diff --git a/LICENSE b/LICENSE
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--- /dev/null
+++ b/LICENSE
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+ GNU GENERAL PUBLIC LICENSE
+ Version 3, 29 June 2007
+
+ Copyright (C) 2007 Free Software Foundation, Inc.
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+reviewing courts shall apply local law that most closely approximates
+an absolute waiver of all civil liability in connection with the
+Program, unless a warranty or assumption of liability accompanies a
+copy of the Program in return for a fee.
+
+ END OF TERMS AND CONDITIONS
+
+ How to Apply These Terms to Your New Programs
+
+ If you develop a new program, and you want it to be of the greatest
+possible use to the public, the best way to achieve this is to make it
+free software which everyone can redistribute and change under these terms.
+
+ To do so, attach the following notices to the program. It is safest
+to attach them to the start of each source file to most effectively
+state the exclusion of warranty; and each file should have at least
+the "copyright" line and a pointer to where the full notice is found.
+
+
+ Copyright (C)
+
+ This program is free software: you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation, either version 3 of the License, or
+ (at your option) any later version.
+
+ This program is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ GNU General Public License for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with this program. If not, see .
+
+Also add information on how to contact you by electronic and paper mail.
+
+ If the program does terminal interaction, make it output a short
+notice like this when it starts in an interactive mode:
+
+ Copyright (C)
+ This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+ This is free software, and you are welcome to redistribute it
+ under certain conditions; type `show c' for details.
+
+The hypothetical commands `show w' and `show c' should show the appropriate
+parts of the General Public License. Of course, your program's commands
+might be different; for a GUI interface, you would use an "about box".
+
+ You should also get your employer (if you work as a programmer) or school,
+if any, to sign a "copyright disclaimer" for the program, if necessary.
+For more information on this, and how to apply and follow the GNU GPL, see
+.
+
+ The GNU General Public License does not permit incorporating your program
+into proprietary programs. If your program is a subroutine library, you
+may consider it more useful to permit linking proprietary applications with
+the library. If this is what you want to do, use the GNU Lesser General
+Public License instead of this License. But first, please read
+.
diff --git a/Pseudopotentials/Ba.psp8 b/Pseudopotentials/Ba.psp8
new file mode 100644
index 00000000..5fec7c4b
--- /dev/null
+++ b/Pseudopotentials/Ba.psp8
@@ -0,0 +1,3680 @@
+Ba ONCVPSP-4.0.1 r_core= 2.94370 2.94370 2.97913 2.55001
+ 56.0000 10.0000 190817 zatom,zion,pspd
+ 8 2 3 4 600 0 pspcod,pspxc,lmax,lloc,mmax,r2well
+ 5.99000000 0.00000000 0.00000000 rchrg fchrg qchrg
+ 2 2 2 2 0 nproj
+ 1 1 extension_switch
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+ 592 5.9100000000000E+00 6.8635250151642E-03 6.8636461718317E-03 1.0786022425202E-11
+ 593 5.9200000000000E+00 6.8052794525383E-03 6.8053992458539E-03 1.0217940107526E-11
+ 594 5.9300000000000E+00 6.7475026504362E-03 6.7476210966992E-03 9.6798261798991E-12
+ 595 5.9400000000000E+00 6.6901909580227E-03 6.6903080733101E-03 9.1700969671179E-12
+ 596 5.9500000000000E+00 6.6333407573737E-03 6.6334565575443E-03 8.6872526887419E-12
+ 597 5.9600000000000E+00 6.5769484629657E-03 6.5770629636634E-03 8.2298729227246E-12
+ 598 5.9700000000000E+00 6.5210105211782E-03 6.5211237378356E-03 7.7966123988230E-12
+ 599 5.9800000000000E+00 6.4655234098107E-03 6.4656353576527E-03 7.3861970865530E-12
+ 600 5.9900000000000E+00 6.4104836376094E-03 6.4105943316564E-03 6.9974203723380E-12
+
+#
+#ONCVPSP (Optimized Norm-Conservinng Vanderbilt PSeudopotential)
+#scalar-relativistic version 4.0.1 06/04/2019
+#
+#While it is not required under the terms of the GNU GPL, it is
+#suggested that you cite D. R. Hamann, Phys. Rev. B 88, 085117 (2013)
+#in any publication utilizing these pseudopotentials.
+#
+# ATOM AND REFERENCE CONFIGURATION
+# atsym z nc nv iexc psfile
+ Ba 56.00 9 4 3 psp8
+#
+# n l f
+ 1 0 2.00
+ 2 0 2.00
+ 2 1 6.00
+ 3 0 2.00
+ 3 1 6.00
+ 3 2 10.00
+ 4 0 2.00
+ 4 1 6.00
+ 4 2 10.00
+ 5 0 2.00
+ 5 1 6.00
+ 5 2 1.00
+ 6 0 1.00
+#
+# PSEUDOPOTENTIAL AND OPTIMIZATION
+# lmax
+ 3
+#
+# l, rc, ep, ncon, nbas, qcut
+ 0 2.93784 -1.19126 5 8 4.58118
+ 1 2.93784 -0.64624 5 8 4.80909
+ 2 2.97309 -0.04970 5 8 5.73962
+ 3 2.54602 0.14815 5 8 7.53728
+#
+# LOCAL POTENTIAL
+# lloc, lpopt, rc(5), dvloc0
+ 4 5 2.31429 0.00000
+#
+# VANDERBILT-KLEINMAN-BYLANDER PROJECTORs
+# l, nproj, debl
+ 0 2 1.08879
+ 1 2 1.60356
+ 2 2 1.83660
+ 3 2 1.30997
+#
+# MODEL CORE CHARGE
+# icmod, fcfact, rcfact
+ 0 0.00000 0.00000
+#
+# LOG DERIVATIVE ANALYSIS
+# epsh1, epsh2, depsh
+ -5.00 3.00 0.02
+#
+# OUTPUT GRID
+# rlmax, drl
+ 6.00 0.01
+#
+# TEST CONFIGURATIONS
+# ncnf
+ 0
+# nvcnf
+# n l f
+
+
+END_PSP
diff --git a/Pseudopotentials/Fe.psp8 b/Pseudopotentials/Fe.psp8
new file mode 100644
index 00000000..47994ac3
--- /dev/null
+++ b/Pseudopotentials/Fe.psp8
@@ -0,0 +1,3071 @@
+Fe ONCVPSP-4.0.1 r_core= 2.09643 2.12167 2.07150
+ 26.0000 16.0000 190723 zatom,zion,pspd
+ 8 2 2 4 600 0 pspcod,pspxc,lmax,lloc,mmax,r2well
+ 5.99000000 0.00000000 0.00000000 rchrg fchrg qchrg
+ 2 2 2 0 0 nproj
+ 1 1 extension_switch
+ 0 -2.7195953571607E+00 -2.1381115667878E+00
+ 1 0.0000000000000E+00 -1.9238866055815E-10 1.8304865956331E-10
+ 2 1.0000000000000E-02 7.4708525910486E-02 -1.8518962348355E-02
+ 3 2.0000000000000E-02 1.4922163531374E-01 -3.6901899100273E-02
+ 4 3.0000000000000E-02 2.2334477480945E-01 -5.5013539563853E-02
+ 5 4.0000000000000E-02 2.9688511139474E-01 -7.2720117411812E-02
+ 6 5.0000000000000E-02 3.6965237817118E-01 -8.9890109299479E-02
+ 7 6.0000000000000E-02 4.4145970279904E-01 -1.0639495733631E-01
+ 8 7.0000000000000E-02 5.1212441317536E-01 -1.2210977024525E-01
+ 9 8.0000000000000E-02 5.8146881500495E-01 -1.3691399822730E-01
+ 10 9.0000000000000E-02 6.4932093617010E-01 -1.5069207677417E-01
+ 11 1.0000000000000E-01 7.1551523308491E-01 -1.6333403493817E-01
+ 12 1.1000000000000E-01 7.7989325453953E-01 -1.7473606387226E-01
+ 13 1.2000000000000E-01 8.4230425889628E-01 -1.8480104179275E-01
+ 14 1.3000000000000E-01 9.0260578089053E-01 -1.9343901188873E-01
+ 15 1.4000000000000E-01 9.6066414470940E-01 -2.0056761010210E-01
+ 16 1.5000000000000E-01 1.0163549204692E+00 -2.0611244012764E-01
+ 17 1.6000000000000E-01 1.0695633216813E+00 -2.1000739342861E-01
+ 18 1.7000000000000E-01 1.1201845417835E+00 -2.1219491252693E-01
+ 19 1.8000000000000E-01 1.1681240283167E+00 -2.1262619630274E-01
+ 20 1.9000000000000E-01 1.2132976938321E+00 -2.1126134652326E-01
+ 21 2.0000000000000E-01 1.2556320631354E+00 -2.0806945530860E-01
+ 22 2.1000000000000E-01 1.2950643569810E+00 -2.0302863373099E-01
+ 23 2.2000000000000E-01 1.3315425128430E+00 -1.9612598222638E-01
+ 24 2.3000000000000E-01 1.3650251438885E+00 -1.8735750397155E-01
+ 25 2.4000000000000E-01 1.3954814377606E+00 -1.7672796283986E-01
+ 26 2.5000000000000E-01 1.4228909972508E+00 -1.6425068799133E-01
+ 27 2.6000000000000E-01 1.4472436253788E+00 -1.4994732757302E-01
+ 28 2.7000000000000E-01 1.4685390578195E+00 -1.3384755440138E-01
+ 29 2.8000000000000E-01 1.4867866460014E+00 -1.1598872686353E-01
+ 30 2.9000000000000E-01 1.5020049945568E+00 -9.6415508608852E-02
+ 31 3.0000000000000E-01 1.5142215571168E+00 -7.5179450900123E-02
+ 32 3.1000000000000E-01 1.5234721947266E+00 -5.2338541754546E-02
+ 33 3.2000000000000E-01 1.5298007013858E+00 -2.7956726225074E-02
+ 34 3.3000000000000E-01 1.5332583014164E+00 -2.1034023515398E-03
+ 35 3.4000000000000E-01 1.5339031235010E+00 2.5147102554082E-02
+ 36 3.5000000000000E-01 1.5317996563382E+00 5.3716070533081E-02
+ 37 3.6000000000000E-01 1.5270181909131E+00 8.3520941714606E-02
+ 38 3.7000000000000E-01 1.5196342543856E+00 1.1447586835825E-01
+ 39 3.8000000000000E-01 1.5097280405582E+00 1.4649226944687E-01
+ 40 3.9000000000000E-01 1.4973838417986E+00 1.7947938116090E-01
+ 41 4.0000000000000E-01 1.4826894871564E+00 2.1334479869744E-01
+ 42 4.1000000000000E-01 1.4657357912396E+00 2.4799500507004E-01
+ 43 4.2000000000000E-01 1.4466160181963E+00 2.8333588273906E-01
+ 44 4.3000000000000E-01 1.4254253648913E+00 3.1927320417239E-01
+ 45 4.4000000000000E-01 1.4022604670718E+00 3.5571309772218E-01
+ 46 4.5000000000000E-01 1.3772189319917E+00 3.9256248552016E-01
+ 47 4.6000000000000E-01 1.3503989006043E+00 4.2972949043980E-01
+ 48 4.7000000000000E-01 1.3218986420514E+00 4.6712380954483E-01
+ 49 4.8000000000000E-01 1.2918161827724E+00 5.0465705183498E-01
+ 50 4.9000000000000E-01 1.2602489721309E+00 5.4224303850953E-01
+ 51 5.0000000000000E-01 1.2272935860207E+00 5.7979806439150E-01
+ 52 5.1000000000000E-01 1.1930454694660E+00 6.1724111958656E-01
+ 53 5.2000000000000E-01 1.1575987187790E+00 6.5449407088652E-01
+ 54 5.3000000000000E-01 1.1210459033857E+00 6.9148180286317E-01
+ 55 5.4000000000000E-01 1.0834779269850E+00 7.2813231903015E-01
+ 56 5.5000000000000E-01 1.0449839272652E+00 7.6437680387341E-01
+ 57 5.6000000000000E-01 1.0056512129778E+00 8.0014964696182E-01
+ 58 5.7000000000000E-01 9.6556523676167E-01 8.3538843074247E-01
+ 59 5.8000000000000E-01 9.2480960172164E-01 8.7003388399885E-01
+ 60 5.9000000000000E-01 8.8346609940710E-01 9.0402980329783E-01
+ 61 6.0000000000000E-01 8.4161477650370E-01 9.3732294507238E-01
+ 62 6.1000000000000E-01 7.9933402725134E-01 9.6986289127616E-01
+ 63 6.2000000000000E-01 7.5670070833852E-01 1.0016018918015E+00
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+
+#
+#ONCVPSP (Optimized Norm-Conservinng Vanderbilt PSeudopotential)
+#scalar-relativistic version 4.0.1 06/04/2019
+#
+#While it is not required under the terms of the GNU GPL, it is
+#suggested that you cite D. R. Hamann, Phys. Rev. B 88, 085117 (2013)
+#in any publication utilizing these pseudopotentials.
+#
+# ATOM AND REFERENCE CONFIGURATION
+# atsym z nc nv iexc psfile
+ Fe 26.00 3 4 3 psp8
+#
+# n l f
+ 1 0 2.00
+ 2 0 2.00
+ 2 1 6.00
+ 3 0 2.00
+ 3 1 6.00
+ 4 0 2.00
+ 3 2 6.00
+#
+# PSEUDOPOTENTIAL AND OPTIMIZATION
+# lmax
+ 2
+#
+# l, rc, ep, ncon, nbas, qcut
+ 0 2.08667 -3.45509 5 8 6.68986
+ 1 2.11172 -2.20653 5 8 7.45338
+ 2 2.06193 -0.27580 5 8 8.55864
+#
+# LOCAL POTENTIAL
+# lloc, lpopt, rc(5), dvloc0
+ 4 5 1.87426 0.00000
+#
+# VANDERBILT-KLEINMAN-BYLANDER PROJECTORs
+# l, nproj, debl
+ 0 2 3.26061
+ 1 2 2.97009
+ 2 2 1.24375
+#
+# MODEL CORE CHARGE
+# icmod, fcfact, rcfact
+ 0 0.00000 0.00000
+#
+# LOG DERIVATIVE ANALYSIS
+# epsh1, epsh2, depsh
+ -5.00 3.00 0.02
+#
+# OUTPUT GRID
+# rlmax, drl
+ 6.00 0.01
+#
+# TEST CONFIGURATIONS
+# ncnf
+ 0
+# nvcnf
+# n l f
+
+
+END_PSP
diff --git a/Pseudopotentials/H.psp8 b/Pseudopotentials/H.psp8
new file mode 100644
index 00000000..d9c2c335
--- /dev/null
+++ b/Pseudopotentials/H.psp8
@@ -0,0 +1,1859 @@
+H ONCVPSP-4.0.1 r_core= 1.14388
+ 1.0000 1.0000 190917 zatom,zion,pspd
+ 8 2 0 4 600 0 pspcod,pspxc,lmax,lloc,mmax,r2well
+ 5.99000000 0.00000000 0.00000000 rchrg fchrg qchrg
+ 2 0 0 0 0 nproj
+ 1 1 extension_switch
+ 0 -1.1032006263972E+00 -3.6404567230487E-01
+ 1 0.0000000000000E+00 -5.6581527685395E-08 3.7836252408940E-08
+ 2 1.0000000000000E-02 7.4447601984748E-02 -2.3526467436927E-02
+ 3 2.0000000000000E-02 1.4876944342101E-01 -4.6690336862065E-02
+ 4 3.0000000000000E-02 2.2284529984472E-01 -6.9134600012058E-02
+ 5 4.0000000000000E-02 2.9656565315452E-01 -9.0513191983275E-02
+ 6 5.0000000000000E-02 3.6983614576580E-01 -1.1049588299796E-01
+ 7 6.0000000000000E-02 4.4258099875140E-01 -1.2877250307955E-01
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+ 597 5.9600000000000E+00 9.1209381959539E-05 9.1213907590474E-05 0.0000000000000E+00
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+
+#
+#ONCVPSP (Optimized Norm-Conservinng Vanderbilt PSeudopotential)
+#scalar-relativistic version 4.0.1 06/04/2019
+#
+#While it is not required under the terms of the GNU GPL, it is
+#suggested that you cite D. R. Hamann, Phys. Rev. B 88, 085117 (2013)
+#in any publication utilizing these pseudopotentials.
+#
+# ATOM AND REFERENCE CONFIGURATION
+# atsym z nc nv iexc psfile
+ H 1.00 0 1 3 psp8
+#
+# n l f
+ 1 0 1.00
+#
+# PSEUDOPOTENTIAL AND OPTIMIZATION
+# lmax
+ 0
+#
+# l, rc, ep, ncon, nbas, qcut
+ 0 1.13748 -0.23860 5 8 9.72141
+#
+# LOCAL POTENTIAL
+# lloc, lpopt, rc(5), dvloc0
+ 4 5 0.49352 0.00000
+#
+# VANDERBILT-KLEINMAN-BYLANDER PROJECTORs
+# l, nproj, debl
+ 0 2 1.27464
+#
+# MODEL CORE CHARGE
+# icmod, fcfact, rcfact
+ 0 0.00000 0.00000
+#
+# LOG DERIVATIVE ANALYSIS
+# epsh1, epsh2, depsh
+ -5.00 3.00 0.02
+#
+# OUTPUT GRID
+# rlmax, drl
+ 6.00 0.01
+#
+# TEST CONFIGURATIONS
+# ncnf
+ 0
+# nvcnf
+# n l f
+
+
+END_PSP
diff --git a/Pseudopotentials/H_GGA.psp8 b/Pseudopotentials/H_GGA.psp8
new file mode 100644
index 00000000..c3dc785c
--- /dev/null
+++ b/Pseudopotentials/H_GGA.psp8
@@ -0,0 +1,1859 @@
+H ONCVPSP-4.0.1 r_core= 1.14388
+ 1.0000 1.0000 190817 zatom,zion,pspd
+ 8 11 0 4 600 0 pspcod,pspxc,lmax,lloc,mmax,r2well
+ 5.99000000 0.00000000 0.00000000 rchrg fchrg qchrg
+ 2 0 0 0 0 nproj
+ 1 1 extension_switch
+ 0 -1.1257865439110E+00 -3.7414728495599E-01
+ 1 0.0000000000000E+00 -5.5911854590640E-08 3.7394794344392E-08
+ 2 1.0000000000000E-02 7.4078151894324E-02 -2.3416239852864E-02
+ 3 2.0000000000000E-02 1.4803859972420E-01 -4.6473052909964E-02
+ 4 3.0000000000000E-02 2.2176896256326E-01 -6.8816494619515E-02
+ 5 4.0000000000000E-02 2.9516714603040E-01 -9.0103352416538E-02
+ 6 5.0000000000000E-02 3.6814560154214E-01 -1.1000594077276E-01
+ 7 6.0000000000000E-02 4.4063456705873E-01 -1.2821623958860E-01
+ 8 7.0000000000000E-02 5.1258401874231E-01 -1.4444920333463E-01
+ 9 8.0000000000000E-02 5.8396411885751E-01 -1.5844510574466E-01
+ 10 9.0000000000000E-02 6.5476401130024E-01 -1.6997082884042E-01
+ 11 1.0000000000000E-01 7.2498888996828E-01 -1.7882005392620E-01
+ 12 1.1000000000000E-01 7.9465534411636E-01 -1.8481236401812E-01
+ 13 1.2000000000000E-01 8.6378506598855E-01 -1.8779131991883E-01
+ 14 1.3000000000000E-01 9.3239708639314E-01 -1.8762162368947E-01
+ 15 1.4000000000000E-01 1.0004987804664E+00 -1.8418553149417E-01
+ 16 1.5000000000000E-01 1.0680759557305E+00 -1.7737872065989E-01
+ 17 1.6000000000000E-01 1.1350823949389E+00 -1.6710585142406E-01
+ 18 1.7000000000000E-01 1.2014292746465E+00 -1.5327609057325E-01
+ 19 1.8000000000000E-01 1.2669749148372E+00 -1.3579888063207E-01
+ 20 1.9000000000000E-01 1.3315153336089E+00 -1.1458024340579E-01
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+ 597 5.9600000000000E+00 8.4377181098059E-05 8.4381645087617E-05 0.0000000000000E+00
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+
+#
+#ONCVPSP (Optimized Norm-Conservinng Vanderbilt PSeudopotential)
+#scalar-relativistic version 4.0.1 06/04/2019
+#
+#While it is not required under the terms of the GNU GPL, it is
+#suggested that you cite D. R. Hamann, Phys. Rev. B 88, 085117 (2013)
+#in any publication utilizing these pseudopotentials.
+#
+# ATOM AND REFERENCE CONFIGURATION
+# atsym z nc nv iexc psfile
+ H 1.00 0 1 4 psp8
+#
+# n l f
+ 1 0 1.00
+#
+# PSEUDOPOTENTIAL AND OPTIMIZATION
+# lmax
+ 0
+#
+# l, rc, ep, ncon, nbas, qcut
+ 0 1.13748 -0.23860 5 8 9.72141
+#
+# LOCAL POTENTIAL
+# lloc, lpopt, rc(5), dvloc0
+ 4 5 0.49352 0.00000
+#
+# VANDERBILT-KLEINMAN-BYLANDER PROJECTORs
+# l, nproj, debl
+ 0 2 1.27464
+#
+# MODEL CORE CHARGE
+# icmod, fcfact, rcfact
+ 0 0.00000 0.00000
+#
+# LOG DERIVATIVE ANALYSIS
+# epsh1, epsh2, depsh
+ -5.00 3.00 0.02
+#
+# OUTPUT GRID
+# rlmax, drl
+ 6.00 0.01
+#
+# TEST CONFIGURATIONS
+# ncnf
+ 0
+# nvcnf
+# n l f
+
+
+END_PSP
diff --git a/Pseudopotentials/O.psp8 b/Pseudopotentials/O.psp8
new file mode 100644
index 00000000..58f5aa79
--- /dev/null
+++ b/Pseudopotentials/O.psp8
@@ -0,0 +1,2464 @@
+O ONCVPSP-3.3.1 r_core= 1.29195 1.47310
+ 8.0000 6.0000 190128 zatom,zion,pspd
+ 8 2 1 4 600 0 pspcod,pspxc,lmax,lloc,mmax,r2well
+ 5.99000000 0.00000000 0.00000000 rchrg fchrg qchrg
+ 2 2 0 0 0 nproj
+ 1 1 extension_switch
+ 0 9.8039458648062E+00 1.3940968705798E+00
+ 1 0.0000000000000E+00 2.8163213983134E-09 -9.8156246741699E-09
+ 2 1.0000000000000E-02 8.9663020185480E-02 -6.4027817020632E-03
+ 3 2.0000000000000E-02 1.7918092483447E-01 -1.3049427776932E-02
+ 4 3.0000000000000E-02 2.6840691548778E-01 -2.0176041044928E-02
+ 5 4.0000000000000E-02 3.5719087019612E-01 -2.8003350708319E-02
+ 6 5.0000000000000E-02 4.4537778693024E-01 -3.6729396702763E-02
+ 7 6.0000000000000E-02 5.3280635113698E-01 -4.6522652323702E-02
+ 8 7.0000000000000E-02 6.1930766545706E-01 -5.7515719480801E-02
+ 9 8.0000000000000E-02 7.0470417680425E-01 -6.9799721117865E-02
+ 10 9.0000000000000E-02 7.8880883257007E-01 -8.3419503369501E-02
+ 11 1.0000000000000E-01 8.7142449371820E-01 -9.8369746103570E-02
+ 12 1.1000000000000E-01 9.5234362803191E-01 -1.1459206484851E-01
+ 13 1.2000000000000E-01 1.0313483018487E+00 -1.3197316998196E-01
+ 14 1.3000000000000E-01 1.1082104833363E+00 -1.5034413074331E-01
+ 15 1.4000000000000E-01 1.1826926648206E+00 -1.6948077242832E-01
+ 16 1.5000000000000E-01 1.2545488059549E+00 -1.8910521534537E-01
+ 17 1.6000000000000E-01 1.3235255937164E+00 -2.0888854408794E-01
+ 18 1.7000000000000E-01 1.3893640094233E+00 -2.2845457573710E-01
+ 19 1.8000000000000E-01 1.4518011872782E+00 -2.4738467608605E-01
+ 20 1.9000000000000E-01 1.5105725434525E+00 -2.6522355420045E-01
+ 21 2.0000000000000E-01 1.5654141495302E+00 -2.8148594791135E-01
+ 22 2.1000000000000E-01 1.6160653192987E+00 -2.9566409648191E-01
+ 23 2.2000000000000E-01 1.6622713735128E+00 -3.0723588197458E-01
+ 24 2.3000000000000E-01 1.7037865434127E+00 -3.1567350802539E-01
+ 25 2.4000000000000E-01 1.7403769705430E+00 -3.2045257403308E-01
+ 26 2.5000000000000E-01 1.7718237578249E+00 -3.2106139438034E-01
+ 27 2.6000000000000E-01 1.7979260249536E+00 -3.1701040638094E-01
+ 28 2.7000000000000E-01 1.8185039200367E+00 -3.0784150729913E-01
+ 29 2.8000000000000E-01 1.8334015390070E+00 -2.9313716009328E-01
+ 30 2.9000000000000E-01 1.8424897047222E+00 -2.7252910951996E-01
+ 31 3.0000000000000E-01 1.8456685588283E+00 -2.4570655488315E-01
+ 32 3.1000000000000E-01 1.8428699213827E+00 -2.1242363296860E-01
+ 33 3.2000000000000E-01 1.8340593758926E+00 -1.7250607445688E-01
+ 34 3.3000000000000E-01 1.8192380407870E+00 -1.2585690922174E-01
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+
+#
+#ONCVPSP (Optimized Norm-Conservinng Vanderbilt PSeudopotential)
+#scalar-relativistic version 3.3.1 12/12/2017
+#
+#While it is not required under the terms of the GNU GPL, it is
+#suggested that you cite D. R. Hamann, Phys. Rev. B 88, 085117 (2013)
+#in any publication utilizing these pseudopotentials.
+#
+# ATOM AND REFERENCE CONFIGURATION
+# atsym z nc nv iexc psfile
+ O 8.00 1 2 3 psp8
+#
+# n l f
+ 1 0 2.00
+ 2 0 2.00
+ 2 1 4.00
+#
+# PSEUDOPOTENTIAL AND OPTIMIZATION
+# lmax
+ 1
+#
+# l, rc, ep, ncon, nbas, qcut
+ 0 1.29195 -0.87291 5 8 8.98916
+ 1 1.47310 -0.33804 5 8 9.14990
+#
+# LOCAL POTENTIAL
+# lloc, lpopt, rc(5), dvloc0
+ 4 5 0.90330 0.00000
+#
+# VANDERBILT-KLEINMAN-BYLANDER PROJECTORs
+# l, nproj, debl
+ 0 2 1.51851
+ 1 2 1.53631
+#
+# MODEL CORE CHARGE
+# icmod, fcfact, rcfact
+ 0 0.00000 0.00000
+#
+# LOG DERIVATIVE ANALYSIS
+# epsh1, epsh2, depsh
+ -5.00 3.00 0.02
+#
+# OUTPUT GRID
+# rlmax, drl
+ 6.00 0.01
+#
+# TEST CONFIGURATIONS
+# ncnf
+ 0
+# nvcnf
+# n l f
+
+
+END_PSP
diff --git a/Pseudopotentials/O_GGA.psp8 b/Pseudopotentials/O_GGA.psp8
new file mode 100644
index 00000000..9f5e268b
--- /dev/null
+++ b/Pseudopotentials/O_GGA.psp8
@@ -0,0 +1,2464 @@
+O ONCVPSP-4.0.1 r_core= 1.29700 1.47943
+ 8.0000 6.0000 190817 zatom,zion,pspd
+ 8 11 1 4 600 0 pspcod,pspxc,lmax,lloc,mmax,r2well
+ 5.99000000 0.00000000 0.00000000 rchrg fchrg qchrg
+ 2 2 0 0 0 nproj
+ 1 1 extension_switch
+ 0 9.6680801733666E+00 1.3229111763523E+00
+ 1 0.0000000000000E+00 -1.4705343609478E-09 1.6270221281367E-09
+ 2 1.0000000000000E-02 9.4366225043070E-02 -2.2483458871271E-02
+ 3 2.0000000000000E-02 1.8847650009829E-01 -4.4904017382368E-02
+ 4 3.0000000000000E-02 2.8207563099975E-01 -6.7197457728292E-02
+ 5 4.0000000000000E-02 3.7490992514494E-01 -8.9296938033718E-02
+ 6 5.0000000000000E-02 4.6672791747527E-01 -1.1113170783406E-01
+ 7 6.0000000000000E-02 5.5728106780097E-01 -1.3262585786135E-01
+ 8 7.0000000000000E-02 6.4632442172347E-01 -1.5369711763780E-01
+ 9 8.0000000000000E-02 7.3361722887858E-01 -1.7425571600687E-01
+ 10 9.0000000000000E-02 8.1892351396876E-01 -1.9420332158876E-01
+ 11 1.0000000000000E-01 9.0201259801480E-01 -2.1343208212556E-01
+ 12 1.1000000000000E-01 9.8265956936861E-01 -2.3182378365880E-01
+ 13 1.2000000000000E-01 1.0606457062200E+00 -2.4924915232645E-01
+ 14 1.3000000000000E-01 1.1357588545220E+00 -2.6556732314189E-01
+ 15 1.4000000000000E-01 1.2077937673785E+00 -2.8062550128718E-01
+ 16 1.5000000000000E-01 1.2765524138989E+00 -2.9425884208617E-01
+ 17 1.6000000000000E-01 1.3418442672660E+00 -3.0629057579758E-01
+ 18 1.7000000000000E-01 1.4034865831996E+00 -3.1653240257823E-01
+ 19 1.8000000000000E-01 1.4613046810808E+00 -3.2478518132341E-01
+ 20 1.9000000000000E-01 1.5151322406691E+00 -3.3083993353059E-01
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+ 571 5.7000000000000E+00 7.9289632947700E-05 7.9297986698583E-05 0.0000000000000E+00
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+ 578 5.7700000000000E+00 6.8949193281657E-05 6.8956513865824E-05 0.0000000000000E+00
+ 579 5.7800000000000E+00 6.7587951994474E-05 6.7595135970297E-05 0.0000000000000E+00
+ 580 5.7900000000000E+00 6.6253951629262E-05 6.6261001585775E-05 0.0000000000000E+00
+ 581 5.8000000000000E+00 6.4946638768431E-05 6.4953557244683E-05 0.0000000000000E+00
+ 582 5.8100000000000E+00 6.3665471430043E-05 6.3672260916090E-05 0.0000000000000E+00
+ 583 5.8200000000000E+00 6.2409918826642E-05 6.2416581764507E-05 0.0000000000000E+00
+ 584 5.8300000000000E+00 6.1179461129501E-05 6.1185999914124E-05 0.0000000000000E+00
+ 585 5.8400000000000E+00 5.9973589238290E-05 5.9980006218456E-05 0.0000000000000E+00
+ 586 5.8500000000000E+00 5.8791804555103E-05 5.8798102034352E-05 0.0000000000000E+00
+ 587 5.8600000000000E+00 5.7633618763612E-05 5.7639799001127E-05 0.0000000000000E+00
+ 588 5.8700000000000E+00 5.6498553613068E-05 5.6504618824548E-05 0.0000000000000E+00
+ 589 5.8800000000000E+00 5.5386140706960E-05 5.5392093065477E-05 0.0000000000000E+00
+ 590 5.8900000000000E+00 5.4295921295894E-05 5.4301762932730E-05 0.0000000000000E+00
+ 591 5.9000000000000E+00 5.3227446075115E-05 5.3233179080581E-05 0.0000000000000E+00
+ 592 5.9100000000000E+00 5.2180274986667E-05 5.2185901410911E-05 0.0000000000000E+00
+ 593 5.9200000000000E+00 5.1153977025277E-05 5.1159498879069E-05 0.0000000000000E+00
+ 594 5.9300000000000E+00 5.0148130048614E-05 5.0153549304119E-05 0.0000000000000E+00
+ 595 5.9400000000000E+00 4.9162320591696E-05 4.9167639183232E-05 0.0000000000000E+00
+ 596 5.9500000000000E+00 4.8196143685335E-05 4.8201363510114E-05 0.0000000000000E+00
+ 597 5.9600000000000E+00 4.7249202678116E-05 4.7254325596969E-05 0.0000000000000E+00
+ 598 5.9700000000000E+00 4.6321109062397E-05 4.6326136900489E-05 0.0000000000000E+00
+ 599 5.9800000000000E+00 4.5411482304252E-05 4.5416416851779E-05 0.0000000000000E+00
+ 600 5.9900000000000E+00 4.4519949676663E-05 4.4524792689533E-05 0.0000000000000E+00
+
+#
+#ONCVPSP (Optimized Norm-Conservinng Vanderbilt PSeudopotential)
+#scalar-relativistic version 4.0.1 06/04/2019
+#
+#While it is not required under the terms of the GNU GPL, it is
+#suggested that you cite D. R. Hamann, Phys. Rev. B 88, 085117 (2013)
+#in any publication utilizing these pseudopotentials.
+#
+# ATOM AND REFERENCE CONFIGURATION
+# atsym z nc nv iexc psfile
+ O 8.00 1 2 4 psp8
+#
+# n l f
+ 1 0 2.00
+ 2 0 2.00
+ 2 1 4.00
+#
+# PSEUDOPOTENTIAL AND OPTIMIZATION
+# lmax
+ 1
+#
+# l, rc, ep, ncon, nbas, qcut
+ 0 1.29195 -0.88057 5 8 8.98916
+ 1 1.47310 -0.33187 5 8 9.14990
+#
+# LOCAL POTENTIAL
+# lloc, lpopt, rc(5), dvloc0
+ 4 5 0.90330 0.00000
+#
+# VANDERBILT-KLEINMAN-BYLANDER PROJECTORs
+# l, nproj, debl
+ 0 2 1.51851
+ 1 2 1.53631
+#
+# MODEL CORE CHARGE
+# icmod, fcfact, rcfact
+ 0 0.00000 0.00000
+#
+# LOG DERIVATIVE ANALYSIS
+# epsh1, epsh2, depsh
+ -5.00 3.00 0.02
+#
+# OUTPUT GRID
+# rlmax, drl
+ 6.00 0.01
+#
+# TEST CONFIGURATIONS
+# ncnf
+ 0
+# nvcnf
+# n l f
+
+
+END_PSP
diff --git a/Pseudopotentials/Si.psp8 b/Pseudopotentials/Si.psp8
new file mode 100644
index 00000000..e5bf09d4
--- /dev/null
+++ b/Pseudopotentials/Si.psp8
@@ -0,0 +1,2464 @@
+Si ONCVPSP-3.3.1 r_core= 2.29275 3.56481
+ 14.0000 4.0000 180913 zatom,zion,pspd
+ 8 2 1 4 600 0 pspcod,pspxc,lmax,lloc,mmax,r2well
+ 5.99000000 0.00000000 0.00000000 rchrg fchrg qchrg
+ 2 2 0 0 0 nproj
+ 1 1 extension_switch
+ 0 5.0237207847988E+00 3.7427701812917E-01
+ 1 0.0000000000000E+00 2.9456992400867E-13 -4.4412806765592E-12
+ 2 1.0000000000000E-02 2.9609322907980E-02 -1.9314684904104E-02
+ 3 2.0000000000000E-02 5.9205263038517E-02 -3.8607377407385E-02
+ 4 3.0000000000000E-02 8.8774428110458E-02 -5.7856062570533E-02
+ 5 4.0000000000000E-02 1.1830340688711E-01 -7.7038680625911E-02
+ 6 5.0000000000000E-02 1.4777875982806E-01 -9.6133105183895E-02
+ 7 6.0000000000000E-02 1.7718700989638E-01 -1.1511712218068E-01
+ 8 7.0000000000000E-02 2.0651463357255E-01 -1.3396840980953E-01
+ 9 8.0000000000000E-02 2.3574805212630E-01 -1.5266451967291E-01
+ 10 9.0000000000000E-02 2.6487362319713E-01 -1.7118285938766E-01
+ 11 1.0000000000000E-01 2.9387763273390E-01 -1.8950067686844E-01
+ 12 1.1000000000000E-01 3.2274628734326E-01 -2.0759504650753E-01
+ 13 1.2000000000000E-01 3.5146570709624E-01 -2.2544285746005E-01
+ 14 1.3000000000000E-01 3.8002191884174E-01 -2.4302080423438E-01
+ 15 1.4000000000000E-01 4.0840085007471E-01 -2.6030537977714E-01
+ 16 1.5000000000000E-01 4.3658832340641E-01 -2.7727287123031E-01
+ 17 1.6000000000000E-01 4.6457005168306E-01 -2.9389935852639E-01
+ 18 1.7000000000000E-01 4.9233163379845E-01 -3.1016071597420E-01
+ 19 1.8000000000000E-01 5.1985855124512E-01 -3.2603261697414E-01
+ 20 1.9000000000000E-01 5.4713616544781E-01 -3.4149054198733E-01
+ 21 2.0000000000000E-01 5.7414971592163E-01 -3.5650978986825E-01
+ 22 2.1000000000000E-01 6.0088431929662E-01 -3.7106549265427E-01
+ 23 2.2000000000000E-01 6.2732496924897E-01 -3.8513263388968E-01
+ 24 2.3000000000000E-01 6.5345653737793E-01 -3.9868607054506E-01
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+ 598 5.9700000000000E+00 1.4080862957769E-03 1.4081193927338E-03 5.0150281963490E-13
+ 599 5.9800000000000E+00 1.3884334297694E-03 1.3884660529922E-03 4.7413766666739E-13
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+
+#
+#ONCVPSP (Optimized Norm-Conservinng Vanderbilt PSeudopotential)
+#scalar-relativistic version 3.3.1 12/12/2017
+#
+#While it is not required under the terms of the GNU GPL, it is
+#suggested that you cite D. R. Hamann, Phys. Rev. B 88, 085117 (2013)
+#in any publication utilizing these pseudopotentials.
+#
+# ATOM AND REFERENCE CONFIGURATION
+# atsym z nc nv iexc psfile
+ Si 14.00 3 2 3 psp8
+#
+# n l f
+ 1 0 2.00
+ 2 0 2.00
+ 2 1 6.00
+ 3 0 2.00
+ 3 1 2.00
+#
+# PSEUDOPOTENTIAL AND OPTIMIZATION
+# lmax
+ 1
+#
+# l, rc, ep, ncon, nbas, qcut
+ 0 2.26557 -0.39999 5 8 4.77946
+ 1 3.56481 -0.15320 5 8 3.13498
+#
+# LOCAL POTENTIAL
+# lloc, lpopt, rc(5), dvloc0
+ 4 5 1.32451 0.00000
+#
+# VANDERBILT-KLEINMAN-BYLANDER PROJECTORs
+# l, nproj, debl
+ 0 2 0.46066
+ 1 2 0.90802
+#
+# MODEL CORE CHARGE
+# icmod, fcfact, rcfact
+ 0 0.00000 0.00000
+#
+# LOG DERIVATIVE ANALYSIS
+# epsh1, epsh2, depsh
+ -5.00 3.00 0.02
+#
+# OUTPUT GRID
+# rlmax, drl
+ 6.00 0.01
+#
+# TEST CONFIGURATIONS
+# ncnf
+ 0
+# nvcnf
+# n l f
+
diff --git a/Pseudopotentials/Ti.psp8 b/Pseudopotentials/Ti.psp8
new file mode 100644
index 00000000..9eda50b7
--- /dev/null
+++ b/Pseudopotentials/Ti.psp8
@@ -0,0 +1,3071 @@
+Ti ONCVPSP-4.0.1 r_core= 2.47760 2.33374 2.27856
+ 22.0000 12.0000 190817 zatom,zion,pspd
+ 8 2 2 4 600 0 pspcod,pspxc,lmax,lloc,mmax,r2well
+ 5.99000000 0.00000000 0.00000000 rchrg fchrg qchrg
+ 2 2 2 0 0 nproj
+ 1 1 extension_switch
+ 0 1.9841871804698E+00 -1.3485599243227E-01
+ 1 0.0000000000000E+00 -8.6664009302240E-12 -8.6870843851727E-11
+ 2 1.0000000000000E-02 5.1858808980582E-02 4.7911631989352E-02
+ 3 2.0000000000000E-02 1.0364091312250E-01 9.5639845666080E-02
+ 4 3.0000000000000E-02 1.5526976056484E-01 1.4300210387284E-01
+ 5 4.0000000000000E-02 2.0666910493778E-01 1.8981762739365E-01
+ 6 5.0000000000000E-02 2.5776315694933E-01 2.3590826302351E-01
+ 7 6.0000000000000E-02 3.0847673458758E-01 2.8109933861828E-01
+ 8 7.0000000000000E-02 3.5873541148730E-01 3.2522050088689E-01
+ 9 8.0000000000000E-02 4.0846566301823E-01 3.6810653177474E-01
+ 10 9.0000000000000E-02 4.5759500966330E-01 4.0959813939529E-01
+ 11 1.0000000000000E-01 5.0605215726772E-01 4.4954271959431E-01
+ 12 1.1000000000000E-01 5.5376713375451E-01 4.8779508437969E-01
+ 13 1.2000000000000E-01 6.0067142191881E-01 5.2421815361620E-01
+ 14 1.3000000000000E-01 6.4669808793141E-01 5.5868360656968E-01
+ 15 1.4000000000000E-01 6.9178190520188E-01 5.9107249008754E-01
+ 16 1.5000000000000E-01 7.3585947327334E-01 6.2127578042083E-01
+ 17 1.6000000000000E-01 7.7886933144364E-01 6.4919489592680E-01
+ 18 1.7000000000000E-01 8.2075206683175E-01 6.7474215813869E-01
+ 19 1.8000000000000E-01 8.6145041663367E-01 6.9784119894989E-01
+ 20 1.9000000000000E-01 9.0090936433823E-01 7.1842731193129E-01
+ 21 2.0000000000000E-01 9.3907622970019E-01 7.3644774608290E-01
+ 22 2.1000000000000E-01 9.7590075229573E-01 7.5186194061142E-01
+ 23 2.2000000000000E-01 1.0113351685139E+00 7.6464169962300E-01
+ 24 2.3000000000000E-01 1.0453342818656E+00 7.7477130592443E-01
+ 25 2.4000000000000E-01 1.0778555265208E+00 7.8224757343333E-01
+ 26 2.5000000000000E-01 1.1088590240138E+00 7.8707983800853E-01
+ 27 2.6000000000000E-01 1.1383076330826E+00 7.8928988682299E-01
+ 28 2.7000000000000E-01 1.1661669926413E+00 7.8891182671236E-01
+ 29 2.8000000000000E-01 1.1924055579061E+00 7.8599189224110E-01
+ 30 2.9000000000000E-01 1.2169946297275E+00 7.8058819453272E-01
+ 31 3.0000000000000E-01 1.2399083772051E+00 7.7277041221036E-01
+ 32 3.1000000000000E-01 1.2611238536878E+00 7.6261942608664E-01
+ 33 3.2000000000000E-01 1.2806210062838E+00 7.5022689952586E-01
+ 34 3.3000000000000E-01 1.2983826790330E+00 7.3569480667623E-01
+ 35 3.4000000000000E-01 1.3143946099088E+00 7.1913491103268E-01
+ 36 3.5000000000000E-01 1.3286454218434E+00 7.0066819704161E-01
+ 37 3.6000000000000E-01 1.3411266079841E+00 6.8042425769494E-01
+ 38 3.7000000000000E-01 1.3518325114079E+00 6.5854064128211E-01
+ 39 3.8000000000000E-01 1.3607602995343E+00 6.3516216067363E-01
+ 40 3.9000000000000E-01 1.3679099334920E+00 6.1044016869667E-01
+ 41 4.0000000000000E-01 1.3732841327049E+00 5.8453180333159E-01
+ 42 4.1000000000000E-01 1.3768883349715E+00 5.5759920660847E-01
+ 43 4.2000000000000E-01 1.3787306523212E+00 5.2980872121002E-01
+ 44 4.3000000000000E-01 1.3788218229345E+00 5.0133006889682E-01
+ 45 4.4000000000000E-01 1.3771751594184E+00 4.7233551495581E-01
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+ 47 4.6000000000000E-01 1.3687341190348E+00 4.1349540399282E-01
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+ 49 4.8000000000000E-01 1.3535633534117E+00 3.5468516070255E-01
+ 50 4.9000000000000E-01 1.3435132945302E+00 3.2572475149437E-01
+ 51 5.0000000000000E-01 1.3318560575878E+00 2.9728797551440E-01
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+ 595 5.9400000000000E+00 3.1325897129850E-03 3.1326424588210E-03 0.0000000000000E+00
+ 596 5.9500000000000E+00 3.0927929806546E-03 3.0928450579004E-03 0.0000000000000E+00
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+ 599 5.9800000000000E+00 2.9763464568710E-03 2.9763965801723E-03 0.0000000000000E+00
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+
+#
+#ONCVPSP (Optimized Norm-Conservinng Vanderbilt PSeudopotential)
+#scalar-relativistic version 4.0.1 06/04/2019
+#
+#While it is not required under the terms of the GNU GPL, it is
+#suggested that you cite D. R. Hamann, Phys. Rev. B 88, 085117 (2013)
+#in any publication utilizing these pseudopotentials.
+#
+# ATOM AND REFERENCE CONFIGURATION
+# atsym z nc nv iexc psfile
+ Ti 22.00 3 4 3 psp8
+#
+# n l f
+ 1 0 2.00
+ 2 0 2.00
+ 2 1 6.00
+ 3 0 2.00
+ 3 1 6.00
+ 4 0 2.00
+ 3 2 2.00
+#
+# PSEUDOPOTENTIAL AND OPTIMIZATION
+# lmax
+ 2
+#
+# l, rc, ep, ncon, nbas, qcut
+ 0 2.46607 -2.30174 5 8 3.75809
+ 1 2.32329 -1.42811 5 8 6.54321
+ 2 2.26852 -0.15651 5 8 7.03480
+#
+# LOCAL POTENTIAL
+# lloc, lpopt, rc(5), dvloc0
+ 4 5 1.64387 0.00000
+#
+# VANDERBILT-KLEINMAN-BYLANDER PROJECTORs
+# l, nproj, debl
+ 0 2 2.13758
+ 1 2 2.12460
+ 2 2 1.17895
+#
+# MODEL CORE CHARGE
+# icmod, fcfact, rcfact
+ 0 0.00000 0.00000
+#
+# LOG DERIVATIVE ANALYSIS
+# epsh1, epsh2, depsh
+ -5.00 3.00 0.02
+#
+# OUTPUT GRID
+# rlmax, drl
+ 6.00 0.01
+#
+# TEST CONFIGURATIONS
+# ncnf
+ 0
+# nvcnf
+# n l f
+
+
+END_PSP
diff --git a/Pseudopotentials/psd_TM_Al.psp b/Pseudopotentials/psd_TM_Al.psp
new file mode 100644
index 00000000..2e85733d
--- /dev/null
+++ b/Pseudopotentials/psd_TM_Al.psp
@@ -0,0 +1,4292 @@
+Al Troulier-Martins r_core= 2.57919 2.57919
+13.0000 3.0000 000000 zatom,zion,pspd
+ 8 2 1 0 1069 0 pspcod,pspxc,lmax,lloc,mmax,r2well
+ 0.00000000 0.00000000 0.00000000 rchrg fchrg qchrg
+ 1 1 0 0 0 nproj
+ 1 1 extension_switch
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+
+#
+#This is a Troulier-Martins pseudopotential file coverted to psp format
+# l, rc, ep, ncon, nbas, qcut
+ 0 2.57919 -0.00000 0 0 0.00000
+ 1 2.57919 -0.00000 0 0 0.00000
+
diff --git a/Pseudopotentials/psd_oncv_C.pot b/Pseudopotentials/psd_oncv_C.pot
new file mode 100644
index 00000000..58de8cc7
--- /dev/null
+++ b/Pseudopotentials/psd_oncv_C.pot
@@ -0,0 +1,2464 @@
+C ONCVPSP-3.3.1 r_core= 1.42330 1.40643
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+ 591 5.9000000000000E+00 2.8666968922192E-04 2.8668653119296E-04 0.0000000000000E+00
+ 592 5.9100000000000E+00 2.8211217434668E-04 2.8212876473707E-04 0.0000000000000E+00
+ 593 5.9200000000000E+00 2.7762882617736E-04 2.7764516885916E-04 0.0000000000000E+00
+ 594 5.9300000000000E+00 2.7321840407260E-04 2.7323450285615E-04 0.0000000000000E+00
+ 595 5.9400000000000E+00 2.6887968882752E-04 2.6889554746246E-04 0.0000000000000E+00
+ 596 5.9500000000000E+00 2.6461148228905E-04 2.6462710446536E-04 0.0000000000000E+00
+ 597 5.9600000000000E+00 2.6041260697140E-04 2.6042799632035E-04 0.0000000000000E+00
+ 598 5.9700000000000E+00 2.5628190569742E-04 2.5629706579253E-04 0.0000000000000E+00
+ 599 5.9800000000000E+00 2.5221824124747E-04 2.5223317560553E-04 0.0000000000000E+00
+ 600 5.9900000000000E+00 2.4822049597501E-04 2.4823520805694E-04 0.0000000000000E+00
+
+#
+#ONCVPSP (Optimized Norm-Conservinng Vanderbilt PSeudopotential)
+#scalar-relativistic version 3.3.1 12/12/2017
+#
+#While it is not required under the terms of the GNU GPL, it is
+#suggested that you cite D. R. Hamann, Phys. Rev. B 88, 085117 (2013)
+#in any publication utilizing these pseudopotentials.
+#
+# ATOM AND REFERENCE CONFIGURATION
+# atsym z nc nv iexc psfile
+ C 6.00 1 2 4 psp8
+#
+# n l f
+ 1 0 2.00
+ 2 0 2.00
+ 2 1 2.00
+#
+# PSEUDOPOTENTIAL AND OPTIMIZATION
+# lmax
+ 1
+#
+# l, rc, ep, ncon, nbas, qcut
+ 0 1.42330 -0.50533 5 8 6.97628
+ 1 1.38975 -0.19424 5 8 8.59046
+#
+# LOCAL POTENTIAL
+# lloc, lpopt, rc(5), dvloc0
+ 4 5 0.82223 0.00000
+#
+# VANDERBILT-KLEINMAN-BYLANDER PROJECTORs
+# l, nproj, debl
+ 0 2 1.09624
+ 1 2 1.27170
+#
+# MODEL CORE CHARGE
+# icmod, fcfact, rcfact
+ 0 0.00000 0.00000
+#
+# LOG DERIVATIVE ANALYSIS
+# epsh1, epsh2, depsh
+ -5.00 3.00 0.02
+#
+# OUTPUT GRID
+# rlmax, drl
+ 6.00 0.01
+#
+# TEST CONFIGURATIONS
+# ncnf
+ 0
+# nvcnf
+# n l f
+
+
+END_PSP
diff --git a/Pseudopotentials/psd_oncv_C_lda.pot b/Pseudopotentials/psd_oncv_C_lda.pot
new file mode 100644
index 00000000..89545a1d
--- /dev/null
+++ b/Pseudopotentials/psd_oncv_C_lda.pot
@@ -0,0 +1,9127 @@
+C ONCVPSP-3.2.3 r_core= 0.93752 1.00708
+ 6.0000 4.0000 170515 zatom,zion,pspd
+ 8 2 1 4 1500 0 pspcod,pspxc,lmax,lloc,mmax,r2well
+ 14.99000000 0.00000000 0.00000000 rchrg fchrg qchrg
+ 2 2 0 0 0 nproj
+ 1 1 extension_switch
+ 0 1.1722384783653E+02 4.3912365035180E+00
+ 1 0.0000000000000E+00 -1.2934599602499E-07 3.9662844064647E-08
+ 2 1.0000000000000E-02 5.0870545049818E-02 4.3951354003865E-02
+ 3 2.0000000000000E-02 9.9501823866258E-02 8.8458053622106E-02
+ 4 3.0000000000000E-02 1.4371640784980E-01 1.3405738103521E-01
+ 5 4.0000000000000E-02 1.8145905201498E-01 1.8125094120203E-01
+ 6 5.0000000000000E-02 2.1085409188771E-01 2.3048793686264E-01
+ 7 6.0000000000000E-02 2.3025850157456E-01 2.8214975071018E-01
+ 8 7.0000000000000E-02 2.3830932288806E-01 3.3653622254999E-01
+ 9 8.0000000000000E-02 2.3396430475829E-01 3.9385396960131E-01
+ 10 9.0000000000000E-02 2.1653474832772E-01 4.5420705022983E-01
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+ 14 1.3000000000000E-01 1.5666168050166E-02 7.2416498751151E-01
+ 15 1.4000000000000E-01 -6.3973962372463E-02 7.9735180888184E-01
+ 16 1.5000000000000E-01 -1.5271360732966E-01 8.7186558475557E-01
+ 17 1.6000000000000E-01 -2.4862230928642E-01 9.4706331073249E-01
+ 18 1.7000000000000E-01 -3.4948845383371E-01 1.0222249417360E+00
+ 19 1.8000000000000E-01 -4.5286797897531E-01 1.0965683256356E+00
+ 20 1.9000000000000E-01 -5.5613944767509E-01 1.1692659792569E+00
+ 21 2.0000000000000E-01 -6.5656425018848E-01 1.2394633262265E+00
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+
+#
+#ONCVPSP (Optimized Norm-Conservinng Vanderbilt PSeudopotential)
+#scalar-relativistic version 3.2.3 08/16/2016
+#
+#While it is not required under the terms of the GNU GPL, it is
+#suggested that you cite E. R. Hamann, Phys. Rev. B 88, 085117 (2013)
+#in any publication utilizing these pseudopotentials.
+#
+# ATOM ANE REFERENCE CONFIGURATION
+# atsym z nc nv iexc psfile
+ C 6.00 1 2 3 psp8
+#
+# n l f
+ 1 0 2.00
+ 2 0 2.00
+ 2 1 2.00
+#
+# PSEUEOPOTENTIAL ANE OPTIMIZATION
+# lmax
+ 1
+#
+# l, rc, ep, ncon, nbas, qcut
+ 0 0.93000 -0.50140 4 7 6.55000
+ 1 1.00000 -0.19918 4 7 7.30000
+#
+# LOCAL POTENTIAL
+# lloc, lpopt, rc(5), dvloc0
+ 4 5 0.93000 0.00000
+#
+# VANEERBILT-KLEINMAN-BYLANEER PROJECTORs
+# l, nproj, debl
+ 0 2 1.50000
+ 1 2 1.50000
+#
+# MOEEL CORE CHARGE
+# icmod, fcfact, rcfact
+ 0 0.00000 0.00000
+#
+# LOG EERIVATIVE ANALYSIS
+# epsh1, epsh2, depsh
+ -12.00 12.00 0.02
+#
+# OUTPUT GRIE
+# rlmax, drl
+ 15.00 0.01
+#
+# TEST CONFIGURATIONS
+# ncnf
+ 0
+# nvcnf
+# n l f
+
+
+ENE_PSP
+
+Begin PSICOEE8
+C ONCVPSP-3.2.3 r_core= 0.93752 1.00708
+ 6.0000 4.0000 170515 zatom,zion,pspd
+ 8 2 1 4 1500 0 pspcod,pspxc,lmax,lloc,mmax,r2well
+ 14.99000000 0.00000000 0.00000000 rchrg fchrg qchrg
+ 2 2 0 0 0 nproj
+ 1 1 extension_switch
+ 1 0.0000000000000E+00 6.9975636396435E-11 5.9366928004284-320
+ 2 1.0000000000000E-02 4.9759726525969E-03 4.7438207051093-319
+ 3 2.0000000000000E-02 9.9605476703491E-03 -1.2934599602499E-07
+ 4 3.0000000000000E-02 1.4962268311548E-02 5.0870545049818E-02
+ 5 4.0000000000000E-02 1.9989560553919E-02 9.9501823866258E-02
+ 6 5.0000000000000E-02 2.5050676768807E-02 1.4371640784980E-01
+ 7 6.0000000000000E-02 3.0153642121528E-02 1.8145905201498E-01
+ 8 7.0000000000000E-02 3.5306204522366E-02 2.1085409188771E-01
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+ 10 9.0000000000000E-02 4.5789456346241E-02 2.3830932288806E-01
+ 11 1.0000000000000E-01 5.1133869066653E-02 2.3396430475829E-01
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+ 16 1.5000000000000E-01 7.9119217546877E-02 1.5666168050166E-02
+ 17 1.6000000000000E-01 8.5002797614491E-02 -6.3973962372463E-02
+ 18 1.7000000000000E-01 9.0990950343719E-02 -1.5271360732966E-01
+ 19 1.8000000000000E-01 9.7086639896632E-02 -2.4862230928642E-01
+ 20 1.9000000000000E-01 1.0329239981995E-01 -3.4948845383371E-01
+ 21 2.0000000000000E-01 1.0961035839053E-01 -4.5286797897531E-01
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+ 23 2.2000000000000E-01 1.2258953713478E-01 -6.5656425018848E-01
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+
+#
+#ONCVPSP (Optimized Norm-Conservinng Vanderbilt PSeudopotential)
+#scalar-relativistic version 3.2.3 08/16/2016
+#
+#While it is not required under the terms of the GNU GPL, it is
+#suggested that you cite E. R. Hamann, Phys. Rev. B 88, 085117 (2013)
+#in any publication utilizing these pseudopotentials.
+#
+# ATOM AND REFERENCE CONFIGURATION
+# atsym z nc nv iexc psfile
+ C 6.00 1 2 3 psp8
+#
+# n l f
+ 1 0 2.00
+ 2 0 2.00
+ 2 1 2.00
+#
+# PSEUDOPOTENTIAL ANE OPTIMIZATION
+# lmax
+ 1
+#
+# l, rc, ep, ncon, nbas, qcut
+ 0 0.93000 -0.50140 4 7 6.55000
+ 1 1.00000 -0.19918 4 7 7.30000
+#
+# LOCAL POTENTIAL
+# lloc, lpopt, rc(5), dvloc0
+ 4 5 0.93000 0.00000
+#
+# VANDERBILT-KLEINMAN-BYLADEER PROJECTORs
+# l, nproj, debl
+ 0 2 1.50000
+ 1 2 1.50000
+#
+# MODEL CORE CHARGE
+# icmod, fcfact, rcfact
+ 0 0.00000 0.00000
+#
+# LOG DERIVATIVE ANALYSIS
+# epsh1, epsh2, depsh
+ -12.00 12.00 0.02
+#
+# OUTPUT GRID
+# rlmax, drl
+ 15.00 0.01
+#
+# TEST CONFIGURATIONS
+# ncnf
+ 0
+# nvcnf
+# n l f
+
+
+ENE_PSI
diff --git a/Pseudopotentials/psd_oncv_H-1.pot b/Pseudopotentials/psd_oncv_H-1.pot
new file mode 100644
index 00000000..8cfcd218
--- /dev/null
+++ b/Pseudopotentials/psd_oncv_H-1.pot
@@ -0,0 +1,1859 @@
+H ONCVPSP-3.3.1 r_core= 1.15113
+ 1.0000 1.0000 190128 zatom,zion,pspd
+ 8 2 0 4 600 0 pspcod,pspxc,lmax,lloc,mmax,r2well
+ 5.99000000 0.00000000 0.00000000 rchrg fchrg qchrg
+ 2 0 0 0 0 nproj
+ 1 1 extension_switch
+ 0 -1.2539437611788E+00 -4.0727290034061E-01
+ 1 0.0000000000000E+00 4.6168487866094E-08 -3.4318619543394E-08
+ 2 1.0000000000000E-02 3.0205697226572E-02 1.2138998345020E-02
+ 3 2.0000000000000E-02 6.1520920405994E-02 2.3897417609999E-02
+ 4 3.0000000000000E-02 9.5025730951330E-02 3.4910538706878E-02
+ 5 4.0000000000000E-02 1.3174187672572E-01 4.4844951510226E-02
+ 6 5.0000000000000E-02 1.7260516197975E-01 5.3413190813061E-02
+ 7 6.0000000000000E-02 2.1843961566096E-01 6.0387175148664E-02
+ 8 7.0000000000000E-02 2.6993400210192E-01 6.5610090721067E-02
+ 9 8.0000000000000E-02 3.2762117192434E-01 6.9006397005503E-02
+ 10 9.0000000000000E-02 3.9186069495896E-01 7.0589672163570E-02
+ 11 1.0000000000000E-01 4.6282515214355E-01 7.0468064425559E-02
+ 12 1.1000000000000E-01 5.4049039096860E-01 6.8847169050086E-02
+ 13 1.2000000000000E-01 6.2462997048174E-01 6.6030208290916E-02
+ 14 1.3000000000000E-01 7.1481393865217E-01 6.2415452799431E-02
+ 15 1.4000000000000E-01 8.1041199864468E-01 5.8490885815360E-02
+ 16 1.5000000000000E-01 9.1060103293295E-01 5.4826175046603E-02
+ 17 1.6000000000000E-01 1.0143768669036E+00 5.2062079989264E-02
+ 18 1.7000000000000E-01 1.1205700683707E+00 5.0897483274831E-02
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+ 592 5.9100000000000E+00 9.9003735996281E-05 9.9008418115630E-05 0.0000000000000E+00
+ 593 5.9200000000000E+00 9.7392971224773E-05 9.7397586040348E-05 0.0000000000000E+00
+ 594 5.9300000000000E+00 9.5808645202972E-05 9.5813193680135E-05 0.0000000000000E+00
+ 595 5.9400000000000E+00 9.4250320017889E-05 9.4254803108201E-05 0.0000000000000E+00
+ 596 5.9500000000000E+00 9.2717565077799E-05 9.2721983719215E-05 0.0000000000000E+00
+ 597 5.9600000000000E+00 9.1209956988643E-05 9.1214312105707E-05 0.0000000000000E+00
+ 598 5.9700000000000E+00 8.9727079432550E-05 8.9731371936586E-05 0.0000000000000E+00
+ 599 5.9800000000000E+00 8.8268523044768E-05 8.8272753834068E-05 0.0000000000000E+00
+ 600 5.9900000000000E+00 8.6833885307547E-05 8.6838055267556E-05 0.0000000000000E+00
+
+#
+#ONCVPSP (Optimized Norm-Conservinng Vanderbilt PSeudopotential)
+#scalar-relativistic version 3.3.1 12/12/2017
+#
+#While it is not required under the terms of the GNU GPL, it is
+#suggested that you cite D. R. Hamann, Phys. Rev. B 88, 085117 (2013)
+#in any publication utilizing these pseudopotentials.
+#
+# ATOM AND REFERENCE CONFIGURATION
+# atsym z nc nv iexc psfile
+ H 1.00 0 1 3 psp8
+#
+# n l f
+ 1 0 1.00
+#
+# PSEUDOPOTENTIAL AND OPTIMIZATION
+# lmax
+ 0
+#
+# l, rc, ep, ncon, nbas, qcut
+ 0 1.13748 -0.23366 5 8 9.72141
+#
+# LOCAL POTENTIAL
+# lloc, lpopt, rc(5), dvloc0
+ 4 5 0.49352 0.00000
+#
+# VANDERBILT-KLEINMAN-BYLANDER PROJECTORs
+# l, nproj, debl
+ 0 2 1.27464
+#
+# MODEL CORE CHARGE
+# icmod, fcfact, rcfact
+ 0 0.00000 0.00000
+#
+# LOG DERIVATIVE ANALYSIS
+# epsh1, epsh2, depsh
+ -5.00 3.00 0.02
+#
+# OUTPUT GRID
+# rlmax, drl
+ 6.00 0.01
+#
+# TEST CONFIGURATIONS
+# ncnf
+ 0
+# nvcnf
+# n l f
+
+
+END_PSP
diff --git a/Pseudopotentials/psd_oncv_H.pot b/Pseudopotentials/psd_oncv_H.pot
new file mode 100644
index 00000000..b7d545e7
--- /dev/null
+++ b/Pseudopotentials/psd_oncv_H.pot
@@ -0,0 +1,1859 @@
+H ONCVPSP-3.3.1 r_core= 1.15113
+ 1.0000 1.0000 181022 zatom,zion,pspd
+ 8 2 0 4 600 0 pspcod,pspxc,lmax,lloc,mmax,r2well
+ 5.99000000 0.00000000 0.00000000 rchrg fchrg qchrg
+ 2 0 0 0 0 nproj
+ 1 1 extension_switch
+ 0 -1.2539439737565E+00 -4.0727292438671E-01
+ 1 0.0000000000000E+00 4.6168852851913E-08 -3.4318795388844E-08
+ 2 1.0000000000000E-02 3.0205698123833E-02 1.2138999894621E-02
+ 3 2.0000000000000E-02 6.1520922213950E-02 2.3897420827784E-02
+ 4 3.0000000000000E-02 9.5025733695607E-02 3.4910543827077E-02
+ 5 4.0000000000000E-02 1.3174188044170E-01 4.4844958876908E-02
+ 6 5.0000000000000E-02 1.7260516670903E-01 5.3413200871546E-02
+ 7 6.0000000000000E-02 2.1843962144675E-01 6.0387188434381E-02
+ 8 7.0000000000000E-02 2.6993400898358E-01 6.5610107846030E-02
+ 9 8.0000000000000E-02 3.2762117993123E-01 6.9006418642692E-02
+ 10 9.0000000000000E-02 3.9186070410377E-01 7.0589699029529E-02
+ 11 1.0000000000000E-01 4.6282516241525E-01 7.0468097261630E-02
+ 12 1.1000000000000E-01 5.4049040232538E-01 6.8847208602560E-02
+ 13 1.2000000000000E-01 6.2462998284408E-01 6.6030255290553E-02
+ 14 1.3000000000000E-01 7.1481395189635E-01 6.2415507940791E-02
+ 15 1.4000000000000E-01 8.1041201259678E-01 5.8490949736338E-02
+ 16 1.5000000000000E-01 9.1060104736392E-01 5.4826248308604E-02
+ 17 1.6000000000000E-01 1.0143768815252E+00 5.2062163058539E-02
+ 18 1.7000000000000E-01 1.1205700828325E+00 5.0897576505106E-02
+ 19 1.8000000000000E-01 1.2278655118024E+00 5.2074395783183E-02
+ 20 1.9000000000000E-01 1.3348252616211E+00 5.6360623420784E-02
+ 21 2.0000000000000E-01 1.4399145570289E+00 6.4531943866096E-02
+ 22 2.1000000000000E-01 1.5415301204920E+00 7.7352212873843E-02
+ 23 2.2000000000000E-01 1.6380304623197E+00 9.5553269898473E-02
+ 24 2.3000000000000E-01 1.7277675102081E+00 1.1981451833395E-01
+ 25 2.4000000000000E-01 1.8091189638291E+00 1.5074273421057E-01
+ 26 2.5000000000000E-01 1.8805207421258E+00 1.8885257042057E-01
+ 27 2.6000000000000E-01 1.9404988852717E+00 2.3454822050832E-01
+ 28 2.7000000000000E-01 1.9877002799046E+00 2.8810669354086E-01
+ 29 2.8000000000000E-01 2.0209215950848E+00 3.4966312979816E-01
+ 30 2.9000000000000E-01 2.0391358470307E+00 4.1919855641786E-01
+ 31 3.0000000000000E-01 2.0415160523672E+00 4.9653044333234E-01
+ 32 3.1000000000000E-01 2.0274554814604E+00 5.8130637366996E-01
+ 33 3.2000000000000E-01 1.9965840842465E+00 6.7300109025463E-01
+ 34 3.3000000000000E-01 1.9487807294427E+00 7.7091712208724E-01
+ 35 3.4000000000000E-01 1.8841809725969E+00 8.7418913301621E-01
+ 36 3.5000000000000E-01 1.8031801474277E+00 9.8179207059461E-01
+ 37 3.6000000000000E-01 1.7064316565035E+00 1.0925531278522E+00
+ 38 3.7000000000000E-01 1.5948404196609E+00 1.2051674658903E+00
+ 39 3.8000000000000E-01 1.4695515197464E+00 1.3182175823609E+00
+ 40 3.9000000000000E-01 1.3319341634125E+00 1.4301961515097E+00
+ 41 4.0000000000000E-01 1.1835611479508E+00 1.5395321069808E+00
+ 42 4.1000000000000E-01 1.0261840917857E+00 1.6446196903315E+00
+ 43 4.2000000000000E-01 8.6170474467269E-01 1.7438501473933E+00
+ 44 4.3000000000000E-01 6.9214274243191E-01 1.8356457222819E+00
+ 45 4.4000000000000E-01 5.1960020899615E-01 1.9184955758636E+00
+ 46 4.5000000000000E-01 3.4622363470335E-01 1.9909932424592E+00
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+ 48 4.7000000000000E-01 5.5319019760563E-03 2.1000604241940E+00
+ 49 4.8000000000000E-01 -1.5764082770728E-01 2.1346898118682E+00
+ 50 4.9000000000000E-01 -3.1345101831895E-01 2.1551663157985E+00
+ 51 5.0000000000000E-01 -4.6016649792851E-01 2.1611930828304E+00
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+ 54 5.3000000000000E-01 -8.3145175977382E-01 2.0931785488942E+00
+ 55 5.4000000000000E-01 -9.2854663029546E-01 2.0427795755611E+00
+ 56 5.5000000000000E-01 -1.0110136801338E+00 1.9793684284129E+00
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+ 58 5.7000000000000E-01 -1.1306001647514E+00 1.8165626593171E+00
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+ 590 5.8900000000000E+00 1.0230637078830E-04 1.0231119047851E-04 0.0000000000000E+00
+ 591 5.9000000000000E+00 1.0064138486664E-04 1.0064613527999E-04 0.0000000000000E+00
+ 592 5.9100000000000E+00 9.9003735985569E-05 9.9008418115630E-05 0.0000000000000E+00
+ 593 5.9200000000000E+00 9.7392971214214E-05 9.7397586040348E-05 0.0000000000000E+00
+ 594 5.9300000000000E+00 9.5808645192565E-05 9.5813193680135E-05 0.0000000000000E+00
+ 595 5.9400000000000E+00 9.4250320007631E-05 9.4254803108201E-05 0.0000000000000E+00
+ 596 5.9500000000000E+00 9.2717565067688E-05 9.2721983719215E-05 0.0000000000000E+00
+ 597 5.9600000000000E+00 9.1209956978677E-05 9.1214312105707E-05 0.0000000000000E+00
+ 598 5.9700000000000E+00 8.9727079422726E-05 8.9731371936586E-05 0.0000000000000E+00
+ 599 5.9800000000000E+00 8.8268523035085E-05 8.8272753834068E-05 0.0000000000000E+00
+ 600 5.9900000000000E+00 8.6833885298002E-05 8.6838055267556E-05 0.0000000000000E+00
+
+#
+#ONCVPSP (Optimized Norm-Conservinng Vanderbilt PSeudopotential)
+#scalar-relativistic version 3.3.1 12/12/2017
+#
+#While it is not required under the terms of the GNU GPL, it is
+#suggested that you cite D. R. Hamann, Phys. Rev. B 88, 085117 (2013)
+#in any publication utilizing these pseudopotentials.
+#
+# ATOM AND REFERENCE CONFIGURATION
+# atsym z nc nv iexc psfile
+ H 1.00 0 1 3 psp8
+#
+# n l f
+ 1 0 1.00
+#
+# PSEUDOPOTENTIAL AND OPTIMIZATION
+# lmax
+ 0
+#
+# l, rc, ep, ncon, nbas, qcut
+ 0 1.13748 -0.23366 5 8 9.72141
+#
+# LOCAL POTENTIAL
+# lloc, lpopt, rc(5), dvloc0
+ 4 5 0.49352 0.00000
+#
+# VANDERBILT-KLEINMAN-BYLANDER PROJECTORs
+# l, nproj, debl
+ 0 2 1.27464
+#
+# MODEL CORE CHARGE
+# icmod, fcfact, rcfact
+ 0 0.00000 0.00000
+#
+# LOG DERIVATIVE ANALYSIS
+# epsh1, epsh2, depsh
+ -5.00 3.00 0.02
+#
+# OUTPUT GRID
+# rlmax, drl
+ 6.00 0.01
+#
+# TEST CONFIGURATIONS
+# ncnf
+ 0
+# nvcnf
+# n l f
+
+
+END_PSP
diff --git a/Pseudopotentials/psd_oncv_Li.pot b/Pseudopotentials/psd_oncv_Li.pot
new file mode 100644
index 00000000..1f56fc90
--- /dev/null
+++ b/Pseudopotentials/psd_oncv_Li.pot
@@ -0,0 +1,2470 @@
+Li ONCVPSP-3.3.1 r_core= 2.01415 3.02155
+ 3.0000 3.0000 171225 zatom,zion,pspd
+ 8 2 1 4 600 0 pspcod,pspxc,lmax,lloc,mmax,r2well
+ 5.99000000 0.00000000 0.00000000 rchrg fchrg qchrg
+ 2 2 0 0 0 nproj
+ 1 1 extension_switch
+ 0 -2.4888884197835E+00 -1.1495118168115E+00
+ 1 0.0000000000000E+00 -1.1087575302327E-11 5.8103744038362E-11
+ 2 1.0000000000000E-02 4.3746550455598E-02 -2.1019598436744E-02
+ 3 2.0000000000000E-02 8.7449264078380E-02 -4.1956356607637E-02
+ 4 3.0000000000000E-02 1.3106435581465E-01 -6.2727770456412E-02
+ 5 4.0000000000000E-02 1.7454814390919E-01 -8.3252006290510E-02
+ 6 5.0000000000000E-02 2.1785710090785E-01 -1.0344823083906E-01
+ 7 6.0000000000000E-02 2.6094790389215E-01 -1.2323693520351E-01
+ 8 7.0000000000000E-02 3.0377748370286E-01 -1.4254025073356E-01
+ 9 8.0000000000000E-02 3.4630307292077E-01 -1.6128225491939E-01
+ 10 9.0000000000000E-02 3.8848225238647E-01 -1.7938926546275E-01
+ 11 1.0000000000000E-01 4.3027299605712E-01 -1.9679012077499E-01
+ 12 1.1000000000000E-01 4.7163371401657E-01 -2.1341644524795E-01
+ 13 1.2000000000000E-01 5.1252329347616E-01 -2.2920289775351E-01
+ 14 1.3000000000000E-01 5.5290113762581E-01 -2.4408740194888E-01
+ 15 1.4000000000000E-01 5.9272720221982E-01 -2.5801135709667E-01
+ 16 1.5000000000000E-01 6.3196202980771E-01 -2.7091982824967E-01
+ 17 1.6000000000000E-01 6.7056678154789E-01 -2.8276171480031E-01
+ 18 1.7000000000000E-01 7.0850326657053E-01 -2.9348989655209E-01
+ 19 1.8000000000000E-01 7.4573396888539E-01 -3.0306135663369E-01
+ 20 1.9000000000000E-01 7.8222207186021E-01 -3.1143728074585E-01
+ 21 2.0000000000000E-01 8.1793148032585E-01 -3.1858313240357E-01
+ 22 2.1000000000000E-01 8.5282684039413E-01 -3.2446870401200E-01
+ 23 2.2000000000000E-01 8.8687355710489E-01 -3.2906814379171E-01
+ 24 2.3000000000000E-01 9.2003781004759E-01 -3.3235995874609E-01
+ 25 2.4000000000000E-01 9.5228656713161E-01 -3.3432699403973E-01
+ 26 2.5000000000000E-01 9.8358759670650E-01 -3.3495638933058E-01
+ 27 2.6000000000000E-01 1.0139094782592E+00 -3.3423951276814E-01
+ 28 2.7000000000000E-01 1.0432216119391E+00 -3.3217187353472E-01
+ 29 2.8000000000000E-01 1.0714942271839E+00 -3.2875301396535E-01
+ 30 2.9000000000000E-01 1.0986983907384E+00 -3.2398638243178E-01
+ 31 3.0000000000000E-01 1.1248060143747E+00 -3.1787918831851E-01
+ 32 3.1000000000000E-01 1.1497898626377E+00 -3.1044224054954E-01
+ 33 3.2000000000000E-01 1.1736235609492E+00 -3.0168977124531E-01
+ 34 3.3000000000000E-01 1.1962816044104E+00 -2.9163924619721E-01
+ 35 3.4000000000000E-01 1.2177393676506E+00 -2.8031116394198E-01
+ 36 3.5000000000000E-01 1.2379731160636E+00 -2.6772884529874E-01
+ 37 3.6000000000000E-01 1.2569600187767E+00 -2.5391821529769E-01
+ 38 3.7000000000000E-01 1.2746781636834E+00 -2.3890757947933E-01
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+ 40 3.9000000000000E-01 1.3062252326976E+00 -2.0541004961566E-01
+ 41 4.0000000000000E-01 1.3200150969578E+00 -1.8698961745074E-01
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+ 591 5.9000000000000E+00 2.5832894238534E-03 2.5832916829923E-03 0.0000000000000E+00
+ 592 5.9100000000000E+00 2.5585766059558E-03 2.5585788329446E-03 0.0000000000000E+00
+ 593 5.9200000000000E+00 2.5340883697883E-03 2.5340905651367E-03 0.0000000000000E+00
+ 594 5.9300000000000E+00 2.5098228484912E-03 2.5098250127010E-03 0.0000000000000E+00
+ 595 5.9400000000000E+00 2.4857781880947E-03 2.4857803216600E-03 0.0000000000000E+00
+ 596 5.9500000000000E+00 2.4619525474723E-03 2.4619546508796E-03 0.0000000000000E+00
+ 597 5.9600000000000E+00 2.4383440982940E-03 2.4383461720222E-03 0.0000000000000E+00
+ 598 5.9700000000000E+00 2.4149510249799E-03 2.4149530695006E-03 0.0000000000000E+00
+ 599 5.9800000000000E+00 2.3917715246481E-03 2.3917735404255E-03 0.0000000000000E+00
+ 600 5.9900000000000E+00 2.3688038070678E-03 2.3688057945589E-03 0.0000000000000E+00
+
+#
+#ONCVPSP (Optimized Norm-Conservinng Vanderbilt PSeudopotential)
+#scalar-relativistic version 3.3.1 12/12/2017
+#
+#While it is not required under the terms of the GNU GPL, it is
+#suggested that you cite E. R. Hamann, Phys. Rev. B 88, 085117 (2013)
+#in any publication utilizing these pseudopotentials.
+#
+# ATOM AND REFERENCE CONFIGURATION
+# atsym z nc nv iexc psfile
+ Li 3.00 0 2 3 psp8
+#
+# n l f
+ 1 0 2.00
+ 2 0 1.00
+#
+# PSEUDOPOTENTIAL AND OPTIMIZATION
+# lmax
+ 1
+#
+# l, rc, ep, ncon, nbas, qcut
+ 0 2.00000 -1.87794 4 8 6.00000
+ 1 3.00000 0.10000 4 8 4.00000
+#
+# LOCAL POTENTIAL
+# lloc, lpopt, rc(5), dvloc0
+ 4 5 1.00000 0.00000
+#
+# VANDERBILT-KLEINMAN-BYLANDER PROJECTORs
+# l, nproj, debl
+ 0 2 1.77222
+ 1 2 0.75000
+#
+# MODEL CORE CHARGE
+# icmod, fcfact, rcfact
+ 0 0.00000 0.00000
+#
+# LOG DERIVATIVE ANALYSIS
+# epsh1, epsh2, depsh
+ -2.00 2.00 0.02
+#
+# OUTPUT GRID
+# rlmax, drl
+ 6.00 0.01
+#
+# TEST CONFIGURATIONS
+# ncnf
+ 2
+# nvcnf
+# n l f
+ 1
+ 1 0 2.00
+#
+ 2
+ 1 0 2.00
+ 2 1 1.00
+#
+
+
+END_PSP
diff --git a/Pseudopotentials/psd_oncv_N.pot b/Pseudopotentials/psd_oncv_N.pot
new file mode 100644
index 00000000..8ee01930
--- /dev/null
+++ b/Pseudopotentials/psd_oncv_N.pot
@@ -0,0 +1,2464 @@
+N ONCVPSP-3.3.1 r_core= 1.60510 1.53031
+ 7.0000 5.0000 190128 zatom,zion,pspd
+ 8 2 1 4 600 0 pspcod,pspxc,lmax,lloc,mmax,r2well
+ 5.99000000 0.00000000 0.00000000 rchrg fchrg qchrg
+ 2 2 0 0 0 nproj
+ 1 1 extension_switch
+ 0 7.1189760403912E+00 1.0033398890710E+00
+ 1 0.0000000000000E+00 4.2585712733967E-11 -1.9294615904997E-10
+ 2 1.0000000000000E-02 8.6914272051891E-02 -3.8148756626366E-02
+ 3 2.0000000000000E-02 1.7359947088499E-01 -7.6072070347601E-02
+ 4 3.0000000000000E-02 2.5982720651986E-01 -1.1354525670945E-01
+ 5 4.0000000000000E-02 3.4537045418939E-01 -1.5034514860629E-01
+ 6 5.0000000000000E-02 4.3000423376761E-01 -1.8625085602257E-01
+ 7 6.0000000000000E-02 5.1350628535460E-01 -2.2104452691501E-01
+ 8 7.0000000000000E-02 5.9565773968488E-01 -2.5451210938535E-01
+ 9 8.0000000000000E-02 6.7624378198414E-01 -2.8644411510059E-01
+ 10 9.0000000000000E-02 7.5505430784770E-01 -3.1663638368204E-01
+ 11 1.0000000000000E-01 8.3188456965481E-01 -3.4489084751081E-01
+ 12 1.1000000000000E-01 9.0653581196705E-01 -3.7101629608864E-01
+ 13 1.2000000000000E-01 9.7881589428817E-01 -3.9482913875523E-01
+ 14 1.3000000000000E-01 1.0485398994886E+00 -4.1615416420196E-01
+ 15 1.4000000000000E-01 1.1155307261214E+00 -4.3482529484194E-01
+ 16 1.5000000000000E-01 1.1796196627816E+00 -4.5068633370567E-01
+ 17 1.6000000000000E-01 1.2406469425861E+00 -4.6359170113564E-01
+ 18 1.7000000000000E-01 1.2984622757821E+00 -4.7340715815937E-01
+ 19 1.8000000000000E-01 1.3529253584299E+00 -4.8001051303560E-01
+ 20 1.9000000000000E-01 1.4039063550491E+00 -4.8329230709987E-01
+ 21 2.0000000000000E-01 1.4512863530729E+00 -4.8315647568984E-01
+ 22 2.1000000000000E-01 1.4949577869236E+00 -4.7952097961573E-01
+ 23 2.2000000000000E-01 1.5348248295026E+00 -4.7231840236185E-01
+ 24 2.3000000000000E-01 1.5708037488853E+00 -4.6149650796982E-01
+ 25 2.4000000000000E-01 1.6028232280274E+00 -4.4701875436664E-01
+ 26 2.5000000000000E-01 1.6308246453210E+00 -4.2886475676849E-01
+ 27 2.6000000000000E-01 1.6547623138942E+00 -4.0703069571731E-01
+ 28 2.7000000000000E-01 1.6746036776218E+00 -3.8152966429731E-01
+ 29 2.8000000000000E-01 1.6903294619129E+00 -3.5239194913497E-01
+ 30 2.9000000000000E-01 1.7019337774600E+00 -3.1966523991247E-01
+ 31 3.0000000000000E-01 1.7094241752787E+00 -2.8341476232241E-01
+ 32 3.1000000000000E-01 1.7128216515311E+00 -2.4372332966130E-01
+ 33 3.2000000000000E-01 1.7121606008171E+00 -2.0069130860276E-01
+ 34 3.3000000000000E-01 1.7074887168267E+00 -1.5443649510562E-01
+ 35 3.4000000000000E-01 1.6988668394820E+00 -1.0509389689701E-01
+ 36 3.5000000000000E-01 1.6863687479475E+00 -5.2815419523021E-02
+ 37 3.6000000000000E-01 1.6700808991627E+00 2.2305464246313E-03
+ 38 3.7000000000000E-01 1.6501021118390E+00 5.9859638621421E-02
+ 39 3.8000000000000E-01 1.6265431961681E+00 1.1987213784806E-01
+ 40 3.9000000000000E-01 1.5995265298091E+00 1.8205368456172E-01
+ 41 4.0000000000000E-01 1.5691855810482E+00 2.4617609658915E-01
+ 42 4.1000000000000E-01 1.5356643803662E+00 3.1199828647809E-01
+ 43 4.2000000000000E-01 1.4991169419884E+00 3.7926727616540E-01
+ 44 4.3000000000000E-01 1.4597066373407E+00 4.4771930572599E-01
+ 45 4.4000000000000E-01 1.4176055226774E+00 5.1708103206526E-01
+ 46 4.5000000000000E-01 1.3729936234903E+00 5.8707081251824E-01
+ 47 4.6000000000000E-01 1.3260581786409E+00 6.5740006743128E-01
+ 48 4.7000000000000E-01 1.2769928474820E+00 7.2777471493757E-01
+ 49 4.8000000000000E-01 1.2259968835450E+00 7.9789667030427E-01
+ 50 4.9000000000000E-01 1.1732742786626E+00 8.6746540143784E-01
+ 51 5.0000000000000E-01 1.1190328816678E+00 9.3617953139578E-01
+ 52 5.1000000000000E-01 1.0634834960622E+00 1.0037384780731E+00
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+
+#
+#ONCVPSP (Optimized Norm-Conservinng Vanderbilt PSeudopotential)
+#scalar-relativistic version 3.3.1 12/12/2017
+#
+#While it is not required under the terms of the GNU GPL, it is
+#suggested that you cite D. R. Hamann, Phys. Rev. B 88, 085117 (2013)
+#in any publication utilizing these pseudopotentials.
+#
+# ATOM AND REFERENCE CONFIGURATION
+# atsym z nc nv iexc psfile
+ N 7.00 1 2 3 psp8
+#
+# n l f
+ 1 0 2.00
+ 2 0 2.00
+ 2 1 3.00
+#
+# PSEUDOPOTENTIAL AND OPTIMIZATION
+# lmax
+ 1
+#
+# l, rc, ep, ncon, nbas, qcut
+ 0 1.60510 -0.67703 5 8 8.23432
+ 1 1.51217 -0.26614 5 8 9.22597
+#
+# LOCAL POTENTIAL
+# lloc, lpopt, rc(5), dvloc0
+ 4 5 1.10894 0.00000
+#
+# VANDERBILT-KLEINMAN-BYLANDER PROJECTORs
+# l, nproj, debl
+ 0 2 2.24547
+ 1 2 2.62189
+#
+# MODEL CORE CHARGE
+# icmod, fcfact, rcfact
+ 0 0.00000 0.00000
+#
+# LOG DERIVATIVE ANALYSIS
+# epsh1, epsh2, depsh
+ -5.00 3.00 0.02
+#
+# OUTPUT GRID
+# rlmax, drl
+ 6.00 0.01
+#
+# TEST CONFIGURATIONS
+# ncnf
+ 0
+# nvcnf
+# n l f
+
+
+END_PSP
diff --git a/Pseudopotentials/psd_oncv_O.pot b/Pseudopotentials/psd_oncv_O.pot
new file mode 100644
index 00000000..58f5aa79
--- /dev/null
+++ b/Pseudopotentials/psd_oncv_O.pot
@@ -0,0 +1,2464 @@
+O ONCVPSP-3.3.1 r_core= 1.29195 1.47310
+ 8.0000 6.0000 190128 zatom,zion,pspd
+ 8 2 1 4 600 0 pspcod,pspxc,lmax,lloc,mmax,r2well
+ 5.99000000 0.00000000 0.00000000 rchrg fchrg qchrg
+ 2 2 0 0 0 nproj
+ 1 1 extension_switch
+ 0 9.8039458648062E+00 1.3940968705798E+00
+ 1 0.0000000000000E+00 2.8163213983134E-09 -9.8156246741699E-09
+ 2 1.0000000000000E-02 8.9663020185480E-02 -6.4027817020632E-03
+ 3 2.0000000000000E-02 1.7918092483447E-01 -1.3049427776932E-02
+ 4 3.0000000000000E-02 2.6840691548778E-01 -2.0176041044928E-02
+ 5 4.0000000000000E-02 3.5719087019612E-01 -2.8003350708319E-02
+ 6 5.0000000000000E-02 4.4537778693024E-01 -3.6729396702763E-02
+ 7 6.0000000000000E-02 5.3280635113698E-01 -4.6522652323702E-02
+ 8 7.0000000000000E-02 6.1930766545706E-01 -5.7515719480801E-02
+ 9 8.0000000000000E-02 7.0470417680425E-01 -6.9799721117865E-02
+ 10 9.0000000000000E-02 7.8880883257007E-01 -8.3419503369501E-02
+ 11 1.0000000000000E-01 8.7142449371820E-01 -9.8369746103570E-02
+ 12 1.1000000000000E-01 9.5234362803191E-01 -1.1459206484851E-01
+ 13 1.2000000000000E-01 1.0313483018487E+00 -1.3197316998196E-01
+ 14 1.3000000000000E-01 1.1082104833363E+00 -1.5034413074331E-01
+ 15 1.4000000000000E-01 1.1826926648206E+00 -1.6948077242832E-01
+ 16 1.5000000000000E-01 1.2545488059549E+00 -1.8910521534537E-01
+ 17 1.6000000000000E-01 1.3235255937164E+00 -2.0888854408794E-01
+ 18 1.7000000000000E-01 1.3893640094233E+00 -2.2845457573710E-01
+ 19 1.8000000000000E-01 1.4518011872782E+00 -2.4738467608605E-01
+ 20 1.9000000000000E-01 1.5105725434525E+00 -2.6522355420045E-01
+ 21 2.0000000000000E-01 1.5654141495302E+00 -2.8148594791135E-01
+ 22 2.1000000000000E-01 1.6160653192987E+00 -2.9566409648191E-01
+ 23 2.2000000000000E-01 1.6622713735128E+00 -3.0723588197458E-01
+ 24 2.3000000000000E-01 1.7037865434127E+00 -3.1567350802539E-01
+ 25 2.4000000000000E-01 1.7403769705430E+00 -3.2045257403308E-01
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+
+#
+#ONCVPSP (Optimized Norm-Conservinng Vanderbilt PSeudopotential)
+#scalar-relativistic version 3.3.1 12/12/2017
+#
+#While it is not required under the terms of the GNU GPL, it is
+#suggested that you cite D. R. Hamann, Phys. Rev. B 88, 085117 (2013)
+#in any publication utilizing these pseudopotentials.
+#
+# ATOM AND REFERENCE CONFIGURATION
+# atsym z nc nv iexc psfile
+ O 8.00 1 2 3 psp8
+#
+# n l f
+ 1 0 2.00
+ 2 0 2.00
+ 2 1 4.00
+#
+# PSEUDOPOTENTIAL AND OPTIMIZATION
+# lmax
+ 1
+#
+# l, rc, ep, ncon, nbas, qcut
+ 0 1.29195 -0.87291 5 8 8.98916
+ 1 1.47310 -0.33804 5 8 9.14990
+#
+# LOCAL POTENTIAL
+# lloc, lpopt, rc(5), dvloc0
+ 4 5 0.90330 0.00000
+#
+# VANDERBILT-KLEINMAN-BYLANDER PROJECTORs
+# l, nproj, debl
+ 0 2 1.51851
+ 1 2 1.53631
+#
+# MODEL CORE CHARGE
+# icmod, fcfact, rcfact
+ 0 0.00000 0.00000
+#
+# LOG DERIVATIVE ANALYSIS
+# epsh1, epsh2, depsh
+ -5.00 3.00 0.02
+#
+# OUTPUT GRID
+# rlmax, drl
+ 6.00 0.01
+#
+# TEST CONFIGURATIONS
+# ncnf
+ 0
+# nvcnf
+# n l f
+
+
+END_PSP
diff --git a/Pseudopotentials/psd_oncv_Si.pot b/Pseudopotentials/psd_oncv_Si.pot
new file mode 100644
index 00000000..e5bf09d4
--- /dev/null
+++ b/Pseudopotentials/psd_oncv_Si.pot
@@ -0,0 +1,2464 @@
+Si ONCVPSP-3.3.1 r_core= 2.29275 3.56481
+ 14.0000 4.0000 180913 zatom,zion,pspd
+ 8 2 1 4 600 0 pspcod,pspxc,lmax,lloc,mmax,r2well
+ 5.99000000 0.00000000 0.00000000 rchrg fchrg qchrg
+ 2 2 0 0 0 nproj
+ 1 1 extension_switch
+ 0 5.0237207847988E+00 3.7427701812917E-01
+ 1 0.0000000000000E+00 2.9456992400867E-13 -4.4412806765592E-12
+ 2 1.0000000000000E-02 2.9609322907980E-02 -1.9314684904104E-02
+ 3 2.0000000000000E-02 5.9205263038517E-02 -3.8607377407385E-02
+ 4 3.0000000000000E-02 8.8774428110458E-02 -5.7856062570533E-02
+ 5 4.0000000000000E-02 1.1830340688711E-01 -7.7038680625911E-02
+ 6 5.0000000000000E-02 1.4777875982806E-01 -9.6133105183895E-02
+ 7 6.0000000000000E-02 1.7718700989638E-01 -1.1511712218068E-01
+ 8 7.0000000000000E-02 2.0651463357255E-01 -1.3396840980953E-01
+ 9 8.0000000000000E-02 2.3574805212630E-01 -1.5266451967291E-01
+ 10 9.0000000000000E-02 2.6487362319713E-01 -1.7118285938766E-01
+ 11 1.0000000000000E-01 2.9387763273390E-01 -1.8950067686844E-01
+ 12 1.1000000000000E-01 3.2274628734326E-01 -2.0759504650753E-01
+ 13 1.2000000000000E-01 3.5146570709624E-01 -2.2544285746005E-01
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+ 593 5.9200000000000E+00 1.5106935073865E-03 1.5107290828459E-03 6.6396729328403E-13
+ 594 5.9300000000000E+00 1.4895787039257E-03 1.4896137686543E-03 6.2772308715753E-13
+ 595 5.9400000000000E+00 1.4687649389805E-03 1.4687995006112E-03 5.9346012793235E-13
+ 596 5.9500000000000E+00 1.4482478218766E-03 1.4482818879235E-03 5.6106994665419E-13
+ 597 5.9600000000000E+00 1.4280230275894E-03 1.4280566054500E-03 5.3044977719248E-13
+ 598 5.9700000000000E+00 1.4080862957769E-03 1.4081193927338E-03 5.0150281963490E-13
+ 599 5.9800000000000E+00 1.3884334297694E-03 1.3884660529922E-03 4.7413766666739E-13
+ 600 5.9900000000000E+00 1.3690602955766E-03 1.3690924521236E-03 4.4826777571297E-13
+
+#
+#ONCVPSP (Optimized Norm-Conservinng Vanderbilt PSeudopotential)
+#scalar-relativistic version 3.3.1 12/12/2017
+#
+#While it is not required under the terms of the GNU GPL, it is
+#suggested that you cite D. R. Hamann, Phys. Rev. B 88, 085117 (2013)
+#in any publication utilizing these pseudopotentials.
+#
+# ATOM AND REFERENCE CONFIGURATION
+# atsym z nc nv iexc psfile
+ Si 14.00 3 2 3 psp8
+#
+# n l f
+ 1 0 2.00
+ 2 0 2.00
+ 2 1 6.00
+ 3 0 2.00
+ 3 1 2.00
+#
+# PSEUDOPOTENTIAL AND OPTIMIZATION
+# lmax
+ 1
+#
+# l, rc, ep, ncon, nbas, qcut
+ 0 2.26557 -0.39999 5 8 4.77946
+ 1 3.56481 -0.15320 5 8 3.13498
+#
+# LOCAL POTENTIAL
+# lloc, lpopt, rc(5), dvloc0
+ 4 5 1.32451 0.00000
+#
+# VANDERBILT-KLEINMAN-BYLANDER PROJECTORs
+# l, nproj, debl
+ 0 2 0.46066
+ 1 2 0.90802
+#
+# MODEL CORE CHARGE
+# icmod, fcfact, rcfact
+ 0 0.00000 0.00000
+#
+# LOG DERIVATIVE ANALYSIS
+# epsh1, epsh2, depsh
+ -5.00 3.00 0.02
+#
+# OUTPUT GRID
+# rlmax, drl
+ 6.00 0.01
+#
+# TEST CONFIGURATIONS
+# ncnf
+ 0
+# nvcnf
+# n l f
+
diff --git a/Pseudopotentials/psd_oncv_Si_old.pot b/Pseudopotentials/psd_oncv_Si_old.pot
new file mode 100644
index 00000000..76c1a113
--- /dev/null
+++ b/Pseudopotentials/psd_oncv_Si_old.pot
@@ -0,0 +1,2587 @@
+Si ONCVPSP-3.3.1 r_core= 2.01081 2.01081 2.70947
+ 14.0000 12.0000 171225 zatom,zion,pspd
+ 8 2 2 4 500 0 pspcod,pspxc,lmax,lloc,mmax,r2well
+ 4.99000000 0.00000000 0.00000000 rchrg fchrg qchrg
+ 2 2 2 0 0 nproj
+ 1 1 extension_switch
+ 0 -6.0026638345423E+00 -1.6732868177866E+00
+ 1 0.0000000000000E+00 -1.9296231279498E-11 1.7473034130688E-10
+ 2 1.0000000000000E-02 5.5164655313872E-02 -4.3383565003698E-02
+ 3 2.0000000000000E-02 1.1024314389505E-01 -8.6602445020537E-02
+ 4 3.0000000000000E-02 1.6514950722339E-01 -1.2949269441229E-01
+ 5 4.0000000000000E-02 2.1979820241189E-01 -1.7189184123761E-01
+ 6 5.0000000000000E-02 2.7410430804862E-01 -2.1363961164434E-01
+ 7 6.0000000000000E-02 3.2798372768261E-01 -2.5457863943938E-01
+ 8 7.0000000000000E-02 3.8135339019138E-01 -2.9455515610231E-01
+ 9 8.0000000000000E-02 4.3413144628681E-01 -3.3341965668364E-01
+ 10 9.0000000000000E-02 4.8623746044003E-01 -3.7102753724354E-01
+ 11 1.0000000000000E-01 5.3759259753399E-01 -4.0723969974040E-01
+ 12 1.1000000000000E-01 5.8811980358468E-01 -4.4192312056717E-01
+ 13 1.2000000000000E-01 6.3774397990783E-01 -4.7495137925574E-01
+ 14 1.3000000000000E-01 6.8639215014742E-01 -5.0620514422016E-01
+ 15 1.4000000000000E-01 7.3399361962511E-01 -5.3557261278763E-01
+ 16 1.5000000000000E-01 7.8048012651472E-01 -5.6294990316514E-01
+ 17 1.6000000000000E-01 8.2578598439415E-01 -5.8824139640816E-01
+ 18 1.7000000000000E-01 8.6984821577666E-01 -6.1136002688925E-01
+ 19 1.8000000000000E-01 9.1260667627501E-01 -6.3222752020716E-01
+ 20 1.9000000000000E-01 9.5400416910451E-01 -6.5077457792356E-01
+ 21 2.0000000000000E-01 9.9398654968439E-01 -6.6694100896386E-01
+ 22 2.1000000000000E-01 1.0325028201507E+00 -6.8067580796304E-01
+ 23 2.2000000000000E-01 1.0695052136474E+00 -6.9193718127547E-01
+ 24 2.3000000000000E-01 1.1049492683150E+00 -7.0069252179256E-01
+ 25 2.4000000000000E-01 1.1387938909496E+00 -7.0691833412201E-01
+ 26 2.5000000000000E-01 1.1710014103538E+00 -7.1060011207132E-01
+ 27 2.6000000000000E-01 1.2015376204516E+00 -7.1173217074393E-01
+ 28 2.7000000000000E-01 1.2303718132860E+00 -7.1031743589468E-01
+ 29 2.8000000000000E-01 1.2574768020630E+00 -7.0636719349885E-01
+ 30 2.9000000000000E-01 1.2828289344454E+00 -6.9990080276404E-01
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+
+#
+#ONCVPSP (Optimized Norm-Conservinng Vanderbilt PSeudopotential)
+#scalar-relativistic version 3.3.1 12/12/2017
+#
+#While it is not required under the terms of the GNU GPL, it is
+#suggested that you cite E. R. Hamann, Phys. Rev. B 88, 085117 (2013)
+#in any publication utilizing these pseudopotentials.
+#
+# ATOM AND REFERENCE CONFIGURATION
+# atsym z nc nv iexc psfile
+ Si 14.00 1 4 3 psp8
+#
+# n l f
+ 1 0 2.00
+ 2 0 2.00
+ 2 1 6.00
+ 3 0 2.00
+ 3 1 2.00
+#
+# PSEUDOPOTENTIAL AND OPTIMIZATION
+# lmax
+ 2
+#
+# l, rc, ep, ncon, nbas, qcut
+ 0 2.00000 -5.09839 5 9 7.00000
+ 1 2.00000 -3.51325 5 10 8.00000
+ 2 2.70000 0.10000 5 8 5.00000
+#
+# LOCAL POTENTIAL
+# lloc, lpopt, rc(5), dvloc0
+ 4 5 2.00000 0.00000
+#
+# VANDERBILT-KLEINMAN-BYLANDER PROJECTORs
+# l, nproj, debl
+ 0 2 4.69839
+ 1 2 3.36006
+ 2 2 0.75000
+#
+# MODEL CORE CHARGE
+# icmod, fcfact, rcfact
+ 0 0.00000 0.00000
+#
+# LOG DERIVATIVE ANALYSIS
+# epsh1, epsh2, depsh
+ -6.00 2.00 0.02
+#
+# OUTPUT GRID
+# rlmax, drl
+ 5.00 0.01
+#
+# TEST CONFIGURATIONS
+# ncnf
+ 3
+# nvcnf
+# n l f
+ 4
+ 2 0 2.00
+ 2 1 6.00
+ 3 0 1.00
+ 3 1 2.00
+#
+ 4
+ 2 0 2.00
+ 2 1 6.00
+ 3 0 2.00
+ 3 1 1.00
+#
+ 4
+ 2 0 2.00
+ 2 1 6.00
+ 3 0 1.00
+ 3 1 1.00
+#
+
+
+END_PSP
diff --git a/README.md b/README.md
new file mode 100644
index 00000000..c6ebd5db
--- /dev/null
+++ b/README.md
@@ -0,0 +1,76 @@
+## M-SPARC Usage
+### (1) Brief:
+Matlab-Simulation Package for Ab-initio Real-space Calculations (M-SPARC) is a real-space code for performing electronic structure calculations based on Kohn-Sham Density Functional Theory (DFT). Its primary purpose is the rapid development and testing of new algorithms and methods within DFT. The main features of M-SPARC 1.0 include
+
+* Boundary conditions for crystals, surfaces, wires, and molecules.
+* Calculation of ground state energy, atomic forces, and stress tensor.
+* Unconstrained collinear magnetization via spin polarized calculations.
+* Structural relaxation and molecular dynamics (MD).
+* LDA and GGA exchange correlation functionals.
+* ONCV and TM pseudopotentials in psp8 (ABINIT) format.
+
+### (2) Input files:
+The required input files to run a simulation with M-SPARC are (with shared names)
+(a) ".inpt" -- User options and parameters.
+(b) ".ion" -- Atomic information.
+A more detailed description of the input options can be found in the user manual loated in M-SPARC/docs. Examples of input files can be found in the directory M-SPARC/tests. In addition, M-SPARC requires pseudopotential files of psp8 format which can be generated by D. R. Hamann's open-source pseudopotential code [ONCVPSP](http://www.mat-simresearch.com/). Pseudopotential files are specified in the ".ion" file.
+
+### (3) Execution:
+M-SPARC can be executed in matlab by calling the `msparc` function (which is located under src/ directory). It is required that the ".inpt" and ".ion" files are located in the same directory and share the same name. For example, to run a simulation with input files as "filename.inpt" and "filename.ion" in the src/ directory, use the following command:
+```
+S = msparc('filename');
+```
+In many cases, we would not want to put the input files inside the src/ directory. In such cases, we need to provide the path to the input file name, without any extension. As an example, one can run a test located in M-SPARC/tests/MeshConvergence as follows. First go to src/ directory. Run a DC silicon system with mesh = 0.4 bohr by:
+
+```
+S = msparc('../tests/MeshConvergence/Si8-ONCV-0.4');
+```
+The result is printed to an output file named "Si8-ONCV-0.4.out", located in the same directory as the input files. If the file "Si8-ONCV-0.4.out" is already present, the result will be printed to "Si8-ONCV-0.4.out_1" instead. The max number of ".out" files allowed with the same name is 100. Once this number is reached, the result will instead overwrite the "Si8-ONCV-0.4.out" file. One can compare the result with the reference out file named "Si8-ONCV-0.4.refout".
+
+In the examples/ directory, we also provide a sample script file `run_examples.m`, which launches four example tests one by one. To run these examples, simply change directory to examples/ directory, and run
+```
+run_examples
+```
+Note that in this case, we're trying to call the `msparc` function from a different directory. This is achieved by using the MATLAB function `addpath` to add the src/ directory to search path.
+
+One can also run M-SPARC using the MATLAB parallel pool to parallelize over k-points and spin by providing a second argument, `parallel_switch`, when running M-SPARC:
+```
+S = msparc('filename',parallel_switch);
+```
+If `parallel_switch = 1`, M-SPARC will start using the parallel pool, and if `parallel_switch = 0`, M-SPARC will not use the parallel pool, which is the default. Only turn on parallel pool if k-points or spin are present.
+
+### (4) Output:
+
+Upon successful execution of the
+```
+S = msparc(fname);
+```
+command, an output structure is returned and stored in `S`. The structure `S` contains detailed information that can be useful for post-processing and debugging. Information such as the input parameters, densities, wavefunctions, eigenvalues, and all electronic ground-state properties calculated are stored in the output structure.
+
+Apart from the output structure returned, depending on the calculations performed, some output files will be created in the same location as the input files too.
+
+**Single point calculations**
+
+- `.out` file
+The `.out` file contains general information about the test, including input parameters, SCF convergence progress, ground state properties and timing information.
+- `.static` file
+The `.static` file contains the atomic positions and atomic forces if the user chooses to print these information.
+
+**Structrual relaxation calculations**
+- `.out` file
+See above.
+- `.geopt` file
+The `.geopt` file contains the atomic positions and atomic forces for each relaxation step. This file is created only when the unit cell is fixed. For cell relaxation a `.cellopt` file is created instead.
+- `.cellopt` file
+The `.cellopt` file contains the cell information (lattice vectors, cell lengths, volume) and stresses for each relaxation step. Only created for cell relaxation.
+- `.restart` file
+The `.restart` file contains information necessary to perform a restarted structural relaxation calculation.
+
+**Molecular dynamics (MD) calculations**
+
+- `.out` file
+See above.
+- `.aimd` file
+The `.aimd` file contains the atomic positions, atomic velocities, atomic forces, electronic temperature, ionic temperature and total energy for each MD step.
+- `.restart` file
+The `.restart` file contains information necessary to perform a restarted MD calculation.
diff --git a/doc/Manual.pdf b/doc/Manual.pdf
new file mode 100644
index 00000000..c70dfb04
Binary files /dev/null and b/doc/Manual.pdf differ
diff --git a/doc/Manual.tex b/doc/Manual.tex
new file mode 100644
index 00000000..cecb779e
--- /dev/null
+++ b/doc/Manual.tex
@@ -0,0 +1,3038 @@
+\documentclass[xcolor=dvipsnames,t]{beamer}
+%\usepackage[utf8]{inputenc}
+\usepackage{verbatim} % for comment
+\usetheme{Madrid}
+\usecolortheme{seahorse}
+\usepackage{beamerouterthemesplit}
+
+
+\title[] {M-SPARC \\ {\small User guide}}
+\author{Qimen Xu, Abhiraj Sharma, Phanish Suryanarayana}
+\institute[]
+{
+Material Physics \& Mechanics Group \\
+Georgia Institute of Technology
+}
+
+\date{}
+\setbeamertemplate{frametitle continuation}{}
+\setbeamertemplate{navigation symbols}{}
+\setbeamercolor{block title}{bg=Apricot!50,fg=black}
+%\addtobeamertemplate{block begin}{\vskip -\smallskipamount}{}
+%\addtobeamertemplate{block end}{}{\vskip -\smallskipamount}
+\addtobeamertemplate{block begin}{\vspace*{-0.6pt}}{}
+\addtobeamertemplate{block end}{}{\vspace*{-0.6pt}}
+\hypersetup{colorlinks,
+citecolor=violet,
+linkcolor=blue,
+menucolor=white,
+anchorcolor=yellow
+filecolor=pink,
+}
+
+
+\setbeamertemplate{footline}{
+ \hbox{%
+ \begin{beamercolorbox}[wd=\paperwidth,ht=1ex,dp=1.5ex,leftskip=2ex,rightskip=2ex]{page footer}%
+ \usebeamerfont{title in head/foot}%
+ \insertshorttitle \hfill
+ \insertsection \hfill
+ \insertframenumber{} / \inserttotalframenumber
+ \end{beamercolorbox}}%
+}
+
+% \setbeamertemplate{headline} [split theme]
+% {%
+% \begin{beamercolorbox}{section in head/foot}
+% \vskip2pt\insertnavigation{\paperwidth}\vskip2pt
+% \end{beamercolorbox}%
+% }
+
+% \defbeamertemplate*{footline}{split theme}
+% {%
+% \leavevmode%
+% \hbox{\begin{beamercolorbox}[wd=.5\paperwidth,ht=2.5ex,dp=1.125ex,leftskip=.3cm plus1fill,rightskip=.3cm]{section in head/foot}%
+% \usebeamerfont{author in head/foot}\insertshortauthor
+% \end{beamercolorbox}%
+% \begin{beamercolorbox}[wd=.5\paperwidth,ht=2.5ex,dp=1.125ex,leftskip=.3cm,rightskip=.3cm plus1fil]{title in head/foot}%
+% \usebeamerfont{title in head/foot}\insertshorttitle
+% \end{beamercolorbox}}%
+% \vskip0pt%
+% }
+
+
+
+\let\otp\titlepage
+\renewcommand{\titlepage}{\otp\addtocounter{framenumber}{-1}}
+
+\begin{document}
+
+%\frame{\titlepage}
+
+\begin{frame}[plain]
+ \titlepage
+\end{frame}
+
+
+\begin{frame}[allowframebreaks]{\textbf{Introduction}} \label{Introduction}
+Matlab-Simulation Package for Ab-initio Real-space Calculations (M-SPARC) is a real-space code for performing electronic structure calculations based on Kohn-Sham Density Functional Theory (DFT). Its primary purpose is the rapid development and testing of new algorithms and methods within DFT. The current features of M-SPARC include
+\begin{itemize}
+ \item Boundary conditions for crystals, surfaces, wires, and molecules.
+ \item Calculation of ground state energy, atomic forces, and stress tensor.
+ \item Unconstrained collinear magnetization via spin polarized calculations.
+ \item Structural relaxation and molecular dynamics (MD).
+ \item LDA and GGA exchange correlation functionals.
+ \item ONCV and TM pseudopotentials in psp8 (ABINIT) format.
+\end{itemize}
+Additional details regarding the formulation and implementation of M-SPARC can be found in the accompanying paper. Please direct any questions and report any bugs to Prof.~Phanish Suryanarayana.
+
+\end{frame}
+
+
+\begin{frame}[allowframebreaks]{\textbf{Input files}} \label{Inputfiles}
+The required input files to run a simulation with M-SPARC are
+\begin{itemize}
+ \item ``.inpt" file -- User options and parameters.
+ \item ``.ion" file -- Atomic information.
+\end{itemize}
+It is required that the ``.inpt" and ``.ion" files are located in the same directory and share the same name. A detailed description of the input options is provided in this document. Examples of input files can be found in the directory \texttt{M-SPARC/tests}. In addition, M-SPARC requires pseudopotential files of psp8 format which can be generated by D. R. Hamann's open-source pseudopotential code \href{http://www.mat-simresearch.com/}{ONCVPSP}. Pseudopotential files are specified in the ``.ion" file.
+\end{frame}
+
+
+
+\begin{frame}[allowframebreaks,fragile]{\textbf{Execution}} \label{Execution}
+M-SPARC can be executed in MATLAB by calling the \texttt{msparc} function (which is located under \texttt{src/} directory). It is required that the ``.inpt" and ``.ion" files are located in the same directory and share the same name. For example, to run a simulation with input files as ``filename.inpt" and ``filename.ion" in the \texttt{src/} directory, use the following command:
+\begin{verbatim}
+S = msparc(`filename');
+\end{verbatim}
+
+In many cases, we would not want to put the input files inside the \texttt{src/} directory. In such cases, we need to provide the path to the input file name, without any extension. As an example, one can run a test located in \texttt{M-SPARC/tests/MeshConvergence}. First go to \texttt{src/} directory. Run a DC silicon system with mesh = 0.4 bohr by:
+\begin{verbatim}
+S = msparc(`../tests/MeshConvergence/Si8-ONCV-0.4');
+\end{verbatim}
+The result is printed to output file ``Si8-ONCV-0.4.out", located in the same directory as the input files. If the file ``Si8-ONCV-0.4.out" is already present, the result will be printed to ``Si8-ONCV-0.4.out\_1" instead. The max number of ``.out" files allowed with the same name is 100. Once this number is reached, the result will instead overwrite the ``Si8-ONCV-0.4.out" file. One can compare the result with the reference out file named ``Si8-ONCV-0.4.refout".\\~\\
+
+In the \texttt{examples/} directory, we also provide a sample script file \texttt{run\_examples.m}, which launches four example tests one by one. To run these examples, simply change directory to \texttt{examples/} directory, and run:
+\begin{verbatim}
+run_examples
+\end{verbatim}
+
+One can also run M-SPARC using the MATLAB parallel pool over k-points/spin by providing a second argument, \texttt{parallel\_switch}, when running M-SPARC:
+\begin{verbatim}
+S = msparc(`filename',parallel_switch);
+\end{verbatim}
+If \texttt{parallel\_switch = 1}, M-SPARC will start using the parallel pool, and if \texttt{parallel\_switch = 0}, M-SPARC will not use the parallel pool, which is the default.
+\end{frame}
+
+
+\begin{frame}[allowframebreaks,fragile]{\textbf{Output}} \label{Output}
+Upon successful execution of the
+%\begin{verbatim}
+``\texttt{S = msparc(`filename');}"
+%\end{verbatim}
+command, an output structure is returned and stored in \texttt{S}. The structure \texttt{S} contains detailed information that can be useful for post-processing and debugging. Information such as the input parameters, densities, wavefunctions, eigenvalues, and all electronic ground-state properties calculated are stored in the output structure.\\
+
+Apart from the output structure returned, depending on the calculations performed, some output files will be created in the same location as the input files too. \\
+
+\textbf{Single point calculations} \\
+\begin{itemize}
+ \item ``.out" file -- Contains general information about the test, including input parameters, SCF convergence progress, ground state properties and timing information.
+ \item ``.static" file -- Contains the atomic positions and atomic forces if the user chooses to print these information..
+\end{itemize}
+
+\textbf{Structrual relaxation calculations} \\
+\begin{itemize}
+ \item ``.out" file -- See above.
+ \item ``.geopt" file -- Contains the atomic positions and atomic forces for each relaxation step. This file is created only when the unit cell is fixed. For cell relaxation a `.cellopt` file is created instead.
+ \item ``.cellopt" file -- Contains the cell information (lattice vectors, cell lengths, volume) and stresses for each relaxation step. Only created for cell relaxation.
+ \item ``.restart" file -- Contains information necessary to perform a restarted structural relaxation calculation.
+\end{itemize}
+
+\textbf{Molecular dynamics (MD) calculations} \\
+\begin{itemize}
+ \item ``.out" file -- See above.
+ \item ``.aimd" file -- Contains the atomic positions, atomic velocities, atomic forces, electronic temperature, ionic temperature and total energy for each MD step.
+ \item ``.restart" file -- Contains information necessary to perform a restarted MD calculation.
+\end{itemize}
+
+\end{frame}
+
+
+\begin{frame}[allowframebreaks]{\textbf{Input file options}} \label{Index}
+\vspace{-2mm}
+\begin{block}{System}
+\hyperlink{CELL}{\texttt{CELL}} $\vert$ \hyperlink{LATVEC}{\texttt{LATVEC}} $\vert$ \hyperlink{FD_GRID}{\texttt{FD\_GRID}} $\vert$ \hyperlink{MESH_SPACING}{\texttt{MESH\_SPACING}} $\vert$ \hyperlink{ECUT}{\texttt{ECUT}} $\vert$ \hyperlink{BC}{\texttt{BC}} $\vert$ \hyperlink{FD_ORDER}{\texttt{FD\_ORDER}} $\vert$ \hyperlink{EXCHANGE_CORRELATION}{\texttt{EXCHANGE\_CORRELATION}} $\vert$ \hyperlink{SPIN_TYP}{\texttt{SPIN\_TYP}} $\vert$ \hyperlink{KPOINT_GRID}{\texttt{KPOINT\_GRID}} $\vert$ \hyperlink{KPOINT_SHIFT}{\texttt{KPOINT\_SHIFT}} $\vert$ \hyperlink{ELEC_TEMP_TYPE}{\texttt{ELEC\_TEMP\_TYPE}} $\vert$ \hyperlink{ELEC_TEMP}{\texttt{ELEC\_TEMP}} $\vert$ \hyperlink{SMEARING}{\texttt{SMEARING}} $\vert$ \hyperlink{NSTATES}{\texttt{NSTATES}} \\
+\hyperlink{ATOM_TYPE}{\texttt{ATOM\_TYPE}} $\vert$ \hyperlink{PSEUDO_POT}{\texttt{PSEUDO\_POT}} $\vert$ \hyperlink{N_TYPE_ATOM}{\texttt{N\_TYPE\_ATOM}} $\vert$ \hyperlink{COORD}{\texttt{COORD}} $\vert$ \hyperlink{COORD_FRAC}{\texttt{COORD\_FRAC}} $\vert$ \hyperlink{RELAX}{\texttt{RELAX}} $\vert$ \hyperlink{SPIN}{\texttt{SPIN}}
+\end{block}
+
+\begin{block}{SCF}
+\hyperlink{CHEB_DEGREE}{\texttt{CHEB\_DEGREE}} $\vert$ \hyperlink{RHO_TRIGGER}{\texttt{RHO\_TRIGGER}} $\vert$ \hyperlink{MAXIT_SCF}{\texttt{MAXIT\_SCF}} $\vert$ \hyperlink{TOL_SCF}{\texttt{TOL\_SCF}} $\vert$ \hyperlink{SCF_FORCE_ACC}{\texttt{SCF\_FORCE\_ACC}} $\vert$ \hyperlink{SCF_ENERGY_ACC}{\texttt{SCF\_ENERGY\_ACC}} $\vert$ \hyperlink{TOL_LANCZOS}{\texttt{TOL\_LANCZOS}} $\vert$ \hyperlink{MIXING_VARIABLE}{\texttt{MIXING\_VARIABLE}} $\vert$ \hyperlink{MIXING_HISTORY}{\texttt{MIXING\_HISTORY}} $\vert$ \hyperlink{MIXING_PARAMETER}{\texttt{MIXING\_PARAMETER}} $\vert$ \hyperlink{PULAY_FREQUENCY}{\texttt{PULAY\_FREQUENCY}} $\vert$ \hyperlink{PULAY_RESTART_FREQ}{\texttt{PULAY\_RESTART\_FREQ}} $\vert$ \hyperlink{MIXING_PRECOND}{\texttt{MIXING\_PRECOND}} $\vert$ \hyperlink{TOL_PRECOND}{\texttt{TOL\_PRECOND}} $\vert$ \hyperlink{PRECOND_KERKER_KTF}{\texttt{PRECOND\_KERKER\_KTF}} $\vert$ \hyperlink{PRECOND_KERKER_THRESH}{\texttt{PRECOND\_KERKER\_THRESH}} $\vert$ \hyperlink{PRECOND_RESTA_Q0}{\texttt{PRECOND\_RESTA\_Q0}} $\vert$ \hyperlink{PRECOND_RESTA_RS}{\texttt{PRECOND\_RESTA\_RS}} $\vert$ \hyperlink{PRECOND_FITPOW}{\texttt{PRECOND\_FITPOW}}
+\end{block}
+
+\vspace{-2mm}
+\begin{block}{Electrostatics}
+\hyperlink{TOL_POISSON}{\texttt{TOL\_POISSON}} $\vert$ \hyperlink{TOL_PSEUDOCHARGE}{\texttt{TOL\_PSEUDOCHARGE}} $\vert$ \hyperlink{REFERENCE_CUTOFF}{\texttt{REFERENCE\_CUTOFF}}
+\end{block}
+
+\vspace{-2mm}
+\begin{block}{Stress calculation}
+\hyperlink{CALC_STRESS}{\texttt{CALC\_STRESS}} $\vert$ \hyperlink{CALC_PRES}{\texttt{CALC\_PRES}}
+\end{block}
+\vspace{-2mm}
+
+\begin{block}{MD}
+\hyperlink{MD_FLAG}{\texttt{MD\_FLAG}} $\vert$ \hyperlink{MD_METHOD}{\texttt{MD\_METHOD}} $\vert$ \hyperlink{MD_NSTEP}{\texttt{MD\_NSTEP}} $\vert$ \hyperlink{MD_TIMESTEP}{\texttt{MD\_TIMESTEP}} $\vert$ \hyperlink{ION_TEMP}{\texttt{ION\_TEMP}} $\vert$ \hyperlink{ION_ELEC_EQT}{\texttt{ION\_ELEC\_EQT}} $\vert$ \hyperlink{RESTART_FLAG}{\texttt{RESTART\_FLAG}}
+\end{block}
+\vspace{-2mm}
+\begin{block}{Structural relaxation}
+\hyperlink{RELAX_FLAG}{\texttt{RELAX\_FLAG}} $\vert$ \hyperlink{RELAX_METHOD}{\texttt{RELAX\_METHOD}} $\vert$ \hyperlink{RELAX_NITER}{\texttt{RELAX\_NITER}} $\vert$ \hyperlink{TOL_RELAX}{\texttt{TOL\_RELAX}} $\vert$ \hyperlink{TOL_RELAX_CELL}{\texttt{TOL\_RELAX\_CELL}} $\vert$ \hyperlink{RELAX_MAXDIAL}{\texttt{RELAX\_MAXDIAL}} $\vert$ \hyperlink{NLCG_SIGMA}{\texttt{NLCG\_SIGMA}} $\vert$ \hyperlink{L_HISTORY}{\texttt{L\_HISTORY}} $\vert$ \hyperlink{L_FINIT_STP}{\texttt{L\_FINIT\_STP}} $\vert$ \hyperlink{L_MAXMOV}{\texttt{L\_MAXMOV}} $\vert$ \hyperlink{L_AUTOSCALE}{\texttt{L\_AUTOSCALE}} $\vert$ \hyperlink{L_LINEOPT}{\texttt{L\_LINEOPT}} $\vert$ \hyperlink{L_ICURV}{\texttt{L\_ICURV}} $\vert$ \hyperlink{FIRE_DT}{\texttt{FIRE\_DT}} $\vert$ \hyperlink{FIRE_MASS}{\texttt{FIRE\_MASS}} $\vert$ \hyperlink{FIRE_MAXMOV}{\texttt{FIRE\_MAXMOV}} $\vert$ \hyperlink{RESTART_FLAG}{\texttt{RESTART\_FLAG}}
+\end{block}
+
+\begin{block}{Print options}
+\hyperlink{PRINT_ATOMS}{\texttt{PRINT\_ATOMS}} $\vert$ \hyperlink{PRINT_FORCES}{\texttt{PRINT\_FORCES}} $\vert$ \hyperlink{PRINT_MDOUT}{\texttt{PRINT\_MDOUT}} $\vert$ \hyperlink{PRINT_RELAXOUT}{\texttt{PRINT\_RELAXOUT}} $\vert$ \hyperlink{PRINT_RESTART}{\texttt{PRINT\_RESTART}} $\vert$ \hyperlink{PRINT_RESTART_FQ}{\texttt{PRINT\_RESTART\_FQ}} $\vert$ \hyperlink{PRINT_VELS}{\texttt{PRINT\_VELS}} $\vert$ \hyperlink{OUTPUT_FILE}{\texttt{OUTPUT\_FILE}}
+\end{block}
+
+
+\end{frame}
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks,c]{} \label{System}
+
+\begin{center}
+\Huge \textbf{System: .inpt file}
+\end{center}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{CELL}} \label{CELL}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+None
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+Bohr
+\end{block}
+
+\begin{block}{Example}
+\texttt{CELL}: 10.20 11.21 7.58
+\end{block}
+\end{columns}
+\begin{block}{Description}
+A set of three whitespace delimited values specifying the cell lengths in the lattice vector (\hyperlink{LATVEC}{\texttt{LATVEC}}) directions, respectively.
+\end{block}
+
+\begin{block}{Remark}
+The values should not be separated by more than one white space character.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{LATVEC}} \label{LATVEC}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double array
+\end{block}
+
+\begin{block}{Default}
+1.0 0.0 0.0\\
+0.0 1.0 0.0\\
+0.0 0.0 1.0\\
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{LATVEC}: \\
+0.5 0.5 0.0\\
+0.0 0.5 0.5\\
+0.5 0.0 0.5\\
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+A set of three vectors in row major order specifying the lattice vectors of the simulation domain (\hyperlink{CELL}{\texttt{CELL}}).
+\end{block}
+
+%\begin{block}{Remark}
+%Lattice vectors need not be unit vectors.
+%\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{FD\_GRID}} \label{FD_GRID}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Integer
+\end{block}
+
+\begin{block}{Default}
+None
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{FD\_GRID}: 26 26 30
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+A set of three whitespace delimited values specifying the number of finite-difference intervals in the lattice vector (\hyperlink{LATVEC}{\texttt{LATVEC}}) directions, respectively.
+\end{block}
+
+\begin{block}{Remark}
+The convergence of results with respect to spatial discretization needs to be verified. \hyperlink{ECUT}{\texttt{ECUT}}, \hyperlink{MESH_SPACING}{\texttt{MESH\_SPACING}}, \hyperlink{FD_GRID}{\texttt{FD\_GRID}} cannot be specified simultaneously.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{MESH\_SPACING}} \label{MESH_SPACING}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+None
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+Bohr
+\end{block}
+
+\begin{block}{Example}
+\texttt{MESH\_SPACING}: 0.4
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Mesh spacing of the finite-difference grid.
+\end{block}
+
+\begin{block}{Remark}
+The exact mesh-size will be determined by the size of the domain. \hyperlink{MESH_SPACING}{\texttt{MESH\_SPACING}}, \hyperlink{FD_GRID}{\texttt{FD\_GRID}}, \hyperlink{ECUT}{\texttt{ECUT}} cannot be specified simultaneously.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{ECUT}} \label{ECUT}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+None
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+Ha
+\end{block}
+
+\begin{block}{Example}
+\texttt{ECUT}: 30
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Equivalent plane-wave energy cutoff, based on which \hyperlink{MESH_SPACING}{\texttt{MESH\_SPACING}} will be automatically calculated.
+\end{block}
+
+\begin{block}{Remark}
+This is not exact, but rather an estimate. \hyperlink{ECUT}{\texttt{ECUT}}, \hyperlink{MESH_SPACING}{\texttt{MESH\_SPACING}}, \hyperlink{FD_GRID}{\texttt{FD\_GRID}} cannot be specified simultaneously.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{BC}} \label{BC}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Character
+\end{block}
+
+\begin{block}{Default}
+None
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{BC}: \texttt{P D D}
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+A set of three whitespace delimited characters specifying the boundary conditions in the lattice vector directions, respectively. \texttt{P} represents periodic boundary conditions and \texttt{D} represents Dirichlet boundary conditions.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{FD\_ORDER}} \label{FD_ORDER}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Integer
+\end{block}
+
+\begin{block}{Default}
+12
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{FD\_ORDER}: 12
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Order of the finite-difference approximation.
+\end{block}
+
+\begin{block}{Remark}
+Restricted to even integers since central finite-differences are employed. The default value of 12 has been found to be an efficient choice for most systems.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{EXCHANGE\_CORRELATION}} \label{EXCHANGE_CORRELATION}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.35\linewidth}
+\begin{block}{Type}
+String
+\end{block}
+
+\begin{block}{Default}
+No Default
+\end{block}
+
+\column{0.55\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{EXCHANGE\_CORRELATION}: \texttt{LDA\_PW}
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Choice of exchange-correlation functional. Options are \texttt{LDA\_PW} (Perdew-Wang LDA), \texttt{LDA\_PZ} (Purdew-Zunger LDA), and \texttt{GGA\_PBE} (PBE GGA).
+\end{block}
+
+\begin{block}{Remark}
+For spin-polarized calculation (\hyperlink{SPIN_TYP}{\texttt{SPIN\_TYP}} = 1), \texttt{LDA\_PZ} is not available.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{SPIN\_TYP}} \label{SPIN_TYP}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Integer
+\end{block}
+
+\begin{block}{Default}
+0
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{SPIN\_TYP}: 1
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+\texttt{SPIN\_TYP}: 0 performs spin unpolarized calculation. \\
+\texttt{SPIN\_TYP}: 1 performs unconstrained collinear spin-polarized calculation.
+\end{block}
+
+\begin{block}{Remark}
+\texttt{SPIN\_TYP} can only take values 0 and 1.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{KPOINT\_GRID}} \label{KPOINT_GRID}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Integer array
+\end{block}
+
+\begin{block}{Default}
+ 1 1 1
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{KPOINT\_GRID}: 2 3 4
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Number of k-points in each direction of the Monkhorst-Pack grid for Brillouin zone integration.
+\end{block}
+
+\begin{block}{Remark}
+Time-reversal symmetry is assumed to hold.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{KPOINT\_SHIFT}} \label{KPOINT_SHIFT}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double array
+\end{block}
+
+\begin{block}{Default}
+ 0.0 0.0 0.0
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{KPOINT\_SHIFT}: 0.5 0.5 0.5
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Shift of k-points in each direction of the k-point lattice.
+\end{block}
+
+\begin{block}{Remark}
+The shift is in reduced coordinates. The default zero shift corresponds to the Monkhorst-Pack grid.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{ELEC\_TEMP\_TYPE}} \label{ELEC_TEMP_TYPE}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+String
+\end{block}
+
+\begin{block}{Default}
+\texttt{gaussian}
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{ELEC\_TEMP\_TYPE}: \texttt{fd}
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Function used for the smearing (electronic temperature). Options are: \texttt{fermi-dirac} (or \texttt{fd}), \texttt{gaussian}.
+\end{block}
+
+\begin{block}{Remark}
+Use \hyperlink{ELEC_TEMP}{\texttt{ELEC\_TEMP}} or \hyperlink{SMEARING}{\texttt{SMEARING}} to set smearing value.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{ELEC\_TEMP}} \label{ELEC_TEMP}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+1160.452
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+Kelvin
+\end{block}
+
+\begin{block}{Example}
+\texttt{ELEC\_TEMP}: 315.773
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Electronic temperature.
+\end{block}
+
+\begin{block}{Remark}
+This is equivalent to setting \hyperlink{SMEARING}{\texttt{SMEARING}} (0.001 Ha = 315.773 Kelvin).
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{SMEARING}} \label{SMEARING}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+0.003675 for \texttt{gaussian} \\
+0.007350 for \texttt{fermi-dirac}
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+Ha
+\end{block}
+
+\begin{block}{Example}
+\texttt{SMEARING}: 0.001
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Value of smearing.
+\end{block}
+
+\begin{block}{Remark}
+Equivalent to setting \hyperlink{ELEC_TEMP}{\texttt{ELEC\_TEMP}} (0.001 Ha = 315.773 Kelvin).
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{NSTATES}} \label{NSTATES}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Integer
+\end{block}
+
+\begin{block}{Default}
+$N_e/2 \times 1.2 + 5$
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{NSTATES}: 24
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+The number of Kohn-Sham states/orbitals.
+\end{block}
+
+\begin{block}{Remark}
+This number should not be smaller than half of
+the total number of valence electrons ($N_e$) in the system. Note that the number of additional states required increases with increasing values of \hyperlink{ELEC_TEMP}{\texttt{ELEC\_TEMP}}/\hyperlink{SMEARING}{\texttt{SMEARING}}.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks,c]{} \label{System:ion}
+
+\begin{center}
+\Huge \textbf{System: .ion file}
+\end{center}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{ATOM\_TYPE}} \label{ATOM_TYPE}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+String
+\end{block}
+
+\begin{block}{Default}
+None
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{ATOM\_TYPE: Fe}
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Atomic type symbol.
+\end{block}
+
+\begin{block}{Remark}
+The atomic type symbol can be attached with a number, e.g., Fe1 and Fe2. This feature is useful if one needs to provide two different pseudopotential files (\hyperlink{PSEUDO_POT}{\texttt{PSEUDO\_POT}}) for the same element.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{PSEUDO\_POT}} \label{PSEUDO_POT}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+String
+\end{block}
+
+\begin{block}{Default}
+None
+\end{block}
+
+\column{0.5\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{PSEUDO\_POT: ../psp/Fe.psp8}
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Path to the pseudopotential file.
+\end{block}
+
+\begin{block}{Remark}
+The default directory for the pseudopotential files is the same as the input files. For example, if a pseudopotential Fe.psp8 is put in the same directory as the input files, one can simply specify \texttt{PSEUDO\_POT: Fe.psp8}.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{N\_TYPE\_ATOM}} \label{N_TYPE_ATOM}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Integer
+\end{block}
+
+\begin{block}{Default}
+None
+\end{block}
+
+\column{0.5\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{N\_TYPE\_ATOM: 2}
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+The number of atoms of a \hyperlink{ATOM_TYPE}{\texttt{ATOM\_TYPE}} specified immediately before this variable.
+\end{block}
+
+\begin{block}{Remark}
+For a system with different types of atoms, one has to specify the number of atoms for every type.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{COORD}} \label{COORD}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+None
+\end{block}
+
+\column{0.5\linewidth}
+\begin{block}{Unit}
+Bohr
+\end{block}
+
+\begin{block}{Example}
+\texttt{COORD: \\}
+0.0 0.0 0.0 \\
+2.5 2.5 2.5
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+The Cartesian coordinates of atoms of a \hyperlink{ATOM_TYPE}{\texttt{ATOM\_TYPE}} specified before this variable. If the coordinates are outside the fundamental domain (see \hyperlink{CELL}{\texttt{CELL}} and \hyperlink{LATVEC}{\texttt{LATVEC}}) in the periodic directions (see \hyperlink{BC}{\texttt{BC}}), it will be automatically mapped back to the domain.
+\end{block}
+
+\begin{block}{Remark}
+For a system with different types of atoms, one has to specify the coordinates for every \hyperlink{ATOM_TYPE}{\texttt{ATOM\_TYPE}}. One can also specify the coordinates of the atoms using \hyperlink{COORD_FRAC}{\texttt{COORD\_FRAC}}.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{COORD\_FRAC}} \label{COORD_FRAC}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+None
+\end{block}
+
+\column{0.5\linewidth}
+\begin{block}{Unit}
+None
+\end{block}
+
+\begin{block}{Example}
+\texttt{COORD\_FRAC: \\}
+0.5 0.5 0.0 \\
+0.0 0.5 0.5
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+The fractional coordinates of atoms of a \hyperlink{ATOM_TYPE}{\texttt{ATOM\_TYPE}} specified before this variable. \texttt{COORD\_FRAC}$(i,j)$ $\times$ \hyperlink{CELL}{\texttt{CELL}}$(j)$, $(j = 1,2,3)$ gives the coordinate of the $i^{th}$ atom along the $j^{th}$ \hyperlink{LATVEC}{\texttt{LATVEC}} direction. If the coordinates are outside the fundamental domain (see \hyperlink{CELL}{\texttt{CELL}} and \hyperlink{LATVEC}{\texttt{LATVEC}}) in the periodic directions (see \hyperlink{BC}{\texttt{BC}}), it will be automatically mapped back to the domain.
+\end{block}
+
+\begin{block}{Remark}
+For a system with different types of atoms, one has to specify the coordinates for every \hyperlink{ATOM_TYPE}{\texttt{ATOM\_TYPE}}. One can also specify the coordinates of the atoms using \hyperlink{COORD}{\texttt{COORD}}.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{RELAX}} \label{RELAX}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Integer
+\end{block}
+
+\begin{block}{Default}
+1 1 1
+\end{block}
+
+\column{0.5\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{RELAX: \\}
+1 0 1 \\
+0 1 0
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Atomic coordinate with the corresponding \texttt{RELAX} value 0 is held fixed during relaxation/MD.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{SPIN}} \label{SPIN}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+0.0
+\end{block}
+
+\column{0.5\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{SPIN: \\}
+1.0 \\
+-1.0
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Specifies the net initial spin on each atom for a spin-polarized calculation.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks,c]{} \label{SCF}
+
+\begin{center}
+\Huge \textbf{SCF}
+\end{center}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{CHEB\_DEGREE}} \label{CHEB_DEGREE}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Integer
+\end{block}
+
+\begin{block}{Default}
+Automatically set.
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{CHEB\_DEGEE}: 25
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Degree of polynomial used for Chebyshev filtering.
+\end{block}
+
+\begin{block}{Remark}
+For larger mesh-sizes, smaller values of \texttt{CHEB\_DEGREE} are generally more efficient, and vice-versa.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{RHO\_TRIGGER}} \label{RHO_TRIGGER}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Integer
+\end{block}
+
+\begin{block}{Default}
+4
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{RHO\_TRIGGER}: 5
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+The number of times Chebyshev filtering is repeated before updating the electron density in the very first SCF iteration.
+\end{block}
+
+\begin{block}{Remark}
+Values smaller than the default value of 4 can result in a significant increase in the number of SCF
+iterations. Larger values can sometimes reduce the number of SCF iterations.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{{MAXIT\_SCF}}} \label{MAXIT_SCF}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Integer
+\end{block}
+
+\begin{block}{Default}
+100
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{MAXIT\_SCF}: 50
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Maximum number of SCF iterations.
+\end{block}
+
+\begin{block}{Remark}
+Larger values than the default of 100 may be required for highly inhomogeneous systems, particularly when small values of \hyperlink{SMEARING}{\texttt{SMEARING}}/\hyperlink{ELEC_TEMP}{\texttt{ELEC\_TEMP}} are chosen.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{TOL\_SCF}} \label{TOL_SCF}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+Automatically set for $10^{-3}$ Ha/Bohr accuracy in force
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{TOL\_SCF}: 1e-5
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+The tolerance on the normalized residual of the effective potential or the electron density for convergence of the SCF iteration.
+\end{block}
+
+\begin{block}{Remark}
+Only one of \hyperlink{TOL_SCF}{\texttt{TOL\_SCF}}, \hyperlink{SCF_ENERGY_ACC}{\texttt{SCF\_ENERGY\_ACC}}, or \hyperlink{SCF_FORCE_ACC}{\texttt{SCF\_FORCE\_ACC}} can be specified.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{SCF\_FORCE\_ACC}} \label{SCF_FORCE_ACC}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+None
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+Ha/Bohr
+\end{block}
+
+\begin{block}{Example}
+\texttt{SCF\_FORCE\_ACC}: 1e-4
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+The tolerance on the atomic forces for convergence of the SCF iteration.
+\end{block}
+
+\begin{block}{Remark}
+Only one of \hyperlink{SCF_FORCE_ACC}{\texttt{SCF\_FORCE\_ACC}}, \hyperlink{TOL_SCF}{\texttt{TOL\_SCF}} or \hyperlink{SCF_ENERGY_ACC}{\texttt{SCF\_ENERGY\_ACC}} can be specified.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{SCF\_ENERGY\_ACC}} \label{SCF_ENERGY_ACC}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+None
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+Ha/atom
+\end{block}
+
+\begin{block}{Example}
+\texttt{SCF\_ENERGY\_ACC}: 1e-5
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+The tolerance on the free energy for the convergence of the SCF iteration.
+\end{block}
+
+\begin{block}{Remark}
+Only one of \hyperlink{SCF_ENERGY_ACC}{\texttt{SCF\_ENERGY\_ACC}}, \hyperlink{SCF_FORCE_ACC}{\texttt{SCF\_FORCE\_ACC}}, or \hyperlink{TOL_SCF}{\texttt{TOL\_SCF}} can be specified.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{TOL\_LANCZOS}} \label{TOL_LANCZOS}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+1e-2
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{TOL\_LANCZOS}: 1e-3
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+The tolerance within the Lanczos algorithm for calculating the extremal eigenvalues of the Hamiltonian, required as part of the CheFSI method.
+\end{block}
+
+\begin{block}{Remark}
+Typically, the Lanczos tolerance does not need to be very strict.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{MIXING\_VARIABLE}} \label{MIXING_VARIABLE}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+String
+\end{block}
+
+\begin{block}{Default}
+\texttt{potential}
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{MIXING\_VARIABLE}: \texttt{density}
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+This specifies whether potential or density mixing is performed in the SCF iteration. Available options are: \texttt{potential} and \texttt{density}.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{MIXING\_HISTORY}} \label{MIXING_HISTORY}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Integer
+\end{block}
+
+\begin{block}{Default}
+7
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{MIXING\_HISTORY}: 40
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+The mixing history used in Pulay mixing.
+\end{block}
+
+\begin{block}{Remark}
+Too small values of \hyperlink{MIXING_HISTORY}{\texttt{MIXING\_HISTORY}} can result in poor SCF convergence.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{MIXING\_PARAMETER}} \label{MIXING_PARAMETER}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+0.3
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{MIXING\_PARAMETER}: 0.1
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+The value of the relaxation parameter used in Pulay/simple mixing.
+\end{block}
+
+\begin{block}{Remark}
+Values larger than the default value of 0.3 can be used for insulating systems, whereas smaller values are generally required for metallic systems, particularly at small values of \hyperlink{SMEARING}{\texttt{SMEARING}} or \hyperlink{ELEC_TEMP}{\texttt{ELEC\_TEMP}}.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{PULAY\_FREQUENCY}} \label{PULAY_FREQUENCY}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Integer
+\end{block}
+
+\begin{block}{Default}
+1
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{PULAY\_FREQUENCY}: 4
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+The frequency of Pulay mixing in Periodic Pulay.
+\end{block}
+
+\begin{block}{Remark}
+The default value of 1 corresponds to Pulay mixing.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{PULAY\_RESTART\_FREQ}} \label{PULAY_RESTART_FREQ}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Integer
+\end{block}
+
+\begin{block}{Default}
+0
+\end{block}
+
+\column{0.5\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{PULAY\_RESTART\_FREQ}: 4
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+The frequency for restarting the `Periodic Pulay' mixing. If set to 0, the restarted Pulay method is turned off.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{MIXING\_PRECOND}} \label{MIXING_PRECOND}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+String
+\end{block}
+
+\begin{block}{Default}
+none
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{MIXING\_PRECOND}: \texttt{kerker}
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+This specifies the preconditioner used in the SCF iteration. Available options are: \texttt{none}, \texttt{kerker}, \texttt{resta} and \texttt{truncated\_kerker}.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{TOL\_PRECOND}} \label{TOL_PRECOND}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+$h^2\times0.001$
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{TOL\_PRECOND}: 1e-4
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+The tolerance on the relative residual for the linear systems arising during the real-space preconditioning of the SCF.
+\end{block}
+
+\begin{block}{Remark}
+The linear systems do not need to be solved very accurately. $h$ is the mesh spacing.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{PRECOND\_KERKER\_KTF}} \label{PRECOND_KERKER_KTF}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+1.0
+\end{block}
+
+\column{0.5\linewidth}
+\begin{block}{Unit}
+$\textrm{Bohr}^{-1}$
+\end{block}
+
+\begin{block}{Example}
+\texttt{PRECOND\_KERKER\_KTF}: 0.8
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+The Thomas-Fermi screening length appearing in the \texttt{kerker} and \texttt{truncated\_kerker} preconditioners (\hyperlink{MIXING_PRECOND}{\texttt{MIXING\_PRECOND}}).
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{PRECOND\_KERKER\_THRESH}} \label{PRECOND_KERKER_THRESH}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+0.25
+\end{block}
+
+\column{0.5\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{PRECOND\_KERKER\_THRESH}: 0.1
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+The threshold for the \texttt{truncated\_kerker} preconditioner (\hyperlink{MIXING_PRECOND}{\texttt{MIXING\_PRECOND}}).
+\end{block}
+
+\begin{block}{Remark}
+This threshold will be scaled by the \hyperlink{MIXING_PARAMETER}{\texttt{MIXING\_PARAMETER}}. If the threshold is set to 0, the \texttt{kerker} preconditioner is recovered.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{PRECOND\_RESTA\_Q0}} \label{PRECOND_RESTA_Q0}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+1.36
+\end{block}
+
+\column{0.5\linewidth}
+\begin{block}{Unit}
+$\textrm{Bohr}^{-1}$
+\end{block}
+
+\begin{block}{Example}
+\texttt{PRECOND\_RESTA\_Q0}: 1.10
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+The Fermi-momentum-related quantity appearing in \texttt{resta} preconditioner (\hyperlink{MIXING_PRECOND}{\texttt{MIXING\_PRECOND}}).
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{PRECOND\_RESTA\_RS}} \label{PRECOND_RESTA_RS}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+2.76
+\end{block}
+
+\column{0.5\linewidth}
+\begin{block}{Unit}
+Bohr
+\end{block}
+
+\begin{block}{Example}
+\texttt{PRECOND\_RESTA\_RS}: 4.28
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+The screening length appearing in the \texttt{resta} preconditioner (\hyperlink{MIXING_PRECOND}{\texttt{MIXING\_PRECOND}}).
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{PRECOND\_FITPOW}} \label{PRECOND_FITPOW}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Integer
+\end{block}
+
+\begin{block}{Default}
+2
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{PRECOND\_FITPOW}: 3
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Half of the highest degree of rational polynomials used for the real-space preconditioning of the SCF iteration.
+\end{block}
+
+\begin{block}{Remark}
+Currently this number cannot be larger than 5. Used only for the \texttt{resta} and \texttt{truncated\_kerker} preconditioners.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks,c]{} \label{Electrostatics}
+
+\begin{center}
+\Huge \textbf{Electrostatics}
+\end{center}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{TOL\_POISSON}} \label{TOL_POISSON}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Integer
+\end{block}
+
+\begin{block}{Default}
+\hyperlink{TOL_SCF}{\texttt{TOL\_SCF}}$\times 0.01$
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{TOL\_POISSON}: 1e-6
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+The tolerance on the norm of the relative residual for the Poisson equation.
+\end{block}
+
+\begin{block}{Remark}
+The tolerance for poisson solver should not be worse than \hyperlink{TOL_SCF}{\texttt{TOL\_SCF}}, otherwise it might seriously affect the convergence of the SCF iteration.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{TOL\_PSEUDOCHARGE}} \label{TOL_PSEUDOCHARGE}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+\hyperlink{TOL_SCF}{\texttt{TOL\_SCF}}$\times 0.01$
+\end{block}
+
+\column{0.45\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{TOL\_PSEUDOCHARGE}: 1e-6
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+The normalized error in the net enclosed charge for the pseudocharge density of each atom.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{REFERENCE\_CUTOFF}} \label{REFERENCE_CUTOFF}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+0.5
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+Bohr
+\end{block}
+
+\begin{block}{Example}
+\texttt{REFERENCE\_CUTOFF}: 1.0
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+The cutoff radius of the reference potential used for evaluating the electrostatic correction arising from overlapping pseudocharge densities.
+\end{block}
+
+\begin{block}{Remark}
+This number should be smaller than half the smallest interatomic distance.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks,c]{} \label{Stress calculation}
+
+\begin{center}
+\Huge \textbf{Stress calculation}
+\end{center}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{CALC\_STRESS}} \label{CALC_STRESS}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Integer
+\end{block}
+
+\begin{block}{Default}
+0
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{CALC\_STRESS}: 1
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Flag for calculation of the Hellmann-Feynman stress tensor (in cartesian coordinates).
+\end{block}
+
+%\begin{block}{Remark}
+%\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{CALC\_PRES}} \label{CALC_PRES}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Integer
+\end{block}
+
+\begin{block}{Default}
+0
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{CALC\_PRES}: 1
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Flag for calculation of the pressure.
+\end{block}
+
+\begin{block}{Remark}
+Pressure is directly calculated, without calculation of the stress tensor.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks,c]{} \label{MD}
+
+\begin{center}
+\Huge \textbf{MD}
+\end{center}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{MD\_FLAG}} \label{MD_FLAG}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Integer
+\end{block}
+
+\begin{block}{Default}
+0
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{MD\_FLAG}: 1
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+MD simulations are performed if the flag is set to 1.
+\end{block}
+
+\begin{block}{Remark}
+\hyperlink{MD_FLAG}{\texttt{MD\_FLAG}} and \hyperlink{RELAX_FLAG}{\texttt{RELAX\_FLAG}} both cannot be set to 1.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{MD\_METHOD}} \label{MD_METHOD}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+String
+\end{block}
+
+\begin{block}{Default}
+NVE
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{MD\_METHOD}: NVE
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Type of MD to be performed.
+\end{block}
+
+\begin{block}{Remark}
+Only NVE (microcanonical ensemble) is supported.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{MD\_NSTEP}} \label{MD_NSTEP}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Integer
+\end{block}
+
+\begin{block}{Default}
+0
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{MD\_NSTEP}: 100
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Specifies the number of MD steps.
+\end{block}
+
+\begin{block}{Remark}
+If MD\_NSTEP $= N$, the MD runs from $0$ to $(N-1) \times$ \hyperlink{MD_TIMESTEP}{\texttt{MD\_TIMESTEP}} fs.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{MD\_TIMESTEP}} \label{MD_TIMESTEP}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+1
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+Femtosecond
+\end{block}
+
+\begin{block}{Example}
+\texttt{MD\_TIMESTEP}: 0.1
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+MD time step.
+\end{block}
+
+\begin{block}{Remark}
+Total MD time is given by: \hyperlink{MD_TIMESTEP}{\texttt{MD\_TIMESTEP}} $\times$ \hyperlink{MD_NSTEP}{\texttt{MD\_NSTEP}}.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{ION\_TEMP}} \label{ION_TEMP}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+No Default
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+Kelvin
+\end{block}
+
+\begin{block}{Example}
+\texttt{ION\_TEMP}: 315
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Starting ionic temperature in MD, used to generate initial velocity distribution.
+\end{block}
+
+\begin{block}{Remark}
+Must be specified if \hyperlink{MD_FLAG}{\texttt{MD\_FLAG}} is set to $1$.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{ION\_ELEC\_EQT}} \label{ION_ELEC_EQT}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Integer
+\end{block}
+
+\begin{block}{Default}
+1
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{ION\_ELEC\_EQT}: 0
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Flag that determines whether the \hyperlink{ELEC_TEMP}{\texttt{ELEC\_TEMP}} will be set equal to \hyperlink{ION_TEMP}{\texttt{ION\_TEMP}} during MD.
+\end{block}
+
+\begin{block}{Remark}
+If the flag is set to 0, the values of \hyperlink{ELEC_TEMP}{\texttt{ELEC\_TEMP}} and \hyperlink{ION_TEMP}{\texttt{ION\_TEMP}} need to be identical.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{RESTART\_FLAG}} \label{RESTART_FLAG}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Integer
+\end{block}
+
+\begin{block}{Default}
+0
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{RESTART\_FLAG}: 0
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Flag for restarting molecular dynamics and structural relaxation.
+\end{block}
+
+\begin{block}{Remark}
+Restarts from the previous configuration which is stored in a .restart file.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks,c]{} \label{Structural relaxation}
+
+\begin{center}
+\Huge \textbf{Structural relaxation}
+\end{center}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{RELAX\_FLAG}} \label{RELAX_FLAG}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Integer
+\end{block}
+
+\begin{block}{Default}
+0
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{RELAX\_FLAG}: 1
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Flag for performing structural relaxation. $0$ means no structural relaxation. $1$ represents relaxation of atom positions. $2$ represents optimization of volume with the fractional coordinates of the atoms fixed.
+\end{block}
+
+\begin{block}{Remark}
+This flag should not be specified if \hyperlink{MD_FLAG}{\texttt{MD\_FLAG}} is set to $1$.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{RELAX\_METHOD}} \label{RELAX_METHOD}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+String
+\end{block}
+
+\begin{block}{Default}
+LBFGS
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{RELAX\_METHOD}: NLCG
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Specifies the algorithm for structural relaxation. The choices are `LBFGS' (limited-memory BFGS), `NLCG' (Non-linear conjugate gradient), and `FIRE' (Fast inertial relaxation engine).
+\end{block}
+
+\begin{block}{Remark}
+LBFGS is typically the best choice.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{RELAX\_NITER}} \label{RELAX_NITER}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Integer
+\end{block}
+
+\begin{block}{Default}
+100
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{RELAX\_NITER}: 25
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Specifies the maximum number of iterations for the structural relaxation (\hyperlink{RELAX_FLAG}{\texttt{RELAX\_FLAG}}).
+\end{block}
+
+\begin{block}{Remark}
+If \hyperlink{RESTART_FLAG}{\texttt{RESTART\_FLAG}} is set to $1$, then relaxation will restart from the last atomic configuration and run for maximum of \hyperlink{RELAX_NITER}{\texttt{RELAX\_NITER}} iterations.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{TOL\_RELAX}} \label{TOL_RELAX}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+5e-4
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+Ha/Bohr
+\end{block}
+
+\begin{block}{Example}
+\texttt{TOL\_RELAX}: 1e-3
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Specifies the tolerance for termination of the structural relaxation. The tolerance is defined on the maximum force component (in absolute sense) over all atoms.
+\end{block}
+
+%\begin{block}{Remark}
+%\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{TOL\_RELAX\_CELL}} \label{TOL_RELAX_CELL}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+1e-2
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+GPa
+\end{block}
+
+\begin{block}{Example}
+\texttt{TOL\_RELAX}: 1e-3
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Specifies the tolerance for termination of the cell relaxation. The tolerance is defined on the maximum principle stress component.
+\end{block}
+
+%\begin{block}{Remark}
+%\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{RELAX\_MAXDIAL}} \label{RELAX_MAXDIAL}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+1.2
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{RELAX\_MAXDIAL}: 1.4
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+The maximum scaling of the volume allowed with respect to the initial volume defined by \hyperlink{CELL}{\texttt{CELL}} and \hyperlink{LATVEC}{\texttt{LATVEC}}. This will determine the upper-bound and lower-bound in the bisection method (Brent's method) for the volume optimization.
+\end{block}
+
+%\begin{block}{Remark}
+%\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{NLCG\_SIGMA}} \label{NLCG_SIGMA}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+0.5
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{NLCG\_SIGMA}: 1
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Parameter in the secant method used to control the step length in NLCG (\hyperlink{RELAX_METHOD}{\texttt{RELAX\_METHOD}}).
+\end{block}
+
+\begin{block}{Remark}
+Default value works well in most cases.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{L\_HISTORY}} \label{L_HISTORY}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Integer
+\end{block}
+
+\begin{block}{Default}
+20
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{L\_HISTORY}: 15
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Size of history in LBFGS (\hyperlink{RELAX_METHOD}{\texttt{RELAX\_METHOD}}).
+\end{block}
+
+\begin{block}{Remark}
+Default value works well in most cases.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{L\_FINIT\_STP}} \label{L_FINIT_STP}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+5e-3
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+Bohr
+\end{block}
+
+\begin{block}{Example}
+\texttt{L\_FINIT\_STP}: 0.01
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Step length for line optimizer in LBFGS (\hyperlink{RELAX_METHOD}{\texttt{RELAX\_METHOD}}).
+\end{block}
+
+\begin{block}{Remark}
+Default value works well in most cases.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{L\_MAXMOV}} \label{L_MAXMOV}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+0.2
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+Bohr
+\end{block}
+
+\begin{block}{Example}
+\texttt{L\_MAXMOV}: 1.0
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+The maximum allowed step size in LBFGS (\hyperlink{RELAX_METHOD}{\texttt{RELAX\_METHOD}}).
+\end{block}
+
+\begin{block}{Remark}
+Default value works well in most cases.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{L\_AUTOSCALE}} \label{L_AUTOSCALE}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Integer
+\end{block}
+
+\begin{block}{Default}
+1
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{L\_AUTOSCALE}: 0
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Flag for automatically determining the inverse curvature that is used to determine the direction for next iteration in LBFGS (\hyperlink{RELAX_METHOD}{\texttt{RELAX\_METHOD}}).
+\end{block}
+
+\begin{block}{Remark}
+Default works well in most cases.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{L\_LINEOPT}} \label{L_LINEOPT}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Integer
+\end{block}
+
+\begin{block}{Default}
+1
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{L\_LINEOPT}: 0
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Flag for atomic force based line minimization in LBFGS (\hyperlink{RELAX_METHOD}{\texttt{RELAX\_METHOD}}).
+\end{block}
+
+\begin{block}{Remark}
+Required only if \hyperlink{L_AUTOSCALE}{\texttt{L\_AUTOSCALE}} is $0$.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{L\_ICURV}} \label{L_ICURV}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+1.0
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{L\_ICURV}: 0.1
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Initial inverse curvature, used to construct the inverse Hessian matrix in LBFGS (\hyperlink{RELAX_METHOD}{\texttt{RELAX\_METHOD}}).
+\end{block}
+
+\begin{block}{Remark}
+Needed only if \hyperlink{L_AUTOSCALE}{\texttt{L\_AUTOSCALE}} is $0$. Default value works well in most cases.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{FIRE\_DT}} \label{FIRE_DT}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+1
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+Femto second
+\end{block}
+
+\begin{block}{Example}
+\texttt{FIRE\_DT}: 0.1
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Time step used in FIRE (\hyperlink{RELAX_METHOD}{\texttt{RELAX\_METHOD}}).
+\end{block}
+
+\begin{block}{Remark}
+Default value works well in most cases.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{FIRE\_MASS}} \label{FIRE_MASS}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+1.0
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+Atomic mass unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{FIRE\_MASS}: 2.5
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Pseudomass used in FIRE (\hyperlink{RELAX_METHOD}{\texttt{RELAX\_METHOD}}).
+\end{block}
+
+\begin{block}{Remark}
+Default value works well in most cases.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{FIRE\_MAXMOV}} \label{FIRE_MAXMOV}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Double
+\end{block}
+
+\begin{block}{Default}
+0.2
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+Bohr
+\end{block}
+
+\begin{block}{Example}
+\texttt{FIRE\_MAXMOV}: 1.0
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Maximum movement for any atom in FIRE (\hyperlink{RELAX_METHOD}{\texttt{RELAX\_METHOD}}).
+\end{block}
+
+\begin{block}{Remark}
+Default value works well in most cases.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks,c]{} \label{Print options}
+
+\begin{center}
+\Huge \textbf{Print options}
+\end{center}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{PRINT\_ATOMS}} \label{PRINT_ATOMS}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+0 or 1
+\end{block}
+
+\begin{block}{Default}
+0
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{PRINT\_ATOMS}: 1
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Flag for writing the atomic positions. For ground-state calculations, atom positions are printed to a `.static' output file. For structural relaxation calculations, atom positions are printed to a `.geopt' file. For MD calculations, atom positions are printed to a `.aimd' file.
+\end{block}
+
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{PRINT\_FORCES}} \label{PRINT_FORCES}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+0 or 1
+\end{block}
+
+\begin{block}{Default}
+0
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{PRINT\_FORCES}: 1
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Flag for writing the atomic forces. For ground-state calculations, forces are printed to a `.static' output file. For structural relaxation calculations, forces are printed to a `.geopt' file. For MD calculations, forces are printed to a `.aimd' file.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{PRINT\_MDOUT}} \label{PRINT_MDOUT}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+0 or 1
+\end{block}
+
+\begin{block}{Default}
+1
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{PRINT\_MDOUT}: 0
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Flag for printing the the MD output into the .aimd file.
+\end{block}
+
+%\begin{block}{Remark}
+%\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{PRINT\_RELAXOUT}} \label{PRINT_RELAXOUT}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+0 or 1
+\end{block}
+
+\begin{block}{Default}
+1
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{PRINT\_RELAXOUT}: 0
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Flag for printing the structural relaxation data in a .geopt file.
+\end{block}
+
+\begin{block}{Remark}
+Required only if \hyperlink{RELAX_FLAG}{\texttt{RELAX\_FLAG}} is set to $1$.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{PRINT\_RESTART}} \label{PRINT_RESTART}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+0 or 1
+\end{block}
+
+\begin{block}{Default}
+1
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{PRINT\_RESTART}: 0
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Flag for writing the .restart file, used to restart MD and structural relaxation simulations.
+\end{block}
+
+\begin{block}{Remark}
+Relevant only if either \hyperlink{MD_FLAG}{\texttt{MD\_FLAG}} is $1$ or \hyperlink{RELAX_FLAG}{\texttt{RELAX\_FLAG}} is $1$.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{PRINT\_RESTART\_FQ}} \label{PRINT_RESTART_FQ}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+Integer
+\end{block}
+
+\begin{block}{Default}
+1
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{PRINT\_RESTART\_FQ}: 10
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Frequency at which .restart file is written in MD and structural optimization simulations.
+\end{block}
+
+\begin{block}{Remark}
+Relevant only if either \hyperlink{MD_FLAG}{\texttt{MD\_FLAG}} is $1$ or \hyperlink{RELAX_FLAG}{\texttt{RELAX\_FLAG}} is $1$.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{PRINT\_VELS}} \label{PRINT_VELS}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+0 or 1
+\end{block}
+
+\begin{block}{Default}
+1
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{PRINT\_VELS}: 0
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+Flag for printing the ion velocities in an MD simulation into the .aimd file.
+\end{block}
+
+\begin{block}{Remark}
+Relevant only if \hyperlink{MD_FLAG}{\texttt{MD\_FLAG}} is set to $1$.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]{\texttt{OUTPUT\_FILE}} \label{OUTPUT_FILE}
+\vspace*{-12pt}
+\begin{columns}
+\column{0.4\linewidth}
+\begin{block}{Type}
+String
+\end{block}
+
+\begin{block}{Default}
+Same as the input file name
+\end{block}
+
+\column{0.4\linewidth}
+\begin{block}{Unit}
+No unit
+\end{block}
+
+\begin{block}{Example}
+\texttt{OUTPUT\_FILE}: myfname
+\end{block}
+\end{columns}
+
+\begin{block}{Description}
+The name of the output files. The output files are attached with a suffix (`.out',`.static',`.geopt' and `.aimd').
+\end{block}
+
+\begin{block}{Remark}
+If an output file with the same name already exist, the results will be written to a file with a number attached, e.g., `myfname.out\_1'. The maximum number of output files with the same name allowed is 100. After that the output files will be overwritten in succession.
+\end{block}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+\begin{frame}[allowframebreaks]{\textbf{Acknowledgments}} \label{Acknowledgments}
+The work was supported by the grant DE-SC0019410 funded by the U.S. Department of Energy, Office of Science. Initial development efforts were supported by the grants 1333500 and 1553212 funded by the U.S. National Science Foundation.
+\end{frame}
+
+
+
+
+
+
+\end{document}
+
diff --git a/examples/BaTiO3.inpt b/examples/BaTiO3.inpt
new file mode 100644
index 00000000..6e2001d5
--- /dev/null
+++ b/examples/BaTiO3.inpt
@@ -0,0 +1,11 @@
+# Test: BaTiO3 #
+CELL: 7.63 7.63 7.63
+FD_GRID: 15 15 15
+BC: P P P
+EXCHANGE_CORRELATION: LDA_PZ
+TOL_SCF: 1e-5
+TOL_PSEUDOCHARGE: 1e-5
+PRINT_FORCES: 1
+PRINT_ATOMS: 1
+
+
diff --git a/examples/BaTiO3.ion b/examples/BaTiO3.ion
new file mode 100644
index 00000000..cbeba8ac
--- /dev/null
+++ b/examples/BaTiO3.ion
@@ -0,0 +1,44 @@
+#=========================
+# format of ion file
+#=========================
+# ATOM_TYPE:
+# PSEUDO_POT:
+# N_TYPE_ATOM:
+# COORD:
+#
+# ...
+# RELAX:
+#
+# ...
+
+# Reminder: when changing number of atoms, change the RELAX flags accordingly
+# as well.
+
+ATOM_TYPE: Ba # atom type
+PSEUDO_POT: ../Pseudopotentials/Ba.psp8
+N_TYPE_ATOM: 1 # number of atoms of this type
+COORD: # coordinates follows
+7.540463013371621 7.248833728543416 7.518607464589964
+
+# 0 0 0
+
+ATOM_TYPE: Ti # atom type
+PSEUDO_POT: ../Pseudopotentials/Ti.psp8
+N_TYPE_ATOM: 1 # number of atoms of this type
+COORD: # coordinates follows
+3.725768164762889 3.878328962888697 3.426961342823767
+
+#0.5 0.5 0.5
+
+ATOM_TYPE: O # atom type
+PSEUDO_POT: ../Pseudopotentials/O.psp8
+N_TYPE_ATOM: 3 # number of atoms of this type
+COORD: # coordinates follows
+ 4.052740031589397 7.190115020153727 3.856885000727702
+ 7.090600941523509 3.476460666072041 3.727807248988862
+ 3.601707961096307 3.648353082729004 0.199860166191001
+
+#0 0.5 0.5
+#0.5 0 0.5
+#0.5 0.5 0
+
diff --git a/examples/BaTiO3.reflog b/examples/BaTiO3.reflog
new file mode 100644
index 00000000..d8e1e7db
--- /dev/null
+++ b/examples/BaTiO3.reflog
@@ -0,0 +1,313 @@
+
+ Reading .inpt file ...
+
+
+
+# $ cat BaTiO3.inpt
+# Test: BaTiO3 #
+CELL: 7.63 7.63 7.63
+FD_GRID: 15 15 15
+BC: P P P
+EXCHANGE_CORRELATION: LDA_PZ
+TOL_SCF: 1e-5
+TOL_PSEUDOCHARGE: 1e-5
+PRINT_FORCES: 1
+PRINT_ATOMS: 1
+
+
+<\INPT>
+
+ Reading .ion file ...
+ Number of atom types : 3
+ Total number of atoms: 5
+ Default atomic mass for Ba is 137.327000
+ Default atomic mass for Ti is 47.867000
+ Default atomic mass for O is 15.999400
+ pseudo_dir # 1 = ../Pseudopotentials/Ba.psp8
+ pseudo_dir # 2 = ../Pseudopotentials/Ti.psp8
+ pseudo_dir # 3 = ../Pseudopotentials/O.psp8
+
+ COORD:
+ 7.540463013371621 7.248833728543416 7.518607464589964
+ 3.725768164762889 3.878328962888697 3.426961342823767
+ 4.052740031589397 7.190115020153727 3.856885000727702
+ 7.090600941523509 3.476460666072041 3.727807248988862
+ 3.601707961096307 3.648353082729004 0.199860166191001
+
+ kpoint grid before symmetry:
+ 0 0 0
+
+ kpoint grid after symmetry:
+ 0 0 0
+
+## Chebyshev polynomial degree not provided, finding npl ...
+## Based on the mesh size, npl is set to: 17
+## Number of states not provided, finding Nev ...
+## Based on the number of electrons, Nev is set to: 29
+## Poisson tolerance not provided, choosing poisson_tol ...
+## poisson_tol is set to: 1.000e-07
+ Creating differentiation matrices ...
+ Done. (0.064 sec)
+
+ Estimated memory usage:
+ Total: 12.41 MB
+ orbitals : 2.99 MB
+ sparse matrices : 8.70 MB
+ global-size vectors : 369.14 kB
+ mixing histories : 369.14 kB
+
+ Finding rb for Ba ...
+ rb = {3.561 3.561 3.561}, int_b = -9.999921525074964, err_rb = 7.847e-05
+ rb = {4.069 4.069 4.069}, int_b = -10.000061099168041, err_rb = 6.110e-05
+ rb = {4.578 4.578 4.578}, int_b = -10.000021197682786, err_rb = 2.120e-05
+ rb = {5.087 5.087 5.087}, int_b = -10.000016308813512, err_rb = 1.631e-05
+ rb = {5.595 5.595 5.595}, int_b = -10.000011153740992, err_rb = 1.115e-05
+ rb = {6.104 6.104 6.104}, int_b = -9.999998575103312, err_rb = 1.425e-06
+ rb = {6.104 6.104 6.104}
+ Finding rb for Ti ...
+ rb = {3.052 3.052 3.052}, int_b = -11.999990899677675, err_rb = 9.100e-06
+ rb = {3.052 3.052 3.052}
+ Finding rb for O ...
+ rb = {2.035 2.035 2.035}, int_b = -5.996295496021606, err_rb = 3.705e-03
+ rb = {2.543 2.543 2.543}, int_b = -6.000228753767169, err_rb = 2.288e-04
+ rb = {3.052 3.052 3.052}, int_b = -6.000040176728949, err_rb = 4.018e-05
+ rb = {3.561 3.561 3.561}, int_b = -6.000040176728949, err_rb = 4.018e-05
+ rb = {4.069 4.069 4.069}, int_b = -6.000026031623906, err_rb = 2.603e-05
+ rb = {4.578 4.578 4.578}, int_b = -6.000018149058158, err_rb = 1.815e-05
+ rb = {5.087 5.087 5.087}, int_b = -6.000016275978431, err_rb = 1.628e-05
+ rb = {5.595 5.595 5.595}, int_b = -6.000012360409576, err_rb = 1.236e-05
+ rb = {6.104 6.104 6.104}, int_b = -5.999998407764163, err_rb = 1.592e-06
+ rb = {6.104 6.104 6.104}
+
+ ###############################################################
+ Relaxation step number: 1
+
+ Starting pseudocharge generation and self energy calculation...
+ Integration b = 39.999320267883
+
+ Integration b_ref = 40.000058593117
+
+ ****************************************
+ * Eself_ref = 588.612037 *
+ ****************************************
+ Done. (0.100750 s)
+ Time for b calculation: 0.110 seconds.
+
+ Starting calculating nonlocal projectors ...
+ Done. (0.100220 s)
+
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+ Starting SCF iteration...
+ AAR converged to a relative residual of 1.47079e-08 in 31 iterations.
+ Poisson problem took 0.033329s
+ =============================================
+ Relaxation iteration: 1
+ SCF iteration number: 1, Chebyshev cycle: 1
+ =============================================
+ Fermi energy = 1.026521
+ This SCF iteration took 0.244 s.
+
+ =============================================
+ Relaxation iteration: 1
+ SCF iteration number: 1, Chebyshev cycle: 2
+ =============================================
+ Fermi energy = 0.185457
+ This SCF iteration took 0.129 s.
+
+ =============================================
+ Relaxation iteration: 1
+ SCF iteration number: 1, Chebyshev cycle: 3
+ =============================================
+ Fermi energy = 0.115219
+ This SCF iteration took 0.107 s.
+
+ =============================================
+ Relaxation iteration: 1
+ SCF iteration number: 1, Chebyshev cycle: 4
+ =============================================
+ Fermi energy = 0.114580
+ AAR converged to a relative residual of 6.02685e-08 in 25 iterations.
+ Poisson problem took 0.013953s
+ Escc = 4.19715058
+ Etot = -130.89166534
+ Eatom = -26.17833307
+ Error in SCF iteration: 2.1656e-01
+ This SCF iteration took 0.157 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 2
+ =========================
+ Fermi energy = 0.236607
+ AAR converged to a relative residual of 6.34624e-08 in 25 iterations.
+ Poisson problem took 0.008918s
+ Escc = 0.02865658
+ Etot = -131.84904641
+ Eatom = -26.36980928
+ Error in SCF iteration: 4.8907e-02
+ This SCF iteration took 0.127 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 3
+ =========================
+ Fermi energy = 0.221328
+ AAR converged to a relative residual of 1.5456e-08 in 25 iterations.
+ Poisson problem took 0.010156s
+ Escc = -0.09452642
+ Etot = -131.87532837
+ Eatom = -26.37506567
+ Error in SCF iteration: 2.4928e-02
+ This SCF iteration took 0.131 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 4
+ =========================
+ Fermi energy = 0.230019
+ AAR converged to a relative residual of 6.56507e-09 in 25 iterations.
+ Poisson problem took 0.012736s
+ Escc = 0.09583663
+ Etot = -131.88135595
+ Eatom = -26.37627119
+ Error in SCF iteration: 1.6272e-02
+ This SCF iteration took 0.139 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 5
+ =========================
+ Fermi energy = 0.228293
+ AAR converged to a relative residual of 9.34526e-08 in 22 iterations.
+ Poisson problem took 0.008703s
+ Escc = -0.02050820
+ Etot = -131.88643419
+ Eatom = -26.37728684
+ Error in SCF iteration: 3.0722e-03
+ This SCF iteration took 0.145 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 6
+ =========================
+ Fermi energy = 0.229349
+ AAR converged to a relative residual of 1.80014e-08 in 19 iterations.
+ Poisson problem took 0.007452s
+ Escc = -0.01149918
+ Etot = -131.88655729
+ Eatom = -26.37731146
+ Error in SCF iteration: 1.1704e-03
+ This SCF iteration took 0.127 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 7
+ =========================
+ Fermi energy = 0.229376
+ AAR converged to a relative residual of 9.93279e-08 in 17 iterations.
+ Poisson problem took 0.006268s
+ Escc = 0.01069114
+ Etot = -131.88656945
+ Eatom = -26.37731389
+ Error in SCF iteration: 4.3965e-04
+ This SCF iteration took 0.128 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 8
+ =========================
+ Fermi energy = 0.229499
+ AAR converged to a relative residual of 9.53422e-08 in 13 iterations.
+ Poisson problem took 0.005107s
+ Escc = -0.00219341
+ Etot = -131.88657110
+ Eatom = -26.37731422
+ Error in SCF iteration: 2.2970e-04
+ This SCF iteration took 0.123 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 9
+ =========================
+ Fermi energy = 0.229402
+ AAR converged to a relative residual of 8.94423e-08 in 13 iterations.
+ Poisson problem took 0.005329s
+ Escc = -0.00204897
+ Etot = -131.88657236
+ Eatom = -26.37731447
+ Error in SCF iteration: 1.3206e-04
+ This SCF iteration took 0.124 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 10
+ =========================
+ Fermi energy = 0.229397
+ AAR converged to a relative residual of 4.18046e-08 in 13 iterations.
+ Poisson problem took 0.005286s
+ Escc = 0.00067438
+ Etot = -131.88657206
+ Eatom = -26.37731441
+ Error in SCF iteration: 3.4174e-05
+ This SCF iteration took 0.124 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 11
+ =========================
+ Fermi energy = 0.229397
+ AAR converged to a relative residual of 1.35098e-08 in 13 iterations.
+ Poisson problem took 0.005585s
+ Escc = -0.00025269
+ Etot = -131.88657250
+ Eatom = -26.37731450
+ Error in SCF iteration: 1.3215e-05
+ This SCF iteration took 0.124 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 12
+ =========================
+ Fermi energy = 0.229397
+ AAR converged to a relative residual of 3.33071e-09 in 13 iterations.
+ Poisson problem took 0.005249s
+ Escc = -0.00002304
+ Etot = -131.88657235
+ Eatom = -26.37731447
+ Error in SCF iteration: 1.2706e-06
+ This SCF iteration took 0.122 s.
+
+
+ Finished SCF iteration in 12 steps!
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+ **********************************************************
+ * Energy per unit cell = -131.886572345 Ha. *
+ * Energy per atom = -26.377314469 Ha. *
+ **********************************************************
+
+ Starting atomic force calculation ...
+ local force calculation: 0.127 s
+ ***********************************************************
+ * Atomic Force *
+ ***********************************************************
+ Drift free forces (Ha/Bohr):
+ 0.002949397730739 -0.069480091917209 -0.176982421133567
+ 0.106587984961503 0.130222142559184 -0.281070874728238
+ -0.061964068165232 0.243780457912813 -0.429316996200704
+ -0.198922472527671 -0.641036343243366 0.539548550100714
+ 0.151349158000660 0.336513834688578 0.347821741961794
+
+ Max magnitude of forces (Ha/Bohr): 0.861168033168400
+
+
+ Time for calculating forces: 0.164726 s.
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+ Final atomic positions (Cartesian) are as follows:
+ 7.540463 7.248834 7.518607
+ 3.725768 3.878329 3.426961
+ 4.052740 7.190115 3.856885
+ 7.090601 3.476461 3.727807
+ 3.601708 3.648353 0.199860
+
+ Run-time of the program: 2.848134 seconds
diff --git a/examples/BaTiO3.refout b/examples/BaTiO3.refout
new file mode 100644
index 00000000..f65ad3eb
--- /dev/null
+++ b/examples/BaTiO3.refout
@@ -0,0 +1,108 @@
+***************************************************************************
+* M-SPARC (Dec 17, 2019) *
+* Copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech *
+* Distributed under GNU General Public License 3 (GPL) *
+* Date: 20-Dec-2019 Start time: 13:53:33 *
+***************************************************************************
+ Input parameters
+***************************************************************************
+CELL: 7.630000 7.630000 7.630000
+FD_GRID: 15 15 15
+FD_ORDER: 12
+BOUNDARY_CONDITION: 2
+KPOINT_GRID: 1 1 1
+KPOINT_SHIFT: 0 0 0
+ELEC_TEMP_TYPE: gaussian
+SMEARING: 0.007349864
+CHEB_DEGREE: 17
+NSTATES: 29
+EXCHANGE_CORRELATION: LDA_PZ
+CALC_STRESS: 0
+CALC_PRES: 0
+MAXIT_SCF: 100
+TOL_SCF: 1.00E-05
+TOL_POISSON: 1.00E-07
+TOL_LANCZOS: 1.00E-02
+TOL_PSEUDOCHARGE: 1.00E-05
+MIXING_VARIABLE: potential
+MIXING_PRECOND: none
+MIXING_PARAMETER: 0.30
+MIXING_HISTORY: 7
+PULAY_FREQUENCY: 1
+PULAY_RESTART_FREQ: 0
+REFERENCE_CUTOFF: 0.50
+RHO_TRIGGER: 4
+FIX_RAND: 0
+PRINT_FORCES: 1
+PRINT_ATOMS: 1
+PRINT_EIGEN: 0
+PRINT_DENSITY: 0
+OUTPUT_FILE: BaTiO3.out
+***************************************************************************
+ Initialization
+***************************************************************************
+Mesh spacing : 0.508667 (Bohr)
+Number of symmetry adapted k-points: 1
+Output printed to : BaTiO3.out
+Total number of atom types : 3
+Total number of atoms : 5
+Total number of electrons : 40
+Atom type 1 (valence electrons) : Ba 10
+Pseudopotential : ../Pseudopotentials/Ba.psp8
+lloc : 4
+Pseudocharge radii of atom type 1 : 6.10 6.10 6.10
+Number of atoms of type 1 : 1
+Atom type 2 (valence electrons) : Ti 12
+Pseudopotential : ../Pseudopotentials/Ti.psp8
+lloc : 4
+Pseudocharge radii of atom type 2 : 3.05 3.05 3.05
+Number of atoms of type 2 : 1
+Atom type 3 (valence electrons) : O 6
+Pseudopotential : ../Pseudopotentials/O.psp8
+lloc : 4
+Pseudocharge radii of atom type 3 : 6.10 6.10 6.10
+Number of atoms of type 3 : 3
+Estimated total memory usage : 12.41 MB
+=====================================================================
+ Self Consistent Field (SCF#1)
+=====================================================================
+Iteration Free Energy (Ha/atom) SCF Error Timing (sec)
+1 -2.6178333067E+01 2.166E-01 0.479
+2 -2.6369809283E+01 4.891E-02 0.157
+3 -2.6375065674E+01 2.493E-02 0.127
+4 -2.6376271190E+01 1.627E-02 0.131
+5 -2.6377286838E+01 3.072E-03 0.139
+6 -2.6377311458E+01 1.170E-03 0.145
+7 -2.6377313890E+01 4.396E-04 0.127
+8 -2.6377314220E+01 2.297E-04 0.128
+9 -2.6377314472E+01 1.321E-04 0.123
+10 -2.6377314413E+01 3.417E-05 0.124
+11 -2.6377314500E+01 1.322E-05 0.124
+12 -2.6377314469E+01 1.271E-06 0.124
+Total number of SCF: 12
+====================================================================
+ Energy
+====================================================================
+Free energy per atom : -2.6377314469E+01 (Ha/atom)
+Total free energy : -1.3188657235E+02 (Ha)
+Band structure energy : -1.1200032124E+01 (Ha)
+Exchange correlation energy : -2.1484725013E+01 (Ha)
+Self and correction energy : -2.0340707365E+02 (Ha)
+Entropy*kb*T : -1.2911789235E-05 (Ha)
+Fermi level : 2.2939659731E-01 (Ha)
+Average force : 4.7671471023E-01 (Ha/Bohr)
+Maximum force : 8.6116803317E-01 (Ha/Bohr)
+Time for force calculation : 0.165 (sec)
+***************************************************************************
+ Timing info
+***************************************************************************
+Total walltime : 2.848 sec
+___________________________________________________________________________
+
+***************************************************************************
+* Material Physics & Mechanics Group, Georgia Tech *
+* PI: Phanish Suryanarayana *
+* Main Developers: Qimen Xu, Abhiraj Sharma *
+* Acknowledgements: U.S. DOE (DE-SC0019410); NSF (1333500,1553212) *
+***************************************************************************
+
diff --git a/examples/BaTiO3.refstatic b/examples/BaTiO3.refstatic
new file mode 100644
index 00000000..6257de6a
--- /dev/null
+++ b/examples/BaTiO3.refstatic
@@ -0,0 +1,15 @@
+***************************************************************************
+ Atom positions
+***************************************************************************
+Cartesian coordinates of atoms (Bohr):
+ 7.5404630134 7.2488337285 7.5186074646
+ 3.7257681648 3.8783289629 3.4269613428
+ 4.0527400316 7.1901150202 3.8568850007
+ 7.0906009415 3.4764606661 3.7278072490
+ 3.6017079611 3.6483530827 0.1998601662
+Atomic forces (Ha/Bohr):
+ 0.0029493977 -0.0694800919 -0.1769824211
+ 0.1065879850 0.1302221426 -0.2810708747
+ -0.0619640682 0.2437804579 -0.4293169962
+ -0.1989224725 -0.6410363432 0.5395485501
+ 0.1513491580 0.3365138347 0.3478217420
diff --git a/examples/H2O_sheet.inpt b/examples/H2O_sheet.inpt
new file mode 100644
index 00000000..7040877f
--- /dev/null
+++ b/examples/H2O_sheet.inpt
@@ -0,0 +1,17 @@
+# Test: H2O sheet in x,y plane #
+CELL: 5.67 5.67 18.90
+FD_GRID: 12 12 38
+FD_ORDER: 12
+BOUNDARY_CONDITION: 3
+EXCHANGE_CORRELATION: GGA_PBE
+ELEC_TEMP_TYPE: fd
+SMEARING: 0.003674932
+TOL_SCF: 1e-4
+TOL_PSEUDOCHARGE: 1e-5
+MIXING_VARIABLE: potential
+MIXING_PRECOND: none
+NSTATES: 8
+PRINT_FORCES: 1
+PRINT_ATOMS: 1
+
+
diff --git a/examples/H2O_sheet.ion b/examples/H2O_sheet.ion
new file mode 100644
index 00000000..035854e2
--- /dev/null
+++ b/examples/H2O_sheet.ion
@@ -0,0 +1,29 @@
+#=========================
+# format of ion file
+#=========================
+# ATOM_TYPE:
+# PSEUDO_POT:
+# N_TYPE_ATOM:
+# COORD:
+#
+# ...
+# RELAX:
+#
+# ...
+
+# Reminder: when changing number of atoms, change the RELAX flags accordingly
+# as well.
+
+ATOM_TYPE: H # atom type
+PSEUDO_POT: ../Pseudopotentials/H_GGA.psp8
+N_TYPE_ATOM: 2 # number of atoms of this type
+COORD: # coordinates follows
+ 4.265111864110533 2.834589187490385 10.556010134214192
+ 1.404066510870237 2.834589187490385 10.556010134214192
+
+ATOM_TYPE: O # atom type
+PSEUDO_POT: ../Pseudopotentials/O_GGA.psp8
+N_TYPE_ATOM: 1 # number of atoms of this type
+COORD: # coordinates follows
+ 2.834589187490385 2.834589187490385 9.448630624967949
+
diff --git a/examples/H2O_sheet.reflog b/examples/H2O_sheet.reflog
new file mode 100644
index 00000000..d45b989a
--- /dev/null
+++ b/examples/H2O_sheet.reflog
@@ -0,0 +1,265 @@
+
+ Reading .inpt file ...
+
+
+
+# $ cat H2O_sheet.inpt
+# Test: H2O sheet in x,y plane #
+CELL: 5.67 5.67 18.90
+FD_GRID: 12 12 38
+FD_ORDER: 12
+BOUNDARY_CONDITION: 3
+EXCHANGE_CORRELATION: GGA_PBE
+ELEC_TEMP_TYPE: fd
+SMEARING: 0.003674932
+TOL_SCF: 1e-4
+TOL_PSEUDOCHARGE: 1e-5
+MIXING_VARIABLE: potential
+MIXING_PRECOND: none
+NSTATES: 8
+PRINT_FORCES: 1
+PRINT_ATOMS: 1
+
+
+<\INPT>
+
+Warning: "BOUNDARY_CONDITION" is obsolete, use "BC" instead!
+ Reading .ion file ...
+ Number of atom types : 2
+ Total number of atoms: 3
+ Default atomic mass for H is 1.007975
+ Default atomic mass for O is 15.999400
+ pseudo_dir # 1 = ../Pseudopotentials/H_GGA.psp8
+ pseudo_dir # 2 = ../Pseudopotentials/O_GGA.psp8
+
+ COORD:
+ 4.265111864110533 2.834589187490385 10.556010134214192
+ 1.404066510870237 2.834589187490385 10.556010134214192
+ 2.834589187490385 2.834589187490385 9.448630624967949
+
+ kpoint grid before symmetry:
+ 0 0 0
+
+ kpoint grid after symmetry:
+ 0 0 0
+
+## Chebyshev polynomial degree not provided, finding npl ...
+## Based on the mesh size, npl is set to: 18
+## Poisson tolerance not provided, choosing poisson_tol ...
+## poisson_tol is set to: 1.000e-06
+ Creating differentiation matrices ...
+ Done. (0.027 sec)
+
+ Estimated memory usage:
+ Total: 17.05 MB
+ orbitals : 1.37 MB
+ sparse matrices : 14.48 MB
+ global-size vectors : 614.25 kB
+ mixing histories : 614.25 kB
+
+ Finding rb for H ...
+ rb = {1.890 1.989 1.989}, int_b = -0.999547097929057, err_rb = 4.529e-04
+ rb = {2.362 2.487 2.487}, int_b = -1.000055797672791, err_rb = 5.580e-05
+ rb = {2.835 2.984 2.984}, int_b = -1.000002348367600, err_rb = 2.348e-06
+ rb = {2.835 2.984 2.984}
+ Finding rb for O ...
+ rb = {2.362 2.362 1.989}, int_b = -5.998970768580525, err_rb = 1.029e-03
+ rb = {2.835 2.835 2.487}, int_b = -6.000075749215827, err_rb = 7.575e-05
+ rb = {3.308 3.308 2.984}, int_b = -6.000019461398413, err_rb = 1.946e-05
+ rb = {3.780 3.780 3.482}, int_b = -6.000013611721441, err_rb = 1.361e-05
+ rb = {4.253 4.253 3.979}, int_b = -6.000023798963386, err_rb = 2.380e-05
+ rb = {4.725 4.725 4.476}, int_b = -6.000023639904740, err_rb = 2.364e-05
+ rb = {5.198 5.198 4.974}, int_b = -6.000018956303236, err_rb = 1.896e-05
+ rb = {5.670 5.670 5.471}, int_b = -6.000015300858329, err_rb = 1.530e-05
+ rb = {6.143 6.143 5.968}, int_b = -5.999998449235370, err_rb = 1.551e-06
+ rb = {6.143 6.143 5.968}
+
+ ###############################################################
+ Relaxation step number: 1
+
+ Starting pseudocharge generation and self energy calculation...
+ Integration b = 8.000036459878
+
+ Integration b_ref = 8.000019301376
+
+ ****************************************
+ * Eself_ref = 83.273893 *
+ ****************************************
+ Done. (0.042385 s)
+ Time for b calculation: 0.042 seconds.
+
+ Starting calculating nonlocal projectors ...
+ Done. (0.016983 s)
+
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+ Starting SCF iteration...
+ AAR converged to a relative residual of 8.60911e-07 in 67 iterations.
+ Poisson problem took 0.106965s
+ =============================================
+ Relaxation iteration: 1
+ SCF iteration number: 1, Chebyshev cycle: 1
+ =============================================
+ Fermi energy = 1.031388
+ This SCF iteration took 0.113 s.
+
+ =============================================
+ Relaxation iteration: 1
+ SCF iteration number: 1, Chebyshev cycle: 2
+ =============================================
+ Fermi energy = -0.119891
+ This SCF iteration took 0.052 s.
+
+ =============================================
+ Relaxation iteration: 1
+ SCF iteration number: 1, Chebyshev cycle: 3
+ =============================================
+ Fermi energy = -0.180751
+ This SCF iteration took 0.051 s.
+
+ =============================================
+ Relaxation iteration: 1
+ SCF iteration number: 1, Chebyshev cycle: 4
+ =============================================
+ Fermi energy = -0.182187
+ AAR converged to a relative residual of 4.99747e-07 in 61 iterations.
+ Poisson problem took 0.036048s
+ Escc = 3.01822684
+ Etot = -16.96614061
+ Eatom = -5.65538020
+ Error in SCF iteration: 4.6391e-01
+ This SCF iteration took 0.094 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 2
+ =========================
+ Fermi energy = -0.173805
+ AAR converged to a relative residual of 3.03865e-07 in 61 iterations.
+ Poisson problem took 0.036303s
+ Escc = 0.52165662
+ Etot = -17.09861056
+ Eatom = -5.69953685
+ Error in SCF iteration: 8.4916e-02
+ This SCF iteration took 0.096 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 3
+ =========================
+ Fermi energy = -0.172765
+ AAR converged to a relative residual of 5.54952e-07 in 49 iterations.
+ Poisson problem took 0.029013s
+ Escc = 0.03948861
+ Etot = -17.10144939
+ Eatom = -5.70048313
+ Error in SCF iteration: 2.9190e-02
+ This SCF iteration took 0.086 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 4
+ =========================
+ Fermi energy = -0.173366
+ AAR converged to a relative residual of 7.60036e-07 in 43 iterations.
+ Poisson problem took 0.035120s
+ Escc = 0.08628931
+ Etot = -17.10140280
+ Eatom = -5.70046760
+ Error in SCF iteration: 3.6104e-02
+ This SCF iteration took 0.101 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 5
+ =========================
+ Fermi energy = -0.175128
+ AAR converged to a relative residual of 4.27273e-07 in 43 iterations.
+ Poisson problem took 0.022818s
+ Escc = -0.00689903
+ Etot = -17.10173318
+ Eatom = -5.70057773
+ Error in SCF iteration: 1.2689e-02
+ This SCF iteration took 0.080 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 6
+ =========================
+ Fermi energy = -0.179039
+ AAR converged to a relative residual of 1.39952e-07 in 43 iterations.
+ Poisson problem took 0.024749s
+ Escc = -0.01374837
+ Etot = -17.10175263
+ Eatom = -5.70058421
+ Error in SCF iteration: 6.1743e-03
+ This SCF iteration took 0.080 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 7
+ =========================
+ Fermi energy = -0.178701
+ AAR converged to a relative residual of 7.94664e-07 in 25 iterations.
+ Poisson problem took 0.015546s
+ Escc = -0.00902935
+ Etot = -17.10175542
+ Eatom = -5.70058514
+ Error in SCF iteration: 2.8208e-03
+ This SCF iteration took 0.071 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 8
+ =========================
+ Fermi energy = -0.178725
+ AAR converged to a relative residual of 9.97799e-07 in 29 iterations.
+ Poisson problem took 0.015206s
+ Escc = -0.00000460
+ Etot = -17.10175516
+ Eatom = -5.70058505
+ Error in SCF iteration: 2.0049e-04
+ This SCF iteration took 0.070 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 9
+ =========================
+ Fermi energy = -0.178654
+ AAR converged to a relative residual of 8.24044e-07 in 13 iterations.
+ Poisson problem took 0.008210s
+ Escc = -0.00017173
+ Etot = -17.10175564
+ Eatom = -5.70058521
+ Error in SCF iteration: 7.1829e-05
+ This SCF iteration took 0.061 s.
+
+
+ Finished SCF iteration in 9 steps!
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+ **********************************************************
+ * Energy per unit cell = -17.101755641 Ha. *
+ * Energy per atom = -5.700585214 Ha. *
+ **********************************************************
+
+ Starting atomic force calculation ...
+ local force calculation: 0.054 s
+ ***********************************************************
+ * Atomic Force *
+ ***********************************************************
+ Drift free forces (Ha/Bohr):
+ -0.031040528694906 0.001290039333674 0.016116671183374
+ 0.032443316980656 0.001297175279174 0.016046084191571
+ -0.001402788285750 -0.002587214612848 -0.032162755374946
+
+ Max magnitude of forces (Ha/Bohr): 0.036217789804117
+
+
+ Time for calculating forces: 0.072760 s.
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+ Final atomic positions (Cartesian) are as follows:
+ 4.265112 2.834589 10.556010
+ 1.404067 2.834589 10.556010
+ 2.834589 2.834589 9.448631
+
+ Run-time of the program: 1.323179 seconds
diff --git a/examples/H2O_sheet.refout b/examples/H2O_sheet.refout
new file mode 100644
index 00000000..80865186
--- /dev/null
+++ b/examples/H2O_sheet.refout
@@ -0,0 +1,102 @@
+***************************************************************************
+* M-SPARC (Dec 17, 2019) *
+* Copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech *
+* Distributed under GNU General Public License 3 (GPL) *
+* Date: 20-Dec-2019 Start time: 13:53:35 *
+***************************************************************************
+ Input parameters
+***************************************************************************
+CELL: 5.670000 5.670000 18.900000
+FD_GRID: 12 12 38
+FD_ORDER: 12
+BOUNDARY_CONDITION: 3
+KPOINT_GRID: 1 1 1
+KPOINT_SHIFT: 0 0 0
+ELEC_TEMP_TYPE: fermi-dirac
+SMEARING: 0.003674932
+CHEB_DEGREE: 18
+NSTATES: 8
+EXCHANGE_CORRELATION: GGA_PBE
+CALC_STRESS: 0
+CALC_PRES: 0
+MAXIT_SCF: 100
+TOL_SCF: 1.00E-04
+TOL_POISSON: 1.00E-06
+TOL_LANCZOS: 1.00E-02
+TOL_PSEUDOCHARGE: 1.00E-05
+MIXING_VARIABLE: potential
+MIXING_PRECOND: none
+MIXING_PARAMETER: 0.30
+MIXING_HISTORY: 7
+PULAY_FREQUENCY: 1
+PULAY_RESTART_FREQ: 0
+REFERENCE_CUTOFF: 0.50
+RHO_TRIGGER: 4
+FIX_RAND: 0
+PRINT_FORCES: 1
+PRINT_ATOMS: 1
+PRINT_EIGEN: 0
+PRINT_DENSITY: 0
+OUTPUT_FILE: H2O_sheet.out
+***************************************************************************
+ Initialization
+***************************************************************************
+Mesh spacing in x-direction : 0.472500 (Bohr)
+Mesh spacing in y-direction : 0.472500 (Bohr)
+Mesh spacing in z direction : 0.497368 (Bohr)
+Number of symmetry adapted k-points: 1
+Output printed to : H2O_sheet.out
+Total number of atom types : 2
+Total number of atoms : 3
+Total number of electrons : 8
+Atom type 1 (valence electrons) : H 1
+Pseudopotential : ../Pseudopotentials/H_GGA.psp8
+lloc : 4
+Pseudocharge radii of atom type 1 : 2.83 2.98 2.98
+Number of atoms of type 1 : 2
+Atom type 2 (valence electrons) : O 6
+Pseudopotential : ../Pseudopotentials/O_GGA.psp8
+lloc : 4
+Pseudocharge radii of atom type 2 : 6.14 6.14 5.97
+Number of atoms of type 2 : 1
+Estimated total memory usage : 17.05 MB
+=====================================================================
+ Self Consistent Field (SCF#1)
+=====================================================================
+Iteration Free Energy (Ha/atom) SCF Error Timing (sec)
+1 -5.6553802020E+00 4.639E-01 0.216
+2 -5.6995368544E+00 8.492E-02 0.094
+3 -5.7004831313E+00 2.919E-02 0.096
+4 -5.7004676000E+00 3.610E-02 0.086
+5 -5.7005777281E+00 1.269E-02 0.101
+6 -5.7005842098E+00 6.174E-03 0.080
+7 -5.7005851410E+00 2.821E-03 0.080
+8 -5.7005850544E+00 2.005E-04 0.071
+9 -5.7005852138E+00 7.183E-05 0.070
+Total number of SCF: 9
+====================================================================
+ Energy
+====================================================================
+Free energy per atom : -5.7005852138E+00 (Ha/atom)
+Total free energy : -1.7101755641E+01 (Ha)
+Band structure energy : -4.0196453479E+00 (Ha)
+Exchange correlation energy : -4.3051177228E+00 (Ha)
+Self and correction energy : -3.6101055082E+01 (Ha)
+Entropy*kb*T : -1.6062354104E-06 (Ha)
+Fermi level : -1.7865360782E-01 (Ha)
+Average force : 3.4504618079E-02 (Ha/Bohr)
+Maximum force : 3.6217789804E-02 (Ha/Bohr)
+Time for force calculation : 0.073 (sec)
+***************************************************************************
+ Timing info
+***************************************************************************
+Total walltime : 1.323 sec
+___________________________________________________________________________
+
+***************************************************************************
+* Material Physics & Mechanics Group, Georgia Tech *
+* PI: Phanish Suryanarayana *
+* Main Developers: Qimen Xu, Abhiraj Sharma *
+* Acknowledgements: U.S. DOE (DE-SC0019410); NSF (1333500,1553212) *
+***************************************************************************
+
diff --git a/examples/H2O_sheet.refstatic b/examples/H2O_sheet.refstatic
new file mode 100644
index 00000000..59817cfd
--- /dev/null
+++ b/examples/H2O_sheet.refstatic
@@ -0,0 +1,11 @@
+***************************************************************************
+ Atom positions
+***************************************************************************
+Cartesian coordinates of atoms (Bohr):
+ 4.2651118641 2.8345891875 10.5560101342
+ 1.4040665109 2.8345891875 10.5560101342
+ 2.8345891875 2.8345891875 9.4486306250
+Atomic forces (Ha/Bohr):
+ -0.0310405287 0.0012900393 0.0161166712
+ 0.0324433170 0.0012971753 0.0160460842
+ -0.0014027883 -0.0025872146 -0.0321627554
diff --git a/examples/H2O_wire.inpt b/examples/H2O_wire.inpt
new file mode 100644
index 00000000..051b892e
--- /dev/null
+++ b/examples/H2O_wire.inpt
@@ -0,0 +1,17 @@
+# Test: H2O wire in z direction #
+CELL: 14.00 14.00 6.00
+FD_GRID: 28 28 12
+FD_ORDER: 12
+BC: D D P
+#BOUNDARY_CONDITION: 4
+EXCHANGE_CORRELATION: LDA_PZ
+ELEC_TEMP_TYPE: fd
+SMEARING: 0.003674932
+TOL_SCF: 1e-5
+TOL_PSEUDOCHARGE: 1e-4
+NSTATES: 8
+#MIXING_VARIABLE: density
+PRINT_FORCES: 1
+PRINT_ATOMS: 1
+
+
diff --git a/examples/H2O_wire.ion b/examples/H2O_wire.ion
new file mode 100644
index 00000000..dcb18e5b
--- /dev/null
+++ b/examples/H2O_wire.ion
@@ -0,0 +1,29 @@
+#=========================
+# format of ion file
+#=========================
+# ATOM_TYPE:
+# PSEUDO_POT:
+# N_TYPE_ATOM:
+# COORD:
+#
+# ...
+# RELAX:
+#
+# ...
+
+# Reminder: when changing number of atoms, change the RELAX flags accordingly
+# as well.
+
+ATOM_TYPE: H # atom type
+PSEUDO_POT: ../Pseudopotentials/H.psp8
+N_TYPE_ATOM: 2 # number of atoms of this type
+COORD: # coordinates follows
+ 7.369126503082081 7.000000000000000 4.430522676620148
+ 7.369126503082081 7.000000000000000 1.569477323379852
+
+ATOM_TYPE: O # atom type
+PSEUDO_POT: ../Pseudopotentials/O.psp8
+N_TYPE_ATOM: 1 # number of atoms of this type
+COORD: # coordinates follows
+ 6.261746993835837 7.000000000000000 3.000000000000000
+
diff --git a/examples/H2O_wire.reflog b/examples/H2O_wire.reflog
new file mode 100644
index 00000000..11ebf91c
--- /dev/null
+++ b/examples/H2O_wire.reflog
@@ -0,0 +1,283 @@
+
+ Reading .inpt file ...
+
+
+
+# $ cat H2O_wire.inpt
+# Test: H2O wire in z direction #
+CELL: 14.00 14.00 6.00
+FD_GRID: 28 28 12
+FD_ORDER: 12
+BC: D D P
+#BOUNDARY_CONDITION: 4
+EXCHANGE_CORRELATION: LDA_PZ
+ELEC_TEMP_TYPE: fd
+SMEARING: 0.003674932
+TOL_SCF: 1e-5
+TOL_PSEUDOCHARGE: 1e-4
+NSTATES: 8
+#MIXING_VARIABLE: density
+PRINT_FORCES: 1
+PRINT_ATOMS: 1
+
+
+<\INPT>
+
+ Reading .ion file ...
+ Number of atom types : 2
+ Total number of atoms: 3
+ Default atomic mass for H is 1.007975
+ Default atomic mass for O is 15.999400
+ pseudo_dir # 1 = ../Pseudopotentials/H.psp8
+ pseudo_dir # 2 = ../Pseudopotentials/O.psp8
+
+ COORD:
+ 7.369126503082081 7.000000000000000 4.430522676620148
+ 7.369126503082081 7.000000000000000 1.569477323379852
+ 6.261746993835837 7.000000000000000 3.000000000000000
+
+ kpoint grid before symmetry:
+ 0 0 0
+
+ kpoint grid after symmetry:
+ 0 0 0
+
+## Chebyshev polynomial degree not provided, finding npl ...
+## Based on the mesh size, npl is set to: 17
+## Poisson tolerance not provided, choosing poisson_tol ...
+## poisson_tol is set to: 1.000e-07
+ Creating differentiation matrices ...
+ Done. (0.047 sec)
+
+ Estimated memory usage:
+ Total: 30.64 MB
+ orbitals : 2.46 MB
+ sparse matrices : 26.02 MB
+ global-size vectors : 1.08 MB
+ mixing histories : 1.08 MB
+
+ Finding rb for H ...
+ rb = {2.000 2.000 2.000}, int_b = -0.999561794045042, err_rb = 4.382e-04
+ rb = {2.500 2.500 2.500}, int_b = -1.000054837166567, err_rb = 5.484e-05
+ rb = {2.500 2.500 2.500}
+ Finding rb for O ...
+ rb = {2.000 2.000 2.000}, int_b = -5.996408445447010, err_rb = 3.592e-03
+ rb = {2.500 2.500 2.500}, int_b = -6.000208106728446, err_rb = 2.081e-04
+ rb = {3.000 3.000 3.000}, int_b = -6.000042257126758, err_rb = 4.226e-05
+ rb = {3.000 3.000 3.000}
+
+ ###############################################################
+ Relaxation step number: 1
+
+ Starting pseudocharge generation and self energy calculation...
+ Integration b = 8.000154770260
+
+ Integration b_ref = 8.000103702045
+
+ ****************************************
+ * Eself_ref = 69.600500 *
+ ****************************************
+ Done. (0.028609 s)
+ Time for b calculation: 0.029 seconds.
+
+ Starting calculating nonlocal projectors ...
+ Done. (0.009295 s)
+
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+ Starting SCF iteration...
+ AAR converged to a relative residual of 7.327e-08 in 55 iterations.
+ Poisson problem took 0.064257s
+ =============================================
+ Relaxation iteration: 1
+ SCF iteration number: 1, Chebyshev cycle: 1
+ =============================================
+ Fermi energy = 1.093137
+ This SCF iteration took 0.107 s.
+
+ =============================================
+ Relaxation iteration: 1
+ SCF iteration number: 1, Chebyshev cycle: 2
+ =============================================
+ Fermi energy = -0.032877
+ This SCF iteration took 0.055 s.
+
+ =============================================
+ Relaxation iteration: 1
+ SCF iteration number: 1, Chebyshev cycle: 3
+ =============================================
+ Fermi energy = -0.125812
+ This SCF iteration took 0.055 s.
+
+ =============================================
+ Relaxation iteration: 1
+ SCF iteration number: 1, Chebyshev cycle: 4
+ =============================================
+ Fermi energy = -0.128359
+ AAR converged to a relative residual of 3.56833e-08 in 49 iterations.
+ Poisson problem took 0.060542s
+ Escc = 2.05913843
+ Etot = -17.10340446
+ Eatom = -5.70113482
+ Error in SCF iteration: 2.2099e-01
+ This SCF iteration took 0.120 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 2
+ =========================
+ Fermi energy = -0.118560
+ AAR converged to a relative residual of 9.39638e-08 in 45 iterations.
+ Poisson problem took 0.051591s
+ Escc = 0.28347306
+ Etot = -17.17408420
+ Eatom = -5.72469473
+ Error in SCF iteration: 1.0788e-01
+ This SCF iteration took 0.109 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 3
+ =========================
+ Fermi energy = -0.124013
+ AAR converged to a relative residual of 3.53366e-08 in 43 iterations.
+ Poisson problem took 0.052884s
+ Escc = -0.08920046
+ Etot = -17.17614589
+ Eatom = -5.72538196
+ Error in SCF iteration: 6.5251e-02
+ This SCF iteration took 0.112 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 4
+ =========================
+ Fermi energy = -0.141157
+ AAR converged to a relative residual of 1.79335e-08 in 37 iterations.
+ Poisson problem took 0.053225s
+ Escc = 0.05937320
+ Etot = -17.17634157
+ Eatom = -5.72544719
+ Error in SCF iteration: 4.3684e-03
+ This SCF iteration took 0.113 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 5
+ =========================
+ Fermi energy = -0.140892
+ AAR converged to a relative residual of 4.34103e-08 in 37 iterations.
+ Poisson problem took 0.046158s
+ Escc = -0.04344019
+ Etot = -17.17646166
+ Eatom = -5.72548722
+ Error in SCF iteration: 5.1207e-03
+ This SCF iteration took 0.106 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 6
+ =========================
+ Fermi energy = -0.141842
+ AAR converged to a relative residual of 3.20914e-08 in 37 iterations.
+ Poisson problem took 0.045316s
+ Escc = 0.02806782
+ Etot = -17.17646887
+ Eatom = -5.72548962
+ Error in SCF iteration: 2.8767e-03
+ This SCF iteration took 0.105 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 7
+ =========================
+ Fermi energy = -0.141507
+ AAR converged to a relative residual of 8.99764e-08 in 31 iterations.
+ Poisson problem took 0.039337s
+ Escc = -0.00248727
+ Etot = -17.17648405
+ Eatom = -5.72549468
+ Error in SCF iteration: 2.3504e-04
+ This SCF iteration took 0.099 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 8
+ =========================
+ Fermi energy = -0.141579
+ AAR converged to a relative residual of 7.79978e-08 in 25 iterations.
+ Poisson problem took 0.034721s
+ Escc = 0.00118292
+ Etot = -17.17648345
+ Eatom = -5.72549448
+ Error in SCF iteration: 1.2833e-04
+ This SCF iteration took 0.095 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 9
+ =========================
+ Fermi energy = -0.141567
+ AAR converged to a relative residual of 4.98006e-08 in 19 iterations.
+ Poisson problem took 0.028619s
+ Escc = 0.00009710
+ Etot = -17.17648396
+ Eatom = -5.72549465
+ Error in SCF iteration: 3.3451e-05
+ This SCF iteration took 0.089 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 10
+ =========================
+ Fermi energy = -0.141553
+ AAR converged to a relative residual of 9.39337e-08 in 7 iterations.
+ Poisson problem took 0.015385s
+ Escc = -0.00008247
+ Etot = -17.17648427
+ Eatom = -5.72549476
+ Error in SCF iteration: 1.6780e-05
+ This SCF iteration took 0.078 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 11
+ =========================
+ Fermi energy = -0.141558
+ AAR converged to a relative residual of 4.36929e-08 in 7 iterations.
+ Poisson problem took 0.013891s
+ Escc = -0.00001438
+ Etot = -17.17648403
+ Eatom = -5.72549468
+ Error in SCF iteration: 2.7812e-06
+ This SCF iteration took 0.082 s.
+
+
+ Finished SCF iteration in 11 steps!
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+ **********************************************************
+ * Energy per unit cell = -17.176484028 Ha. *
+ * Energy per atom = -5.725494676 Ha. *
+ **********************************************************
+
+ Starting atomic force calculation ...
+ local force calculation: 0.036 s
+ ***********************************************************
+ * Atomic Force *
+ ***********************************************************
+ Drift free forces (Ha/Bohr):
+ 0.023972720830750 -0.000000152640035 -0.043481812515439
+ 0.023972723189752 -0.000000152335682 0.043481810467295
+ -0.047945444020502 0.000000304975717 0.000000002048144
+
+ Max magnitude of forces (Ha/Bohr): 0.049652385276844
+
+
+ Time for calculating forces: 0.061581 s.
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+ Final atomic positions (Cartesian) are as follows:
+ 7.369127 7.000000 4.430523
+ 7.369127 7.000000 1.569477
+ 6.261747 7.000000 3.000000
+
+ Run-time of the program: 1.605900 seconds
diff --git a/examples/H2O_wire.refout b/examples/H2O_wire.refout
new file mode 100644
index 00000000..5b54ac45
--- /dev/null
+++ b/examples/H2O_wire.refout
@@ -0,0 +1,102 @@
+***************************************************************************
+* M-SPARC (Dec 17, 2019) *
+* Copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech *
+* Distributed under GNU General Public License 3 (GPL) *
+* Date: 20-Dec-2019 Start time: 13:53:37 *
+***************************************************************************
+ Input parameters
+***************************************************************************
+CELL: 14.000000 14.000000 6.000000
+FD_GRID: 28 28 12
+FD_ORDER: 12
+BOUNDARY_CONDITION: 4
+KPOINT_GRID: 1 1 1
+KPOINT_SHIFT: 0 0 0
+ELEC_TEMP_TYPE: fermi-dirac
+SMEARING: 0.003674932
+CHEB_DEGREE: 17
+NSTATES: 8
+EXCHANGE_CORRELATION: LDA_PZ
+CALC_STRESS: 0
+CALC_PRES: 0
+MAXIT_SCF: 100
+TOL_SCF: 1.00E-05
+TOL_POISSON: 1.00E-07
+TOL_LANCZOS: 1.00E-02
+TOL_PSEUDOCHARGE: 1.00E-04
+MIXING_VARIABLE: potential
+MIXING_PRECOND: none
+MIXING_PARAMETER: 0.30
+MIXING_HISTORY: 7
+PULAY_FREQUENCY: 1
+PULAY_RESTART_FREQ: 0
+REFERENCE_CUTOFF: 0.50
+RHO_TRIGGER: 4
+FIX_RAND: 0
+PRINT_FORCES: 1
+PRINT_ATOMS: 1
+PRINT_EIGEN: 0
+PRINT_DENSITY: 0
+OUTPUT_FILE: H2O_wire.out
+***************************************************************************
+ Initialization
+***************************************************************************
+Mesh spacing : 0.500000 (Bohr)
+Number of symmetry adapted k-points: 1
+Output printed to : H2O_wire.out
+Total number of atom types : 2
+Total number of atoms : 3
+Total number of electrons : 8
+Atom type 1 (valence electrons) : H 1
+Pseudopotential : ../Pseudopotentials/H.psp8
+lloc : 4
+Pseudocharge radii of atom type 1 : 2.50 2.50 2.50
+Number of atoms of type 1 : 2
+Atom type 2 (valence electrons) : O 6
+Pseudopotential : ../Pseudopotentials/O.psp8
+lloc : 4
+Pseudocharge radii of atom type 2 : 3.00 3.00 3.00
+Number of atoms of type 2 : 1
+Estimated total memory usage : 30.64 MB
+=====================================================================
+ Self Consistent Field (SCF#1)
+=====================================================================
+Iteration Free Energy (Ha/atom) SCF Error Timing (sec)
+1 -5.7011348215E+00 2.210E-01 0.217
+2 -5.7246947321E+00 1.079E-01 0.120
+3 -5.7253819617E+00 6.525E-02 0.109
+4 -5.7254471913E+00 4.368E-03 0.112
+5 -5.7254872203E+00 5.121E-03 0.113
+6 -5.7254896243E+00 2.877E-03 0.106
+7 -5.7254946829E+00 2.350E-04 0.105
+8 -5.7254944818E+00 1.283E-04 0.099
+9 -5.7254946540E+00 3.345E-05 0.095
+10 -5.7254947566E+00 1.678E-05 0.089
+11 -5.7254946759E+00 2.781E-06 0.078
+Total number of SCF: 11
+====================================================================
+ Energy
+====================================================================
+Free energy per atom : -5.7254946759E+00 (Ha/atom)
+Total free energy : -1.7176484028E+01 (Ha)
+Band structure energy : -4.2353469274E+00 (Ha)
+Exchange correlation energy : -4.1452177335E+00 (Ha)
+Self and correction energy : -3.5516529308E+01 (Ha)
+Entropy*kb*T : -5.9531339030E-06 (Ha)
+Fermi level : -1.4155811721E-01 (Ha)
+Average force : 4.9083404640E-02 (Ha/Bohr)
+Maximum force : 4.9652385277E-02 (Ha/Bohr)
+Time for force calculation : 0.062 (sec)
+***************************************************************************
+ Timing info
+***************************************************************************
+Total walltime : 1.606 sec
+___________________________________________________________________________
+
+***************************************************************************
+* Material Physics & Mechanics Group, Georgia Tech *
+* PI: Phanish Suryanarayana *
+* Main Developers: Qimen Xu, Abhiraj Sharma *
+* Acknowledgements: U.S. DOE (DE-SC0019410); NSF (1333500,1553212) *
+***************************************************************************
+
diff --git a/examples/H2O_wire.refstatic b/examples/H2O_wire.refstatic
new file mode 100644
index 00000000..2869363d
--- /dev/null
+++ b/examples/H2O_wire.refstatic
@@ -0,0 +1,11 @@
+***************************************************************************
+ Atom positions
+***************************************************************************
+Cartesian coordinates of atoms (Bohr):
+ 7.3691265031 7.0000000000 4.4305226766
+ 7.3691265031 7.0000000000 1.5694773234
+ 6.2617469938 7.0000000000 3.0000000000
+Atomic forces (Ha/Bohr):
+ 0.0239727208 -0.0000001526 -0.0434818125
+ 0.0239727232 -0.0000001523 0.0434818105
+ -0.0479454440 0.0000003050 0.0000000020
diff --git a/examples/SiH4.inpt b/examples/SiH4.inpt
new file mode 100644
index 00000000..1bb8b76b
--- /dev/null
+++ b/examples/SiH4.inpt
@@ -0,0 +1,14 @@
+# Test: SiH4 #
+CELL: 13 13 13
+FD_GRID: 26 26 26
+BOUNDARY_CONDITION: 1
+RHO_TRIGGER: 4
+EXCHANGE_CORRELATION: LDA_PW
+MAXIT_SCF: 30
+TOL_SCF: 1e-5
+TOL_PSEUDOCHARGE: 1e-5
+NSTATES: 10
+PRINT_FORCES: 1
+PRINT_ATOMS: 1
+
+
diff --git a/examples/SiH4.ion b/examples/SiH4.ion
new file mode 100644
index 00000000..6d745d20
--- /dev/null
+++ b/examples/SiH4.ion
@@ -0,0 +1,32 @@
+#=========================
+# format of ion file
+#=========================
+# ATOM_TYPE:
+# N_TYPE_ATOM:
+# COORD:
+#
+# ...
+# RELAX:
+#
+# ...
+
+
+# Reminder: when changing number of atoms, change the RELAX flags accordingly
+# as well.
+
+ATOM_TYPE: Si # atom type followed with valence charge
+PSEUDO_POT: ../Pseudopotentials/Si.psp8 # pseudopotential
+N_TYPE_ATOM: 1 # number of atoms of this type
+COORD: # coordinates follows
+6.5 6.5 6.5
+
+
+ATOM_TYPE: H # atom type followed with valence charge
+PSEUDO_POT: ../Pseudopotentials/H.psp8 # pseudopotential
+N_TYPE_ATOM: 4 # number of atoms of this type
+COORD: # coordinates follows
+8.127432021000001 8.127432021000001 8.127432021000001
+4.872567978999999 4.872567978999999 8.127432021000001
+4.872567978999999 8.127432021000001 4.872567978999999
+8.127432021000001 4.872567978999999 4.872567978999999
+
diff --git a/examples/SiH4.reflog b/examples/SiH4.reflog
new file mode 100644
index 00000000..b7d4b675
--- /dev/null
+++ b/examples/SiH4.reflog
@@ -0,0 +1,264 @@
+
+ Reading .inpt file ...
+
+
+
+# $ cat SiH4.inpt
+# Test: SiH4 #
+CELL: 13 13 13
+FD_GRID: 26 26 26
+BOUNDARY_CONDITION: 1
+RHO_TRIGGER: 4
+EXCHANGE_CORRELATION: LDA_PW
+MAXIT_SCF: 30
+TOL_SCF: 1e-5
+TOL_PSEUDOCHARGE: 1e-5
+NSTATES: 10
+PRINT_FORCES: 1
+PRINT_ATOMS: 1
+
+
+<\INPT>
+
+Warning: "BOUNDARY_CONDITION" is obsolete, use "BC" instead!
+ Reading .ion file ...
+ Number of atom types : 2
+ Total number of atoms: 5
+ Default atomic mass for Si is 28.085000
+ Default atomic mass for H is 1.007975
+ pseudo_dir # 1 = ../Pseudopotentials/Si.psp8
+ pseudo_dir # 2 = ../Pseudopotentials/H.psp8
+
+ COORD:
+ 6.500000000000000 6.500000000000000 6.500000000000000
+ 8.127432021000001 8.127432021000001 8.127432021000001
+ 4.872567978999999 4.872567978999999 8.127432021000001
+ 4.872567978999999 8.127432021000001 4.872567978999999
+ 8.127432021000001 4.872567978999999 4.872567978999999
+
+ kpoint grid before symmetry:
+ 0 0 0
+
+ kpoint grid after symmetry:
+ 0 0 0
+
+## Chebyshev polynomial degree not provided, finding npl ...
+## Based on the mesh size, npl is set to: 17
+## Poisson tolerance not provided, choosing poisson_tol ...
+## poisson_tol is set to: 1.000e-07
+ Creating differentiation matrices ...
+ Done. (0.085 sec)
+
+ Estimated memory usage:
+ Total: 90.51 MB
+ orbitals : 6.01 MB
+ sparse matrices : 49.41 MB
+ global-size vectors : 3.46 MB
+ spherical harmonics : 29.53 MB
+ mixing histories : 2.10 MB
+
+ Finding rb for Si ...
+ rb = {4.500 4.500 4.500}, int_b = -4.000013147891343, err_rb = 1.315e-05
+ rb = {5.000 5.000 5.000}, int_b = -4.000011534604855, err_rb = 1.153e-05
+ rb = {5.500 5.500 5.500}, int_b = -4.000010204534080, err_rb = 1.020e-05
+ rb = {6.000 6.000 6.000}, int_b = -3.999998669764024, err_rb = 1.330e-06
+ rb = {6.000 6.000 6.000}
+ Finding rb for H ...
+ rb = {2.000 2.000 2.000}, int_b = -0.999561794045042, err_rb = 4.382e-04
+ rb = {2.500 2.500 2.500}, int_b = -1.000054837166567, err_rb = 5.484e-05
+ rb = {3.000 3.000 3.000}, int_b = -1.000004107312726, err_rb = 4.107e-06
+ rb = {3.000 3.000 3.000}
+
+ ###############################################################
+ Relaxation step number: 1
+
+ Starting pseudocharge generation and self energy calculation...
+ Integration b = 8.000045981672
+
+ Integration b_ref = 8.000025650897
+
+ ****************************************
+ * Eself_ref = 43.271414 *
+ ****************************************
+ Done. (0.020777 s)
+ Time for b calculation: 0.021 seconds.
+
+ Starting calculating nonlocal projectors ...
+ Done. (0.007898 s)
+
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+ Starting SCF iteration...
+ AAR converged to a relative residual of 6.71363e-08 in 49 iterations.
+ Poisson problem took 0.138020s
+ =============================================
+ Relaxation iteration: 1
+ SCF iteration number: 1, Chebyshev cycle: 1
+ =============================================
+ Fermi energy = 1.088407
+ This SCF iteration took 0.255 s.
+
+ =============================================
+ Relaxation iteration: 1
+ SCF iteration number: 1, Chebyshev cycle: 2
+ =============================================
+ Fermi energy = 0.041695
+ This SCF iteration took 0.124 s.
+
+ =============================================
+ Relaxation iteration: 1
+ SCF iteration number: 1, Chebyshev cycle: 3
+ =============================================
+ Fermi energy = -0.045757
+ This SCF iteration took 0.125 s.
+
+ =============================================
+ Relaxation iteration: 1
+ SCF iteration number: 1, Chebyshev cycle: 4
+ =============================================
+ Fermi energy = -0.056692
+ AAR converged to a relative residual of 5.74149e-08 in 43 iterations.
+ Poisson problem took 0.121506s
+ Escc = 0.84981403
+ Etot = -6.22587715
+ Eatom = -1.24517543
+ Error in SCF iteration: 1.3548e-01
+ This SCF iteration took 0.260 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 2
+ =========================
+ Fermi energy = -0.039170
+ AAR converged to a relative residual of 4.65507e-08 in 37 iterations.
+ Poisson problem took 0.109434s
+ Escc = 0.49757694
+ Etot = -6.23470922
+ Eatom = -1.24694184
+ Error in SCF iteration: 8.6423e-02
+ This SCF iteration took 0.246 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 3
+ =========================
+ Fermi energy = -0.010810
+ AAR converged to a relative residual of 3.16819e-08 in 37 iterations.
+ Poisson problem took 0.109089s
+ Escc = -0.04580423
+ Etot = -6.23991302
+ Eatom = -1.24798260
+ Error in SCF iteration: 2.0754e-02
+ This SCF iteration took 0.245 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 4
+ =========================
+ Fermi energy = -0.015161
+ AAR converged to a relative residual of 3.87781e-08 in 31 iterations.
+ Poisson problem took 0.097162s
+ Escc = 0.01289507
+ Etot = -6.23994091
+ Eatom = -1.24798818
+ Error in SCF iteration: 2.7502e-03
+ This SCF iteration took 0.239 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 5
+ =========================
+ Fermi energy = -0.014696
+ AAR converged to a relative residual of 9.38023e-08 in 25 iterations.
+ Poisson problem took 0.084333s
+ Escc = 0.00013549
+ Etot = -6.23994755
+ Eatom = -1.24798951
+ Error in SCF iteration: 8.4361e-04
+ This SCF iteration took 0.225 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 6
+ =========================
+ Fermi energy = -0.014827
+ AAR converged to a relative residual of 9.02788e-08 in 25 iterations.
+ Poisson problem took 0.081397s
+ Escc = 0.00023985
+ Etot = -6.23994956
+ Eatom = -1.24798991
+ Error in SCF iteration: 2.6532e-04
+ This SCF iteration took 0.218 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 7
+ =========================
+ Fermi energy = -0.014910
+ AAR converged to a relative residual of 5.99809e-08 in 13 iterations.
+ Poisson problem took 0.058985s
+ Escc = 0.00065680
+ Etot = -6.23994961
+ Eatom = -1.24798992
+ Error in SCF iteration: 3.0353e-04
+ This SCF iteration took 0.246 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 8
+ =========================
+ Fermi energy = -0.014848
+ AAR converged to a relative residual of 7.2423e-08 in 13 iterations.
+ Poisson problem took 0.059235s
+ Escc = -0.00011138
+ Etot = -6.23994960
+ Eatom = -1.24798992
+ Error in SCF iteration: 2.1644e-05
+ This SCF iteration took 0.254 s.
+
+ =========================
+ Relaxation iteration: 1
+ SCF iteration number: 9
+ =========================
+ Fermi energy = -0.014858
+ AAR converged to a relative residual of 9.91976e-08 in 10 iterations.
+ Poisson problem took 0.047464s
+ Escc = 0.00001114
+ Etot = -6.23994861
+ Eatom = -1.24798972
+ Error in SCF iteration: 9.4035e-06
+ This SCF iteration took 0.217 s.
+
+
+ Finished SCF iteration in 9 steps!
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+ **********************************************************
+ * Energy per unit cell = -6.239948613 Ha. *
+ * Energy per atom = -1.247989723 Ha. *
+ **********************************************************
+
+ Starting atomic force calculation ...
+ local force calculation: 0.031 s
+ ***********************************************************
+ * Atomic Force *
+ ***********************************************************
+ Drift free forces (Ha/Bohr):
+ -0.000000073428623 -0.000000446207082 0.000000152240056
+ -0.004934732182701 -0.004934581894434 -0.004934005185551
+ 0.004935095152163 0.004934306891350 -0.004935939032387
+ 0.004933819717261 -0.004933636206349 0.004935006865413
+ -0.004934109258101 0.004934357416516 0.004934785112468
+
+ Max magnitude of forces (Ha/Bohr): 0.008547867733556
+
+
+ Time for calculating forces: 0.092601 s.
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+ Final atomic positions (Cartesian) are as follows:
+ 6.500000 6.500000 6.500000
+ 8.127432 8.127432 8.127432
+ 4.872568 4.872568 8.127432
+ 4.872568 8.127432 4.872568
+ 8.127432 4.872568 4.872568
+
+ Run-time of the program: 3.195061 seconds
diff --git a/examples/SiH4.refout b/examples/SiH4.refout
new file mode 100644
index 00000000..5c74ce81
--- /dev/null
+++ b/examples/SiH4.refout
@@ -0,0 +1,97 @@
+***************************************************************************
+* M-SPARC (Dec 17, 2019) *
+* Copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech *
+* Distributed under GNU General Public License 3 (GPL) *
+* Date: 20-Dec-2019 Start time: 13:53:38 *
+***************************************************************************
+ Input parameters
+***************************************************************************
+CELL: 13.000000 13.000000 13.000000
+FD_GRID: 26 26 26
+FD_ORDER: 12
+BOUNDARY_CONDITION: 1
+ELEC_TEMP_TYPE: gaussian
+SMEARING: 0.007349864
+CHEB_DEGREE: 17
+NSTATES: 10
+EXCHANGE_CORRELATION: LDA_PW
+CALC_STRESS: 0
+CALC_PRES: 0
+MAXIT_SCF: 30
+TOL_SCF: 1.00E-05
+TOL_POISSON: 1.00E-07
+TOL_LANCZOS: 1.00E-02
+TOL_PSEUDOCHARGE: 1.00E-05
+MIXING_VARIABLE: potential
+MIXING_PRECOND: none
+MIXING_PARAMETER: 0.30
+MIXING_HISTORY: 7
+PULAY_FREQUENCY: 1
+PULAY_RESTART_FREQ: 0
+REFERENCE_CUTOFF: 0.50
+RHO_TRIGGER: 4
+FIX_RAND: 0
+PRINT_FORCES: 1
+PRINT_ATOMS: 1
+PRINT_EIGEN: 0
+PRINT_DENSITY: 0
+OUTPUT_FILE: SiH4.out
+***************************************************************************
+ Initialization
+***************************************************************************
+Mesh spacing : 0.500000 (Bohr)
+Output printed to : SiH4.out
+Total number of atom types : 2
+Total number of atoms : 5
+Total number of electrons : 8
+Atom type 1 (valence electrons) : Si 4
+Pseudopotential : ../Pseudopotentials/Si.psp8
+lloc : 4
+Pseudocharge radii of atom type 1 : 6.00 6.00 6.00
+Number of atoms of type 1 : 1
+Atom type 2 (valence electrons) : H 1
+Pseudopotential : ../Pseudopotentials/H.psp8
+lloc : 4
+Pseudocharge radii of atom type 2 : 3.00 3.00 3.00
+Number of atoms of type 2 : 4
+Estimated total memory usage : 90.51 MB
+=====================================================================
+ Self Consistent Field (SCF#1)
+=====================================================================
+Iteration Free Energy (Ha/atom) SCF Error Timing (sec)
+1 -1.2451754296E+00 1.355E-01 0.503
+2 -1.2469418431E+00 8.642E-02 0.260
+3 -1.2479826042E+00 2.075E-02 0.246
+4 -1.2479881823E+00 2.750E-03 0.245
+5 -1.2479895103E+00 8.436E-04 0.239
+6 -1.2479899127E+00 2.653E-04 0.225
+7 -1.2479899216E+00 3.035E-04 0.218
+8 -1.2479899207E+00 2.164E-05 0.246
+9 -1.2479897227E+00 9.404E-06 0.254
+Total number of SCF: 9
+====================================================================
+ Energy
+====================================================================
+Free energy per atom : -1.2479897227E+00 (Ha/atom)
+Total free energy : -6.2399486133E+00 (Ha)
+Band structure energy : -2.8546194064E+00 (Ha)
+Exchange correlation energy : -2.4796327871E+00 (Ha)
+Self and correction energy : -1.9078384259E+01 (Ha)
+Entropy*kb*T : -1.0838164359E-06 (Ha)
+Fermi level : -1.4858196822E-02 (Ha)
+Average force : 6.8375825236E-03 (Ha/Bohr)
+Maximum force : 8.5478677336E-03 (Ha/Bohr)
+Time for force calculation : 0.093 (sec)
+***************************************************************************
+ Timing info
+***************************************************************************
+Total walltime : 3.195 sec
+___________________________________________________________________________
+
+***************************************************************************
+* Material Physics & Mechanics Group, Georgia Tech *
+* PI: Phanish Suryanarayana *
+* Main Developers: Qimen Xu, Abhiraj Sharma *
+* Acknowledgements: U.S. DOE (DE-SC0019410); NSF (1333500,1553212) *
+***************************************************************************
+
diff --git a/examples/SiH4.refstatic b/examples/SiH4.refstatic
new file mode 100644
index 00000000..34a42850
--- /dev/null
+++ b/examples/SiH4.refstatic
@@ -0,0 +1,15 @@
+***************************************************************************
+ Atom positions
+***************************************************************************
+Cartesian coordinates of atoms (Bohr):
+ 6.5000000000 6.5000000000 6.5000000000
+ 8.1274320210 8.1274320210 8.1274320210
+ 4.8725679790 4.8725679790 8.1274320210
+ 4.8725679790 8.1274320210 4.8725679790
+ 8.1274320210 4.8725679790 4.8725679790
+Atomic forces (Ha/Bohr):
+ -0.0000000734 -0.0000004462 0.0000001522
+ -0.0049347322 -0.0049345819 -0.0049340052
+ 0.0049350952 0.0049343069 -0.0049359390
+ 0.0049338197 -0.0049336362 0.0049350069
+ -0.0049341093 0.0049343574 0.0049347851
diff --git a/examples/run_examples.m b/examples/run_examples.m
new file mode 100644
index 00000000..a62734e5
--- /dev/null
+++ b/examples/run_examples.m
@@ -0,0 +1,23 @@
+% This script launches four example tests
+% Date: Nov 17,2019
+% Author: Qimen Xu
+
+% add src/ folder to path
+% addpath(genpath('../src'));
+addpath(genpath(fullfile('..','src'))); % this works for all OSs
+
+fnames = {'BaTiO3', 'H2O_sheet', 'H2O_wire', 'SiH4'};
+
+t_s = tic;
+for itest = 1:length(fnames)
+ name = fnames{itest};
+ clear S; clc;
+ diary(strcat(name,'.log'));
+ %%%%%%%%%%%%%%%%%
+ S = msparc(name);
+ %%%%%%%%%%%%%%%%%
+ % save(strcat(name,'.mat'), 'S');
+ diary off;
+end
+fprintf(' Total time for running all examples: %.3f s\n', toc(t_s));
+
diff --git a/src/aar.m b/src/aar.m
new file mode 100644
index 00000000..618a9ed4
--- /dev/null
+++ b/src/aar.m
@@ -0,0 +1,74 @@
+function [x] = aar(A,b,x_guess,tol,max_iter,omega,beta,m,p,L,U)
+% @brief Preconditioned Alternating Anderson-Richardson (AAR) MATLAB
+% code. Solves the system Ax = b. Last Modified: 26 March 2018
+%
+% @param A : square matrix (size N x N),
+% @param b : right hand side column vector (size N x 1),
+% @param x_guess : initial guess (of size b),
+% @param tol : convergence tolerance
+% @param max_iter: maximum number of iterations
+% @param omega : relaxation parameter (for Richardson update)
+% @param beta : extrapolation parameter (for Anderson update)
+% @param m : Anderson history, no. of previous iterations to be considered in extrapolation
+% @param p : Perform Anderson extrapolation at every p th iteration
+% @param L : Lower part of LU Preconditioner
+% @param L : Upper part of LU Preconditioner
+% @output x : solution vector
+%
+% NOTE : A and b are to be provided. Other input parameters can be passed as "[]", to use defaults.
+% e.g. : Run code as, tic;x=aar(A,b,[],[],[],[],[],[],[],[]);toc;
+%
+% @ref : Suryanarayana, P., Pratapa, P. P., & Pask, J. E. (2019).
+% Alternating Anderson–Richardson method: An efficient alternative
+% to preconditioned Krylov methods for large, sparse linear systems.
+% Computer Physics Communications, 234, 278-285.
+%
+% @authors Phanish Suryanarayana
+% Phanisri Pradeep Pratapa
+% (In collaboration with John E. Pask.)
+%
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+
+
+N=length(b);
+DX=zeros(N,m);
+DF=zeros(N,m);
+nb = 1/norm(b) ;
+if isempty(x_guess)
+ x_guess = ones(N,1); % initial guess vector
+end
+x_prev = x_guess;
+relres = 1+tol;
+count = 1;
+while count<=max_iter && relres > tol
+ res1 = (b-A*x_prev) ;
+ relres = norm(res1)*nb;
+ res = U\(L\(res1));
+
+ % STORE HISTORY
+ if count>1
+ DX(:,mod(count-2,m)+1) = x_prev-Xold;
+ DF(:,mod(count-2,m)+1) = res-Fold;
+ end
+ Xold = x_prev;
+ Fold = res;
+
+ % UPDATE ITERATE
+ if rem(count,p)~=0 % RICHARDSON UPDATE
+ x_new = x_prev + omega*res;
+ else % ANDERSON UPDATE, apply every p iters
+ x_new = x_prev + beta*res - (DX + beta*DF)*(pinv(DF'*DF)*(DF'*res));
+ end
+
+ x = x_prev;
+ x_prev = x_new;
+ count = count + 1;
+end
+
+if count-1 == max_iter
+ fprintf(' AAR exceeded maximum iterations and converged to a relative residual of %g. \n',relres);
+else
+ fprintf(' AAR converged to a relative residual of %g in %d iterations.\n',relres,count-1);
+end
+
+end
diff --git a/src/andersonWtdAvg.m b/src/andersonWtdAvg.m
new file mode 100644
index 00000000..5126b46e
--- /dev/null
+++ b/src/andersonWtdAvg.m
@@ -0,0 +1,23 @@
+function [x_wavg, f_wavg] = andersonWtdAvg(x_k, f_k, X, F)
+% @brief ANDERSONWTDAVG finds the weighted averages
+% x_wavg := x_k - X*Gamma
+% f_wavg := f_k - F*Gamma
+% where Gamma = inv(F' * F) * F' * f_k, F' denotes the transpose
+% of F.
+%
+% @param x_k Current guess/input vector.
+% @param f_k Current preconditioned residual.
+% @param X Iterate histories, X = [x_{k-m+1}-x_{k-m}, ..., x_k-x_{k-1}].
+% @param F Residual histories, F = [f_{k-m+1}-f_{k-m}, ..., f_k-f_{k-1}].
+%
+% @authors Qimen Xu
+% Abhiraj Sharma
+% Phanish Suryanarayana
+%
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+
+Gamma = pinv(F'*F)*(F'*f_k);
+x_wavg = x_k - X * Gamma;
+f_wavg = f_k - F * Gamma;
+
+end
\ No newline at end of file
diff --git a/src/atomdata_mass.m b/src/atomdata_mass.m
new file mode 100644
index 00000000..3a69af0d
--- /dev/null
+++ b/src/atomdata_mass.m
@@ -0,0 +1,235 @@
+function mass = atomdata_mass(element)
+% @brief Find atomic mass info. for given element type.
+%
+% @param element The element name
+%
+% @authors Qimen Xu
+% Abhiraj Sharma
+% Phanish Suryanarayana
+% @ref NIST (https:%physics.nist.gov/cgi-bin/Compositions/stand_alone.pl?ele=&all=all&ascii=html)
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+%
+
+if (strcmp(element,'H'))
+ mass = 1.007975;
+elseif (strcmp(element,'He'))
+ mass = 4.002602; % avg min&max
+elseif (strcmp(element,'Li'))
+ mass = 6.9675; % avg min&max
+elseif (strcmp(element,'Be'))
+ mass = 9.0121831;
+elseif (strcmp(element,'B'))
+ mass = 10.8135; % avg min&max
+elseif (strcmp(element,'C'))
+ mass = 12.0106; % avg min&max
+elseif (strcmp(element,'N'))
+ mass = 14.006855; % avg min&max
+elseif (strcmp(element,'O'))
+ mass = 15.9994; % avg min&max
+elseif (strcmp(element,'F'))
+ mass = 18.998403163;
+elseif (strcmp(element,'Ne'))
+ mass = 20.1797;
+elseif (strcmp(element,'Na'))
+ mass = 22.98976928;
+elseif (strcmp(element,'Mg'))
+ mass = 24.3055; % avg min&max
+elseif (strcmp(element,'Al'))
+ mass = 26.9815385;
+elseif (strcmp(element,'Si'))
+ mass = 28.085; % avg min&max
+elseif (strcmp(element,'P'))
+ mass = 30.973761998;
+elseif (strcmp(element,'S'))
+ mass = 32.0675; % avg min&max
+elseif (strcmp(element,'Cl'))
+ mass = 35.4515; % avg min&max
+elseif (strcmp(element,'Ar'))
+ mass = 39.948;
+elseif (strcmp(element,'K'))
+ mass = 39.0983;
+elseif (strcmp(element,'Ca'))
+ mass = 40.078;
+elseif (strcmp(element,'Sc'))
+ mass = 44.955908;
+elseif (strcmp(element,'Ti'))
+ mass = 47.867;
+elseif (strcmp(element,'V'))
+ mass = 50.9415;
+elseif (strcmp(element,'Cr'))
+ mass = 51.9961;
+elseif (strcmp(element,'Mn'))
+ mass = 54.938044;
+elseif (strcmp(element,'Fe'))
+ mass = 55.845;
+elseif (strcmp(element,'Co'))
+ mass = 58.933194;
+elseif (strcmp(element,'Ni'))
+ mass = 58.6934;
+elseif (strcmp(element,'Cu'))
+ mass = 63.546;
+elseif (strcmp(element,'Zn'))
+ mass = 65.38;
+elseif (strcmp(element,'Ga'))
+ mass = 69.723;
+elseif (strcmp(element,'Ge'))
+ mass = 72.630;
+elseif (strcmp(element,'As'))
+ mass = 74.921595;
+elseif (strcmp(element,'Se'))
+ mass = 78.971;
+elseif (strcmp(element,'Br'))
+ mass = 79.904; % avg min&max
+elseif (strcmp(element,'Kr'))
+ mass = 83.798;
+elseif (strcmp(element,'Rb'))
+ mass = 85.4678;
+elseif (strcmp(element,'Sr'))
+ mass = 87.62;
+elseif (strcmp(element,'Y'))
+ mass = 88.90584;
+elseif (strcmp(element,'Zr'))
+ mass = 91.224;
+elseif (strcmp(element,'Nb'))
+ mass = 92.90637;
+elseif (strcmp(element,'Mo'))
+ mass = 95.95;
+elseif (strcmp(element,'Tc'))
+ mass = 98;
+elseif (strcmp(element,'Ru'))
+ mass = 101.07;
+elseif (strcmp(element,'Rh'))
+ mass = 102.90550;
+elseif (strcmp(element,'Pd'))
+ mass = 106.42;
+elseif (strcmp(element,'Ag'))
+ mass = 107.8682;
+elseif (strcmp(element,'Cd'))
+ mass = 112.414;
+elseif (strcmp(element,'In'))
+ mass = 114.818;
+elseif (strcmp(element,'Sn'))
+ mass = 118.710;
+elseif (strcmp(element,'Sb'))
+ mass = 121.760;
+elseif (strcmp(element,'Te'))
+ mass = 127.60;
+elseif (strcmp(element,'I'))
+ mass = 126.90447;
+elseif (strcmp(element,'Xe'))
+ mass = 131.293;
+elseif (strcmp(element,'Cs'))
+ mass = 132.90545196;
+elseif (strcmp(element,'Ba'))
+ mass = 137.327;
+elseif (strcmp(element,'La'))
+ mass = 138.90547;
+elseif (strcmp(element,'Ce'))
+ mass = 140.116;
+elseif (strcmp(element,'Pr'))
+ mass = 140.90766;
+elseif (strcmp(element,'Nd'))
+ mass = 144.242;
+elseif (strcmp(element,'Pm'))
+ mass = 145;
+elseif (strcmp(element,'Sm'))
+ mass = 150.36;
+elseif (strcmp(element,'Eu'))
+ mass = 151.964;
+elseif (strcmp(element,'Gd'))
+ mass = 157.25;
+elseif (strcmp(element,'Tb'))
+ mass = 158.92535;
+elseif (strcmp(element,'Dy'))
+ mass = 162.500;
+elseif (strcmp(element,'Ho'))
+ mass = 164.93033;
+elseif (strcmp(element,'Er'))
+ mass = 167.259;
+elseif (strcmp(element,'Tm'))
+ mass = 168.93422;
+elseif (strcmp(element,'Yb'))
+ mass = 173.054;
+elseif (strcmp(element,'Lu'))
+ mass = 174.9668;
+elseif (strcmp(element,'Hf'))
+ mass = 178.49;
+elseif (strcmp(element,'Ta'))
+ mass = 180.94788;
+elseif (strcmp(element,'W'))
+ mass = 183.84;
+elseif (strcmp(element,'Re'))
+ mass = 186.207;
+elseif (strcmp(element,'Os'))
+ mass = 190.23;
+elseif (strcmp(element,'Ir'))
+ mass = 192.217;
+elseif (strcmp(element,'Pt'))
+ mass = 195.084;
+elseif (strcmp(element,'Au'))
+ mass = 196.966569;
+elseif (strcmp(element,'Hg'))
+ mass = 200.592;
+elseif (strcmp(element,'Tl'))
+ mass = 204.3835; % avg min&max
+elseif (strcmp(element,'Pb'))
+ mass = 207.2;
+elseif (strcmp(element,'Bi'))
+ mass = 208.98040;
+elseif (strcmp(element,'Po'))
+ mass = 209;
+elseif (strcmp(element,'At'))
+ mass = 210;
+elseif (strcmp(element,'Rn'))
+ mass = 222;
+elseif (strcmp(element,'Fr'))
+ mass = 223;
+elseif (strcmp(element,'Ra'))
+ mass = 226;
+elseif (strcmp(element,'Ac'))
+ mass = 227;
+elseif (strcmp(element,'Th'))
+ mass = 232.0377;
+elseif (strcmp(element,'Pa'))
+ mass = 231.03588;
+elseif (strcmp(element,'U'))
+ mass = 238.02891;
+elseif (strcmp(element,'Np'))
+ mass = 237;
+elseif (strcmp(element,'Pu'))
+ mass = 244;
+elseif (strcmp(element,'Am'))
+ %mass = ;
+ fprintf('No atomic data for element %s, please provide in input file!\n', element);
+elseif (strcmp(element,'Cm'))
+ %mass = ;
+ fprintf('No atomic data for element %s, please provide in input file!\n', element);
+elseif (strcmp(element,'Bk'))
+ %mass = ;
+ fprintf('No atomic data for element %s, please provide in input file!\n', element);
+elseif (strcmp(element,'Cf'))
+ %mass = ;
+ fprintf('No atomic data for element %s, please provide in input file!\n', element);
+elseif (strcmp(element,'Es'))
+ %mass = ;
+ fprintf('No atomic data for element %s, please provide in input file!\n', element);
+elseif (strcmp(element,'Fm'))
+ %mass = ;
+ fprintf('No atomic data for element %s, please provide in input file!\n', element);
+elseif (strcmp(element,'Md'))
+ %mass = ;
+ fprintf('No atomic data for element %s, please provide in input file!\n', element);
+elseif (strcmp(element,'No'))
+ %mass = ;
+ fprintf('No atomic data for element %s, please provide in input file!\n', element);
+elseif (strcmp(element,'Lw") == 0 || strcmp(element,"Lr'))
+ %mass = ;
+ fprintf('No atomic data for element %s, please provide in input file!\n', element);
+else
+ fprintf('No atomic data for element %s, please provide in input file!\n', element);
+end
+
+
+end
+
+
diff --git a/src/atomicForce.m b/src/atomicForce.m
new file mode 100644
index 00000000..e3b19d0b
--- /dev/null
+++ b/src/atomicForce.m
@@ -0,0 +1,326 @@
+function force = atomicForce(S)
+% @brief atomicForce(S) calculates the atomic force.
+% @authors Qimen Xu
+% Abhiraj Sharma
+% Phanish Suryanarayana
+%
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+%==========================================================================
+
+fprintf('\n Starting atomic force calculation ... \n');
+
+% Calculate local forces
+tic_locforces = tic;
+
+% Dpseudo_x = S.grad_1*(S.b + S.b_ref);
+% Dpseudo_y = S.grad_2*(S.b + S.b_ref);
+% Dpseudo_z = S.grad_3*(S.b + S.b_ref);
+
+Dphi_x = S.grad_1*(S.phi);
+Dphi_y = S.grad_2*(S.phi);
+Dphi_z = S.grad_3*(S.phi);
+
+DVc_x = S.grad_1*S.V_c;
+DVc_y = S.grad_2*S.V_c;
+DVc_z = S.grad_3*S.V_c;
+
+% initialization
+force_corr = zeros(S.n_atm,3);
+force_nloc = zeros(S.n_atm,3);
+force_local = zeros(S.n_atm,3);
+
+count_typ = 1;
+count_typ_atms = 1;
+for JJ_a = 1:S.n_atm % loop over all the atoms
+ % Atom position
+ x0 = S.Atoms(JJ_a,1);
+ y0 = S.Atoms(JJ_a,2);
+ z0 = S.Atoms(JJ_a,3);
+
+ % Note the S.dx, S.dy, S.dz terms are to ensure the image rb-region overlap w/ fund. domain
+ if S.BCx == 0
+ n_image_xl = floor((S.Atoms(JJ_a,1) + S.Atm(count_typ).rb_x)/S.L1);
+ n_image_xr = floor((S.L1 - S.Atoms(JJ_a,1)+S.Atm(count_typ).rb_x-S.dx)/S.L1);
+ else
+ n_image_xl = 0;
+ n_image_xr = 0;
+ end
+
+ if S.BCy == 0
+ n_image_yl = floor((S.Atoms(JJ_a,2) + S.Atm(count_typ).rb_y)/S.L2);
+ n_image_yr = floor((S.L2 - S.Atoms(JJ_a,2)+S.Atm(count_typ).rb_y-S.dy)/S.L2);
+ else
+ n_image_yl = 0;
+ n_image_yr = 0;
+ end
+
+ if S.BCz == 0
+ n_image_zl = floor((S.Atoms(JJ_a,3) + S.Atm(count_typ).rb_z)/S.L3);
+ n_image_zr = floor((S.L3 - S.Atoms(JJ_a,3)+S.Atm(count_typ).rb_z-S.dz)/S.L3);
+ else
+ n_image_zl = 0;
+ n_image_zr = 0;
+ end
+
+ % Total No. of images of atom JJ_a (including atom JJ_a)
+ n_image_total = (n_image_xl+n_image_xr+1) * (n_image_yl+n_image_yr+1) * (n_image_zl+n_image_zr+1);
+ % Find the coordinates for all the images
+ xx_img = (-n_image_xl : n_image_xr) * S.L1 + x0;
+ yy_img = (-n_image_yl : n_image_yr) * S.L2 + y0;
+ zz_img = (-n_image_zl : n_image_zr) * S.L3 + z0;
+ [XX_IMG_3D,YY_IMG_3D,ZZ_IMG_3D] = ndgrid(xx_img,yy_img,zz_img);
+
+ % Loop over all image(s) of atom JJ_a (including atom JJ_a)
+ for count_image = 1:n_image_total
+
+ % Atom position of the image
+ x0_i = XX_IMG_3D(count_image);
+ y0_i = YY_IMG_3D(count_image);
+ z0_i = ZZ_IMG_3D(count_image);
+
+ %**********************************************************************
+ %* Calculate local atomic force term *
+ %**********************************************************************
+
+ % Starting and ending indices of b-region
+ ii_s = ceil ((x0_i - S.Atm(count_typ).rb_x)/S.dx) + 1;
+ ii_e = floor((x0_i + S.Atm(count_typ).rb_x)/S.dx) + 1;
+ jj_s = ceil ((y0_i - S.Atm(count_typ).rb_y)/S.dy) + 1;
+ jj_e = floor((y0_i + S.Atm(count_typ).rb_y)/S.dy) + 1;
+ kk_s = ceil ((z0_i - S.Atm(count_typ).rb_z)/S.dz) + 1;
+ kk_e = floor((z0_i + S.Atm(count_typ).rb_z)/S.dz) + 1;
+
+ % Check if the b-region is inside the domain in Dirichlet BC
+ % direction
+ isInside = (S.BCx == 0 || (S.BCx == 1 && (ii_s>=1) && (ii_e<=S.Nx))) && ...
+ (S.BCy == 0 || (S.BCy == 1 && (jj_s>=1) && (jj_e<=S.Ny))) && ...
+ (S.BCz == 0 || (S.BCz == 1 && (kk_s>=1) && (kk_e<=S.Nz)));
+ % assert(isInside,'Error: Atom too close to boundary for b calculation');
+ if ~isInside
+ fprintf(' WARNING: Atom %d too close to boundary for b calculation\n',JJ_a);
+ end
+ ii_s = max(ii_s,1);
+ ii_e = min(ii_e,S.Nx);
+ jj_s = max(jj_s,1);
+ jj_e = min(jj_e,S.Ny);
+ kk_s = max(kk_s,1);
+ kk_e = min(kk_e,S.Nz);
+
+ xx = S.xin + (ii_s-S.FDn-1:ii_e+S.FDn-1)*S.dx;
+ yy = S.yin + (jj_s-S.FDn-1:jj_e+S.FDn-1)*S.dy;
+ zz = S.zin + (kk_s-S.FDn-1:kk_e+S.FDn-1)*S.dz;
+
+ [XX_3D,YY_3D,ZZ_3D] = ndgrid(xx,yy,zz);
+
+ % Find distances
+ dd = calculateDistance(XX_3D,YY_3D,ZZ_3D,x0_i,y0_i,z0_i,S);
+
+ % Pseudopotential at grid points through interpolation
+ V_PS = zeros(size(dd));
+ IsLargeThanRmax = dd > S.Atm(count_typ).r_grid_vloc(end);
+ V_PS(IsLargeThanRmax) = -S.Atm(count_typ).Z;
+ V_PS(~IsLargeThanRmax) = interp1(S.Atm(count_typ).r_grid_vloc, S.Atm(count_typ).r_grid_vloc.*S.Atm(count_typ).Vloc, dd(~IsLargeThanRmax), 'spline');
+
+ V_PS = V_PS./dd;
+ V_PS(dd
+% Phanish Suryanarayana
+%
+% @param kptvec k-point vector for the current Block diagonalized problem
+% @param grad_dir direction along which gradient has to be calculated
+% @param DG Discrete gradient along grad_dir direction
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+%===================================================================================
+
+if S.cell_typ < 3
+
+ if (grad_dir == 1)
+ I = S.G_I_1;
+ J = S.G_J_1;
+ V = S.G_V_1;
+ BC = S.BCx;
+ if BC == 0
+ isOutl = S.G_JOutl_1;
+ isOutr = S.G_JOutr_1;
+ L = S.L1;
+ kpt = kptvec(1);
+ end
+ elseif (grad_dir == 2)
+ I = S.G_I_2;
+ J = S.G_J_2;
+ V = S.G_V_2;
+ BC = S.BCy;
+ if BC == 0
+ isOutl = S.G_JOutl_2;
+ isOutr = S.G_JOutr_2;
+ L = S.L2;
+ kpt = kptvec(2);
+ end
+ else
+ I = S.G_I_3;
+ J = S.G_J_3;
+ V = S.G_V_3;
+ BC = S.BCz;
+ if BC == 0
+ isOutl = S.G_JOutl_3;
+ isOutr = S.G_JOutr_3;
+ L = S.L3;
+ kpt = kptvec(3);
+ end
+ end
+
+ % Map the elements of discrete laplacian
+ if BC == 0
+ % Phase factor
+ if (kpt == 0)
+ phasefac_l = 1.0;
+ phasefac_r = 1.0;
+ else
+ phasefac_l = exp(-1i*kpt*L);
+ phasefac_r = exp(1i*kpt*L);
+ end
+
+ V(isOutl) = V(isOutl) * phasefac_l;
+ V(isOutr) = V(isOutr) * phasefac_r;
+ end
+
+ DG = sparse(I,J,V,S.N,S.N);
+
+else
+ DG = blochGradient_cychel(S,kptvec,grad_dir);
+end
diff --git a/src/blochLaplacian_1d.m b/src/blochLaplacian_1d.m
new file mode 100644
index 00000000..1ab2e341
--- /dev/null
+++ b/src/blochLaplacian_1d.m
@@ -0,0 +1,124 @@
+function [DL11,DL22,DL33,DG1,DG2,DG3] = blochLaplacian_1d(S,kptvec)
+% @ brief Calculates each component of laplacian in 1D
+% @ authors
+% Abhiraj Sharma
+% Qimen Xu
+% Phanish Suryanarayana
+%
+% @param kptvec k-point vector for the current Block diagonalized problem
+% @param DLii Discrete laplacian component in 1D along ith direction
+% @param DGi Discrete gradient component in 1D along ith direction
+%
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+%============================================================================
+Nx = S.Nx; Ny = S.Ny; Nz = S.Nz;
+
+% Phase factors
+if kptvec(1) == 0
+ x_phasefac_l = 1.0;
+ x_phasefac_r = 1.0;
+else
+ x_phasefac_l = exp(-1i*kptvec(1)*S.L1);
+ x_phasefac_r = exp(1i*kptvec(1)*S.L1);
+end
+
+if kptvec(2) == 0
+ y_phasefac_l = 1.0;
+ y_phasefac_r = 1.0;
+else
+ y_phasefac_l = exp(-1i*kptvec(2)*S.L2);
+ y_phasefac_r = exp(1i*kptvec(2)*S.L2);
+end
+
+if kptvec(3) == 0
+ z_phasefac_l = 1.0;
+ z_phasefac_r = 1.0;
+else
+ z_phasefac_l = exp(-1i*kptvec(3)*S.L3);
+ z_phasefac_r = exp(1i*kptvec(3)*S.L3);
+end
+
+
+% D_xx laplacian in 1D
+%-----------------------
+V = S.V_11;
+
+if S.BCx == 0
+ V(S.isOutl_11) = V(S.isOutl_11) * x_phasefac_l;
+ V(S.isOutr_11) = V(S.isOutr_11) * x_phasefac_r;
+end
+
+% Create discretized Laplacian
+DL11 = sparse(S.I_11,S.II_11,V,Nx,Nx);
+
+% D_yy laplacian in 1D
+%-----------------------
+V = S.V_22;
+
+if S.BCy == 0
+ V(S.isOutl_22) = V(S.isOutl_22) * y_phasefac_l;
+ V(S.isOutr_22) = V(S.isOutr_22) * y_phasefac_r;
+end
+
+% Create discretized Laplacian
+DL22 = sparse(S.I_22,S.II_22,V,Ny,Ny);
+
+% D_zz laplacian in 1D
+%-----------------------
+
+V = S.V_33;
+
+if S.BCz == 0
+ V(S.isOutl_33) = V(S.isOutl_33) * z_phasefac_l;
+ V(S.isOutr_33) = V(S.isOutr_33) * z_phasefac_r;
+end
+
+% Create discretized Laplacian
+DL33 = sparse(S.I_33,S.II_33,V,Nz,Nz);
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+DG1 = zeros(Nx,Nx);
+DG2 = zeros(Ny,Ny);
+DG3 = zeros(Nz,Nz);
+
+if S.cell_typ > 1
+ % x-direction
+ %-------------
+
+ V = S.V_1;
+
+ if S.BCx == 0
+ V(S.isOutl_1) = V(S.isOutl_1) * x_phasefac_l;
+ V(S.isOutr_1) = V(S.isOutr_1) * x_phasefac_r;
+ end
+
+ % Create discretized Laplacian
+ DG1 = sparse(S.I_1,S.II_1,V,Nx,Nx);
+
+ % y-direction
+ %-------------
+
+ V = S.V_2;
+
+ if S.BCy == 0
+ V(S.isOutl_2) = V(S.isOutl_2) * y_phasefac_l;
+ V(S.isOutr_2) = V(S.isOutr_2) * y_phasefac_r;
+ end
+
+ % Create discretized Laplacian
+ DG2 = sparse(S.I_2,S.II_2,V,Ny,Ny);
+
+ % z-direction
+ %-------------
+
+ V = S.V_3;
+
+ if S.BCz == 0
+ V(S.isOutl_3) = V(S.isOutl_3) * z_phasefac_l;
+ V(S.isOutr_3) = V(S.isOutr_3) * z_phasefac_r;
+ end
+
+ % Create discretized Laplacian
+ DG3 = sparse(S.I_3,S.II_3,V,Nz,Nz);
+
+end
diff --git a/src/calculateDistance.m b/src/calculateDistance.m
new file mode 100644
index 00000000..ba2298db
--- /dev/null
+++ b/src/calculateDistance.m
@@ -0,0 +1,32 @@
+function dd = calculateDistance(X,Y,Z,X_ref,Y_ref,Z_ref,S)
+% @ brief Function to perform distance calculation
+% @ authors
+% Abhiraj Sharma
+% Qimen Xu
+% Phanish Suryanarayana
+%
+% @param X X coordinate of the nodes
+% @param Y Y coordinate of the nodes
+% @param Z Z coordinate of the nodes
+% @param X_ref x-coordinate of the reference point
+% @param Y_ref y-coordinate of the reference point
+% @param Z_ref z-coordinate of the reference point
+% @param dd distance of the nodes from the reference point
+%
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+%======================================================================
+ if S.cell_typ == 1
+ XX = bsxfun(@minus,X,X_ref);
+ YY = bsxfun(@minus,Y,Y_ref);
+ ZZ = bsxfun(@minus,Z,Z_ref);
+ dd = sqrt(XX.^2 + YY.^2 + ZZ.^2);
+ elseif S.cell_typ == 2
+ XX = bsxfun(@minus,X,X_ref);
+ YY = bsxfun(@minus,Y,Y_ref);
+ ZZ = bsxfun(@minus,Z,Z_ref);
+ dd = sqrt(S.metric_T(1,1)*XX.^2 + S.metric_T(1,2)*(XX.*YY) + S.metric_T(1,3)*(XX.*ZZ) + ...
+ S.metric_T(2,2)*YY.^2 + S.metric_T(2,3)*(YY.*ZZ) + S.metric_T(3,3)*ZZ.^2);
+ elseif (S.cell_typ == 3 || S.cell_typ == 4 || S.cell_typ == 5)
+ dd = calculateDistance_cychel(X,Y,Z,X_ref,Y_ref,Z_ref,S);
+ end
+end
\ No newline at end of file
diff --git a/src/calculate_b_guessRho_Eself.m b/src/calculate_b_guessRho_Eself.m
new file mode 100644
index 00000000..6f21f778
--- /dev/null
+++ b/src/calculate_b_guessRho_Eself.m
@@ -0,0 +1,221 @@
+function S = calculate_b_guessRho_Eself(S)
+% @brief calculate_b_guessRho_Eself(S) calculates the pseudocharge (& ref),
+% self energy (& ref), electronic density guess, electrostatic
+% energy correction and electrostatic potential correction.
+%
+% @param S A struct that contains the relevant fields.
+%
+% @authors Qimen Xu
+% Abhiraj Sharma
+% Phanish Suryanarayana
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+%
+
+t1 = tic;
+fprintf('\n Starting pseudocharge generation and self energy calculation...\n');
+
+% initialization
+S.b = zeros(S.N,1);
+S.b_ref = zeros(S.N,1);
+S.rho_at = zeros(S.N,1);
+if S.nspin == 2
+ rho_at_up = zeros(S.N,1);
+ rho_at_dn = zeros(S.N,1);
+end
+S.Eself = 0;
+S.Eself_ref = 0;
+S.V_c = zeros(S.N,1);
+
+% Pseudocharge generation and self energy calculation
+count_typ = 1;
+count_typ_atms = 1;
+for JJ_a = 1:S.n_atm % loop over all the atoms
+ % Atom position of atom JJ_a
+ x0 = S.Atoms(JJ_a,1);
+ y0 = S.Atoms(JJ_a,2);
+ z0 = S.Atoms(JJ_a,3);
+
+ % Note the S.dx, S.dy, S.dz terms are to ensure the image rb-region overlap w/ fund. domain
+ if S.BCx == 0
+ n_image_xl = floor((S.Atoms(JJ_a,1) + S.Atm(count_typ).rb_x)/S.L1);
+ n_image_xr = floor((S.L1 - S.Atoms(JJ_a,1)+S.Atm(count_typ).rb_x-S.dx)/S.L1);
+ else
+ n_image_xl = 0;
+ n_image_xr = 0;
+ end
+
+ if S.BCy == 0
+ n_image_yl = floor((S.Atoms(JJ_a,2) + S.Atm(count_typ).rb_y)/S.L2);
+ n_image_yr = floor((S.L2 - S.Atoms(JJ_a,2)+S.Atm(count_typ).rb_y-S.dy)/S.L2);
+ else
+ n_image_yl = 0;
+ n_image_yr = 0;
+ end
+
+ if S.BCz == 0
+ n_image_zl = floor((S.Atoms(JJ_a,3) + S.Atm(count_typ).rb_z)/S.L3);
+ n_image_zr = floor((S.L3 - S.Atoms(JJ_a,3)+S.Atm(count_typ).rb_z-S.dz)/S.L3);
+ else
+ n_image_zl = 0;
+ n_image_zr = 0;
+ end
+
+ % Total No. of images of atom JJ_a (including atom JJ_a)
+ n_image_total = (n_image_xl+n_image_xr+1) * (n_image_yl+n_image_yr+1) * (n_image_zl+n_image_zr+1);
+ % Find the coordinates for all the images
+ xx_img = (-n_image_xl : n_image_xr) * S.L1 + x0;
+ yy_img = (-n_image_yl : n_image_yr) * S.L2 + y0;
+ zz_img = (-n_image_zl : n_image_zr) * S.L3 + z0;
+ [XX_IMG_3D,YY_IMG_3D,ZZ_IMG_3D] = ndgrid(xx_img,yy_img,zz_img);
+
+ % Loop over all image(s) of atom JJ_a (including atom JJ_a)
+ for count_image = 1:n_image_total
+ % Atom position of the image
+ x0_i = XX_IMG_3D(count_image);
+ y0_i = YY_IMG_3D(count_image);
+ z0_i = ZZ_IMG_3D(count_image);
+
+ %************************************************************************
+ %* Calculate b, b_ref, Eself, Eself_ref and rho_at *
+ %************************************************************************
+ % Starting and ending indices of b-region
+ ii_s = ceil ((x0_i - S.Atm(count_typ).rb_x)/S.dx) + 1;
+ ii_e = floor((x0_i + S.Atm(count_typ).rb_x)/S.dx) + 1;
+ jj_s = ceil ((y0_i - S.Atm(count_typ).rb_y)/S.dy) + 1;
+ jj_e = floor((y0_i + S.Atm(count_typ).rb_y)/S.dy) + 1;
+ kk_s = ceil ((z0_i - S.Atm(count_typ).rb_z)/S.dz) + 1;
+ kk_e = floor((z0_i + S.Atm(count_typ).rb_z)/S.dz) + 1;
+
+ % Check if the b-region is inside the domain in Dirichlet BC
+ % direction
+ isInside = (S.BCx == 0 || (S.BCx == 1 && (ii_s>1) && (ii_e1) && (jj_e1) && (kk_e S.Atm(count_typ).r_grid_vloc(end);
+ V_PS(IsLargeThanRmax) = -S.Atm(count_typ).Z;
+ V_PS(~IsLargeThanRmax) = interp1(S.Atm(count_typ).r_grid_vloc, S.Atm(count_typ).r_grid_vloc.*S.Atm(count_typ).Vloc, dd(~IsLargeThanRmax), 'spline');
+
+ V_PS = V_PS./dd;
+ V_PS(dd S.Atm(count_typ).r_grid_rho(end)) = 0;
+
+ % Pseudocharge density, rho_at, Eself calculation
+ II = 1+S.FDn : size(V_PS,1)-S.FDn;
+ JJ = 1+S.FDn : size(V_PS,2)-S.FDn;
+ KK = 1+S.FDn : size(V_PS,3)-S.FDn;
+
+ % Calculate bJ and bJ_ref
+ bJ = pseudochargeDensity_atom(V_PS,II,JJ,KK,xx(1),S);
+ bJ_ref = pseudochargeDensity_atom(V_PS_ref,II,JJ,KK,xx(1),S);
+
+ [II_rb,JJ_rb,KK_rb] = ndgrid(ii_s:ii_e,jj_s:jj_e,kk_s:kk_e);
+ Rowcount_rb = (KK_rb-1)*S.Nx*S.Ny + (JJ_rb-1)*S.Nx + II_rb;
+ sz = size(S.b(Rowcount_rb));
+ S.b(Rowcount_rb) = S.b(Rowcount_rb) + reshape(bJ(II,JJ,KK), sz);
+ S.b_ref(Rowcount_rb) = S.b_ref(Rowcount_rb) + reshape(bJ_ref(II,JJ,KK),sz);
+ rho_add = reshape(rho_isolated_atom(II,JJ,KK),sz);
+ S.rho_at(Rowcount_rb) = S.rho_at(Rowcount_rb) + rho_add;
+ if(S.nspin == 2)
+ rho_at_up(Rowcount_rb) = rho_at_up(Rowcount_rb) + (S.Atm(count_typ).Z + S.Atm(count_typ).mag(count_typ_atms))/(2 * S.Atm(count_typ).Z) * rho_add;
+ rho_at_dn(Rowcount_rb) = rho_at_dn(Rowcount_rb) + (S.Atm(count_typ).Z - S.Atm(count_typ).mag(count_typ_atms))/(2 * S.Atm(count_typ).Z) * rho_add;
+ end
+ S.Eself = S.Eself + 0.5 * sum(sum(sum(bJ(II,JJ,KK).*V_PS(II,JJ,KK).*S.W(Rowcount_rb) )));
+ S.Eself_ref = S.Eself_ref + 0.5 * sum(sum(sum(bJ_ref(II,JJ,KK).*V_PS_ref(II,JJ,KK).*S.W(Rowcount_rb) )));
+ S.V_c(Rowcount_rb) = S.V_c(Rowcount_rb) + reshape(V_PS_ref(II,JJ,KK) - V_PS(II,JJ,KK),sz);
+ end % end of loop over images (including atom JJ_a)
+
+ % Check if same type of atoms are over
+ if count_typ_atms == S.Atm(count_typ).n_atm_typ
+ count_typ_atms = 1;
+ count_typ = count_typ + 1;
+ else
+ count_typ_atms = count_typ_atms + 1;
+ end
+end % end of loop over atoms
+
+% Scaling by factor -1/(4pi) for b
+S.b = (-1/(4*pi))*S.b;
+S.Eself = (-1/(4*pi))*S.Eself;
+
+% Scaling by factor -1/(4pi) for b_ref
+S.b_ref = (-1/(4*pi))*S.b_ref;
+S.Eself_ref = (-1/(4*pi))*S.Eself_ref;
+
+% find positive charges and negative charges
+S.PosCharge = abs(dot(S.W, S.b));
+S.NegCharge = -S.PosCharge + S.NetCharge;
+
+% Check for accuracy of b
+fprintf(' Integration b = %.12f\n\n',abs(dot(S.W,S.b)));
+%assert(abs(dot(S.W,S.b)+S.Nelectron)/S.Nelectron < 1e-4,'Pseudocharge needs improved accuracy!')
+
+% Check for accuracy of b_ref
+fprintf(' Integration b_ref = %.12f\n\n',abs(dot(S.W,S.b_ref)));
+%assert(abs(dot(S.W,S.b_ref)+S.Nelectron)/S.Nelectron < 1e-4,'Rerefence Pseudocharge needs improved accuracy!')
+
+
+%*************************************************************
+%* Designate rho_at *
+%*************************************************************
+% Guess for electron density
+if S.nspin == 2
+ S.rho_at = horzcat(S.rho_at,rho_at_up,rho_at_dn);
+end
+
+%rho_scal = (S.Nelectron/dot(S.W,S.rho_at(:,1)));
+%rho_scal = (-dot(S.W,S.b)/dot(S.W,S.rho_at(:,1)));
+rho_scal = abs(S.NegCharge/dot(S.W,S.rho_at(:,1)));
+S.rho_at = rho_scal*S.rho_at;
+
+if S.nspin == 2
+ netM = dot(S.W,S.rho_at(:,2)) - dot(S.W,S.rho_at(:,3));
+ fprintf('======================================\n');
+ fprintf(' Net initial magnetization is: % .15f \n', netM);
+ fprintf('======================================\n\n');
+end
+
+fprintf(' ****************************************\n');
+fprintf(' * Eself_ref = %f *\n',S.Eself_ref);
+fprintf(' ****************************************\n');
+
+%*************************************************************
+%* Calculate E_corr *
+%*************************************************************
+S.E_corr = 0.5*sum((S.b_ref+S.b).*S.V_c.*S.W) + S.Eself - S.Eself_ref;
+%fprintf('Eself: %.15f, E_corr: %.15f \n',S.Eself,S.E_corr);
+
+fprintf(' Done. (%f s)\n',toc(t1));
+
+end
diff --git a/src/calculate_nloc_projector.m b/src/calculate_nloc_projector.m
new file mode 100644
index 00000000..ef7f1b0a
--- /dev/null
+++ b/src/calculate_nloc_projector.m
@@ -0,0 +1,283 @@
+function Atom = calculate_nloc_projector(S)
+% @brief calculate_nloc_projector(S) calculates nonlocal projectors for
+% each atom.
+%
+% @param S A struct that contains the relevant fields.
+%
+% @authors Qimen Xu
+% Abhiraj Sharma
+% Phanish Suryanarayana
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+%
+
+t1 = tic;
+fprintf('\n Starting calculating nonlocal projectors ...\n');
+
+% initialization
+Atom = repmat(struct([]),[1,S.n_atm]);
+
+% Pseudocharge generation and self energy calculation
+count_typ = 1;
+count_typ_atms = 1;
+
+for JJ_a = 1:S.n_atm % loop over all the atoms
+ % Load pseudopotential file and isolated atom electron density
+ lloc = S.Atm(count_typ).lloc;
+ lmax = S.Atm(count_typ).lmax;
+ Atom(JJ_a).lloc = lloc;
+ Atom(JJ_a).lmax = lmax;
+ Atom(JJ_a).psptyp = S.Atm(count_typ).psptyp;
+ if S.Atm(count_typ).psptyp == 1
+ Atom(JJ_a).nproj = S.Atm(count_typ).nproj;
+ end
+
+ % Atom position of atom JJ_a
+ x0 = S.Atoms(JJ_a,1);
+ y0 = S.Atoms(JJ_a,2);
+ z0 = S.Atoms(JJ_a,3);
+
+ % Note the S.dx, S.dy, S.dz terms are to ensure the image rc-region overlap w/ fund. domain
+ if (S.cell_typ == 1)
+ rcx = S.Atm(count_typ).rc;
+ rcy = S.Atm(count_typ).rc;
+ rcz = S.Atm(count_typ).rc;
+ else
+ rcx = S.Atm(count_typ).rb_x;
+ rcy = S.Atm(count_typ).rb_y;
+ rcz = S.Atm(count_typ).rb_z;
+ end
+
+ if S.BCx == 0
+ n_image_xl = floor((S.Atoms(JJ_a,1) + rcx)/S.L1);
+ n_image_xr = floor((S.L1 - S.Atoms(JJ_a,1)+rcx-S.dx)/S.L1);
+ else
+ n_image_xl = 0;
+ n_image_xr = 0;
+ end
+
+ if S.BCy == 0
+ n_image_yl = floor((S.Atoms(JJ_a,2) + rcy)/S.L2);
+ n_image_yr = floor((S.L2 - S.Atoms(JJ_a,2)+rcy-S.dy)/S.L2);
+ else
+ n_image_yl = 0;
+ n_image_yr = 0;
+ end
+
+ if S.BCz == 0
+ n_image_zl = floor((S.Atoms(JJ_a,3) + rcz)/S.L3);
+ n_image_zr = floor((S.L3 - S.Atoms(JJ_a,3)+rcz-S.dz)/S.L3);
+ else
+ n_image_zl = 0;
+ n_image_zr = 0;
+ end
+
+ % Total No. of images of atom JJ_a (including atom JJ_a)
+ n_image_total = (n_image_xl+n_image_xr+1) * (n_image_yl+n_image_yr+1) * (n_image_zl+n_image_zr+1);
+
+ % Find the coordinates for all the images
+ xx_img = (-n_image_xl : n_image_xr) * S.L1 + x0;
+ yy_img = (-n_image_yl : n_image_yr) * S.L2 + y0;
+ zz_img = (-n_image_zl : n_image_zr) * S.L3 + z0;
+ [XX_IMG_3D,YY_IMG_3D,ZZ_IMG_3D] = ndgrid(xx_img,yy_img,zz_img);
+
+ % Count for rc-images (images whoes rc-domain have influence in fund. domain)
+ imgRcCount = 0;
+ % Loop over all image(s) of atom JJ_a (including atom JJ_a)
+ for count_image = 1:n_image_total
+ % Atom position of the image
+ x0_i = XX_IMG_3D(count_image);
+ y0_i = YY_IMG_3D(count_image);
+ z0_i = ZZ_IMG_3D(count_image);
+
+ % Check if the rc-region is inside the domain in Dirichlet BC
+ % direction
+ % isInside = (S.BCx == 0 || (S.BCx == 1 && (ii_s>1) && (ii_e1) && (jj_e1) && (kk_e
+% Abhiraj Sharma
+% Phanish Suryanarayana
+%
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+
+% max dialation of volume allowed
+% S.max_dilatation = 1.2;
+
+% relax cell in the periodic dims
+S.cellrelax_dims = [1-S.BCx, 1-S.BCy, 1-S.BCz];
+S.cellrelax_ndim = sum(S.cellrelax_dims);
+
+if S.cellrelax_ndim < 1
+ error('Cell relaxation is not allowed for isolated systems!');
+end
+
+V = S.L1 * S.L2 * S.L3; % volume
+
+lower_bound = V / S.max_dilatation;
+upper_bound = V * S.max_dilatation;
+
+[optVol,S,~] = Brent(@volume_relax_fun, S, lower_bound, upper_bound, 1e-4, S.TOL_RELAX_CELL, S.max_relax_it);
+
+% cell size related to optimal volume
+V_old = S.L1 * S.L2 * S.L3;
+scal = nthroot(optVol / V_old, S.cellrelax_ndim);
+if S.cellrelax_dims(1) == 1
+ S.L1 = S.L1 * scal;
+end
+if S.cellrelax_dims(2) == 1
+ S.L2 = S.L2 * scal;
+end
+if S.cellrelax_dims(3) == 1
+ S.L3 = S.L3 * scal;
+end
+S.optVol = optVol; % save optimized volume
+
+fprintf('\n');
+fprintf(' *****************************************************************\n');
+fprintf(' * Optimized volume: %.9f \n', optVol);
+fprintf(' * Optimized cell size: %.9f %.9f %.9f\n',S.L1,S.L2,S.L3);
+fprintf(' *****************************************************************\n');
+fprintf('\n');
+
+end
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+function [max_P_stress,S] = volume_relax_fun(S, Vol)
+% Calculate principle stress for new volume
+
+% update cell length (mesh size) related initialization and atom positions
+% TODO: Need to go through msparc.m and initialization.m to find out full
+% list
+
+
+S = reinitialize_cell_mesh(S, Vol);
+
+fprintf('\n');
+fprintf(' **************************************************\n');
+fprintf(' Reinitialization for relax step # %d\n',S.Relax_iter);
+fprintf(' Volume: %-15.10f\n',Vol);
+fprintf(' Cell : %.10f %.10f %.10f\n',S.L1,S.L2,S.L3);
+fprintf(' Mesh : %f %f %f\n',S.dx,S.dy,S.dz);
+fprintf(' rb : %.2f %.2f %.2f\n',[S.Atm(:).rb_x,S.Atm(:).rb_y,S.Atm(:).rb_z]');
+fprintf(' **************************************************\n');
+
+% evaluate stress
+S.Calc_stress = 1; % make sure stress calculation is on
+[~,~,S] = electronicGroundStateAtomicForce(reshape(S.Atoms',[],1),S);
+
+% print the result in .geopt file
+if S.PrintRelaxout == 1
+ PrintCellRelax(S);
+end
+
+S.ForceCount = S.ForceCount + 1;
+S.Relax_iter = S.Relax_iter + 1;
+
+% find the max principle stress in the relaxed dimensions
+ind = (S.cellrelax_dims ~= 0);
+
+%max_P_stress = max(eig(S.Stress(ind,ind)));
+max_P_stress = sum(diag(S.Stress(ind,ind)))/S.cellrelax_ndim;
+
+end
+
+
+function S = reinitialize_cell_mesh(S, Vol)
+% Once Volume is updated, the cell dimensions and mesh sized will be
+% updated. All variables related to cell length and mesh size have to be
+% updated as well.
+%
+% S.L1, S.L2, S.L3
+% S.dx, S.dy, S.dz, S.dV
+% finite-difference weights
+% S.Atoms
+% S.rb
+% discrete Laplacian, gradient
+
+if Vol <= 0.0
+ error('Volume has become 0 or negative!');
+end
+
+Vol_old = S.L1 * S.L2 * S.L3; % old volume
+
+% scaling factor
+scal = nthroot(Vol / Vol_old, S.cellrelax_ndim);
+
+% Calculate new length corresponding to volume Vol
+if S.cellrelax_dims(1) == 1
+ S.L1 = S.L1 * scal;
+end
+if S.cellrelax_dims(2) == 1
+ S.L2 = S.L2 * scal;
+end
+if S.cellrelax_dims(3) == 1
+ S.L3 = S.L3 * scal;
+end
+
+% Calculate new atom Cartesian coordinates
+if S.cellrelax_dims(1) == 1
+ S.Atoms(:,1) = S.Atoms(:,1) * scal;
+ for ityp = 1:S.n_typ
+ if (S.IsFrac(ityp) == 0)
+ S.Atm(ityp).coords(:,1) = S.Atm(ityp).coords(:,1) * scal;
+ end
+ end
+end
+
+if S.cellrelax_dims(2) == 1
+ S.Atoms(:,2) = S.Atoms(:,2) * scal;
+ for ityp = 1:S.n_typ
+ if (S.IsFrac(ityp) == 0)
+ S.Atm(ityp).coords(:,2) = S.Atm(ityp).coords(:,2) * scal;
+ end
+ end
+end
+
+if S.cellrelax_dims(3) == 1
+ S.Atoms(:,3) = S.Atoms(:,3) * scal;
+ for ityp = 1:S.n_typ
+ if (S.IsFrac(ityp) == 0)
+ S.Atm(ityp).coords(:,3) = S.Atm(ityp).coords(:,3) * scal;
+ end
+ end
+end
+
+
+% update mesh size
+if S.cellrelax_dims(1) == 1
+ S.dx = S.dx * scal;
+end
+if S.cellrelax_dims(2) == 1
+ S.dy = S.dy * scal;
+end
+if S.cellrelax_dims(3) == 1
+ S.dz = S.dz * scal;
+end
+S.dV = S.dx * S.dy * S.dz * S.Jacb;
+
+% Weights for spatial integration over domain
+% Weights for spatial integration over domain
+% S.W = IntgWts(S.Nx,S.Ny,S.Nz,S.BCx,S.BCy,S.BCz,S.xin,S);
+if S.cell_typ == 1 || S.cell_typ == 2
+ S.W = ones(S.N,1) * (S.dx*S.dy*S.dz*S.Jacb);
+else
+ S.W = IntgWts(S.Nx,S.Ny,S.Nz,S.BCx,S.BCy,S.BCz,S.xin,S);
+end
+% Brillouin-Zone Sampling
+S = Generate_kpts(S);
+
+% Create spherical harmonics for poisson solve for isolated clusters
+if (S.BCx == 1 && S.BCy == 1 && S.BCz == 1)
+ % Calculate Spherical Harmonics with origin shifted to the center of the domain
+ xx_aug = (0-S.FDn:S.Nx+S.FDn-1)*S.dx;% - L1/2;
+ yy_aug = (0-S.FDn:S.Ny+S.FDn-1)*S.dy;% - L2/2;
+ zz_aug = (0-S.FDn:S.Nz+S.FDn-1)*S.dz;% - L3/2;
+ [XX_AUG_3D,YY_AUG_3D,ZZ_AUG_3D] = ndgrid(xx_aug,yy_aug,zz_aug);
+ % Find distances
+ RR_AUG_3D = calculateDistance(XX_AUG_3D,YY_AUG_3D,ZZ_AUG_3D,S.L1/2,S.L2/2,S.L3/2,S);
+
+ XX_AUG = reshape(XX_AUG_3D,[],1);
+ YY_AUG = reshape(YY_AUG_3D,[],1);
+ ZZ_AUG = reshape(ZZ_AUG_3D,[],1);
+ RR_AUG = reshape(RR_AUG_3D,[],1);
+
+ S.RR_AUG = RR_AUG;
+ S.RR_AUG_3D = RR_AUG_3D;
+
+ in_flag = ones(S.Nx+2*S.FDn,S.Ny+2*S.FDn,S.Nz+2*S.FDn);
+ in_flag(1:S.FDn,:,:) = 0;
+ in_flag(:,1:S.FDn,:) = 0;
+ in_flag(:,:,1:S.FDn) = 0;
+ in_flag(S.FDn+S.Nx+1:end,:,:) = 0;
+ in_flag(:,S.FDn+S.Ny+1:end,:) = 0;
+ in_flag(:,:,S.FDn+S.Nz+1:end) = 0;
+ isIn = (in_flag~=0);
+
+ S.isIn = isIn;
+ S.RR = RR_AUG(isIn);
+
+ pos_node_cart = coordinateTransformation(S,[XX_AUG,YY_AUG,ZZ_AUG],'noncart2cart_dis');
+ pos_atm_cart = coordinateTransformation(S,[S.L1/2,S.L2/2,S.L3/2],'noncart2cart_dis');
+ XX_AUG = bsxfun(@minus,pos_node_cart(:,1),pos_atm_cart(:,1));
+ YY_AUG = bsxfun(@minus,pos_node_cart(:,2),pos_atm_cart(:,2));
+ ZZ_AUG = bsxfun(@minus,pos_node_cart(:,3),pos_atm_cart(:,3));
+
+ l_cut = 6;
+ SH = repmat(struct([]),l_cut+1,1);
+ for l = 0:l_cut
+ for m = -l:l
+ SH(l+1).Ylm_AUG(:,m+l+1) = sphericalHarmonics(XX_AUG,YY_AUG,ZZ_AUG,l,m,'real');
+ Ylm_AUG_TEMP = SH(l+1).Ylm_AUG(:,m+l+1);
+ SH(l+1).Ylm(:,m+l+1) = Ylm_AUG_TEMP(isIn);
+ % SH(l+1).Ylm(:,m+l+1) = sphericalHarmonics(XX,YY,ZZ,l,m,'real');
+ end
+ end
+
+ S.l_cut = l_cut;
+ S.SH = SH;
+end
+
+% first find effective mesh size
+dx2_inv = 1/(S.dx * S.dx);
+dy2_inv = 1/(S.dy * S.dy);
+dz2_inv = 1/(S.dz * S.dz);
+h_eff = sqrt(3.0 / (dx2_inv + dy2_inv + dz2_inv));
+
+% Update chebyshev polynomial degree if larger npl is required
+S.npl = max(Mesh2ChebDegree(h_eff), S.npl);
+
+% update precond_tol if more strict tol is required for new mesh size
+S.precond_tol = min(h_eff * h_eff * 0.001, S.precond_tol);
+
+% Calculate rb
+S = Calculate_rb(S);
+
+% Calculate discrete laplacian (1D) and discrete gradient indices' values
+S = lapIndicesValues_1d(S);
+S = gradIndicesValues(S);
+
+% Calculate discrete laplacian
+[DL11,DL22,DL33,DG1,DG2,DG3] = blochLaplacian_1d(S,[0 0 0]);
+if S.cell_typ < 3
+ S.Lap_std = S.lapc_T(1,1) * kron(speye(S.Nz),kron(speye(S.Ny),DL11)) + S.lapc_T(2,2) * kron(speye(S.Nz),kron(DL22,speye(S.Nx))) + ...
+ S.lapc_T(3,3) * kron(DL33,kron(speye(S.Ny),speye(S.Nx))) ;
+ if (S.cell_typ == 2)
+ MDL = S.lapc_T(1,2) * kron(speye(S.Nz),kron(DG2,DG1)) + S.lapc_T(2,3) * kron(DG3,kron(DG2,speye(S.Nx))) + ...
+ S.lapc_T(1,3) * kron(DG3,kron(speye(S.Ny),DG1)) ;
+ S.Lap_std = S.Lap_std + MDL;
+ end
+elseif (S.cell_typ == 3 || S.cell_typ == 4 || S.cell_typ == 5)
+ S.Lap_std = kron(speye(S.Nz),kron(speye(S.Ny),(DL11+DG1))) + kron(DL33,kron(speye(S.Ny),speye(S.Nx))) + ...
+ kron(speye(S.Nz),kron(DL22,S.R2inv));
+ if (S.cell_typ == 4 || S.cell_typ == 5)
+ MDL = kron(speye(S.Nz),kron(DL22,speye(S.Nx))) + kron(DG3,kron(DG2,speye(S.Nx)));
+ S.Lap_std = S.Lap_std + MDL;
+ end
+end
+
+% Calculate discrete gradient
+S.grad_1 = blochGradient(S,[0 0 0],1);
+S.grad_2 = blochGradient(S,[0 0 0],2);
+S.grad_3 = blochGradient(S,[0 0 0],3);
+
+% Calculate preconditioners for negative discrete laplacian
+[S.LapPreconL, S.LapPreconU] = ilu(S.Lap_std,struct('droptol',1e-5));
+
+end
+
+
+function [x, S, err] = Brent(FUN, S, x1, x2, tol, tol_f, max_iter)
+%@brief Brent's method for finding the root of a function.
+%
+%@param FUN(x;S) Function handle who's root will be evaluated.
+%@param tol Tolerance for minimum x interval to perform bisection.
+%@param tol_f Tolerance for f(x) to be considered close enough to 0
+%
+%@ref W.H. Press, Numerical recepies 3rd edition: The art of scientific
+% computing, Cambridge university press, 2007.
+%
+EPSILON = eps; % double precision 2^-52 = 2.22e-16
+err = 0;
+
+a = x1;
+b = x2;
+c = x2;
+
+[fa,S] = FUN(S,a);
+[fb,S] = FUN(S,b);
+
+%printf("f(%f) = %f, f(%f) = %f\n", x1, fa, x2, fb);
+if((fa > 0.0 && fb > 0.0) || (fa < 0.0 && fb < 0.0))
+ x = 0.0; err = 1; % error flag
+ error('Root must be within the given range (x1, x2) in Brent''s method');
+end
+fc = fb;
+
+for iter = 1:max_iter
+ if((fb > 0.0 && fc > 0.0) || (fb < 0.0 && fc < 0.0))
+ c = a; fc = fa;
+ e = b-a;
+ d = b-a;
+ end
+ if ( abs(fc) < abs(fb) )
+ a = b; b = c; c = a;
+ fa = fb; fb = fc; fc = fa;
+ end
+ tol1 = 2.0 * EPSILON * abs(b) + 0.5 * tol;
+ xm = 0.5*(c-b);
+ %if(abs(xm) <= tol1 || abs(fb) < EPSILON)
+ if(abs(xm) <= tol1 || abs(fb) < tol_f)
+ x = b;
+ fprintf(' Brent''s (bisection) method converged in %d iterations\n',iter);
+ return;
+ end
+ if(abs(e) >= tol1 && abs(fa) > abs(fb))
+ % attempt inverse quadratic interpolation
+ s = fb / fa;
+ if( a == c)
+ p = 2.0 * xm * s;
+ q = 1.0 - s;
+ else
+ q = fa / fc; r = fb / fc;
+ p = s * (2.0 * xm * q * (q - r) - (b - a) * (r - 1.0));
+ q = (q - 1.0) * (r - 1.0) * (s - 1.0);
+ end
+ if(p > 0.0)
+ %check whether in bounds
+ q = -q;
+ end
+ p = abs(p);
+ tol1q = tol1 * q;
+ min1 = 3.0 * xm * q - abs(tol1q);
+ eq = e * q;
+ min2 = abs(eq);
+ if(2.0 * p < min(min1,min2))
+ %accept interpolation
+ e = d; d = p / q;
+ else
+ % Bounds decreasing too slowly, use bisection
+ d = xm; e = d;
+ end
+ else
+ d = xm; e = d;
+ end
+ % move last best guess to a
+ a = b; fa = fb;
+
+ if (abs(d) > tol1)
+ % evaluate new trial root
+ b = b + d;
+ else
+ b = b + SIGN(tol1, xm);
+ end
+ [fb,S] = FUN(S,b);
+end
+
+%x = 0.0;
+err = 1; % error flag
+fprintf(' Maximum iterations exceeded in brents root finding method...exiting\n');
+
+end
+
+
+%%%%%%%%%%%%%%%%%%%%%%%
+function y = SIGN(a,b)
+% y = abs(a) * sign(b);
+if b > 0.0
+ y = abs(a);
+else
+ y = -abs(a);
+end
+end
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+function npl = Mesh2ChebDegree(h)
+ % the relation between h and npl is fit with a cubic polynomial
+ % p(x) = p3 * x^3 + p2 * x^2 + p1 * x + p0.
+ p3 = -700. / 3.;
+ p2 = 1240. / 3.;
+ p1 = -773. / 3.;
+ p0 = 1078. / 15.;
+ if (h > 0.7)
+ npl = 14;
+ else
+ npl = ((p3 * h + p2) * h + p1) * h + p0;
+ end
+ npl = round(npl);
+end
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+function S = Calculate_rb(S)
+% Starting and ending indices of b-region
+if (S.cell_typ == 1 || S.cell_typ == 2)
+ pos_atm_x = 0; % atom location in x-direction
+ pos_atm_y = 0; % atom location in y-direction
+ pos_atm_z = 0; % atom location in z-direction
+ rb_up_x = 12;
+ f_rby = @(y) y;
+ rb_up_y = f_rby(12);
+ rb_up_z = 12;
+
+elseif (S.cell_typ == 3 || S.cell_typ == 4 || S.cell_typ == 5)
+ pos_atm_x = S.xmax_at; % maximum R coordinate of any atom
+ pos_atm_y = 0; % atom location in theta-direction
+ pos_atm_z = 0; % atom location in z-direction
+ rb_up_x = S.xvac; % Radial direction vacuum
+ f_rby = @(y) acos(1 - y^2/(2*pos_atm_x^2));
+ rb_up_y = f_rby(12); % Theta direction
+ rb_up_z = 12; % z-direction
+
+end
+ii_s_temp = -ceil(rb_up_x/S.dx);
+ii_e_temp = ceil(rb_up_x/S.dx);
+jj_s_temp = -ceil(rb_up_y/S.dy);
+jj_e_temp = ceil(rb_up_y/S.dy);
+kk_s_temp = 0;
+kk_e_temp = ceil(rb_up_z/S.dz);
+xx_temp = pos_atm_x + (ii_s_temp-S.FDn:ii_e_temp+S.FDn)*S.dx;
+yy_temp = pos_atm_y + (jj_s_temp-S.FDn:jj_e_temp+S.FDn)*S.dy;
+zz_temp = pos_atm_z + (kk_s_temp-S.FDn:kk_e_temp+S.FDn)*S.dz;
+[XX_3D_temp,YY_3D_temp,ZZ_3D_temp] = ndgrid(xx_temp,yy_temp,zz_temp);
+Nx = (ii_e_temp-ii_s_temp)+1;
+Ny = (jj_e_temp-jj_s_temp)+1;
+Nz = (kk_e_temp-kk_s_temp)+1;
+% Find distances
+dd_temp = calculateDistance(XX_3D_temp,YY_3D_temp,ZZ_3D_temp,pos_atm_x,pos_atm_y,pos_atm_z,S);
+
+% Find integration weights
+W_temp = IntgWts(Nx,Ny,Nz,1,1,1,xx_temp(S.FDn+1),S); % 1 - dirichlet BC on the boundary nodes
+W_temp = reshape(W_temp,Nx,Ny,Nz);
+
+% Find VJ and bJ
+for ityp = 1:S.n_typ
+ V_PS_temp = zeros(size(dd_temp));
+ IsLargeThanRmax = dd_temp > S.Atm(ityp).r_grid_vloc(end);
+ V_PS_temp(IsLargeThanRmax) = -S.Atm(ityp).Z;
+ V_PS_temp(~IsLargeThanRmax) = interp1(S.Atm(ityp).r_grid_vloc, ...
+ S.Atm(ityp).r_grid_vloc.*S.Atm(ityp).Vloc, dd_temp(~IsLargeThanRmax), 'spline');
+
+ V_PS_temp = V_PS_temp./dd_temp;
+ V_PS_temp(dd_temp S.pseudocharge_tol && count <= 100 && rb_x <= rb_up_x && rb_y <= rb_up_y && rb_z <= rb_up_z )
+ rb_x = rb_x + S.dx;
+ rb_z = rb_z + S.dz;
+ rb_y = f_rby(max(rb_x,rb_z));
+ ii_rb = -1*ii_s_temp+S.FDn-floor(rb_x/S.dx)+1:-1*ii_s_temp+S.FDn+floor(rb_x/S.dx)+1;
+ jj_rb = -1*jj_s_temp+S.FDn-floor(rb_y/S.dy)+1:-1*jj_s_temp+S.FDn+floor(rb_y/S.dy)+1;
+ kk_rb = S.FDn+1:S.FDn+floor(rb_z/S.dz)+1;
+ err_rb = abs(sum(sum(sum(W_temp(ii_rb-S.FDn,jj_rb-S.FDn,kk_rb-S.FDn).*b_temp(ii_rb,jj_rb,kk_rb))))*2 + S.Atm(ityp).Z);
+ fprintf(' rb = {%.3f %.3f %.3f}, int_b = %.15f, err_rb = %.3e\n',rb_x,rb_y,rb_z,2*sum(sum(sum(W_temp(ii_rb-S.FDn,jj_rb-S.FDn,kk_rb-S.FDn).*b_temp(ii_rb,jj_rb,kk_rb)))),err_rb);
+ count = count + 1;
+ end
+
+ assert(rb_x<=rb_up_x && rb_y<=rb_up_y && rb_z<=rb_up_z,'Need to increase upper bound for rb!');
+ S.Atm(ityp).rb_x = rb_x;
+ S.Atm(ityp).rb_y = rb_y;
+ S.Atm(ityp).rb_z = rb_z;
+ % S.Atm(ityp).rb_x = ceil(rb_x/S.dx-1e-12)*S.dx; % + S.dx;
+ % S.Atm(ityp).rb_y = ceil(rb_y/S.dy-1e-12)*S.dy; % + S.dy;
+ % S.Atm(ityp).rb_z = ceil(rb_z/S.dz-1e-12)*S.dz; % + S.dz;
+ fprintf(' rb = {%.3f %.3f %.3f}\n',S.Atm(ityp).rb_x,S.Atm(ityp).rb_y,S.Atm(ityp).rb_z);
+end
+
+end
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+function [W] = IntgWts(Nx,Ny,Nz,BCx,BCy,BCz,xin,S)
+ if S.cell_typ == 1 || S.cell_typ == 2
+ W_x = ones(Nx,1)*S.dx;
+ W_x(1) = W_x(1) * (1-BCx*0.5);
+ W_x(Nx) = W_x(Nx) * (1-BCx*0.5);
+
+ W_y = ones(Ny,1)*S.dy;
+ W_y(1) = W_y(1) * (1-BCy*0.5);
+ W_y(Ny) = W_y(Ny) * (1-BCy*0.5);
+
+ W_z = ones(Nz,1)*S.dz;
+ W_z(1) = W_z(1) * (1-BCz*0.5);
+ W_z(Nz) = W_z(Nz) * (1-BCz*0.5);
+
+ W = kron(W_z,kron(W_y,W_x)) * S.Jacb;
+ elseif (S.cell_typ == 3 || S.cell_typ == 4 || S.cell_typ == 5)
+ W = IntgWts_cychel(Nx,Ny,Nz,BCx,BCy,BCz,xin,S);
+ end
+end
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+function PrintCellRelax(S)
+% @ brief Function to write relaxation output in .cellopt file
+%================================================================
+ if S.Relax_iter == 1
+ fileID = fopen(S.relaxfname,'w');
+ else
+ fileID = fopen(S.relaxfname,'a');
+ end
+ fprintf(fileID,':RELAXSTEP: %d\n',S.Relax_iter);
+
+ fprintf(fileID,':CELL: %18.10E %18.10E %18.10E\n',S.L1,S.L2,S.L3);
+ fprintf(fileID,':VOLUME: %18.10E\n',S.L1*S.L2*S.L3);
+ fprintf(fileID,':LATVEC:\n');
+ fprintf(fileID,'%18.10E %18.10E %18.10E \n',S.lat_vec(1,:));
+ fprintf(fileID,'%18.10E %18.10E %18.10E \n',S.lat_vec(2,:));
+ fprintf(fileID,'%18.10E %18.10E %18.10E \n',S.lat_vec(3,:));
+ fprintf(fileID,':STRESS:\n');
+ fprintf(fileID,'%18.10E %18.10E %18.10E \n',S.Stress(1,:));
+ fprintf(fileID,'%18.10E %18.10E %18.10E \n',S.Stress(2,:));
+ fprintf(fileID,'%18.10E %18.10E %18.10E \n',S.Stress(3,:));
+
+ fclose(fileID);
+end
+
+
+
+
+function [S] = Generate_kpts(S)
+ nkpt = S.nkpt;
+ if (S.BCx == 1 && nkpt(1) > 1)
+ error(' nkpt cannot be greater than 1 in Dirichlet boundary direction (x)');
+ end
+ if (S.BCy == 1 && nkpt(2) > 1)
+ error(' nkpt cannot be greater than 1 in Dirichlet boundary direction (y)');
+ end
+ if (S.BCz == 1 && nkpt(3) > 1)
+ error(' nkpt cannot be greater than 1 in Dirichlet boundary direction (z)');
+ end
+
+ % Monkhorst-pack grid for Brillouin zone sampling
+ MPG_typ1 = @(nkpt) (2*(1:nkpt) - nkpt - 1)/2; % MP grid points for infinite group order
+ MPG_typ2 = @(nkpt) (0:nkpt-1); % MP grid points for finite group order
+
+ if S.cell_typ < 3
+ kptgrid_x = (1/nkpt(1)) * MPG_typ1(nkpt(1));
+ kptgrid_y = (1/nkpt(2)) * MPG_typ1(nkpt(2));
+ kptgrid_z = (1/nkpt(3)) * MPG_typ1(nkpt(3));
+ sumx = 0;
+ sumy = 0;
+ sumz = 0;
+ % shift kpoint grid
+ kptgrid_x = kptgrid_x + S.kptshift(1) * (1/nkpt(1));
+ kptgrid_y = kptgrid_y + S.kptshift(2) * (1/nkpt(2));
+ kptgrid_z = kptgrid_z + S.kptshift(3) * (1/nkpt(3));
+
+ % map k-points back to BZ
+ temp_epsilon = eps; % include the right boundary k-points instead of left
+ kptgrid_x = mod(kptgrid_x + 0.5 - temp_epsilon, 1) - 0.5 + temp_epsilon;
+ kptgrid_y = mod(kptgrid_y + 0.5 - temp_epsilon, 1) - 0.5 + temp_epsilon;
+ kptgrid_z = mod(kptgrid_z + 0.5 - temp_epsilon, 1) - 0.5 + temp_epsilon;
+ elseif (S.cell_typ == 3 || S.cell_typ == 4 || S.cell_typ == 5)
+ kptgrid_x = (1/nkpt(1)) * MPG_typ1(nkpt(1));
+ kptgrid_y = (1/nkpt(2)) * MPG_typ2(nkpt(2));
+ kptgrid_z = (1/nkpt(3)) * MPG_typ1(nkpt(3));
+ sumx = 0;
+ sumy = nkpt(2);
+ sumz = 0;
+ end
+
+ % Scale kpoints
+ kptgrid_x = (2*pi/S.L1) * kptgrid_x;
+ kptgrid_y = (2*pi/S.L2) * kptgrid_y;
+ kptgrid_z = (2*pi/S.L3) * kptgrid_z;
+
+ [kptgrid_X, kptgrid_Y, kptgrid_Z] = ndgrid(kptgrid_x,kptgrid_y,kptgrid_z);
+ kptgrid = [reshape(kptgrid_X,[],1),reshape(kptgrid_Y,[],1),reshape(kptgrid_Z,[],1)];
+ disp('kpoint grid before symmetry:');
+ disp(kptgrid);
+
+ tnkpt = prod(nkpt);
+ wkpt = ones(tnkpt,1)/tnkpt;% weights for k-points
+ TOL = 1e-8;
+ % Time-Reversal Symmetry to reduce k-points
+ if S.TimeRevSym == 1
+ Ikpt = zeros(tnkpt,1);
+ Ikpt_rev = zeros(tnkpt,1);
+ for ii = 1:tnkpt
+ for jj = ii+1:tnkpt
+ if (abs(kptgrid(ii,1) + kptgrid(jj,1) - sumx) < TOL) && (abs(kptgrid(ii,2) + kptgrid(jj,2) - sumy) < TOL) && (abs(kptgrid(ii,3) + kptgrid(jj,3) - sumz) < TOL)
+ Ikpt(ii) = 1;
+ Ikpt_rev(jj) = 1;
+ end
+ end
+ end
+ Ikpt = Ikpt>0.5;
+ Ikpt_rev = Ikpt_rev>0.5;
+ wkpt(Ikpt_rev) = 2*wkpt(Ikpt_rev);
+ kptgrid = kptgrid(~Ikpt,:);
+ wkpt = wkpt(~Ikpt);
+ tnkpt = size(wkpt,1);
+ end
+
+ disp('kpoint grid after symmetry:');
+ disp(kptgrid);
+ % Store into the structure
+ S.kptgrid = kptgrid;
+ S.tnkpt = tnkpt;
+ S.wkpt = wkpt;
+end
+
+
diff --git a/src/chargeExtrapolation.m b/src/chargeExtrapolation.m
new file mode 100644
index 00000000..5bd6aa41
--- /dev/null
+++ b/src/chargeExtrapolation.m
@@ -0,0 +1,56 @@
+function S = chargeExtrapolation(S)
+% @brief Perform charge extrapolation to get better guess density for
+% MD/Relax.
+%
+% @authors Qimen Xu
+% Abhiraj Sharma
+% Phanish Suryanarayana
+%
+% @ref: Dario Alfe, Computer Physics Communication 118 (1999) 31-33
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+
+% update charge difference (rho_SC - rho_at) histories
+S.delta_rho_tm2 = S.delta_rho_tm1;
+S.delta_rho_tm1 = S.delta_rho_t;
+
+% find the difference between the current converged density and rho_at
+% note that this is done before new rho_at is calculated
+if (S.ForceCount >= 2)
+ S.delta_rho_t = S.rho(:,1) - S.rho_at(:,1);
+end
+
+% find new extrapolation of charge difference for new rho_guess
+% NOTE: this differs from delta_rho_t, delta_rho_tm1, delta_rho_tm2, since
+% it is not actually a difference between self-consistent rho and rho_at.
+% Instead, it's an extrapolation of the three
+if (S.ForceCount >= 4)
+ A = zeros(2,2); b = zeros(2,1);
+ r_t_tm1 = S.atom_pos_t(:) - S.atom_pos_tm1(:);
+ r_tm1_tm2 = S.atom_pos_tm1(:) - S.atom_pos_tm2(:);
+ r_tp1_t = S.atom_pos_tp1(:) - S.atom_pos_t(:);
+ A(1,1) = dot(r_t_tm1, r_t_tm1);
+ A(1,2) = dot(r_t_tm1, r_tm1_tm2);
+ A(2,2) = dot(r_tm1_tm2, r_tm1_tm2);
+ A(2,1) = A(1,2);
+ b(1) = dot(r_tp1_t, r_t_tm1);
+ b(2) = dot(r_tp1_t, r_tm1_tm2);
+ % find extrapolation coeff
+ x = pinv(A) * b; % A might be singular
+ alpha = x(1); beta = x(2);
+ S.delta_rho_in_tp1 = (1+alpha) * S.delta_rho_t + ...
+ (beta-alpha) * S.delta_rho_tm1 - beta * S.delta_rho_tm2;
+ % S.delta_rho_in_tp1 = (1+alpha)*(S.dV_t/S.dV_tp1) * S.delta_rho_t + ...
+ % (beta-alpha)*(S.dV_tm1/S.dV_tp1) * S.delta_rho_tm1 - beta*(S.dV_tm2/S.dV_tp1) * S.delta_rho_tm2;
+end
+
+% update atomic position histories
+S.atom_pos_tm2 = S.atom_pos_tm1;
+S.atom_pos_tm1 = S.atom_pos_t;
+S.atom_pos_t = S.atom_pos_tp1;
+
+% S.dV_tm2 = S.dV_tm1;
+% S.dV_tm1 = S.dV_t;
+% S.dV_t = S.dV_tp1;
+
+end
+
diff --git a/src/chebyshev_filter.m b/src/chebyshev_filter.m
new file mode 100644
index 00000000..ce16880a
--- /dev/null
+++ b/src/chebyshev_filter.m
@@ -0,0 +1,44 @@
+function Y = chebyshev_filter(X,m,a,b,a0,DL11,DL22,DL33,DG1,DG2,DG3,Veff,S,kpt_vec)
+% @brief CHEBYSHEV_FILTER performs chebyshev fitering on the given
+% states.
+%
+% @param X Current states to be filtered.
+% @param m Chebyshev polynomial degree.
+% @param a Lower bound of the filter.
+% @param b Upper bound of the filter.
+% @param a0 Cutoff of the filter.
+%
+% @ref:
+% Y. Zhou, et al, 2016. Parallel Self-Consistent-Field Calculations via
+% Chebyshev-Filtered Subspace Acceleration.
+% https://www-users.cs.umn.edu/~saad/PDF/umsi-2006-101.pdf
+%
+% @authors Qimen Xu
+% Abhiraj Sharma
+% Phanish Suryanarayana
+%
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+
+
+% Note: the nonlocal pseudopotential is taken into account
+e = (b-a)/2;
+c = (b+a)/2;
+sigma = e/(a0 - c); sigma1 = sigma;
+gamma = 2/sigma1;
+% HX = H * X;
+HX = h_nonlocal_vector_mult(DL11,DL22,DL33,DG1,DG2,DG3,Veff,X,S,kpt_vec);
+Y = (sigma1/e)*(HX-c*X);
+
+ii = 2;
+while(ii <= m)
+ sigma2 = 1/(gamma - sigma);
+ % HX = H * Y;
+ HX = h_nonlocal_vector_mult(DL11,DL22,DL33,DG1,DG2,DG3,Veff,Y,S,kpt_vec);
+ Ynew = (2*sigma2/e)*(HX - c*Y) - ((sigma*sigma2)*X);
+ X = Y;
+ Y = Ynew;
+ sigma = sigma2;
+ ii = ii + 1;
+end
+
+end
diff --git a/src/coordinateTransformation.m b/src/coordinateTransformation.m
new file mode 100644
index 00000000..ffcbc221
--- /dev/null
+++ b/src/coordinateTransformation.m
@@ -0,0 +1,35 @@
+function Y = coordinateTransformation(S, X, transfrm_typ)
+% @ brief Function to perform transformation of quantities like
+% distance, gradient etc. from one coordinate system to another
+% @ authors
+% Abhiraj Sharma
+% Qimen Xu
+% Phanish Suryanarayana
+%
+% @param X(Input) N x 3 matrix
+% @param Y(Output) N x 3 matrix
+%
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+%======================================================================
+
+ % Non cartesian coordinate -> cartesian coordinate
+ if (strcmp(transfrm_typ,'noncart2cart_dis'))
+ if S.cell_typ == 1
+ Y = X;
+ elseif S.cell_typ == 2
+ Y = transpose(S.lat_uvec) * X';
+ Y = Y';
+ elseif (S.cell_typ == 3 || S.cell_typ == 4 || S.cell_typ == 5)
+ Y = coordinateTransformation_cychel(S,X,transfrm_typ);
+ end
+ elseif (strcmp(transfrm_typ,'cart2noncart_dis'))
+ if S.cell_typ == 1
+ Y = X;
+ elseif S.cell_typ == 2
+ Y = S.grad_T * X';
+ Y = Y';
+ elseif (S.cell_typ == 3 || S.cell_typ == 4 || S.cell_typ == 5)
+ Y = coordinateTransformation_cychel(S,X,transfrm_typ);
+ end
+ end
+end
\ No newline at end of file
diff --git a/src/dpseudopot.m b/src/dpseudopot.m
new file mode 100644
index 00000000..3daad8a6
--- /dev/null
+++ b/src/dpseudopot.m
@@ -0,0 +1,20 @@
+function [DX_x,DX_y,DX_z] = dpseudopot(X,II,JJ,KK,XX,YY,ZZ,S)
+% @ brief Function to perform gradient of a 3d matrix.
+% @ authors
+% Abhiraj Sharma
+% Qimen Xu
+% Phanish Suryanarayana
+%
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+%======================================================================
+ if S.cell_typ <= 2
+ DX_x = zeros(size(X)); DX_y = zeros(size(X)); DX_z = zeros(size(X));
+ for p = 1:S.FDn
+ DX_x(II,JJ,KK) = DX_x(II,JJ,KK) + S.w1(p+1)/S.dx*(X(II+p,JJ,KK)-X(II-p,JJ,KK));
+ DX_y(II,JJ,KK) = DX_y(II,JJ,KK) + S.w1(p+1)/S.dy*(X(II,JJ+p,KK)-X(II,JJ-p,KK));
+ DX_z(II,JJ,KK) = DX_z(II,JJ,KK) + S.w1(p+1)/S.dz*(X(II,JJ,KK+p)-X(II,JJ,KK-p));
+ end
+ elseif (S.cell_typ == 3 || S.cell_typ == 4 || S.cell_typ == 5)
+ [DX_x,DX_y,DX_z] = dpseudopot_cychel(X,II,JJ,KK,XX,YY,ZZ,S);
+ end
+end
\ No newline at end of file
diff --git a/src/eigSolver.m b/src/eigSolver.m
new file mode 100644
index 00000000..c29126dd
--- /dev/null
+++ b/src/eigSolver.m
@@ -0,0 +1,224 @@
+function [upper_bound_guess_vecs,psi,EigVal,a0,bup,lambda_cutoff] = eigSolver(S,count,upper_bound_guess_vecs,psi,EigVal,a0,bup,lambda_cutoff)
+% @brief Solve the linearized Hamiltonian eigenproblem.
+%
+% @param count : SCF iteration count.
+% @param upper_bound_guess_vecs : guess vector for maximum eigenvector of
+% the linearized Hamiltonian.
+% @param psi : eigenvectors of the previous linearized
+% Hamiltonian.
+% @param EigVal : previous eigenvalues
+% @param a0 : lower bound for Chebyshev filtering (1st SCF).
+% @param bup : upper bound for Chebyshev filtering (1st SCF).
+% @param lambda_cutoff : cut-off for chebyshev filtering (1st SCF).
+%
+% @authors Qimen Xu
+% Abhiraj Sharma
+% Phanish Suryanarayana
+%
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+%
+
+if S.ForceCount > 1
+ S.rhoTrigger = 1;
+end
+
+if S.parallel ~= 1
+ for ks = 1:S.tnkpt*S.nspin
+ if ks <= S.tnkpt
+ kpt = ks;
+ spin = 1;
+ else
+ kpt = ks - S.tnkpt;
+ spin = 2;
+ end
+ % Heff = spdiags(S.Veff(:,spin),0,S.N,S.N);
+ Heff = S.Veff(:,spin);
+ rng('default'); % Initialize random number generator
+ rng(ks+1);
+ %opts = struct('maxit', 10000, 'tol', 1e-6, 'p', S.Nev+10, 'v0', rand(S.N,1), 'isreal', true);
+ opts = struct('maxit', 100, 'tol', S.TOL_LANCZOS, 'v0', rand(S.N,1));
+ kpt_vec = S.kptgrid(kpt,:);
+ [DL11,DL22,DL33,DG1,DG2,DG3] = blochLaplacian_1d(S,kpt_vec);
+ Hfun = @(x) h_nonlocal_vector_mult(DL11,DL22,DL33,DG1,DG2,DG3,Heff,x,S,kpt_vec);
+ if ~(isreal(DL11) && isreal(DL22) && isreal(DL33))
+ opts.isreal = false;
+ end
+
+ if(count == 1)
+ % Upper bound estimator
+ opts.maxit = 300; % WARNING: might need more accuracy
+ if(S.ForceCount == 1)
+ % For first relaxation step
+ [upper_bound_guess_vecs(:,ks), bup(ks)] = (eigs(Hfun,S.N,1,'lr',opts));
+ bup(ks) = real(bup(ks)) * 1.01;
+ else
+ % For subsequent relaxation steps
+ opts.v0 = S.upper_bound_guess_vecs(:,ks);
+ [upper_bound_guess_vecs(:,ks), bup(ks)] = eigs(Hfun,S.N,1,'lr',opts) ;
+ bup(ks) = real(bup(ks)) * 1.01;
+ end
+ % Lower bound estimator
+ if(S.ForceCount == 1)
+ % For first relaxation step
+ a0(ks) = real(eigs(Hfun,S.N,1,'sr',opts)) - 0.1;
+ else
+ % For subsequent relaxation steps use lowest eigenvalue
+ a0(ks) = S.EigVal(1,ks);
+ end
+ % Always use this on every first SCF of relaxation
+ %lambda_cutoff(ks) = 0.5 * (bup(ks) + a0(ks));
+ else
+ % For subsequent steps
+ if (count > S.rhoTrigger)
+ if S.chefsibound_flag == 1
+ % Upper bound
+ opts.tol = S.TOL_LANCZOS; % WARNING: might need more accuracy than the default
+ opts.v0 = S.upper_bound_guess_vecs(:,ks);
+ [upper_bound_guess_vecs(:,ks), bup(ks)] = eigs(Hfun,S.N,1,'lr',opts);
+ bup(ks) = real(bup(ks)) * 1.01;
+ end
+ % Lower bound
+ a0(ks) = S.EigVal(1,ks);
+ end
+ % Set the filter cut off
+ %S.lambda_f + log10(1e6-1)/S.bet + 0.5;
+ %lambda_cutoff(ks) = S.EigVal(S.Nev,ks) + 0.10;
+ end
+
+ if count == 1 && S.ForceCount == 1
+ lambda_cutoff(ks) = 0.5 * (bup(ks) + a0(ks));
+ else
+ % Set the filter cut off
+ %S.lambda_f + log10(1e6-1)/S.bet + 0.5;
+ lambda_cutoff(ks) = S.EigVal(S.Nev,ks) + 0.10;
+ end
+
+ % fprintf('filter cutoff = %f, lower bound = %f, upper bound = %f\n',lambda_cutoff(ks),a0(ks),bup(ks));
+ % Chebyshev filtering
+ psi(:,:,ks) = chebyshev_filter(psi(:,:,ks),S.npl,lambda_cutoff(ks),bup(ks),a0(ks),DL11,DL22,DL33,DG1,DG2,DG3,Heff,S,kpt_vec);
+ psi(:,:,ks) = orth(psi(:,:,ks));
+ Nev1 = size(psi(:,:,ks),2); % WARNING: ORTH(psi) might change the size of psi, that's why we update Nev
+ assert(Nev1 == S.Nev,'Number of states have changed within SCF');
+
+ % Subspace Hamiltonian
+ Hs = psi(:,:,ks)' * h_nonlocal_vector_mult(DL11,DL22,DL33,DG1,DG2,DG3,Heff,psi(:,:,ks),S,kpt_vec);
+
+ % Solve subspace eigenproblem,
+ if S.cell_typ < 3
+ Hs = 0.5 * (Hs + Hs');
+ end
+ [Q, Q1] = eig(Hs);
+ EigVal(:,ks) = real(diag(Q1)); % WARNING: Taking real part only!
+
+ % subspace rotation
+ psi(:,:,ks) = psi(:,:,ks) * Q;
+
+ % Normalize psi, s.t. integral(psi_new' * psi_new) = 1
+ scfac = 1 ./ sqrt(sum(repmat(S.W,1,S.Nev) .* (psi(:,:,ks) .* conj(psi(:,:,ks))),1));
+ % psi(:,:,ks) = psi(:,:,ks) * diag(scfac);
+ psi(:,:,ks) = bsxfun(@times, psi(:,:,ks), scfac);
+ end
+else
+ % Before getting into parfor, set to use only one thread
+ LASTN = maxNumCompThreads(1);
+ parfor (ks = 1:S.tnkpt*S.nspin, S.num_worker_heuristic)
+ if ks <= S.tnkpt
+ kpt = ks;
+ spin = 1;
+ else
+ kpt = ks - S.tnkpt;
+ spin = 2;
+ end
+ % Heff = spdiags(S.Veff(:,spin),0,S.N,S.N);
+ Heff = S.Veff(:,spin);
+ rng('default'); % Initialize random number generator
+ rng(ks+1);
+ %opts = struct('maxit', 10000, 'tol', 1e-6, 'p', S.Nev+10, 'v0', rand(S.N,1), 'isreal', true);
+ opts = struct('maxit', 100, 'tol', S.TOL_LANCZOS, 'v0', rand(S.N,1));
+ kpt_vec = S.kptgrid(kpt,:);
+ [DL11,DL22,DL33,DG1,DG2,DG3] = blochLaplacian_1d(S,kpt_vec);
+ Hfun = @(x) h_nonlocal_vector_mult(DL11,DL22,DL33,DG1,DG2,DG3,Heff,x,S,kpt_vec);
+ if ~(isreal(DL11) && isreal(DL22) && isreal(DL33))
+ opts.isreal = false;
+ end
+
+ if (count == 1)
+ % Upper bound estimator
+ opts.maxit = 300; % WARNING: might need more accuracy
+ if(S.ForceCount == 1)
+ % For first relaxation step
+ [upper_bound_guess_vecs(:,ks), bup(ks)] = (eigs(Hfun,S.N,1,'lr',opts));
+ bup(ks) = real(bup(ks)) * 1.01;
+ else
+ % For subsequent relaxation steps
+ opts.v0 = S.upper_bound_guess_vecs(:,ks);
+ [upper_bound_guess_vecs(:,ks), bup(ks)] = eigs(Hfun,S.N,1,'lr',opts) ;
+ bup(ks) = real(bup(ks)) * 1.01;
+ end
+ % Lower bound estimator
+ if(S.ForceCount == 1)
+ % For first relaxation step
+ a0(ks) = real(eigs(Hfun,S.N,1,'sr',opts)) - 0.1;
+ else
+ % For subsequent relaxation steps use lowest eigenvalue
+ a0(ks) = S.EigVal(1,ks);
+ end
+ % Always use this on every first SCF of relaxation
+ %lambda_cutoff(ks) = 0.5 * (bup(ks) + a0(ks));
+ else
+ % For subsequent steps
+ if (count > S.rhoTrigger)
+ if S.chefsibound_flag == 1
+ % Upper bound
+ opts.tol = S.TOL_LANCZOS; % WARNING: might need more accuracy than the default
+ opts.v0 = S.upper_bound_guess_vecs(:,ks);
+ [upper_bound_guess_vecs(:,ks), bup(ks)] = eigs(Hfun,S.N,1,'lr',opts);
+ bup(ks) = real(bup(ks)) * 1.01;
+ end
+ % Lower bound
+ a0(ks) = S.EigVal(1,ks);
+ end
+ % Set the filter cut off
+ %S.lambda_f + log10(1e6-1)/S.bet + 0.5;
+ %lambda_cutoff(ks) = S.EigVal(S.Nev,ks) + 0.10;
+ end
+
+ if count == 1 && S.ForceCount == 1
+ lambda_cutoff(ks) = 0.5 * (bup(ks) + a0(ks));
+ else
+ % Set the filter cut off
+ %S.lambda_f + log10(1e6-1)/S.bet + 0.5;
+ lambda_cutoff(ks) = S.EigVal(S.Nev,ks) + 0.10;
+ end
+
+ % fprintf('filter cutoff = %f, lower bound = %f, upper bound = %f\n',lambda_cutoff(ks),a0(ks),bup(ks));
+ % Chebyshev filtering
+ psi(:,:,ks) = chebyshev_filter(psi(:,:,ks),S.npl,lambda_cutoff(ks),bup(ks),a0(ks),DL11,DL22,DL33,DG1,DG2,DG3,Heff,S,kpt_vec);
+ psi(:,:,ks) = orth(psi(:,:,ks));
+ Nev1 = size(psi(:,:,ks),2); % WARNING: ORTH(psi) might change the size of psi, that's why we update Nev
+ assert(Nev1 == S.Nev,'Number of states have changed within SCF');
+
+ % Subspace Hamiltonian
+ Hs = psi(:,:,ks)' * h_nonlocal_vector_mult(DL11,DL22,DL33,DG1,DG2,DG3,Heff,psi(:,:,ks),S,kpt_vec);
+
+ % Solve subspace eigenproblem,
+ if S.cell_typ < 3
+ Hs = 0.5 * (Hs + Hs');
+ end
+ [Q, Q1] = eig(Hs);
+ EigVal(:,ks) = real(diag(Q1)); % WARNING: Taking real part only!
+
+ % subspace rotation
+ psi(:,:,ks) = psi(:,:,ks) * Q;
+
+ % Normalize psi, s.t. integral(psi_new' * psi_new) = 1
+ scfac = 1 ./ sqrt(sum(repmat(S.W,1,S.Nev) .* (psi(:,:,ks) .* conj(psi(:,:,ks))),1));
+ % psi(:,:,ks) = psi(:,:,ks) * diag(scfac);
+ psi(:,:,ks) = bsxfun(@times, psi(:,:,ks), scfac);
+ end
+
+ % After parfor, reset the number of threads as before
+ maxNumCompThreads(LASTN);
+end
+
+
diff --git a/src/electronDensity.m b/src/electronDensity.m
new file mode 100644
index 00000000..525d93ce
--- /dev/null
+++ b/src/electronDensity.m
@@ -0,0 +1,30 @@
+function S = electronDensity(S)
+% @brief Calculate new density based on the new states.
+%
+% @param S A struct that contains the relevant fields.
+%
+% @authors Qimen Xu
+% Abhiraj Sharma
+% Phanish Suryanarayana
+%
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+%
+S.rho = 0 * S.rho;
+if S.nspin == 1
+ for kpt =1:S.tnkpt
+ S.rho = S.rho + 2*S.wkpt(kpt)* sum( bsxfun(@times,S.psi(:,:,kpt).*conj(S.psi(:,:,kpt)),S.occ(:,kpt)'),2);
+ end
+ S.rho = real(S.rho);
+else
+ ks = 1;
+ for spin =1:S.nspin
+ for kpt =1:S.tnkpt
+ S.rho(:,spin+1) = S.rho(:,spin+1) + S.wkpt(kpt)* sum( bsxfun(@times,S.psi(:,:,ks).*conj(S.psi(:,:,ks)),S.occ(:,ks)'),2);
+ ks = ks + 1;
+ end
+ end
+ S.rho(:,2:3) = real(S.rho(:,2:3));
+ S.rho(:,1) = S.rho(:,2) + S.rho(:,3);
+end
+
+end
\ No newline at end of file
diff --git a/src/electronicGroundStateAtomicForce.m b/src/electronicGroundStateAtomicForce.m
new file mode 100644
index 00000000..eb455c10
--- /dev/null
+++ b/src/electronicGroundStateAtomicForce.m
@@ -0,0 +1,308 @@
+function [atompos_next,AtmForce,S] = electronicGroundStateAtomicForce(atom_pos,S)
+% @brief electronicGroundStateAtomicForce(atom_pos,S) calculates the electronic ground
+% state atomic force corresponding to the given atom positions.
+%
+% @param atom_pos Given atom positions (stretched into a (3*n_atoms)-by-1 vector)
+% @param atompos_next Atom position for the next relaxation/MD step (in cartesian coordinates)
+% @param AtmForce Atomic force as a 3*N x 1 vector
+% @authors Qimen Xu
+% Abhiraj Sharma
+% Phanish Suryanarayana
+%
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+%==============================================================================================
+
+tic_relax = tic;
+fprintf('\n');
+fprintf(' ###############################################################\n');
+fprintf(' Relaxation step number: %d \n', S.Relax_iter);
+
+if (S.RelaxFlag || S.MDFlag)
+ % Reshaping atom positions
+ atom_pos = transpose(reshape(atom_pos,3,[]));
+ % update un-mapped atomic positions, for charge extrapolation
+ S.atom_pos_tp1 = S.atom_pos_tp1 + (atom_pos - S.Atoms_old);
+ % S.dV_tp1 = S.dV;
+ % Convert atom coordinates from cartesian to cell coordinates
+ S.Atoms = coordinateTransformation(S, atom_pos, 'cart2noncart_dis');
+end
+
+% Check position of atom near the boundary and apply wraparound in case of PBC
+S = check_atomlocation(S);
+
+% perform charge extrapolation (before rho_at is updated)
+if (S.RelaxFlag == 1 || S.MDFlag)
+ S = chargeExtrapolation(S);
+end
+
+% Pseudocharge (and reference), sum atomic charge density, self energy
+% (and reference), electrostatic correction
+% S.b,S.b_ref,S.Eself,S.Eself_ref,S.rho_at,S.E_corr,S.V_c, S.NegCharge,
+% S.PosCharge, S.NetCharge
+t_calc_b = tic;
+
+S = calculate_b_guessRho_Eself(S);
+
+fprintf(' Time for b calculation: %.3f seconds.\n',toc(t_calc_b));
+
+% set up guess electron density (guess rho)
+S = initElectrondensity(S);
+
+% Calculate nonlocal projectors
+S.Atom = calculate_nloc_projector(S);
+
+% Self-consistent Field (SCF) method
+S = scf(S);
+
+%save('rho.mat','-struct','S','rho');
+S.S_Debug.relax(S.Relax_iter).Eself = S.Eself;
+S.S_Debug.relax(S.Relax_iter).Eself_ref = S.Eself_ref;
+S.S_Debug.relax(S.Relax_iter).E_corr = S.E_corr;
+
+if abs(1-S.occ(1))>1e-6 || abs(S.occ(end))>1e-6
+ fprintf('[\b Warning: No. of states is not enough!]\b \n');
+ S.S_Debug.relax(S.Relax_iter).occ_check = 1; % 1 means not satisfied
+else
+ S.S_Debug.relax(S.Relax_iter).occ_check = 0;
+end
+
+% Etotal = evaluateTotalEnergy(EigVal,occ,rho,S.b,phi,Vxc,S.W,S.bet,S.Eself,S.E_corr,1) ;
+
+fprintf('\n');
+fprintf(' **********************************************************\n');
+fprintf(' * Energy per unit cell = %11.9f Ha. *\n', S.Etotal);
+fprintf(' * Energy per atom = %11.9f Ha. *\n', S.Etotal / S.n_atm);
+fprintf(' **********************************************************\n');
+
+% write to output file
+outfname = S.outfname;
+fileID = fopen(outfname,'a');
+if (fileID == -1)
+ error('\n Cannot open file "%s"\n',outfname);
+end
+fprintf(fileID,'====================================================================\n');
+fprintf(fileID,' Energy \n');
+fprintf(fileID,'====================================================================\n');
+fprintf(fileID,'Free energy per atom :%18.10E (Ha/atom)\n', S.Etotal / S.n_atm);
+fprintf(fileID,'Total free energy :%18.10E (Ha)\n', S.Etotal);
+fprintf(fileID,'Band structure energy :%18.10E (Ha)\n', S.Eband);
+fprintf(fileID,'Exchange correlation energy :%18.10E (Ha)\n', S.Exc);
+fprintf(fileID,'Self and correction energy :%18.10E (Ha)\n', S.E_corr-S.Eself);
+fprintf(fileID,'Entropy*kb*T :%18.10E (Ha)\n', S.Eent);
+fprintf(fileID,'Fermi level :%18.10E (Ha)\n', S.lambda_f);
+if S.nspin ~= 1
+ fprintf(fileID,'Net Magnetization :%18.10E \n', S.netM);
+end
+fclose(fileID);
+
+
+% Atomic force calculation
+tic_force = tic;
+S.force = atomicForce(S);
+%S.force = zeros(S.n_atm,3);
+force_mat = S.force;
+sz_fmat = size(force_mat);
+force_corr = sum(force_mat, 1) / sz_fmat(1);
+if S.cell_typ == 3 || S.cell_typ == 4 || S.cell_typ == 5
+ force_corr(1) = 0.0; % x - component
+ force_corr(2) = 0.0; % y - component
+end
+S.force = force_mat - repmat(force_corr, sz_fmat(1),1);
+
+% Apply constraint on atoms by making forces on fixed atoms zero
+if S.RelaxFlag || S.MDFlag
+ S.force = S.force .* S.mvAtmConstraint;
+end
+
+fprintf(' ***********************************************************\n');
+fprintf(' * Atomic Force *\n');
+fprintf(' ***********************************************************\n');
+fprintf(' Drift free forces (Ha/Bohr):\n');
+S.S_Debug.relax(S.Relax_iter).force = S.force;
+disp(S.force);
+S.abs_force = sqrt(sum(abs(S.force).^2,2));
+fprintf(' Max magnitude of forces (Ha/Bohr):');
+disp(max(S.abs_force));
+
+t_force = toc(tic_force);
+fprintf('\n Time for calculating forces: %f s.\n', t_force);
+
+% write forces into .static file if required
+if (S.PrintForceFlag == 1 && S.MDFlag == 0 && S.RelaxFlag == 0)
+ staticfname = S.staticfname;
+ fileID = fopen(staticfname,'a');
+ if (fileID == -1)
+ error('\n Cannot open file "%s"\n',staticfname);
+ end
+ fprintf(fileID, 'Atomic forces (Ha/Bohr):\n');
+ fprintf(fileID, '%18.10f %18.10f %18.10f\n', S.force');
+ fclose(fileID);
+end
+
+% write force magnitude and timing info. to .out file
+outfname = S.outfname;
+fileID = fopen(outfname,'a');
+if (fileID == -1)
+ error('\n Cannot open file "%s"\n',outfname);
+end
+
+force_magnitude = sqrt(sum(S.force .* S.force, 2));
+avgF = sum(force_magnitude) / length(force_magnitude);
+maxF = max(force_magnitude);
+
+fprintf(fileID,'Average force :%18.10E (Ha/Bohr)\n',avgF);
+fprintf(fileID,'Maximum force :%18.10E (Ha/Bohr)\n',maxF);
+fprintf(fileID,'Time for force calculation : %.3f (sec)\n',t_force);
+fclose(fileID);
+
+
+% Assign output of function
+AtmForce = reshape(S.force',[],1);
+AtmForce = - AtmForce;
+
+
+% Perform stress and pressure calculation
+if S.Calc_stress
+ t1 = tic;
+ Stress = evaluateStress(S);
+ sigma_inGPa = Stress*2.94210119*(10^4);
+ pressure = -trace(sigma_inGPa)/3.0;
+ S.Stress = sigma_inGPa; % store stress tensor
+ S.Pressure = pressure; % store pressure
+ fprintf('\n[\b"Stress in GPa"\n\n\n]\b');
+ disp(sigma_inGPa);
+ fprintf('\n Time for calculating stress: %f s.\n\n', toc(t1));
+
+ outfname = S.outfname;
+ fileID = fopen(outfname,'a');
+ if (fileID == -1)
+ error('\n Cannot open file "%s"\n',outfname);
+ end
+ if (S.MDFlag == 0 && S.RelaxFlag == 0)
+ fprintf(fileID, 'Stress (GPa):\n');
+ fprintf(fileID,'%18.10f %18.10f %18.10f\n', sigma_inGPa');
+ end
+ fprintf(fileID,'Pressure :%18.10E (GPa)\n',pressure);
+ fprintf(fileID,'Maximum stress :%18.10E (GPa)\n',max(max(abs(sigma_inGPa))));
+ fprintf(fileID,'Time for stress calculation : %.3f (sec)\n',toc(t1));
+
+ fclose(fileID);
+end
+
+if (S.Calc_pres && ~S.Calc_stress)
+ t1 = tic;
+ Pressure = evaluatePressure(S);
+ PinGPa = Pressure*2.94210119*(10^4);
+ S.Pressure = PinGPa; % store pressure
+ fprintf('\n[\b"Pressure %f Ha/Bohr^3 %f GPa"\n\n\n]\b',Pressure,PinGPa);
+ fprintf('\n Time for calculating pressure: %f s.\n\n', toc(t1));
+
+ outfname = S.outfname;
+ fileID = fopen(outfname,'a');
+ if (fileID == -1)
+ error('\n Cannot open file "%s"\n',outfname);
+ end
+ fprintf(fileID,'Pressure :%18.10E (GPa)\n',PinGPa);
+ fprintf(fileID,'Time for pressure calculation : %.3f (sec)\n',toc(t1));
+
+ fclose(fileID);
+end
+
+% Updating relaxation iteration number
+S.S_Debug.relax(S.Relax_iter).relax_time = toc(tic_relax);
+if (S.RelaxFlag || S.MDFlag)
+ fprintf('\n Relaxation step number %d completed in %f s.\n',S.Relax_iter, S.S_Debug.relax(S.Relax_iter).relax_time);
+
+ outfname = S.outfname;
+ fileID = fopen(outfname,'a');
+ if (fileID == -1)
+ error('\n Cannot open file "%s"\n',outfname);
+ end
+ fprintf(fileID,'Relax time : %.3f (sec)\n',toc(tic_relax));
+ fclose(fileID);
+
+end
+fprintf(' ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \n');
+
+atompos_next = 0;
+% Reshape the atomic positions for Relax/MD
+if S.RelaxFlag || S.MDFlag
+ %atompos_next = transpose(S.lat_uvec) * S.Atoms';
+ atompos_next = coordinateTransformation(S, S.Atoms, 'noncart2cart_dis');
+ % update mapped Atomic position history, for keeping track of un-mapped
+ % positions that are used in charge extrapolation
+ S.Atoms_old = atompos_next;
+ atompos_next = reshape(atompos_next',[],1);
+end
+
+end
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+function S = initElectrondensity(S)
+if (S.ForceCount == 1)
+ % use sum of the atomic charge densities as rho_guess
+ S.rho = S.rho_at;
+else
+ % perform charge extrapolation
+ if ((S.RelaxFlag == 1 || S.MDFlag) && S.ForceCount >= 4)
+ S.rho(:,1) = S.rho_at(:,1) + S.delta_rho_in_tp1;
+ S.rho(S.rho(:,1) < 0,1) = S.xc_rhotol;
+ % update spin up/down densities
+ if S.nspin ~= 1
+ rho_mag = S.rho(:,2) - S.rho(:,3);
+ S.rho(:,2) = (S.rho(:,1) + rho_mag) * 0.5;
+ S.rho(:,3) = (S.rho(:,1) - rho_mag) * 0.5;
+ end
+ end
+ % need to scale the density
+ S.rho = S.rho * abs(S.NegCharge/dot(S.W,S.rho(:,1)));
+end
+
+end
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+function S = check_atomlocation(S)
+% map atom positions back to the domain if atoms are outside the domain in
+% periodic directions or throw an error in Dirichlet directions
+if S.BCx == 1
+ if (sum(S.Atoms(:,1) >= S.L1 | S.Atoms(:,1) < 0) > 0)
+ error('Atom coordinates in the first lattice vector direction are out of cell');
+ end
+else
+ S.Atoms(S.Atoms(:,1) >= S.L1,1) = S.Atoms(S.Atoms(:,1) >= S.L1,1) - S.L1;
+ S.Atoms(S.Atoms(:,1) < 0,1) = S.Atoms(S.Atoms(:,1) < 0,1) + S.L1;
+end
+
+if S.BCy == 1
+ if (sum(S.Atoms(:,2) >= S.L2 | S.Atoms(:,2) < 0) > 0)
+ error('Atom coordinates in the second lattice vector direction are out of cell');
+ end
+else
+ S.Atoms(S.Atoms(:,2) >= S.L2,2) = S.Atoms(S.Atoms(:,2) >= S.L2,2) - S.L2;
+ S.Atoms(S.Atoms(:,2) < 0,2) = S.Atoms(S.Atoms(:,2) < 0,2) + S.L2;
+end
+
+if S.BCz == 1
+ if (sum(S.Atoms(:,3) >= S.L3 | S.Atoms(:,3) < 0) > 0)
+ error('Atom coordinates in the third lattice vector direction are out of cell');
+ end
+else
+ S.Atoms(S.Atoms(:,3) >= S.L3,3) = S.Atoms(S.Atoms(:,3) >= S.L3,3) - S.L3;
+ S.Atoms(S.Atoms(:,3) < 0,3) = S.Atoms(S.Atoms(:,3) < 0,3) + S.L3;
+end
+
+end
+
+
+
+
+
+
+
+
+
+
diff --git a/src/evaluatePressure.m b/src/evaluatePressure.m
new file mode 100644
index 00000000..8ba01276
--- /dev/null
+++ b/src/evaluatePressure.m
@@ -0,0 +1,808 @@
+function pressure = evaluatePressure(S)
+% @brief Function to calculate pressure in periodic systems (O(N^3))
+% @authors
+% Abhiraj Sharma
+% Phanish Suryanarayana
+%
+% @references
+% "On the calculation of the stress tensor in real-space Kohn-Sham
+% density functional theory (Sharma et. al. 2018)"
+%
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+%=================================================================================
+
+% Component from Energy related terms calculated explicitly
+Dphi_x = S.grad_1*(S.phi);
+Dphi_y = S.grad_2*(S.phi);
+Dphi_z = S.grad_3*(S.phi);
+
+P_eng = 0.0;
+ks = 1;
+for spin = 1:S.nspin
+ for kpt = 1:S.tnkpt
+ P_eng = P_eng - S.occfac*2*S.wkpt(kpt)*sum(S.EigVal(:,ks).*S.occ(:,ks)) ;
+ ks = ks + 1;
+ end
+end
+
+Drho_x = S.grad_1 * S.rho;
+Drho_y = S.grad_2 * S.rho;
+Drho_z = S.grad_3 * S.rho;
+
+P_eng = P_eng + 0.5 * sum(S.rho(:,1) .* S.phi .* S.W) + ...
+ (1.5 * sum(S.b .* S.phi .* S.W)) + (3*S.E_corr) - 3*S.Eself + ...
+ (1/4/pi) * sum( S.W .* (S.lapc_T(1,1)*Dphi_x.*Dphi_x + S.lapc_T(2,2)*Dphi_y.*Dphi_y + S.lapc_T(3,3)*Dphi_z.*Dphi_z +...
+ S.lapc_T(1,2)*Dphi_x.*Dphi_y + S.lapc_T(2,3)*Dphi_y.*Dphi_z + S.lapc_T(1,3)*Dphi_x.*Dphi_z )) ;
+
+% Contribution from exchange-correlation
+if S.nspin == 1
+ P_eng = P_eng - sum(S.rho .* S.Vxc .* S.W) + (3*S.Exc) + ...
+ - S.W' * (S.dvxcdgrho .* (S.lapc_T(1,1)*Drho_x.*Drho_x + S.lapc_T(2,2)*Drho_y.*Drho_y + S.lapc_T(3,3)*Drho_z.*Drho_z +...
+ S.lapc_T(1,2)*Drho_x.*Drho_y + S.lapc_T(2,3)*Drho_y.*Drho_z + S.lapc_T(1,3)*Drho_z.*Drho_x ));
+else
+ P_eng = P_eng - sum(sum(S.Vxc.*S.rho(:,2:3),2).*S.W) + (3*S.Exc) + ...
+ - sum(S.W' * (S.dvxcdgrho .* (S.lapc_T(1,1)*Drho_x.*Drho_x + S.lapc_T(2,2)*Drho_y.*Drho_y + S.lapc_T(3,3)*Drho_z.*Drho_z +...
+ S.lapc_T(1,2)*Drho_x.*Drho_y + S.lapc_T(2,3)*Drho_y.*Drho_z + S.lapc_T(1,3)*Drho_z.*Drho_x )));
+end
+% Components from gradient terms
+
+% initialization
+
+P_elec = 0;
+P_corr = 0;
+%psdfilepath = sprintf('%s/PseudopotFiles',S.inputfile_path);
+count_typ = 1;
+count_typ_atms = 1;
+for JJ_a = 1:S.n_atm % loop over all the atoms
+ % Atom position
+ x0 = S.Atoms(JJ_a,1);
+ y0 = S.Atoms(JJ_a,2);
+ z0 = S.Atoms(JJ_a,3);
+ % Note the S.dx, S.dy, S.dz terms are to ensure the image rb-region overlap w/ fund. domain
+ if S.BCx == 0
+ n_image_xl = floor((S.Atoms(JJ_a,1) + S.Atm(count_typ).rb_x)/S.L1);
+ n_image_xr = floor((S.L1 - S.Atoms(JJ_a,1)+S.Atm(count_typ).rb_x-S.dx)/S.L1);
+ else
+ n_image_xl = 0;
+ n_image_xr = 0;
+ end
+
+ if S.BCy == 0
+ n_image_yl = floor((S.Atoms(JJ_a,2) + S.Atm(count_typ).rb_y)/S.L2);
+ n_image_yr = floor((S.L2 - S.Atoms(JJ_a,2)+S.Atm(count_typ).rb_y-S.dy)/S.L2);
+ else
+ n_image_yl = 0;
+ n_image_yr = 0;
+ end
+
+ if S.BCz == 0
+ n_image_zl = floor((S.Atoms(JJ_a,3) + S.Atm(count_typ).rb_z)/S.L3);
+ n_image_zr = floor((S.L3 - S.Atoms(JJ_a,3)+S.Atm(count_typ).rb_z-S.dz)/S.L3);
+ else
+ n_image_zl = 0;
+ n_image_zr = 0;
+ end
+
+ % Total No. of images of atom JJ_a (including atom JJ_a)
+ n_image_total = (n_image_xl+n_image_xr+1) * (n_image_yl+n_image_yr+1) * (n_image_zl+n_image_zr+1);
+ % Find the coordinates for all the images
+ xx_img = [-n_image_xl : n_image_xr] * S.L1 + x0;
+ yy_img = [-n_image_yl : n_image_yr] * S.L2 + y0;
+ zz_img = [-n_image_zl : n_image_zr] * S.L3 + z0;
+ [XX_IMG_3D,YY_IMG_3D,ZZ_IMG_3D] = ndgrid(xx_img,yy_img,zz_img);
+
+ % Loop over all image(s) of atom JJ_a (including atom JJ_a)
+ for count_image = 1:n_image_total
+
+ % Atom position of the image
+ x0_i = XX_IMG_3D(count_image);
+ y0_i = YY_IMG_3D(count_image);
+ z0_i = ZZ_IMG_3D(count_image);
+
+ % Indices of closest grid point to atom
+ pos_ii = round((x0_i-S.xin) / S.dx) + 1;
+ pos_jj = round((y0_i-S.yin) / S.dy) + 1;
+ pos_kk = round((z0_i-S.zin) / S.dz) + 1;
+
+ % Starting and ending indices of b-region
+ ii_s = pos_ii - ceil(S.Atm(count_typ).rb_x/S.dx+0.5);
+ ii_e = pos_ii + ceil(S.Atm(count_typ).rb_x/S.dx+0.5);
+ jj_s = pos_jj - ceil(S.Atm(count_typ).rb_y/S.dy+0.5);
+ jj_e = pos_jj + ceil(S.Atm(count_typ).rb_y/S.dy+0.5);
+ kk_s = pos_kk - ceil(S.Atm(count_typ).rb_z/S.dz+0.5);
+ kk_e = pos_kk + ceil(S.Atm(count_typ).rb_z/S.dz+0.5);
+
+ % Check if the b-region is inside the domain in Dirichlet BC
+ % direction
+ isInside = (S.BCx == 0 || (S.BCx == 1 && (ii_s>1) && (ii_e1) && (jj_e1) && (kk_e S.Atm(count_typ).r_grid_vloc(end);
+ V_PS(IsLargeThanRmax) = -S.Atm(count_typ).Z;
+ V_PS(~IsLargeThanRmax) = interp1(S.Atm(count_typ).r_grid_vloc, S.Atm(count_typ).r_grid_vloc.*S.Atm(count_typ).Vloc, dd(~IsLargeThanRmax), 'spline');
+
+ V_PS = V_PS./dd;
+ V_PS(dd 1e-10);
+% yr = yr(dd_nl > 1e-10);
+% zr = zr(dd_nl > 1e-10);
+% pos = S.Atom(JJ_a).rcImage(img).rc_pos(dd_nl > 1e-10);
+% dd_nl = dd_nl(dd_nl > 1e-10);
+% [datasites,IA,IC] = unique(dd_nl,'stable');
+%
+% UdV_Jl = interp1(S.Atm(count_typ).r_grid_vloc,UdV(:,l+1),datasites,'spline');
+% Chi_spline = spline(datasites,UdV_Jl);
+% DChi_spline = ppval(fnder(Chi_spline,1),datasites);
+% Chi = UdV_Jl(IC);
+% DChi = DChi_spline(IC);
+% Ylm = sphericalHarmonics(S.lat_uvec,xr,yr,zr,l,m,'real');
+% [DYlm_dx,DYlm_dy,DYlm_dz] = DYlm(S.lat_uvec,xr,yr,zr,l,m);
+%
+% integral_2_x = integral_2_x + transpose(conj((DChi.*xr.*Ylm)./dd_nl + Chi.*DYlm_dx) .* S.W(pos)) * ...
+% (S.psi(pos,:,kpt).*repmat(xr,1,S.Nev)) * phase_fac;
+% integral_2_y = integral_2_y + transpose(conj((DChi.*yr.*Ylm)./dd_nl + Chi.*DYlm_dy) .* S.W(pos)) * ...
+% (S.psi(pos,:,kpt).*repmat(yr,1,S.Nev)) * phase_fac;
+% integral_2_z = integral_2_z + transpose(conj((DChi.*zr.*Ylm)./dd_nl + Chi.*DYlm_dz) .* S.W(pos)) * ...
+% (S.psi(pos,:,kpt).*repmat(zr,1,S.Nev)) * phase_fac;
+% end
+%
+% tf_x = (real(integral_1.*integral_2_x))*S.occ(:,kpt);
+% tf_y = (real(integral_1.*integral_2_y))*S.occ(:,kpt);
+% tf_z = (real(integral_1.*integral_2_z))*S.occ(:,kpt);
+% P_nl = P_nl + 4 * S.wkpt(kpt) * S.Atom(count_typ).gamma_Jl(l+1) * (tf_x + tf_y + tf_z);
+% end
+% end
+%
+% end
+% % Check if same type of atoms are over
+% if count_typ_atms == S.Atm(count_typ).n_atm_typ
+% count_typ_atms = 1;
+% count_typ = count_typ + 1;
+% else
+% count_typ_atms = count_typ_atms + 1;
+% end
+%
+%
+% end % end of loop over atoms
+% %
+
+%disp(P_nl);
+%disp(E_nl);
+
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% DENSITY MATRIX APPROACH - O(N) PRESSURE CALCULATION
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% function pressure = evaluatePressure(S)
+
+% % Gradient of phi calculation
+% Dphi_x = S.grad_1 * S.phi;
+% Dphi_y = S.grad_2 * S.phi;
+% Dphi_z = S.grad_3 * S.phi;
+
+% % Gradient of rho calculation
+% Drho_x = S.grad_1 * S.rho;
+% Drho_y = S.grad_2 * S.rho;
+% Drho_z = S.grad_3 * S.rho;
+
+% % Component from Energy related terms calculated explicitly
+
+% P_eng = - (sum(S.rho .* (3*S.Vxc + 1.5*S.phi) .* S.W)) + (3*S.Exc) + ...
+% (1.5*sum(S.b .* S.phi .* S.W)) + (3*S.E_corr) + ...
+% - 2*sum(S.W .* S.vdrho_xc .* (S.lapc_T(1,1)*Drho_x.*Drho_x + S.lapc_T(2,2)*Drho_y.*Drho_y + S.lapc_T(3,3)*Drho_z.*Drho_z +...
+% (S.lapc_T(1,2) + S.lapc_T(2,1))*Drho_x.*Drho_y + (S.lapc_T(2,3) + S.lapc_T(3,2))*Drho_y.*Drho_z +...
+% (S.lapc_T(1,3) + S.lapc_T(3,1))*Drho_z.*Drho_x )) + ...
+% (1/4/pi) * sum( (S.lapc_T(1,1)*Dphi_x.*Dphi_x + S.lapc_T(2,2)*Dphi_y.*Dphi_y + S.lapc_T(3,3)*Dphi_z.*Dphi_z +...
+% (S.lapc_T(1,2) + S.lapc_T(2,1))*Dphi_x.*Dphi_y + (S.lapc_T(2,3) + S.lapc_T(3,2))*Dphi_y.*Dphi_z +...
+% (S.lapc_T(1,3) + S.lapc_T(3,1))*Dphi_x.*Dphi_z ) .*S.W ) - 3*S.Eself;
+
+% % Components from gradient terms
+
+% % initialization
+
+% %P_Eself = 3*S.Eself;
+% P_elec = 0;
+% P_corr = 0;
+% dx2 = S.dx*S.dx;
+% dy2 = S.dy*S.dy;
+% dz2 = S.dz*S.dz;
+% dxdy = S.dx*S.dy;
+% dydz = S.dy*S.dz;
+% dzdx = S.dz*S.dx;
+% coeff = S.w2(1) * (S.lapc_T(1,1)/dx2 + S.lapc_T(2,2)/dy2 + S.lapc_T(3,3)/dz2);
+% count_typ = 1;
+% count_typ_atms = 1;
+% for JJ_a = 1:S.n_atm % loop over all the atoms
+% % Load pseudopotential file
+% if count_typ_atms == 1
+% filename = strcat('./Pseudopotentials/Pseudopotential_', S.Atm(count_typ).typ);
+% load(filename)
+% end
+
+% % Atom position
+% x0 = S.Atoms(JJ_a,1);
+% y0 = S.Atoms(JJ_a,2);
+% z0 = S.Atoms(JJ_a,3);
+% if(S.BC == 2)
+% % Note the S.dx, S.dy, S.dz terms are to ensure the image rb-region overlap w/ fund. domain
+% n_image_xl = floor((S.Atoms(JJ_a,1) + S.Atm(count_typ).rb)/S.L1);
+% n_image_xr = floor((S.L1 - S.Atoms(JJ_a,1)+S.Atm(count_typ).rb-S.dx)/S.L1);
+% n_image_yl = floor((S.Atoms(JJ_a,2) + S.Atm(count_typ).rb)/S.L2);
+% n_image_yr = floor((S.L2 - S.Atoms(JJ_a,2)+S.Atm(count_typ).rb-S.dy)/S.L2);
+% n_image_zl = floor((S.Atoms(JJ_a,3) + S.Atm(count_typ).rb)/S.L3);
+% n_image_zr = floor((S.L3 - S.Atoms(JJ_a,3)+S.Atm(count_typ).rb-S.dz)/S.L3);
+% % Total No. of images of atom JJ_a (including atom JJ_a)
+% n_image_total = (n_image_xl+n_image_xr+1) * (n_image_yl+n_image_yr+1) * (n_image_zl+n_image_zr+1);
+% % Find the coordinates for all the images
+% xx_img = [-n_image_xl : n_image_xr] * S.L1 + x0;
+% yy_img = [-n_image_yl : n_image_yr] * S.L2 + y0;
+% zz_img = [-n_image_zl : n_image_zr] * S.L3 + z0;
+% [XX_IMG_3D,YY_IMG_3D,ZZ_IMG_3D] = meshgrid(xx_img,yy_img,zz_img);
+% XX_IMG_3D = permute(XX_IMG_3D,[2 1 3]);
+% YY_IMG_3D = permute(YY_IMG_3D,[2 1 3]);
+% ZZ_IMG_3D = permute(ZZ_IMG_3D,[2 1 3]);
+% elseif(S.BC == 3)
+% n_image_xl = floor((S.Atoms(JJ_a,1) + S.Atm(count_typ).rb)/S.L1);
+% n_image_xr = floor((S.L1 - S.Atoms(JJ_a,1)+S.Atm(count_typ).rb-S.dx)/S.L1);
+% n_image_yl = floor((S.Atoms(JJ_a,2) + S.Atm(count_typ).rb)/S.L2);
+% n_image_yr = floor((S.L2 - S.Atoms(JJ_a,2)+S.Atm(count_typ).rb-S.dy)/S.L2);
+% % Total No. of images of atom JJ_a (including atom JJ_a)
+% n_image_total = (n_image_xl+n_image_xr+1) * (n_image_yl+n_image_yr+1);
+% % Find the coordinates for all the images
+% xx_img = [-n_image_xl : n_image_xr] * S.L1 + x0;
+% yy_img = [-n_image_yl : n_image_yr] * S.L2 + y0;
+% zz_img = z0;
+% [XX_IMG_3D,YY_IMG_3D,ZZ_IMG_3D] = meshgrid(xx_img,yy_img,zz_img);
+% XX_IMG_3D = permute(XX_IMG_3D,[2 1 3]);
+% YY_IMG_3D = permute(YY_IMG_3D,[2 1 3]);
+% ZZ_IMG_3D = permute(ZZ_IMG_3D,[2 1 3]);
+% elseif(S.BC == 4)
+% n_image_zl = floor((S.Atoms(JJ_a,3) + S.Atm(count_typ).rb)/S.L3);
+% n_image_zr = floor((S.L3 - S.Atoms(JJ_a,3)+S.Atm(count_typ).rb-S.dz)/S.L3);
+
+% % Total No. of images of atom JJ_a (including atom JJ_a)
+% n_image_total = n_image_zl+n_image_zr+1;
+% % Find the coordinates for all the images
+% xx_img = x0;
+% yy_img = y0;
+% zz_img = [-n_image_zl : n_image_zr] * S.L3 + z0;
+% [XX_IMG_3D,YY_IMG_3D,ZZ_IMG_3D] = meshgrid(xx_img,yy_img,zz_img);
+% XX_IMG_3D = permute(XX_IMG_3D,[2 1 3]);
+% YY_IMG_3D = permute(YY_IMG_3D,[2 1 3]);
+% ZZ_IMG_3D = permute(ZZ_IMG_3D,[2 1 3]);
+% end
+
+% % Loop over all image(s) of atom JJ_a (including atom JJ_a)
+% for count_image = 1:n_image_total
+
+% % Atom position of the image
+% x0_i = XX_IMG_3D(count_image);
+% y0_i = YY_IMG_3D(count_image);
+% z0_i = ZZ_IMG_3D(count_image);
+
+% % Indices of closest grid point to atom
+% pos_ii = round(x0_i / S.dx) + 1;
+% pos_jj = round(y0_i / S.dy) + 1;
+% pos_kk = round(z0_i / S.dz) + 1;
+
+% % Starting and ending indices of b-region
+% ii_s = pos_ii - ceil(S.Atm(count_typ).rb/S.dx+0.5);
+% ii_e = pos_ii + ceil(S.Atm(count_typ).rb/S.dx+0.5);
+% jj_s = pos_jj - ceil(S.Atm(count_typ).rb/S.dy+0.5);
+% jj_e = pos_jj + ceil(S.Atm(count_typ).rb/S.dy+0.5);
+% kk_s = pos_kk - ceil(S.Atm(count_typ).rb/S.dz+0.5);
+% kk_e = pos_kk + ceil(S.Atm(count_typ).rb/S.dz+0.5);
+
+% if(S.BC == 2)
+% % For periodic systems, find the overlap of rb-region and the fund. domain
+% ii_s = max(ii_s,1);
+% ii_e = min(ii_e,S.Nx);
+% jj_s = max(jj_s,1);
+% jj_e = min(jj_e,S.Ny);
+% kk_s = max(kk_s,1);
+% kk_e = min(kk_e,S.Nz);
+% elseif(S.BC == 3)
+% ii_s = max(ii_s,1);
+% ii_e = min(ii_e,S.Nx);
+% jj_s = max(jj_s,1);
+% jj_e = min(jj_e,S.Ny);
+% isInside = (kk_s>1) && (kk_e1) && (ii_e1) && (jj_e
+% Phanish Suryanarayana
+%
+% @ references
+% "On the calculation of the stress tensor in real-space Kohn-Sham
+% density functional theory (Sharma et. al. 2018)"
+%
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+%===============================================================================
+stress = zeros(3,3);
+S_T = transpose(S.lat_uvec);
+
+% Stress contribution from Kinetic component
+ks = 1;
+for spin = 1:S.nspin
+ for kpt = 1:S.tnkpt
+ kpt_vec = S.kptgrid(kpt,:);
+
+ Dpsi_x = blochGradient(S,kpt_vec,1)*S.psi(:,:,ks);
+ Dpsi_y = blochGradient(S,kpt_vec,2)*S.psi(:,:,ks);
+ Dpsi_z = blochGradient(S,kpt_vec,3)*S.psi(:,:,ks);
+
+ TDpsi_1 = S.grad_T(1,1)*Dpsi_x + S.grad_T(2,1)*Dpsi_y + S.grad_T(3,1)*Dpsi_z;
+ TDpsi_2 = S.grad_T(1,2)*Dpsi_x + S.grad_T(2,2)*Dpsi_y + S.grad_T(3,2)*Dpsi_z;
+ TDpsi_3 = S.grad_T(1,3)*Dpsi_x + S.grad_T(2,3)*Dpsi_y + S.grad_T(3,3)*Dpsi_z;
+ TDcpsi_1 = conj(TDpsi_1);
+ TDcpsi_2 = conj(TDpsi_2);
+ TDcpsi_3 = conj(TDpsi_3);
+
+ stress(1,1) = stress(1,1) + real(-S.occfac * S.wkpt(kpt) * (transpose(S.W) * ...
+ (TDcpsi_1.*TDpsi_1)) * S.occ(:,ks));
+ stress(1,2) = stress(1,2) + real(-S.occfac * S.wkpt(kpt) * (transpose(S.W) * ...
+ (TDcpsi_1.*TDpsi_2)) * S.occ(:,ks));
+ stress(1,3) = stress(1,3) + real(-S.occfac * S.wkpt(kpt) * (transpose(S.W) * ...
+ (TDcpsi_1.*TDpsi_3)) * S.occ(:,ks));
+ stress(2,1) = stress(2,1) + real(-S.occfac * S.wkpt(kpt) * (transpose(S.W) * ...
+ (TDcpsi_2.*TDpsi_1)) * S.occ(:,ks));
+ stress(2,2) = stress(2,2) + real(-S.occfac * S.wkpt(kpt) * (transpose(S.W) * ...
+ (TDcpsi_2.*TDpsi_2)) * S.occ(:,ks));
+ stress(2,3) = stress(2,3) + real(-S.occfac * S.wkpt(kpt) * (transpose(S.W) * ...
+ (TDcpsi_2.*TDpsi_3)) * S.occ(:,ks));
+ stress(3,1) = stress(3,1) + real(-S.occfac * S.wkpt(kpt) * (transpose(S.W) * ...
+ (TDcpsi_3.*TDpsi_1)) * S.occ(:,ks));
+ stress(3,2) = stress(3,2) + real(-S.occfac * S.wkpt(kpt) * (transpose(S.W) * ...
+ (TDcpsi_3.*TDpsi_2)) * S.occ(:,ks));
+ stress(3,3) = stress(3,3) + real(-S.occfac * S.wkpt(kpt) * (transpose(S.W) * ...
+ (TDcpsi_3.*TDpsi_3)) * S.occ(:,ks));
+
+ ks = ks + 1;
+ end
+end
+
+% Stress contribution from exchange-correlation and energy terms from electrostatics
+Drho_x = S.grad_1 * S.rho;
+Drho_y = S.grad_2 * S.rho;
+Drho_z = S.grad_3 * S.rho;
+
+if S.nspin == 1
+ for alpha = 1:3
+ for beta = 1:3
+ Drho_alpha = S.grad_T(1,alpha)*Drho_x + S.grad_T(2,alpha)*Drho_y + S.grad_T(3,alpha)*Drho_z ;
+ Drho_beta = S.grad_T(1,beta)*Drho_x + S.grad_T(2,beta)*Drho_y + S.grad_T(3,beta)*Drho_z ;
+ stress(alpha,beta) = stress(alpha,beta) + (alpha == beta) * ( S.Exc - sum(S.W .* S.Vxc .* S.rho) ) + ...
+ -sum(S.W' * (S.dvxcdgrho .* Drho_alpha .* Drho_beta)) +...
+ (alpha == beta) * ( 0.5 * sum( S.W .* (S.b - S.rho) .* S.phi ) - S.Eself + S.E_corr ) ;
+ end
+ end
+
+else
+ for alpha = 1:3
+ for beta = 1:3
+ Drho_alpha = S.grad_T(1,alpha)*Drho_x + S.grad_T(2,alpha)*Drho_y + S.grad_T(3,alpha)*Drho_z ;
+ Drho_beta = S.grad_T(1,beta)*Drho_x + S.grad_T(2,beta)*Drho_y + S.grad_T(3,beta)*Drho_z ;
+ stress(alpha,beta) = stress(alpha,beta) + (alpha == beta) * ( S.Exc - sum(S.W'*(S.Vxc.*S.rho(:,2:3)))) + ...
+ -sum(S.W' * (S.dvxcdgrho .* Drho_alpha .* Drho_beta)) +...
+ (alpha == beta) * ( 0.5 * sum( S.W .* (S.b - S.rho(:,1)) .* S.phi ) - S.Eself + S.E_corr ) ;
+ end
+ end
+end
+
+% Stress contribution from remaining terms in electrostatics
+Dphi_x = S.grad_1*(S.phi);
+Dphi_y = S.grad_2*(S.phi);
+Dphi_z = S.grad_3*(S.phi);
+
+TDphi_1 = S.grad_T(1,1)*Dphi_x + S.grad_T(2,1)*Dphi_y + S.grad_T(3,1)*Dphi_z ;
+TDphi_2 = S.grad_T(1,2)*Dphi_x + S.grad_T(2,2)*Dphi_y + S.grad_T(3,2)*Dphi_z ;
+TDphi_3 = S.grad_T(1,3)*Dphi_x + S.grad_T(2,3)*Dphi_y + S.grad_T(3,3)*Dphi_z ;
+stress(1,1) = stress(1,1) + (1/4/pi) * sum( TDphi_1.*TDphi_1.*S.W);
+stress(1,2) = stress(1,2) + (1/4/pi) * sum( TDphi_1.*TDphi_2.*S.W);
+stress(1,3) = stress(1,3) + (1/4/pi) * sum( TDphi_1.*TDphi_3.*S.W);
+stress(2,1) = stress(2,1) + (1/4/pi) * sum( TDphi_2.*TDphi_1.*S.W);
+stress(2,2) = stress(2,2) + (1/4/pi) * sum( TDphi_2.*TDphi_2.*S.W);
+stress(2,3) = stress(2,3) + (1/4/pi) * sum( TDphi_2.*TDphi_3.*S.W);
+stress(3,1) = stress(3,1) + (1/4/pi) * sum( TDphi_3.*TDphi_1.*S.W);
+stress(3,2) = stress(3,2) + (1/4/pi) * sum( TDphi_3.*TDphi_2.*S.W);
+stress(3,3) = stress(3,3) + (1/4/pi) * sum( TDphi_3.*TDphi_3.*S.W);
+
+%psdfilepath = sprintf('%s/PseudopotFiles',S.inputfile_path);
+count_typ = 1;
+count_typ_atms = 1;
+for JJ_a = 1:S.n_atm % loop over all the atoms
+ % Atom position
+ x0 = S.Atoms(JJ_a,1);
+ y0 = S.Atoms(JJ_a,2);
+ z0 = S.Atoms(JJ_a,3);
+ % Note the S.dx, S.dy, S.dz terms are to ensure the image rb-region overlap w/ fund. domain
+ if S.BCx == 0
+ n_image_xl = floor((S.Atoms(JJ_a,1) + S.Atm(count_typ).rb_x)/S.L1);
+ n_image_xr = floor((S.L1 - S.Atoms(JJ_a,1)+S.Atm(count_typ).rb_x-S.dx)/S.L1);
+ else
+ n_image_xl = 0;
+ n_image_xr = 0;
+ end
+
+ if S.BCy == 0
+ n_image_yl = floor((S.Atoms(JJ_a,2) + S.Atm(count_typ).rb_y)/S.L2);
+ n_image_yr = floor((S.L2 - S.Atoms(JJ_a,2)+S.Atm(count_typ).rb_y-S.dy)/S.L2);
+ else
+ n_image_yl = 0;
+ n_image_yr = 0;
+ end
+
+ if S.BCz == 0
+ n_image_zl = floor((S.Atoms(JJ_a,3) + S.Atm(count_typ).rb_z)/S.L3);
+ n_image_zr = floor((S.L3 - S.Atoms(JJ_a,3)+S.Atm(count_typ).rb_z-S.dz)/S.L3);
+ else
+ n_image_zl = 0;
+ n_image_zr = 0;
+ end
+
+ % Total No. of images of atom JJ_a (including atom JJ_a)
+ n_image_total = (n_image_xl+n_image_xr+1) * (n_image_yl+n_image_yr+1) * (n_image_zl+n_image_zr+1);
+ % Find the coordinates for all the images
+ xx_img = [-n_image_xl : n_image_xr] * S.L1 + x0;
+ yy_img = [-n_image_yl : n_image_yr] * S.L2 + y0;
+ zz_img = [-n_image_zl : n_image_zr] * S.L3 + z0;
+ [XX_IMG_3D,YY_IMG_3D,ZZ_IMG_3D] = ndgrid(xx_img,yy_img,zz_img);
+
+ % Loop over all image(s) of atom JJ_a (including atom JJ_a)
+ for count_image = 1:n_image_total
+
+ % Atom position of the image
+ x0_i = XX_IMG_3D(count_image);
+ y0_i = YY_IMG_3D(count_image);
+ z0_i = ZZ_IMG_3D(count_image);
+
+ % Indices of closest grid point to atom
+ pos_ii = round((x0_i-S.xin) / S.dx) + 1;
+ pos_jj = round((y0_i-S.yin) / S.dy) + 1;
+ pos_kk = round((z0_i-S.zin) / S.dz) + 1;
+
+ % Starting and ending indices of b-region
+ ii_s = pos_ii - ceil(S.Atm(count_typ).rb_x/S.dx+0.5);
+ ii_e = pos_ii + ceil(S.Atm(count_typ).rb_x/S.dx+0.5);
+ jj_s = pos_jj - ceil(S.Atm(count_typ).rb_y/S.dy+0.5);
+ jj_e = pos_jj + ceil(S.Atm(count_typ).rb_y/S.dy+0.5);
+ kk_s = pos_kk - ceil(S.Atm(count_typ).rb_z/S.dz+0.5);
+ kk_e = pos_kk + ceil(S.Atm(count_typ).rb_z/S.dz+0.5);
+
+ % Check if the b-region is inside the domain in Dirichlet BC
+ % direction
+ %isInside = (S.BCx == 0 || (S.BCx == 1 && (ii_s>1) && (ii_e1) && (jj_e1) && (kk_e S.Atm(count_typ).r_grid_vloc(end);
+ V_PS(IsLargeThanRmax) = -S.Atm(count_typ).Z;
+ V_PS(~IsLargeThanRmax) = interp1(S.Atm(count_typ).r_grid_vloc, S.Atm(count_typ).r_grid_vloc.*S.Atm(count_typ).Vloc, dd(~IsLargeThanRmax), 'spline');
+
+ V_PS = V_PS./dd;
+ V_PS(dd1) && (kk_e1) && (ii_e1) && (jj_e
+% Abhiraj Sharma
+% Phanish Suryanarayana
+%
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+%
+
+% Band structure energy
+Eband = 0;
+ks = 1;
+for spin = 1:S.nspin
+ for kpt = 1:S.tnkpt
+ Eband = Eband + S.occfac * S.wkpt(kpt) * sum(S.EigVal(:,ks).*S.occ(:,ks)) ;
+ ks = ks + 1;
+ end
+end
+
+% Exchange-correlation energy
+rho = S.rho;
+% Check if density is too small
+INDX_zerorho = (rho < S.xc_rhotol);
+rho(INDX_zerorho) = S.xc_rhotol;
+
+if S.nspin == 1
+ if S.xc == 0 % LDA_PW
+ C2 = 0.73855876638202 ; % constant for exchange energy
+ %rho = rho+(1e-50) ; % to avoid divide by zero error
+ p = 1 ;
+ A = 0.031091 ;
+ alpha1 = 0.21370 ;
+ beta1 = 7.5957 ;
+ beta2 = 3.5876 ;
+ beta3 = 1.6382 ;
+ beta4 = 0.49294 ;
+ CEnergyPotential = (0.75./(pi*rho)).^(1/3) ;
+ CEnergyPotential = -2*A*(1+alpha1*CEnergyPotential).*log(1+1./(2*A*( beta1*(CEnergyPotential.^0.5) ...
+ + beta2*CEnergyPotential + beta3*(CEnergyPotential.^1.5) + beta4*(CEnergyPotential.^(p+1.0))))) ;
+ %rho = rho-(1e-50) ;
+ Exc = sum(CEnergyPotential.*rho.*S.W) - C2*sum((rho.^(4/3)).*S.W) ;
+ elseif S.xc == 1 % LDA_PZ
+ A = 0.0311;
+ B = -0.048 ;
+ C = 0.002 ;
+ D = -0.0116 ;
+ gamma1 = -0.1423 ;
+ beta1 = 1.0529 ;
+ beta2 = 0.3334 ;
+ C2 = 0.73855876638202;
+ %rho = rho+(1e-50) ; % to avoid divide by zero error
+ CEnergyPotential = (0.75./(pi*rho)).^(1/3) ;
+ islt1 = (CEnergyPotential < 1.0);
+ CEnergyPotential(islt1) = A * log(CEnergyPotential(islt1)) + B ...
+ + C * CEnergyPotential(islt1) .* log(CEnergyPotential(islt1)) ...
+ + D * CEnergyPotential(islt1);
+ CEnergyPotential(~islt1) = gamma1./(1.0+beta1*sqrt(CEnergyPotential(~islt1))+beta2*CEnergyPotential(~islt1));
+ %rho = rho-(1e-50) ;
+ Exc = sum(CEnergyPotential.*rho.*S.W) - C2*sum((rho.^(4/3)).*S.W) ;
+ elseif S.xc == 2
+ Exc = sum(S.e_xc.*rho.*S.W);
+ end
+ % Exchange-correlation energy double counting correction
+ Exc_dc = sum(S.Vxc.*rho.*S.W) ;
+else
+ Exc = sum(S.e_xc.*rho(:,1).*S.W);
+ % Exchange-correlation energy double counting correction
+ Exc_dc = sum(sum(S.Vxc.*rho(:,2:3),2).*S.W) ;
+end
+
+% Electrostatic energy double counting correction
+Eelec_dc = 0.5*sum((S.b-S.rho(:,1)).*S.phi.*S.W);
+
+% Electronic entropy
+Eent = 0 ;
+ks = 1;
+for spin = 1:S.nspin
+ for kpt = 1:S.tnkpt
+ if S.elec_T_type == 0 % fermi-dirac smearing
+ Eent_v = S.occfac*(1/S.bet)*(S.occ(:,ks).*log(S.occ(:,ks))+(1-S.occ(:,ks)).*log(1-S.occ(:,ks)));
+ Eent_v(isnan(Eent_v)) = 0.0 ;
+ elseif S.elec_T_type == 1 % gaussian smearing
+ Eent_v = -S.occfac*(1/S.bet)*1/(2*sqrt(pi)) .* exp(-(S.bet * (S.EigVal(:,ks)-S.lambda_f)).^2);
+ end
+ Eent = Eent + S.wkpt(kpt)*sum(Eent_v);
+ ks = ks + 1;
+ end
+end
+
+% Total free energy
+Etot = Eband + Exc - Exc_dc + Eelec_dc - S.Eself + S.E_corr + Eent;
+
+%fprintf(2,' ------------------\n');
+% fprintf(' Eband = %.8f\n', Eband);
+% fprintf(' Exc = %.8f\n', Exc);
+% fprintf(' Exc_dc = %.8f\n', Exc_dc);
+% fprintf(' Eelec_dc = %.8f\n', Eelec_dc);
+% fprintf(' Eent = %.8f\n', Eent);
+% fprintf(' E_corr = %.8f\n', S.E_corr);
+% fprintf(' Eself = %.8f\n', S.Eself);
+% fprintf(' Etot = %.8f\n', Etot);
+%fprintf(2,' ------------------\n');
+
+end
diff --git a/src/exchangeCorrelationPotential.m b/src/exchangeCorrelationPotential.m
new file mode 100644
index 00000000..7eeda468
--- /dev/null
+++ b/src/exchangeCorrelationPotential.m
@@ -0,0 +1,637 @@
+function [S] = exchangeCorrelationPotential(S)
+% @ brief Calculates exchange correlation potential(LDA, GGA) and
+% exchange correlation energy density(GGA). Purdew-Wang LDA
+% and PBE GGA are implemented for both spin polarized and
+% non-spin polarized calculations.
+% @ authors
+% Abhiraj Sharma
+% Qimen Xu
+% Phanish Suryanarayana
+%
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+%==========================================================================
+
+%--------------------------------------------------------------------------
+% Parameters
+%
+XC = struct;
+XC.alpha_zeta2 = 1.0 - 1.0e-6; XC.alpha_zeta = 1.0 - 1.0e-6; % ABINIT
+%XC.alpha_zeta2 = 1.0; XC.alpha_zeta = 1.0; %LIBXC
+XC.beta = 0.066725;
+%XC.beta = 0.06672455060314922;
+XC.fsec_inv = 1.0/1.709921;
+XC.kappa_pbe = 0.804;
+XC.mu = 0.2195149727645171;
+XC.rsfac = 0.6203504908994000;
+XC.kappa = XC.kappa_pbe;
+XC.mu_divkappa_pbe = XC.mu/XC.kappa_pbe;
+XC.mu_divkappa = XC.mu_divkappa_pbe;
+
+XC.ec0_aa = 0.031091; XC.ec1_aa = 0.015545; XC.mac_aa = 0.016887; % ABINIT
+%XC.ec0_aa = 0.0310907; XC.ec1_aa = 0.01554535; XC.mac_aa = 0.0168869; % LIBXC
+XC.ec0_a1 = 0.21370; XC.ec1_a1 = 0.20548; XC.mac_a1 = 0.11125;
+XC.ec0_b1 = 7.5957; XC.ec1_b1 = 14.1189; XC.mac_b1 = 10.357;
+XC.ec0_b2 = 3.5876; XC.ec1_b2 = 6.1977; XC.mac_b2 = 3.6231;
+XC.ec0_b3 = 1.6382; XC.ec1_b3 = 3.3662; XC.mac_b3 = 0.88026;
+XC.ec0_b4 = 0.49294; XC.ec1_b4 = 0.62517; XC.mac_b4 = 0.49671;
+
+% Constants
+XC.piinv = 1.0/pi;
+XC.third = 1.0/3.0;
+XC.twom1_3 = 2.0^(-XC.third);
+XC.sixpi2_1_3 = (6.0 * pi^2)^XC.third;
+XC.sixpi2m1_3 = 1.0/XC.sixpi2_1_3;
+XC.threefourth_divpi = (3.0/4.0) * XC.piinv;
+XC.gamma = (1.0 - log(2.0)) * XC.piinv^2;
+XC.gamma_inv = 1.0/XC.gamma;
+%beta_gamma = XC.beta * XC.gamma_inv;
+XC.factf_zeta = 1.0/(2.0^(4.0/3.0) - 2.0);
+XC.factfp_zeta = 4.0/3.0 * XC.factf_zeta * XC.alpha_zeta2;
+XC.coeff_tt = 1.0/(4.0 * 4.0 * XC.piinv * (3.0 * pi^2)^XC.third);
+XC.sq_rsfac = sqrt(XC.rsfac);
+XC.sq_rsfac_inv = 1.0/XC.sq_rsfac;
+
+
+if S.nspin == 1
+ if S.xc == 0
+ S = LDA_PW(S);
+ elseif S.xc == 1
+ S = LDA_PZ(S);
+ elseif S.xc == 2
+ S = GGA_PBE(S,XC);
+ end
+else
+ if S.xc == 0
+ S = LSDA_PW(S,XC);
+ elseif S.xc == 1
+ S = LSDA_PZ(S,XC);
+ elseif S.xc == 2
+ S = GSGA_PBE(S,XC);
+ end
+end
+
+end
+%--------------------------------------------------------------------------
+
+function [S] = LDA_PW(S)
+ rho = S.rho;
+ rho(rho < S.xc_rhotol) = S.xc_rhotol;
+ % correlation parameters
+ p = 1 ;
+ A = 0.031091 ;
+ alpha1 = 0.21370 ;
+ beta1 = 7.5957 ;
+ beta2 = 3.5876 ;
+ beta3 = 1.6382 ;
+ beta4 = 0.49294 ;
+
+ % exchange parameters
+ C3 = 0.9847450218427;
+
+ % exchange-correlation potential
+ %rho = rho+(1e-50) ;
+ S.Vxc = (0.75./(pi*rho)).^(1/3) ;
+ S.Vxc = - C3*(rho.^(1/3)) + (-2*A*(1+alpha1*S.Vxc)).*log(1+1./(2*A*(beta1*(S.Vxc.^0.5) + beta2*S.Vxc + beta3*(S.Vxc.^1.5) + beta4*(S.Vxc.^(p+1))))) ...
+ - (S.Vxc/3).*(-2*A*alpha1*log(1+1./(2*A*( beta1*(S.Vxc.^0.5) + beta2*S.Vxc + beta3*(S.Vxc.^1.5) + beta4*(S.Vxc.^(p+1))))) ...
+ - ((-2*A*(1+alpha1*S.Vxc)).*(A*( beta1*(S.Vxc.^-0.5)+ 2*beta2 + 3*beta3*(S.Vxc.^0.5) + 2*(p+1)*beta4*(S.Vxc.^p) ))) ...
+ ./((2*A*( beta1*(S.Vxc.^0.5) + beta2*S.Vxc + beta3*(S.Vxc.^1.5) + beta4*(S.Vxc.^(p+1)) ) ) ...
+ .*(2*A*( beta1*(S.Vxc.^0.5) + beta2*S.Vxc + beta3*(S.Vxc.^1.5) + beta4*(S.Vxc.^(p+1)) ) )+(2*A*( beta1*(S.Vxc.^0.5) + beta2*S.Vxc + beta3*(S.Vxc.^1.5) + beta4*(S.Vxc.^(p+1)) ) )) ) ;
+ S.dvxcdgrho = zeros(size(S.Vxc));
+end
+%--------------------------------------------------------------------------
+
+function [S] = LDA_PZ(S)
+ rho = S.rho;
+ rho(rho < S.xc_rhotol) = S.xc_rhotol;
+ % correlation parameters
+ A = 0.0311;
+ B = -0.048;
+ C = 0.002;
+ D = -0.0116;
+ gamma1 = -0.1423;
+ beta1 = 1.0529;
+ beta2 = 0.3334;
+ % exchange parameters
+ C3 = 0.9847450218427;
+ % exchange-correlation potential
+ %rho = rho+(1e-50);
+ S.Vxc = (0.75./(pi*rho)).^(1/3);
+ islessthan1 = (S.Vxc < 1.0);
+ S.Vxc(islessthan1) = log(S.Vxc(islessthan1)).*(A+(2.0/3.0)*C*S.Vxc(islessthan1)) ...
+ + (B-(1.0/3.0)*A) + (1.0/3.0)*(2.0*D-C)* S.Vxc(islessthan1);
+ S.Vxc(~islessthan1) = (gamma1 + (7.0/6.0)*gamma1*beta1*sqrt(S.Vxc(~islessthan1)) ...
+ + (4.0/3.0)*gamma1*beta2*S.Vxc(~islessthan1))./(1+beta1*sqrt(S.Vxc(~islessthan1))+beta2*S.Vxc(~islessthan1)).^2;
+ S.Vxc = S.Vxc - C3*(rho.^(1/3));
+ isRhoZero = (abs(rho) < 1e-15);
+ S.Vxc(isRhoZero) = 0;
+ %rho = rho-(1e-50) ;
+ S.dvxcdgrho = zeros(size(rho,1),1);
+end
+%------------------------------------------------------------------------------------------------------------------------------
+
+function [S] = GGA_PBE(S,XC)
+ rho = S.rho;
+ rho(rho < S.xc_rhotol) = S.xc_rhotol;
+ drho_1 = S.grad_1 * rho;
+ drho_2 = S.grad_2 * rho;
+ drho_3 = S.grad_3 * rho;
+
+ if S.cell_typ ~= 2
+ sigma = drho_1.*drho_1 + drho_2.*drho_2 + drho_3.*drho_3;
+ else
+ sigma = (S.lapc_T(1,1)*drho_1.*drho_1 + S.lapc_T(2,2)*drho_2.*drho_2 + S.lapc_T(3,3)*drho_3.*drho_3 +...
+ S.lapc_T(1,2)*drho_1.*drho_2 + S.lapc_T(2,3)*drho_2.*drho_3 + S.lapc_T(1,3)*drho_3.*drho_1 ) ; % grad_rho . grad_rho
+ end
+ % -------------------------------------------------------------------------------------------------------------------
+ % Calling inbuilt Libxc functions
+ % -------------------------------------------------------------------------------------------------------------------
+
+% func_id_x = 101; % Perdew-Burke-Ernzerhof GGA functional with exchange only
+% %mex -I/home/users/asharma424/libxc/src -I/home/users/asharma424/libxc -L/opt/etsf/lib -lxc -lm /home/users/asharma424/libxc/examples/xc.c ;
+% fprintf('\n\n');
+% mex -I/home/users/asharma424/Downloads/Softwares/libxc-4.3.3/src -I/home/users/asharma424/Downloads/Softwares/libxc-4.3.3 -L/usr/lib64 -lxc -lm /home/users/asharma424/Downloads/Softwares/libxc-4.3.3/examples/xc.c ;
+% [e_x, v_x, dvxdgrho] = xc(func_id_x, rho, sigma);% e_x = exchange energy per unit particle, v_x = d(rho*e_x)/drho = e_x + rho*de_x/drho, dvxdgrho = d(rho*e_x)/dsigma = rho*de_x/dsigma + 0
+%
+% func_id_c = 130; % Perdew-Burke-Ernzerhof GGA functional with correlation only
+% mex -I/home/users/asharma424/Downloads/Softwares/libxc-4.3.3/src -I/home/users/asharma424/Downloads/Softwares/libxc-4.3.3 -L/usr/lib64 -lxc -lm /home/users/asharma424/Downloads/Softwares/libxc-4.3.3/examples/xc.c ;
+% [e_c, v_c, dvcdgrho] = xc(func_id_c, rho, sigma);% e_c = correlation energy per unit particle, v_c = d(rho*e_c)/drho = e_c + rho*de_c/drho, dvcdgrho = d(rho*e_c)/dsigma = rho*de_c/dsigma + 0
+% fprintf('\n\n');
+% S.e_xc = e_x + e_c ;
+% v_xc = v_x + v_c ;
+% S.dvxcdgrho = dvxdgrho + dvcdgrho ;
+% %
+% S.Vxc = v_xc - 2*( S.lapc_T(1,1)*grad_1*(S.dvxcdgrho.*drho_1) + S.lapc_T(2,2)*grad_2*(S.dvxcdgrho.*drho_2) + S.lapc_T(3,3)*grad_3*(S.dvxcdgrho.*drho_3) +...
+% S.lapc_T(2,1)*grad_1*(S.dvxcdgrho.*drho_2) + S.lapc_T(2,1)*grad_2*(S.dvxcdgrho.*drho_1) + S.lapc_T(3,2)*grad_2*(S.dvxcdgrho.*drho_3) +...
+% S.lapc_T(3,2)*grad_3*(S.dvxcdgrho.*drho_2) + S.lapc_T(3,1)*grad_1*(S.dvxcdgrho.*drho_3) + S.lapc_T(3,1)*grad_3*(S.dvxcdgrho.*drho_1) );
+ % --------------------------------------------------------------------------------------------------------------------------
+ % Direct computation
+ % (taken from ABINIT)
+ % --------------------------------------------------------------------------------------------------------------------------
+
+
+ % Arrays
+ rho_updn = rho/2.0;
+ rho_updnm1_3 = rho_updn.^(-XC.third);
+ rhom1_3 = XC.twom1_3 * rho_updnm1_3;
+
+ rhotot_inv = rhom1_3 .* rhom1_3 .* rhom1_3;
+ rhotmo6 = sqrt(rhom1_3);
+ rhoto6 = rho .* rhom1_3 .* rhom1_3 .* rhotmo6;
+
+ % -----------------------------------------------------------------------
+ % First take care of the exchange part of the functional
+
+ rhomot = rho_updnm1_3;
+ ex_lsd = -XC.threefourth_divpi * XC.sixpi2_1_3 * (rhomot .* rhomot .* rho_updn);
+
+ % Perdew-Burke-Ernzerhof GGA, exchange part
+
+ rho_inv = rhomot .* rhomot .* rhomot;
+ coeffss = (1.0/4.0) * XC.sixpi2m1_3 * XC.sixpi2m1_3 * (rho_inv .* rho_inv .* rhomot .* rhomot);
+ ss = (sigma/4.0) .* coeffss;
+ divss = 1.0./(1.0 + XC.mu_divkappa * ss);
+ dfxdss = XC.mu * (divss .* divss);
+ %d2fxdss2 = -XC.mu * 2.0 * XC.mu_divkappa * (divss .* divss .* divss);
+ fx = 1.0 + XC.kappa * (1.0 - divss);
+ ex_gga = ex_lsd .* fx;
+ dssdn = (-8.0/3.0) * (ss .* rho_inv);
+ dfxdn = dfxdss .* dssdn;
+ v_xc = ex_lsd .* ((4.0/3.0) * fx + rho_updn .* dfxdn);
+
+ dssdg = 2.0 * coeffss;
+ dfxdg = dfxdss .* dssdg;
+ dvxcdgrho1 = ex_lsd .* rho_updn .* dfxdg;
+ exc = ex_gga .* rho_updn;
+
+ % If non spin-polarized, treat spin down contribution now, similar to spin up
+
+ exc = exc * 2.0;
+ S.e_xc = exc .* rhotot_inv;
+
+ % -----------------------------------------------------------------------------
+ % Then takes care of the LSD correlation part of the functional
+
+ rs = XC.rsfac * rhom1_3;
+ sqr_rs = XC.sq_rsfac * rhotmo6;
+ rsm1_2 = XC.sq_rsfac_inv * rhoto6;
+
+ % Formulas A6-A8 of PW92LSD
+
+ ec0_q0 = -2.0 * XC.ec0_aa * (1.0 + XC.ec0_a1 * rs);
+ ec0_q1 = 2.0 * XC.ec0_aa *(XC.ec0_b1 * sqr_rs + XC.ec0_b2 * rs + XC.ec0_b3 * rs .* sqr_rs + XC.ec0_b4 * rs .* rs);
+ ec0_q1p = XC.ec0_aa * (XC.ec0_b1 * rsm1_2 + 2.0 * XC.ec0_b2 + 3.0 * XC.ec0_b3 * sqr_rs + 4.0 * XC.ec0_b4 * rs);
+ ec0_den = 1.0./(ec0_q1 .* ec0_q1 + ec0_q1);
+ ec0_log = -log(ec0_q1 .* ec0_q1 .* ec0_den);
+ ecrs0 = ec0_q0 .* ec0_log;
+ decrs0_drs = -2.0 * XC.ec0_aa * XC.ec0_a1 * ec0_log - ec0_q0 .* ec0_q1p .* ec0_den;
+
+ ecrs = ecrs0;
+ decrs_drs = decrs0_drs;
+ %decrs_dzeta = 0.0;
+ %zeta = 0.0;
+
+ % Add LSD correlation functional to GGA exchange functional
+ S.e_xc = S.e_xc + ecrs;
+ v_xc = v_xc + ecrs - (rs/3.0) .* decrs_drs;
+
+ % -----------------------------------------------------------------------------
+ % Eventually add the GGA correlation part of the PBE functional
+ % Note : the computation of the potential in the spin-unpolarized
+ % case could be optimized much further. Other optimizations are left to do.
+
+ %phi_zeta = 1.0;
+ %phip_zeta = 0.0;
+ phi_zeta_inv = 1.0;
+ %phi_logder = 0.0;
+ phi3_zeta = 1.0;
+ gamphi3inv = XC.gamma_inv;
+ %phipp_zeta = (-2.0/9.0) * XC.alpha_zeta * XC.alpha_zeta;
+
+ % From ec to bb
+ bb = ecrs * gamphi3inv;
+ dbb_drs = decrs_drs * gamphi3inv;
+ %dbb_dzeta = gamphi3inv * (decrs_dzeta - 3.0 * ecrs * phi_logder);
+
+ % From bb to cc
+ exp_pbe = exp(-bb);
+ cc = 1.0./(exp_pbe - 1.0);
+ dcc_dbb = cc .* cc .* exp_pbe;
+ dcc_drs = dcc_dbb .* dbb_drs;
+ %dcc_dzeta = dcc_dbb .* dbb_dzeta;
+
+ % From cc to aa
+ coeff_aa = XC.beta * XC.gamma_inv * phi_zeta_inv * phi_zeta_inv;
+ aa = coeff_aa * cc;
+ daa_drs = coeff_aa * dcc_drs;
+ %daa_dzeta = -2.0 * aa * phi_logder + coeff_aa * dcc_dzeta;
+
+ % Introduce tt : do not assume that the spin-dependent gradients are collinear
+ grrho2 = sigma;
+ dtt_dg = 2.0 * rhotot_inv .* rhotot_inv .* rhom1_3 * XC.coeff_tt;
+ % Note that tt is (the t variable of PBE divided by phi) squared
+ tt = 0.5 * grrho2 .* dtt_dg;
+
+ % Get xx from aa and tt
+ xx = aa .* tt;
+ dxx_drs = daa_drs .* tt;
+ %dxx_dzeta = daa_dzeta .* tt;
+ dxx_dtt = aa;
+
+ % From xx to pade
+ pade_den = 1.0./(1.0 + xx .* (1.0 + xx));
+ pade = (1.0 + xx) .* pade_den;
+ dpade_dxx = -xx .* (2.0 + xx) .* (pade_den.^2);
+ dpade_drs = dpade_dxx .* dxx_drs;
+ dpade_dtt = dpade_dxx .* dxx_dtt;
+ %dpade_dzeta = dpade_dxx .* dxx_dzeta;
+
+ % From pade to qq
+ coeff_qq = tt * phi_zeta_inv * phi_zeta_inv;
+ qq = coeff_qq .* pade;
+ dqq_drs = coeff_qq .* dpade_drs;
+ dqq_dtt = pade * phi_zeta_inv * phi_zeta_inv + coeff_qq .* dpade_dtt;
+ %dqq_dzeta = coeff_qq .* (dpade_dzeta - 2.0 * pade * phi_logder);
+
+ % From qq to rr
+ arg_rr = 1.0 + XC.beta * XC.gamma_inv * qq;
+ div_rr = 1.0./arg_rr;
+ rr = XC.gamma * log(arg_rr);
+ drr_dqq = XC.beta * div_rr;
+ drr_drs = drr_dqq .* dqq_drs;
+ drr_dtt = drr_dqq .* dqq_dtt;
+ %drr_dzeta = drr_dqq .* dqq_dzeta;
+
+ % From rr to hh
+ hh = phi3_zeta * rr;
+ dhh_drs = phi3_zeta * drr_drs;
+ dhh_dtt = phi3_zeta * drr_dtt;
+ %dhh_dzeta = phi3_zeta * (drr_dzeta + 3.0 * rr * phi_logder);
+
+ % The GGA correlation energy is added
+ S.e_xc = S.e_xc + hh;
+
+ % From hh to the derivative of the energy wrt the density
+ drhohh_drho = hh - XC.third * rs .* dhh_drs - (7.0/3.0) * tt .* dhh_dtt; %- zeta * dhh_dzeta
+ v_xc = v_xc + drhohh_drho;
+
+ % From hh to the derivative of the energy wrt to the gradient of the
+ % density, divided by the gradient of the density
+ % (The v3.3 definition includes the division by the norm of the gradient)
+
+ S.dvxcdgrho = 0.5 * dvxcdgrho1 + (rho .* dtt_dg .* dhh_dtt);
+
+ if S.cell_typ ~= 2
+ S.Vxc = v_xc - S.grad_1 * (S.dvxcdgrho.*drho_1) - S.grad_2 * (S.dvxcdgrho.*drho_2) - S.grad_3 * (S.dvxcdgrho.*drho_3);
+ else
+ S.Vxc = v_xc - ( S.lapc_T(1,1)*S.grad_1*(S.dvxcdgrho.*drho_1) + S.lapc_T(2,2)*S.grad_2*(S.dvxcdgrho.*drho_2) + S.lapc_T(3,3)*S.grad_3*(S.dvxcdgrho.*drho_3) +...
+ S.lapc_T(2,1)*S.grad_1*(S.dvxcdgrho.*drho_2) + S.lapc_T(2,1)*S.grad_2*(S.dvxcdgrho.*drho_1) + S.lapc_T(3,2)*S.grad_2*(S.dvxcdgrho.*drho_3) +...
+ S.lapc_T(3,2)*S.grad_3*(S.dvxcdgrho.*drho_2) + S.lapc_T(3,1)*S.grad_1*(S.dvxcdgrho.*drho_3) + S.lapc_T(3,1)*S.grad_3*(S.dvxcdgrho.*drho_1) );
+ end
+end
+%--------------------------------------------------------------------------
+
+function [S] = LSDA_PW(S,XC)
+ rho = S.rho;
+ rho(rho < S.xc_rhotol) = S.xc_rhotol;
+ rho(:,1) = rho(:,2) + rho(:,3);
+ % Arrays
+ %rho = rho+(1e-50) ;
+ rho_updnm1_3 = rho(:,2:3).^(-XC.third);
+ rhom1_3 = rho(:,1).^(-XC.third);
+ rhotot_inv = rhom1_3.^3;
+ zeta = (rho(:,2) - rho(:,3)) .* rhotot_inv; % Check whether it is rho_up-rho_dn or rho_dn-rho_up
+ zetp = 1 + zeta * XC.alpha_zeta;
+ zetm = 1 - zeta * XC.alpha_zeta;
+ zetpm1_3 = zetp.^(-XC.third);
+ zetmm1_3 = zetm.^(-XC.third);
+
+ rhotmo6 = sqrt(rhom1_3);
+ rhoto6 = rho(:,1) .* rhom1_3 .* rhom1_3 .* rhotmo6;
+
+ % -----------------------------------------------------------------------
+ % First take care of the exchange part of the functional
+
+ rhomot = rho_updnm1_3;
+ ex_lsd = -XC.threefourth_divpi * XC.sixpi2_1_3 * (rhomot .* rhomot .* rho(:,2:3));
+
+ v_xc = (4/3) * ex_lsd;
+ exc = sum(ex_lsd .* rho(:,2:3),2);
+ S.e_xc = exc .* rhotot_inv;
+
+ % -----------------------------------------------------------------------------
+ % Then takes care of the LSD correlation part of the functional
+
+ rs = XC.rsfac * rhom1_3;
+ sqr_rs = XC.sq_rsfac * rhotmo6;
+ rsm1_2 = XC.sq_rsfac_inv * rhoto6;
+
+ % Formulas A6-A8 of PW92LSD
+
+ ec0_q0 = -2.0 * XC.ec0_aa * (1.0 + XC.ec0_a1 * rs);
+ ec0_q1 = 2.0 * XC.ec0_aa *(XC.ec0_b1 * sqr_rs + XC.ec0_b2 * rs + XC.ec0_b3 * rs .* sqr_rs + XC.ec0_b4 * rs .* rs);
+ ec0_q1p = XC.ec0_aa * (XC.ec0_b1 * rsm1_2 + 2.0 * XC.ec0_b2 + 3.0 * XC.ec0_b3 * sqr_rs + 4.0 * XC.ec0_b4 * rs);
+ ec0_den = 1.0./(ec0_q1 .* ec0_q1 + ec0_q1);
+ ec0_log = -log(ec0_q1 .* ec0_q1 .* ec0_den);
+ ecrs0 = ec0_q0 .* ec0_log;
+ decrs0_drs = -2.0 * XC.ec0_aa * XC.ec0_a1 * ec0_log - ec0_q0 .* ec0_q1p .* ec0_den;
+
+ mac_q0 = -2.0 * XC.mac_aa * (1.0 + XC.mac_a1 * rs);
+ mac_q1 = 2.0 * XC.mac_aa * (XC.mac_b1 * sqr_rs + XC.mac_b2 * rs + XC.mac_b3 * rs .* sqr_rs + XC.mac_b4 * rs .* rs);
+ mac_q1p = XC.mac_aa * (XC.mac_b1 * rsm1_2 + 2 * XC.mac_b2 + 3 * XC.mac_b3 * sqr_rs + 4 * XC.mac_b4 * rs);
+ mac_den = 1.0./(mac_q1 .* mac_q1 + mac_q1);
+ mac_log = -log( mac_q1 .* mac_q1 .* mac_den );
+ macrs = mac_q0 .* mac_log;
+ dmacrs_drs = -2.0 * XC.mac_aa * XC.mac_a1 * mac_log - mac_q0 .* mac_q1p .* mac_den;
+
+ %zeta = (rho(:,2) - rho(:,3)) .* rhotot_inv;
+ ec1_q0 = -2.0 * XC.ec1_aa * (1.0 + XC.ec1_a1 * rs);
+ ec1_q1 = 2.0 * XC.ec1_aa * (XC.ec1_b1 * sqr_rs + XC.ec1_b2 * rs + XC.ec1_b3 * rs .* sqr_rs + XC.ec1_b4 * rs .* rs);
+ ec1_q1p = XC.ec1_aa * (XC.ec1_b1 * rsm1_2 + 2 * XC.ec1_b2 + 3 * XC.ec1_b3 * sqr_rs + 4 * XC.ec1_b4 * rs);
+ ec1_den = 1.0./(ec1_q1 .* ec1_q1 + ec1_q1);
+ ec1_log = -log( ec1_q1 .* ec1_q1 .* ec1_den );
+ ecrs1 = ec1_q0 .* ec1_log;
+ decrs1_drs = -2.0 * XC.ec1_aa * XC.ec1_a1 * ec1_log - ec1_q0 .* ec1_q1p .* ec1_den;
+
+ % XC.alpha_zeta is introduced in order to remove singularities for fully polarized systems.
+ zetp_1_3 = (1.0 + zeta * XC.alpha_zeta) .* (zetpm1_3.^2);
+ zetm_1_3 = (1.0 - zeta * XC.alpha_zeta) .* (zetmm1_3.^2);
+
+ f_zeta = ( (1.0 + zeta * XC.alpha_zeta2) .* zetp_1_3 + (1.0 - zeta * XC.alpha_zeta2) .* zetm_1_3 - 2.0 ) * XC.factf_zeta;
+ fp_zeta = ( zetp_1_3 - zetm_1_3 ) * XC.factfp_zeta;
+ zeta4 = zeta.^4;
+
+ gcrs = ecrs1 - ecrs0 + macrs * XC.fsec_inv;
+ ecrs = ecrs0 + f_zeta .* (zeta4 .* gcrs - macrs * XC.fsec_inv);
+ dgcrs_drs = decrs1_drs - decrs0_drs + dmacrs_drs * XC.fsec_inv;
+ decrs_drs = decrs0_drs + f_zeta .* (zeta4 .* dgcrs_drs - dmacrs_drs * XC.fsec_inv);
+ dfzeta4_dzeta = 4.0 * zeta.^3 .* f_zeta + fp_zeta .* zeta4;
+ decrs_dzeta = dfzeta4_dzeta .* gcrs - fp_zeta .* macrs * XC.fsec_inv;
+
+ S.e_xc = S.e_xc + ecrs;
+ vxcadd = ecrs - rs * XC.third .* decrs_drs - zeta .* decrs_dzeta;
+ v_xc(:,1) = v_xc(:,1) + vxcadd + decrs_dzeta;
+ v_xc(:,2) = v_xc(:,2) + vxcadd - decrs_dzeta;
+ S.Vxc = v_xc;
+
+ S.dvxcdgrho = zeros(S.N,3);
+end
+%--------------------------------------------------------------------------
+
+
+function [S] = LSDA_PZ(S,XC)
+ error('LSDA_PZ is not implemented!');
+end
+
+
+%--------------------------------------------------------------------------
+function [S] = GSGA_PBE(S,XC)
+ rho = S.rho;
+ rho(rho < S.xc_rhotol) = S.xc_rhotol;
+ rho(:,1) = rho(:,2) + rho(:,3);
+ drho_1 = S.grad_1 * rho;
+ drho_2 = S.grad_2 * rho;
+ drho_3 = S.grad_3 * rho;
+ if S.cell_typ ~= 2
+ sigma = drho_1.*drho_1 + drho_2.*drho_2 + drho_3.*drho_3;
+ else
+ sigma = (S.lapc_T(1,1)*drho_1.*drho_1 + S.lapc_T(2,2)*drho_2.*drho_2 + S.lapc_T(3,3)*drho_3.*drho_3 +...
+ S.lapc_T(1,2)*drho_1.*drho_2 + S.lapc_T(2,3)*drho_2.*drho_3 + S.lapc_T(1,3)*drho_3.*drho_1 ) ; % grad_rho . grad_rho
+ end
+
+
+ % Arrays
+ rho_updnm1_3 = rho(:,2:3).^(-XC.third);
+ rhom1_3 = rho(:,1).^(-XC.third);
+ rhotot_inv = rhom1_3.^3;
+ zeta = (rho(:,2) - rho(:,3)) .* rhotot_inv;
+ zetp = 1.0 + zeta * XC.alpha_zeta;
+ zetm = 1.0 - zeta * XC.alpha_zeta;
+ zetpm1_3 = zetp.^(-XC.third);
+ zetmm1_3 = zetm.^(-XC.third);
+
+ rhotmo6 = sqrt(rhom1_3);
+ rhoto6 = rho(:,1) .* rhom1_3 .* rhom1_3 .* rhotmo6;
+
+ % -----------------------------------------------------------------------
+ % First take care of the exchange part of the functional
+
+ rhomot = rho_updnm1_3;
+ ex_lsd = -XC.threefourth_divpi * XC.sixpi2_1_3 * (rhomot .* rhomot .* rho(:,2:3));
+
+ rho_inv = rhomot .* rhomot .* rhomot;
+ coeffss = (1.0/4.0) * XC.sixpi2m1_3 * XC.sixpi2m1_3 * (rho_inv .* rho_inv .* rhomot .* rhomot);
+ ss = sigma(:,2:3) .* coeffss;
+ divss = 1.0./(1.0 + XC.mu_divkappa * ss);
+ dfxdss = XC.mu * (divss .* divss);
+ fx = 1.0 + XC.kappa * (1.0 - divss);
+ ex_gga = ex_lsd .* fx;
+ dssdn = (-8.0/3.0) * (ss .* rho_inv);
+ dfxdn = dfxdss .* dssdn;
+ v_xc = ex_lsd .* ((4.0/3.0) * fx + rho(:,2:3) .* dfxdn);
+
+ dssdg = 2.0 * coeffss;
+ dfxdg = dfxdss .* dssdg;
+ dvxcdgrho1 = ex_lsd .* rho(:,2:3) .* dfxdg;
+ exc = sum(ex_gga .* rho(:,2:3),2);
+
+ S.e_xc = exc .* rhotot_inv;
+
+ % -----------------------------------------------------------------------------
+ % Then takes care of the LSD correlation part of the functional
+
+ rs = XC.rsfac * rhom1_3;
+ sqr_rs = XC.sq_rsfac * rhotmo6;
+ rsm1_2 = XC.sq_rsfac_inv * rhoto6;
+
+ % Formulas A6-A8 of PW92LSD
+
+ ec0_q0 = -2.0 * XC.ec0_aa * (1.0 + XC.ec0_a1 * rs);
+ ec0_q1 = 2.0 * XC.ec0_aa *(XC.ec0_b1 * sqr_rs + XC.ec0_b2 * rs + XC.ec0_b3 * rs .* sqr_rs + XC.ec0_b4 * rs .* rs);
+ ec0_q1p = XC.ec0_aa * (XC.ec0_b1 * rsm1_2 + 2.0 * XC.ec0_b2 + 3.0 * XC.ec0_b3 * sqr_rs + 4.0 * XC.ec0_b4 * rs);
+ ec0_den = 1.0./(ec0_q1 .* ec0_q1 + ec0_q1);
+ ec0_log = -log(ec0_q1 .* ec0_q1 .* ec0_den);
+ %ec0_log = log( 1.0 + 1.0./ec0_q1);
+ ecrs0 = ec0_q0 .* ec0_log;
+ decrs0_drs = -2.0 * XC.ec0_aa * XC.ec0_a1 * ec0_log - ec0_q0 .* ec0_q1p .* ec0_den;
+
+ mac_q0 = -2.0 * XC.mac_aa * (1.0 + XC.mac_a1 * rs);
+ mac_q1 = 2.0 * XC.mac_aa * (XC.mac_b1 * sqr_rs + XC.mac_b2 * rs + XC.mac_b3 * rs .* sqr_rs + XC.mac_b4 * rs .* rs);
+ mac_q1p = XC.mac_aa * (XC.mac_b1 * rsm1_2 + 2 * XC.mac_b2 + 3 * XC.mac_b3 * sqr_rs + 4 * XC.mac_b4 * rs);
+ mac_den = 1.0./(mac_q1 .* mac_q1 + mac_q1);
+ mac_log = -log( mac_q1 .* mac_q1 .* mac_den );
+ macrs = mac_q0 .* mac_log;
+ dmacrs_drs = -2.0 * XC.mac_aa * XC.mac_a1 * mac_log - mac_q0 .* mac_q1p .* mac_den;
+
+ %zeta = (rho(:,2) - rho(:,3)) .* rhotot_inv;
+ ec1_q0 = -2.0 * XC.ec1_aa * (1.0 + XC.ec1_a1 * rs);
+ ec1_q1 = 2.0 * XC.ec1_aa * (XC.ec1_b1 * sqr_rs + XC.ec1_b2 * rs + XC.ec1_b3 * rs .* sqr_rs + XC.ec1_b4 * rs .* rs);
+ ec1_q1p = XC.ec1_aa * (XC.ec1_b1 * rsm1_2 + 2 * XC.ec1_b2 + 3 * XC.ec1_b3 * sqr_rs + 4 * XC.ec1_b4 * rs);
+ ec1_den = 1.0./(ec1_q1 .* ec1_q1 + ec1_q1);
+ ec1_log = -log( ec1_q1 .* ec1_q1 .* ec1_den );
+ ecrs1 = ec1_q0 .* ec1_log;
+ decrs1_drs = -2.0 * XC.ec1_aa * XC.ec1_a1 * ec1_log - ec1_q0 .* ec1_q1p .* ec1_den;
+ % XC.alpha_zeta is introduced in order to remove singularities for fully polarized systems.
+ zetp_1_3 = (1.0 + zeta * XC.alpha_zeta) .* (zetpm1_3.^2);
+ zetm_1_3 = (1.0 - zeta * XC.alpha_zeta) .* (zetmm1_3.^2);
+
+ f_zeta = ( (1.0 + zeta * XC.alpha_zeta2) .* zetp_1_3 + (1.0 - zeta * XC.alpha_zeta2) .* zetm_1_3 - 2.0 ) * XC.factf_zeta;
+ fp_zeta = ( zetp_1_3 - zetm_1_3 ) * XC.factfp_zeta;
+ zeta4 = zeta.^4;
+
+ gcrs = ecrs1 - ecrs0 + macrs * XC.fsec_inv;
+ ecrs = ecrs0 + f_zeta .* (zeta4 .* gcrs - macrs * XC.fsec_inv);
+
+ %ecrs = ecrs0 + f_zeta .* (-macrs.* (1.0-zeta4) * XC.fsec_inv + (ecrs1-ecrs0) .* zeta4);
+ dgcrs_drs = decrs1_drs - decrs0_drs + dmacrs_drs * XC.fsec_inv;
+ decrs_drs = decrs0_drs + f_zeta .* (zeta4 .* dgcrs_drs - dmacrs_drs * XC.fsec_inv);
+ %decrs_drs = decrs0_drs + f_zeta .* (-dmacrs_drs .* (1.0 - zeta4) * XC.fsec_inv + (decrs1_drs-decrs0_drs) .* zeta4);
+ dfzeta4_dzeta = 4.0 * zeta.^3 .* f_zeta + fp_zeta .* zeta4;
+ decrs_dzeta = dfzeta4_dzeta .* gcrs - fp_zeta .* macrs * XC.fsec_inv;
+
+ % Add LSD correlation functional to GGA exchange functional
+ S.e_xc = S.e_xc + ecrs;
+ vxcadd = ecrs - rs * XC.third .* decrs_drs - zeta .* decrs_dzeta;
+ v_xc(:,1) = v_xc(:,1) + vxcadd + decrs_dzeta;
+ v_xc(:,2) = v_xc(:,2) + vxcadd - decrs_dzeta;
+ %[S.e_xc(1:20) v_xc(1:20,1) v_xc(1:20,2)]
+ % -----------------------------------------------------------------------------
+ % Eventually add the GGA correlation part of the PBE functional
+
+ % The definition of phi has been slightly changed, because
+ % the original PBE one gives divergent behaviour for fully polarized points
+
+ phi_zeta = ( zetpm1_3 .* (1.0 + zeta * XC.alpha_zeta) + zetmm1_3 .* (1.0 - zeta * XC.alpha_zeta) ) * 0.5;
+ phip_zeta = (zetpm1_3 - zetmm1_3) * XC.third * XC.alpha_zeta;
+ phi_zeta_inv = 1.0./phi_zeta;
+ phi_logder = phip_zeta .* phi_zeta_inv;
+ phi3_zeta = phi_zeta .* phi_zeta .* phi_zeta;
+ gamphi3inv = XC.gamma_inv * phi_zeta_inv .* phi_zeta_inv .* phi_zeta_inv;
+
+ % From ec to bb
+ bb = ecrs .* gamphi3inv;
+ dbb_drs = decrs_drs .* gamphi3inv;
+ dbb_dzeta = gamphi3inv .* (decrs_dzeta - 3.0 * ecrs .* phi_logder);
+
+ % From bb to cc
+ exp_pbe = exp(-bb);
+ cc = 1.0./(exp_pbe - 1.0);
+ dcc_dbb = cc .* cc .* exp_pbe;
+ dcc_drs = dcc_dbb .* dbb_drs;
+ dcc_dzeta = dcc_dbb .* dbb_dzeta;
+
+ % From cc to aa
+ coeff_aa = XC.beta * XC.gamma_inv * phi_zeta_inv .* phi_zeta_inv;
+ aa = coeff_aa .* cc;
+ daa_drs = coeff_aa .* dcc_drs;
+ daa_dzeta = -2.0 * aa .* phi_logder + coeff_aa .* dcc_dzeta;
+
+ % Introduce tt : do not assume that the spin-dependent gradients are collinear
+ grrho2 = sigma(:,1);
+ dtt_dg = 2.0 * rhotot_inv .* rhotot_inv .* rhom1_3 * XC.coeff_tt;
+ % Note that tt is (the t variable of PBE divided by phi) squared
+ tt = 0.5 * grrho2 .* dtt_dg;
+
+ % Get xx from aa and tt
+ xx = aa .* tt;
+ dxx_drs = daa_drs .* tt;
+ dxx_dzeta = daa_dzeta .* tt;
+ dxx_dtt = aa;
+
+ % From xx to pade
+ pade_den = 1.0./(1.0 + xx .* (1.0 + xx));
+ pade = (1.0 + xx) .* pade_den;
+ dpade_dxx = -xx .* (2.0 + xx) .* (pade_den.^2);
+ dpade_drs = dpade_dxx .* dxx_drs;
+ dpade_dtt = dpade_dxx .* dxx_dtt;
+ dpade_dzeta = dpade_dxx .* dxx_dzeta;
+
+ % From pade to qq
+ coeff_qq = tt .* phi_zeta_inv .* phi_zeta_inv;
+ qq = coeff_qq .* pade;
+ dqq_drs = coeff_qq .* dpade_drs;
+ dqq_dtt = pade .* phi_zeta_inv .* phi_zeta_inv + coeff_qq .* dpade_dtt;
+ dqq_dzeta = coeff_qq .* (dpade_dzeta - 2.0 * pade .* phi_logder);
+
+ % From qq to rr
+ arg_rr = 1.0 + XC.beta * XC.gamma_inv * qq;
+ div_rr = 1.0./arg_rr;
+ rr = XC.gamma * log(arg_rr);
+ drr_dqq = XC.beta * div_rr;
+ drr_drs = drr_dqq .* dqq_drs;
+ drr_dtt = drr_dqq .* dqq_dtt;
+ drr_dzeta = drr_dqq .* dqq_dzeta;
+
+ % From rr to hh
+ hh = phi3_zeta .* rr;
+ dhh_drs = phi3_zeta .* drr_drs;
+ dhh_dtt = phi3_zeta .* drr_dtt;
+ dhh_dzeta = phi3_zeta .* (drr_dzeta + 3.0 * rr .* phi_logder);
+ % The GGA correlation energy is added
+ S.e_xc = S.e_xc + hh;
+
+ % From hh to the derivative of the energy wrt the density
+ drhohh_drho = hh - XC.third * rs .* dhh_drs - zeta .* dhh_dzeta - (7.0/3.0) * tt .* dhh_dtt;
+ v_xc(:,1) = v_xc(:,1) + drhohh_drho + dhh_dzeta;
+ v_xc(:,2) = v_xc(:,2) + drhohh_drho - dhh_dzeta;
+
+
+ % From hh to the derivative of the energy wrt to the gradient of the
+ % density, divided by the gradient of the density
+ % (The v3.3 definition includes the division by the norm of the gradient)
+
+ S.dvxcdgrho(:,1) = rho(:,1) .* dtt_dg .* dhh_dtt;
+ S.dvxcdgrho(:,2) = dvxcdgrho1(:,1) ;
+ S.dvxcdgrho(:,3) = dvxcdgrho1(:,2) ;
+
+ if S.cell_typ ~= 2
+ Vxc_temp = S.grad_1 * (S.dvxcdgrho.*drho_1) + S.grad_2 * (S.dvxcdgrho.*drho_2) + S.grad_3 * (S.dvxcdgrho.*drho_3);
+ else
+ Vxc_temp = S.lapc_T(1,1)*S.grad_1*(S.dvxcdgrho.*drho_1) + S.lapc_T(2,2)*S.grad_2*(S.dvxcdgrho.*drho_2) + S.lapc_T(3,3)*S.grad_3*(S.dvxcdgrho.*drho_3) +...
+ S.lapc_T(2,1)*S.grad_1*(S.dvxcdgrho.*drho_2) + S.lapc_T(2,1)*S.grad_2*(S.dvxcdgrho.*drho_1) + S.lapc_T(3,2)*S.grad_2*(S.dvxcdgrho.*drho_3) +...
+ S.lapc_T(3,2)*S.grad_3*(S.dvxcdgrho.*drho_2) + S.lapc_T(3,1)*S.grad_1*(S.dvxcdgrho.*drho_3) + S.lapc_T(3,1)*S.grad_3*(S.dvxcdgrho.*drho_1) ;
+ end
+ S.Vxc(:,1) = v_xc(:,1) - Vxc_temp(:,2) - Vxc_temp(:,1);
+ S.Vxc(:,2) = v_xc(:,2) - Vxc_temp(:,3) - Vxc_temp(:,1);
+end
+
+
diff --git a/src/gradIndicesValues.m b/src/gradIndicesValues.m
new file mode 100644
index 00000000..9f506404
--- /dev/null
+++ b/src/gradIndicesValues.m
@@ -0,0 +1,135 @@
+function S = gradIndicesValues(S)
+if S.cell_typ < 3
+ Nx = S.Nx; Ny = S.Ny; Nz = S.Nz;
+ N = S.N;
+ n0 = S.FDn;
+ w1 = S.w1;
+ dx = S.dx;
+ dy = S.dy;
+ dz = S.dz;
+
+ % Initial number of non-zeros: including ghost nodes
+ nnz_count = 2*n0*N ;
+
+ % Row numbers and non-zero values
+ I = zeros(nnz_count,1) ;
+ V = zeros(nnz_count,1) ;
+
+ % Indices of the columns
+ II = zeros(nnz_count,1);
+ JJ = zeros(nnz_count,1) ;
+ KK = zeros(nnz_count,1) ;
+
+ % Gradient along x_direction
+ row_count = 1;
+ count = 1 ;
+ for kk=1:Nz
+ for jj=1:Ny
+ for ii=1:Nx
+ % off-diagonal elements
+ for p=1:n0
+ % ii+p
+ I(count) = row_count; II(count) = ii+p; JJ(count) = jj; KK(count) = kk;
+ V(count) = w1(p+1)/dx;
+ count = count + 1;
+ % ii-p
+ I(count) = row_count; II(count) = ii-p ; JJ(count) = jj; KK(count) = kk;
+ V(count) = -w1(p+1)/dx;
+ count = count + 1;
+ end
+ row_count = row_count+1;
+ end
+ end
+ end
+
+ if S.BCx == 1
+ % Removing outside domain entries (for periodic code this is unnecessary)
+ isIn = (II >= 1) & (II <= Nx);
+ I = I(isIn); II = II(isIn); JJ = JJ(isIn); KK = KK(isIn); V = V(isIn);
+ elseif S.BCx == 0
+ S.G_JOutl_1 = (II<1); S.G_JOutr_1 = (II>Nx); % Warning: Assumed influence of only neighboring cells
+ II = mod(II+(Nx-1),Nx)+1;
+ end
+
+ % Getting linear indices of the columns
+ S.G_J_1 = (KK-1)*Nx*Ny + (JJ-1)*Nx + II;
+ S.G_I_1 = I;
+ S.G_V_1 = V;
+
+ % Gradient along y_direction
+ row_count = 1;
+ count = 1 ;
+ for kk=1:Nz
+ for jj=1:Ny
+ for ii=1:Nx
+ % off-diagonal elements
+ for p=1:n0
+ % ii+p
+ I(count) = row_count; II(count) = ii; JJ(count) = jj+p; KK(count) = kk;
+ V(count) = w1(p+1)/dy;
+ count = count + 1;
+ % ii-p
+ I(count) = row_count; II(count) = ii ; JJ(count) = jj-p; KK(count) = kk;
+ V(count) = -w1(p+1)/dy;
+ count = count + 1;
+ end
+ row_count = row_count+1;
+ end
+ end
+ end
+
+ if S.BCy == 1
+ % Removing outside domain entries (for periodic code this is unnecessary)
+ isIn = (JJ >= 1) & (JJ <= Ny);
+ I = I(isIn); II = II(isIn); JJ = JJ(isIn); KK = KK(isIn); V = V(isIn);
+ elseif S.BCy == 0
+ S.G_JOutl_2 = (JJ<1); S.G_JOutr_2 = (JJ>Ny); % Warning: Assumed influence of only neighboring cells
+ JJ = mod(JJ+(Ny-1),Ny)+1;
+ end
+
+ % Getting linear indices of the columns
+ S.G_J_2 = (KK-1)*Nx*Ny + (JJ-1)*Nx + II;
+ S.G_I_2 = I;
+ S.G_V_2 = V;
+
+ % Gradient along z_direction
+ row_count = 1;
+ count = 1 ;
+ for kk=1:Nz
+ for jj=1:Ny
+ for ii=1:Nx
+ % off-diagonal elements
+ for p=1:n0
+ % ii+p
+ I(count) = row_count; II(count) = ii; JJ(count) = jj; KK(count) = kk+p;
+ V(count) = w1(p+1)/dz;
+ count = count + 1;
+ % ii-p
+ I(count) = row_count; II(count) = ii ; JJ(count) = jj; KK(count) = kk-p;
+ V(count) = -w1(p+1)/dz;
+ count = count + 1;
+ end
+ row_count = row_count+1;
+ end
+ end
+ end
+
+ if S.BCz == 1
+ % Removing outside domain entries (for periodic code this is unnecessary)
+ isIn = (KK >= 1) & (KK <= Nz);
+ I = I(isIn); II = II(isIn); JJ = JJ(isIn); KK = KK(isIn); V = V(isIn);
+ elseif S.BCz == 0
+ S.G_JOutl_3 = (KK<1); S.G_JOutr_3 = (KK>Nz); % Warning: Assumed influence of only neighboring cells
+ KK = mod(KK+(Nz-1),Nz)+1;
+ end
+
+ % Getting linear indices of the columns
+ S.G_J_3 = (KK-1)*Nx*Ny + (JJ-1)*Nx + II;
+ S.G_I_3 = I;
+ S.G_V_3 = V;
+
+else
+ S = gradIndicesValues_cychel(S);
+end
+
+
diff --git a/src/h_nonlocal_vector_mult.m b/src/h_nonlocal_vector_mult.m
new file mode 100644
index 00000000..3578f69e
--- /dev/null
+++ b/src/h_nonlocal_vector_mult.m
@@ -0,0 +1,43 @@
+function Hnlx = h_nonlocal_vector_mult(DL11,DL22,DL33,DG1,DG2,DG3,Veff,X,S,kptvec)
+% @brief Calculates Hamiltonian vector product, where Vnl is the nonlocal
+% pseudopotential to be determined using the info stored in S.
+%
+% @authors Abhiraj Sharma
+% Qimen Xu
+% Phanish Suryanarayana
+%
+% @param DLii Discrete laplacian component in 1D along ith direction
+% @param DGi Discrete gradient component in 1D along ith direction
+% @param Veff Effective potential N x 1 vector
+% @param X N x Ns matrix of eigenfunctions of Hamiltonian
+% @param kptvec k-point vector for the current Block diagonalized problem
+% @param Hnlx Hamiltonian times vector
+%
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+%========================================================================================
+
+% (-0.5*Lap + Veff) * X
+%Hnlx = -0.5*(lapVec(DL11,DL22,DL33,DG1,DG2,DG3,X,S)) + Veff * X;
+Hnlx = -0.5*(lapVec(DL11,DL22,DL33,DG1,DG2,DG3,X,S)) + bsxfun(@times,Veff,X);
+
+% Vnl * X
+if (kptvec(1) == 0 && kptvec(2) == 0 && kptvec(3) == 0)
+ fac = 1.0;
+else
+ fac = 1.0i;
+end
+
+for J = 1:S.n_atm
+ Chi_X_mult = zeros(S.Atom(J).angnum,size(X,2));
+ for img = 1:S.Atom(J).n_image_rc
+ % Chi_X_mult = Chi_X_mult + (S.Atom(J).rcImage(img).Chi_mat .* S.W(S.Atom(J).rcImage(img).rc_pos))' * X(S.Atom(J).rcImage(img).rc_pos,:)* ...
+ Chi_X_mult = Chi_X_mult + ( bsxfun(@times, S.Atom(J).rcImage(img).Chi_mat, S.W(S.Atom(J).rcImage(img).rc_pos)) )' * X(S.Atom(J).rcImage(img).rc_pos,:) * ...
+ (exp(dot(kptvec,(S.Atoms(J,:)-S.Atom(J).rcImage(img).coordinates)*fac)));
+ end
+ % Chi_X_mult = Chi_X_mult .* S.Atom(J).gamma_Jl;
+ Chi_X_mult = bsxfun(@times,Chi_X_mult, S.Atom(J).gamma_Jl);
+ for img = 1:S.Atom(J).n_image_rc
+ Chi = S.Atom(J).rcImage(img).Chi_mat * (exp(-dot(kptvec,(S.Atoms(J,:)-S.Atom(J).rcImage(img).coordinates)*fac)));
+ Hnlx(S.Atom(J).rcImage(img).rc_pos,:) = Hnlx(S.Atom(J).rcImage(img).rc_pos,:) + Chi * Chi_X_mult;
+ end
+end
diff --git a/src/initialization.m b/src/initialization.m
new file mode 100644
index 00000000..625973f5
--- /dev/null
+++ b/src/initialization.m
@@ -0,0 +1,1609 @@
+function S = initialization(filename)
+% @brief initialization(filename) reads data from input file 'filename'
+% and creates a struct 'S' to store all the data read and initialized.
+%
+% @param filename The input filename.
+%
+% @authors Qimen Xu
+% Abhiraj Sharma
+% Phanish Suryanarayana
+%
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+
+% Set up inpt defaults
+S = inpt_defaults();
+
+% Read .inpt file
+S = read_inpt(S, filename);
+
+% Read .ion file
+S = read_ion(S, filename);
+
+% Read pseudopotential files
+for ityp = 1:S.n_typ
+ if (S.Atm(ityp).psptyp == 0)
+ % WARNING: for TM format, lloc has to be set before reading
+ S = ReadPseudoPot(S.Atm(ityp).lloc,S.Atm(ityp).typ);
+ elseif (S.Atm(ityp).psptyp == 1)
+ S = readPseudopot(S, ityp, S.Atm(ityp).psdfname, S.Atm(ityp).typ);
+ else
+ error('Cannot recognize pseudopotential format!');
+ end
+end
+
+% Set up more defaults based on input files
+S = setup_defaults(S, filename);
+
+% Calculate rb
+S = Calculate_rb(S);
+
+% write initialized parameters into output file
+S = Write_output_init(S, filename);
+
+end
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+function S = Calculate_rb(S)
+% Starting and ending indices of b-region
+if (S.cell_typ == 1 || S.cell_typ == 2)
+ pos_atm_x = 0; % atom location in x-direction
+ pos_atm_y = 0; % atom location in y-direction
+ pos_atm_z = 0; % atom location in z-direction
+ rb_up_x = 12;
+ f_rby = @(y) y;
+ rb_up_y = f_rby(12);
+ rb_up_z = 12;
+
+elseif (S.cell_typ == 3 || S.cell_typ == 4 || S.cell_typ == 5)
+ pos_atm_x = S.xmax_at; % maximum R coordinate of any atom
+ pos_atm_y = 0; % atom location in theta-direction
+ pos_atm_z = 0; % atom location in z-direction
+ rb_up_x = S.xvac; % Radial direction vacuum
+ f_rby = @(y) acos(1 - y^2/(2*pos_atm_x^2));
+ rb_up_y = f_rby(12); % Theta direction
+ rb_up_z = 12; % z-direction
+
+end
+ii_s_temp = -ceil(rb_up_x/S.dx);
+ii_e_temp = ceil(rb_up_x/S.dx);
+jj_s_temp = -ceil(rb_up_y/S.dy);
+jj_e_temp = ceil(rb_up_y/S.dy);
+kk_s_temp = 0;
+kk_e_temp = ceil(rb_up_z/S.dz);
+xx_temp = pos_atm_x + (ii_s_temp-S.FDn:ii_e_temp+S.FDn)*S.dx;
+yy_temp = pos_atm_y + (jj_s_temp-S.FDn:jj_e_temp+S.FDn)*S.dy;
+zz_temp = pos_atm_z + (kk_s_temp-S.FDn:kk_e_temp+S.FDn)*S.dz;
+[XX_3D_temp,YY_3D_temp,ZZ_3D_temp] = ndgrid(xx_temp,yy_temp,zz_temp);
+Nx = (ii_e_temp-ii_s_temp)+1;
+Ny = (jj_e_temp-jj_s_temp)+1;
+Nz = (kk_e_temp-kk_s_temp)+1;
+% Find distances
+dd_temp = calculateDistance(XX_3D_temp,YY_3D_temp,ZZ_3D_temp,pos_atm_x,pos_atm_y,pos_atm_z,S);
+
+% Find integration weights
+W_temp = IntgWts(Nx,Ny,Nz,1,1,1,xx_temp(S.FDn+1),S); % 1 - dirichlet BC on the boundary nodes
+W_temp = reshape(W_temp,Nx,Ny,Nz);
+
+% Find VJ and bJ
+for ityp = 1:S.n_typ
+ V_PS_temp = zeros(size(dd_temp));
+ IsLargeThanRmax = dd_temp > S.Atm(ityp).r_grid_vloc(end);
+ V_PS_temp(IsLargeThanRmax) = -S.Atm(ityp).Z;
+ V_PS_temp(~IsLargeThanRmax) = interp1(S.Atm(ityp).r_grid_vloc, ...
+ S.Atm(ityp).r_grid_vloc.*S.Atm(ityp).Vloc, dd_temp(~IsLargeThanRmax), 'spline');
+
+ V_PS_temp = V_PS_temp./dd_temp;
+ V_PS_temp(dd_temp S.pseudocharge_tol && count <= 100 && rb_x <= rb_up_x && rb_y <= rb_up_y && rb_z <= rb_up_z )
+ rb_x = rb_x + S.dx;
+ rb_z = rb_z + S.dz;
+ rb_y = f_rby(max(rb_x,rb_z));
+ ii_rb = -1*ii_s_temp+S.FDn-floor(rb_x/S.dx)+1:-1*ii_s_temp+S.FDn+floor(rb_x/S.dx)+1;
+ jj_rb = -1*jj_s_temp+S.FDn-floor(rb_y/S.dy)+1:-1*jj_s_temp+S.FDn+floor(rb_y/S.dy)+1;
+ kk_rb = S.FDn+1:S.FDn+floor(rb_z/S.dz)+1;
+ err_rb = abs(sum(sum(sum(W_temp(ii_rb-S.FDn,jj_rb-S.FDn,kk_rb-S.FDn).*b_temp(ii_rb,jj_rb,kk_rb))))*2 + S.Atm(ityp).Z);
+ fprintf(' rb = {%.3f %.3f %.3f}, int_b = %.15f, err_rb = %.3e\n',rb_x,rb_y,rb_z,2*sum(sum(sum(W_temp(ii_rb-S.FDn,jj_rb-S.FDn,kk_rb-S.FDn).*b_temp(ii_rb,jj_rb,kk_rb)))),err_rb);
+ count = count + 1;
+ end
+
+ assert(rb_x<=rb_up_x && rb_y<=rb_up_y && rb_z<=rb_up_z,'Need to increase upper bound for rb!');
+ S.Atm(ityp).rb_x = rb_x;
+ S.Atm(ityp).rb_y = rb_y;
+ S.Atm(ityp).rb_z = rb_z;
+ % S.Atm(ityp).rb_x = ceil(rb_x/S.dx-1e-12)*S.dx; % + S.dx;
+ % S.Atm(ityp).rb_y = ceil(rb_y/S.dy-1e-12)*S.dy; % + S.dy;
+ % S.Atm(ityp).rb_z = ceil(rb_z/S.dz-1e-12)*S.dz; % + S.dz;
+ fprintf(' rb = {%.3f %.3f %.3f}\n',S.Atm(ityp).rb_x,S.Atm(ityp).rb_y,S.Atm(ityp).rb_z);
+end
+
+end
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+function S = setup_defaults(S, filename)
+% After reading the input files, set up remaining default values
+S.temp_tol = 1e-12;
+
+% Density tolerance for exchange-correlation
+S.xc_rhotol = 1e-14;
+
+% exchange correlation
+if strcmp(S.XC, 'LDA_PW') || strcmp(S.XC, 'LDA')
+ S.xc = 0;
+elseif strcmp(S.XC, 'LDA_PZ')
+ S.xc = 1; % TODO: Implement PZ LDA!
+elseif strcmp(S.XC, 'GGA_PBE') || strcmp(S.XC, 'GGA')
+ S.xc = 2;
+end
+
+% calculate Nelectron
+S.Nelectron = 0;
+for ityp = 1:S.n_typ
+ S.Nelectron = S.Nelectron + S.Atm(ityp).Z * S.Atm(ityp).n_atm_typ;
+end
+
+% Save the initial positions, since later S.Atoms will be changed
+S.Atoms_init = S.Atoms;
+
+% Cychel parameters
+if (S.cell_typ == 3 || S.cell_typ == 4 || S.cell_typ == 5)
+ % Add the folder containing all the Cychel files to the path
+ addpath('../Cychel');
+ count_prev = 0;
+ count = 0;
+ for ityp = 1:S.n_typ
+ if(S.IsFrac(ityp) == 0)
+ S.Atm(ityp).coords = coordinateTransformation_cychel(S,S.Atm(ityp).coords,'cart2noncart_dis');
+ count = count + S.Atm(ityp).n_atm_typ;
+ S.Atoms(count_prev+1:count,:) = S.Atm(ityp).coords;
+ count_prev = count;
+ else
+ count = count + S.Atm(ityp).n_atm_typ;
+ count_prev = count;
+ end
+ end
+
+ % Find minimum and maximum radial coordinate among all atoms
+ S.xmin_at = min(S.Atoms(:,1));
+ S.xmax_at = max(S.Atoms(:,1));
+
+ % Find vacuum
+ S.xvac = (S.L1 - (S.xmax_at - S.xmin_at))/2;
+
+ % Find inner and outer radius
+ S.xin = S.xmin_at - S.xvac;
+ S.xout = S.xmax_at + S.xvac;
+ fprintf('Cychel radial direction parameters: \n');
+ fprintf('Vacuum %f, Inner radius %f, Outer radius %f\n',S.xvac,S.xin,S.xout);
+
+ % Rotational matrix
+ theta1 = S.L2;
+ S.RotM1 = [cos(theta1),-sin(theta1),0; sin(theta1),cos(theta1),0; 0 0 1];
+ theta2 = S.alph*S.L3;
+ S.RotM2 = [cos(theta2),-sin(theta2),0; sin(theta2),cos(theta2),0; 0 0 1];
+end
+
+% Check the cell typ (orthogonal or non-orthogonal)
+if(abs(dot(S.lat_vec(1,:),S.lat_vec(2,:))) > S.temp_tol ||...
+ abs(dot(S.lat_vec(2,:),S.lat_vec(3,:))) > S.temp_tol ||...
+ abs(dot(S.lat_vec(3,:),S.lat_vec(1,:))) > S.temp_tol)
+ S.cell_typ = 2;
+end
+
+S.lat_uvec(1,:) = S.lat_vec(1,:)/norm(S.lat_vec(1,:));
+S.lat_uvec(2,:) = S.lat_vec(2,:)/norm(S.lat_vec(2,:));
+S.lat_uvec(3,:) = S.lat_vec(3,:)/norm(S.lat_vec(3,:));
+
+% Set up transformation matrices for non orthogonal cells
+if S.cell_typ == 2
+ % Jacobian
+ S.Jacb = det(S.lat_uvec');
+ assert(S.Jacb > 0.0,'Volume is negative!');
+
+ % metric_T, Gradient and laplacian transformation matrices
+ S.metric_T = S.lat_uvec * S.lat_uvec' ;
+ S.metric_T(1,2) = 2*S.metric_T(1,2);
+ S.metric_T(2,3) = 2*S.metric_T(2,3);
+ S.metric_T(1,3) = 2*S.metric_T(1,3);
+ S.grad_T = inv(S.lat_uvec') ;
+ S.lapc_T = S.grad_T * S.grad_T' ;
+ S.lapc_T(1,2) = 2*S.lapc_T(1,2);
+ S.lapc_T(2,3) = 2*S.lapc_T(2,3);
+ S.lapc_T(1,3) = 2*S.lapc_T(1,3);
+
+ count_prev = 0;
+ count = 0;
+ for ityp = 1:S.n_typ
+ if(S.IsFrac(ityp) == 0)
+ S.Atm(ityp).coords = transpose(S.grad_T * transpose(S.Atm(ityp).coords));
+ count = count + S.Atm(ityp).n_atm_typ;
+ S.Atoms(count_prev+1:count,:) = S.Atm(ityp).coords;
+ count_prev = count;
+ else
+ count = count + S.Atm(ityp).n_atm_typ;
+ count_prev = count;
+ end
+ end
+end
+
+% Set up number of spin
+if S.spin_typ == 0
+ S.nspin = 1;
+else
+ S.nspin = 2;
+end
+
+% Provide default spin if not provided
+if S.nspin == 2
+ rng('default');
+ for ityp = 1:S.n_typ
+ if(S.IsSpin(ityp) == 0)
+ S.Atm(ityp).mag = -S.Atm(ityp).Z + 2 * S.Atm(ityp).Z * rand(S.Atm(ityp).n_atm_typ,1);
+ end
+ end
+end
+
+% set up default smearing if not provided
+if S.bet < 0
+ if S.elec_T_type == 0 % fermi-dirac
+ % The electronic temperature corresponding to 0.1 eV is 1160.452211 K
+ S.bet = 27.21138602 / 0.1; % smearing = 0.1 eV = 0.00367493225 Ha, Beta := 1 / smearing
+ elseif S.elec_T_type == 1 % gaussian smearing
+ % The electronic temperature corresponding to 0.2 eV is 2320.904422 K
+ S.bet = 27.21138602 / 0.2; % smearing = 0.2 eV = 0.00734986450 Ha, Beta := 1 / smearing
+ end
+ S.Temp = 1./(3.166810501187400e-06 * S.bet);
+end
+
+% BCx = 0 -> periodic, BCx = 1 -> dirichlet
+if S.BC >= 0 % if user provides BOUNDARY_CONDITION: 1-4
+ if(S.BC == 1)
+ S.BCx = 1; S.BCy = 1; S.BCz = 1;
+ elseif(S.BC == 2)
+ S.BCx = 0; S.BCy = 0; S.BCz = 0;
+ elseif(S.BC == 3)
+ S.BCx = 0; S.BCy = 0; S.BCz = 1;
+ elseif(S.BC == 4)
+ %S.BCx = 0; S.BCy = 1; S.BCz = 1;
+ S.BCx = 1; S.BCy = 1; S.BCz = 0;
+ else
+ error('Boundary condition should be one among {1,2,3,4}');
+ end
+elseif S.BCx >= 0 && S.BCy >= 0 && S.BCz >= 0 % if user provides BCx,BCy,BCz
+ n_Dirichlet = S.BCx + S.BCy + S.BCz;
+ if n_Dirichlet == 0
+ S.BC = 2; % Periodic BC in all 3D
+ elseif n_Dirichlet == 1
+ S.BC = 3; % Surface, Periodic in 2D, Dirichlet in 1D
+ elseif n_Dirichlet == 2
+ S.BC = 4; % Wire, Periodic in 1D, Dirichlet in 2D
+ elseif n_Dirichlet == 3
+ S.BC = 1; % Dirichlet in all 3D
+ end
+else
+ % if user does not provide any BC, set default to periodic in 3D
+ S.BC = 2;
+ S.BCx = 0; S.BCy = 0; S.BCz = 0;
+end
+
+L1 = S.L1; L2 = S.L2; L3 = S.L3;
+
+% S.Nx, S.Ny, S.Nz is number of intervals now
+if S.Nx > 0 && S.Ny > 0 && S.Nz > 0
+ S.dx = S.L1 / S.Nx;
+ S.dy = S.L2 / S.Ny;
+ S.dz = S.L3 / S.Nz;
+elseif S.ecut > 0
+ S.mesh_spacing = Ecut2h(S.ecut, S.FDn);
+ S.Nx = max(round(S.L1/S.mesh_spacing),1);
+ S.Ny = max(round(S.L2/S.mesh_spacing),1);
+ S.Nz = max(round(S.L3/S.mesh_spacing),1);
+ S.dx = S.L1 / S.Nx;
+ S.dy = S.L2 / S.Ny;
+ S.dz = S.L3 / S.Nz;
+elseif S.mesh_spacing > 0
+ S.Nx = max(round(S.L1/S.mesh_spacing),1);
+ S.Ny = max(round(S.L2/S.mesh_spacing),1);
+ S.Nz = max(round(S.L3/S.mesh_spacing),1);
+ S.dx = S.L1 / S.Nx;
+ S.dy = S.L2 / S.Ny;
+ S.dz = S.L3 / S.Nz;
+end
+
+dx = S.dx; dy = S.dy; dz = S.dz;
+S.dV = S.dx * S.dy * S.dz * S.Jacb;
+
+% Finite-difference discretization
+S.Nx = S.Nx + S.BCx;
+S.Ny = S.Ny + S.BCy;
+S.Nz = S.Nz + S.BCz;
+Nx = S.Nx; Ny = S.Ny; Nz = S.Nz;
+S.N = S.Nx * S.Ny * S.Nz;
+
+% map atom positions back to domain for periodic domain
+% in x direction
+isAtomOutx = sum(S.Atoms(:,1) < 0 | S.Atoms(:,1) >= S.L1) > 0;
+if (isAtomOutx)
+ if S.BCx == 0
+ S.Atoms(:,1) = mod(S.Atoms(:,1), S.L1);
+ for ityp = 1:S.n_typ
+ S.Atm(ityp).coords(:,1) = mod(S.Atm(ityp).coords(:,1),S.L1);
+ end
+ fprintf(' Warning: mapped atom position back to domain in x dir!\n');
+ else
+ error('Atom out of domain in x dir!');
+ end
+end
+% in y direction
+isAtomOuty = sum(S.Atoms(:,2) < 0 | S.Atoms(:,2) >= S.L2) > 0;
+if (isAtomOuty)
+ if S.BCy == 0
+ S.Atoms(:,2) = mod(S.Atoms(:,2), S.L2);
+ for ityp = 1:S.n_typ
+ S.Atm(ityp).coords(:,2) = mod(S.Atm(ityp).coords(:,2),S.L2);
+ end
+ fprintf(' Warning: mapped atom position back to domain in y dir!\n');
+ else
+ error('Atom out of domain in y dir!');
+ end
+end
+% in z direction
+isAtomOutz = sum(S.Atoms(:,3) < 0 | S.Atoms(:,3) >= S.L3) > 0;
+if (isAtomOutz)
+ if S.BCz == 0
+ S.Atoms(:,3) = mod(S.Atoms(:,3), S.L3);
+ for ityp = 1:S.n_typ
+ S.Atm(ityp).coords(:,3) = mod(S.Atm(ityp).coords(:,3),S.L3);
+ end
+ fprintf(' Warning: mapped atom position back to domain in z dir!\n');
+ else
+ error('Atom out of domain in z dir!');
+ end
+end
+
+if (isAtomOutx || isAtomOuty || isAtomOutz)
+ fprintf(' After mapping\n COORD:\n');
+ disp(S.Atoms);
+end
+
+% Finite difference weights of the second derivative
+FDn = S.FDn;
+w2 = zeros(1,FDn+1) ;
+for k=1:FDn
+ w2(k+1) = (2*(-1)^(k+1))*(factorial(FDn)^2)/...
+ (k*k*factorial(FDn-k)*factorial(FDn+k));
+ w2(1) = w2(1)-2*(1/(k*k));
+end
+S.w2 = w2;
+
+% Finite difference weights of the first derivative
+w1 = zeros(1,FDn) ;
+for k=1:FDn
+ w1(k+1) = ((-1)^(k+1))*(factorial(FDn)^2)/...
+ (k*factorial(FDn-k)*factorial(FDn+k));
+end
+S.w1 = w1;
+
+% Weights for spatial integration over domain
+% S.W = IntgWts(S.Nx,S.Ny,S.Nz,S.BCx,S.BCy,S.BCz,S.xin,S);
+if S.cell_typ == 1 || S.cell_typ == 2
+ S.W = ones(S.N,1) * (S.dx*S.dy*S.dz*S.Jacb);
+else
+ S.W = IntgWts(S.Nx,S.Ny,S.Nz,S.BCx,S.BCy,S.BCz,S.xin,S);
+end
+
+% assert(abs(sum(S.W)-pi*(S.xout*S.xout-S.xin*S.xin)*S.L3/25)<1e-6, ...
+% 'Incorrect weights for spatial integration!');
+
+% Brillouin-Zone Sampling
+S = Generate_kpts(S);
+
+% Create spherical harmonics for poisson solve for isolated clusters
+if (S.BCx == 1 && S.BCy == 1 && S.BCz == 1)
+ % Calculate Spherical Harmonics with origin shifted to the center of the domain
+ xx_aug = (0-FDn:Nx+FDn-1)*dx;% - L1/2;
+ yy_aug = (0-FDn:Ny+FDn-1)*dy;% - L2/2;
+ zz_aug = (0-FDn:Nz+FDn-1)*dz;% - L3/2;
+ [XX_AUG_3D,YY_AUG_3D,ZZ_AUG_3D] = ndgrid(xx_aug,yy_aug,zz_aug);
+ % Find distances
+ RR_AUG_3D = calculateDistance(XX_AUG_3D,YY_AUG_3D,ZZ_AUG_3D,L1/2,L2/2,L3/2,S);
+
+ XX_AUG = reshape(XX_AUG_3D,[],1);
+ YY_AUG = reshape(YY_AUG_3D,[],1);
+ ZZ_AUG = reshape(ZZ_AUG_3D,[],1);
+ RR_AUG = reshape(RR_AUG_3D,[],1);
+
+ S.RR_AUG = RR_AUG;
+ S.RR_AUG_3D = RR_AUG_3D;
+
+ in_flag = ones(Nx+2*FDn,Ny+2*FDn,Nz+2*FDn);
+ in_flag(1:FDn,:,:) = 0;
+ in_flag(:,1:FDn,:) = 0;
+ in_flag(:,:,1:FDn) = 0;
+ in_flag(FDn+Nx+1:end,:,:) = 0;
+ in_flag(:,FDn+Ny+1:end,:) = 0;
+ in_flag(:,:,FDn+Nz+1:end) = 0;
+ isIn = (in_flag~=0);
+
+ S.isIn = isIn;
+ S.RR = RR_AUG(isIn);
+
+ pos_node_cart = coordinateTransformation(S,[XX_AUG,YY_AUG,ZZ_AUG],'noncart2cart_dis');
+ pos_atm_cart = coordinateTransformation(S,[L1/2,L2/2,L3/2],'noncart2cart_dis');
+ XX_AUG = bsxfun(@minus,pos_node_cart(:,1),pos_atm_cart(:,1));
+ YY_AUG = bsxfun(@minus,pos_node_cart(:,2),pos_atm_cart(:,2));
+ ZZ_AUG = bsxfun(@minus,pos_node_cart(:,3),pos_atm_cart(:,3));
+
+ l_cut = 6;
+ SH = repmat(struct([]),l_cut+1,1);
+ for l = 0:l_cut
+ for m = -l:l
+ SH(l+1).Ylm_AUG(:,m+l+1) = sphericalHarmonics(XX_AUG,YY_AUG,ZZ_AUG,l,m,'real');
+ Ylm_AUG_TEMP = SH(l+1).Ylm_AUG(:,m+l+1);
+ SH(l+1).Ylm(:,m+l+1) = Ylm_AUG_TEMP(isIn);
+ % SH(l+1).Ylm(:,m+l+1) = sphericalHarmonics(XX,YY,ZZ,l,m,'real');
+ end
+ end
+
+ S.l_cut = l_cut;
+ S.SH = SH;
+end
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% set default values to the same default as SPARC %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% first find effective mesh size
+if S.cell_typ < 3
+ dx2_inv = 1/(S.dx * S.dx);
+ dy2_inv = 1/(S.dy * S.dy);
+ dz2_inv = 1/(S.dz * S.dz);
+ h_eff = sqrt(3.0 / (dx2_inv + dy2_inv + dz2_inv));
+elseif (S.cell_typ == 3 || S.cell_typ == 4 || S.cell_typ == 5)
+ dx2_inv = 1/(S.dx * S.dx);
+ dy2_inv = 1/(((S.xin+S.xout)/2)*S.dy)^2;
+ dz2_inv = 1/(S.dz * S.dz);
+ h_eff = sqrt(3.0 / (dx2_inv + dy2_inv + dz2_inv));
+end
+% find npl
+if S.npl < 0
+ fprintf('## Chebyshev polynomial degree not provided, finding npl ...\n');
+ S.npl = Mesh2ChebDegree(h_eff);
+ fprintf('## Based on the mesh size, npl is set to: %d\n',S.npl);
+end
+
+% Nev
+if S.Nev < 0
+ fprintf('## Number of states not provided, finding Nev ...\n');
+ S.Nev = floor(S.Nelectron / 2) * 1.2 + 5;
+ S.Nev = round(S.Nev);
+ fprintf('## Based on the number of electrons, Nev is set to: %d\n',S.Nev);
+end
+
+% SCF_tol
+if S.SCF_tol < 0
+ log10_neatom = log10(S.Nelectron / S.n_atm);
+ target_force_accuracy = -1.0;
+ target_energy_accuracy = -1.0;
+ if S.accuracy_level >= 0
+ target_force_accuracy = 10^(S.accuracy_level + 1);
+ elseif S.target_force_accuracy > 0
+ target_force_accuracy = S.target_force_accuracy;
+ elseif S.target_energy_accuracy > 0
+ target_energy_accuracy = S.target_energy_accuracy;
+ end
+
+ % if none of the accuracy levels are specified, set force_accuracy to
+ % 1e-3
+ if target_force_accuracy < 0 && target_energy_accuracy < 0
+ target_force_accuracy = 1e-3;
+ end
+
+ % choose SCF tol based on the desired accuracy
+ if target_force_accuracy > 0
+ a = 1.03;
+ b = -0.33145 + 1.1761 * log10_neatom;
+ S.SCF_tol = 10^((log10(target_force_accuracy) - b)/a);
+ elseif target_energy_accuracy > 0
+ a = 2.02;
+ b = -0.25440 + 1.0000 * log10_neatom;
+ S.SCF_tol = 10^((log10(target_energy_accuracy) - b)/a);
+ end
+ fprintf('## Based on the desired accuracy, SCF_tol is set to: %.3e\n',S.SCF_tol);
+end
+
+% poisson_tol
+if S.poisson_tol < 0
+ fprintf('## Poisson tolerance not provided, choosing poisson_tol ...\n')
+ S.poisson_tol = S.SCF_tol * 0.01;
+ fprintf('## poisson_tol is set to: %.3e\n',S.poisson_tol);
+end
+
+% pseudocharge_tol
+if S.pseudocharge_tol < 0
+ fprintf('## Pseudocharge tolerance not provided, choosing pseudocharge_tol ...\n')
+ S.pseudocharge_tol = S.SCF_tol * 0.01;
+ fprintf('## pseudocharge_tol is set to: %.3e\n',S.pseudocharge_tol);
+end
+
+% % kerker_tol
+% if S.kerker_tol < 0
+% S.kerker_tol = h_eff * h_eff * 0.001;
+% end
+
+% precond_tol
+if S.precond_tol < 0
+ S.precond_tol = h_eff * h_eff * 0.001;
+end
+
+% mixing parameter for simple mixing
+if S.MixingParameterSimple < 0
+ S.MixingParameterSimple = S.MixingParameter;
+end
+
+% Preconditioner for SCF convergence
+if S.MixingVariable < 0
+ % L_diag = sqrt(S.L1 * S.L1 + S.L2 * S.L2 + S.L3 * S.L3);
+ % if (L_diag <= 20 || (S.BC ~= 2 && S.BC ~= 0))
+ % S.MixingVariable = 1;
+ % else
+ % S.MixingVariable = 0;
+ % end
+ S.MixingVariable = 1; % set default mixing var to potential
+end
+
+if S.MixingPrecond < 0
+ % if S.MixingVariable == 0
+ % S.MixingPrecond = 1;
+ % else
+ % S.MixingPrecond = 0;
+ % end
+ S.MixingPrecond = 0; % set default precond to none
+end
+
+% set up coefficients
+if S.MixingPrecond == 1 % kerker
+ S.precondcoeff_a = 1.0;
+ S.precondcoeff_lambda_TF = S.precond_kTF * S.precond_kTF;
+ S.precondcoeff_k = 0;
+elseif S.MixingPrecond == 2 % resta
+ % put these in input options
+ %max_q = sqrt(3) * 2*pi/0.08; % Maximum q in the domain of fit
+ max_q = 100;
+ % mpower = 2; % The power used in the fit
+ % a0 = 0.25; % parameters of the preconditioner
+ % ktf = 1; % parameters of the preconditioner
+ % q0 = 1.36; % parameters of the preconditioner
+ % e0 = 5.7; % parameters of the preconditioner
+ % Rs = 2.76; % parameters of the preconditioner
+ mpower = S.precond_fitpow;
+ ktf = S.precond_kTF;
+ a0 = S.precond_thresh;
+ q0 = S.precond_resta_q0;
+ Rs = S.precond_resta_Rs;
+ e0 = sinh(q0*Rs)/(q0*Rs); % parameters of the preconditioner
+ %[a_temp, lambda_TF_temp, const_temp] = fit_mixing_preconditioner(...
+ % 100,1.36,5.7,2.76,0.25,1,2,2);
+ [a_temp, lambda_TF_temp, const_temp] = fit_mixing_preconditioner(...
+ max_q, q0, e0, Rs, a0, ktf, mpower, 2);
+ % store coeffs in S
+ S.precondcoeff_a = a_temp;
+ S.precondcoeff_lambda_TF = lambda_TF_temp;
+ S.precondcoeff_k = const_temp;
+elseif S.MixingPrecond == 3 % truncated kerker
+ % put these in input options
+ %max_q = sqrt(3) * 2*pi/0.08; % Maximum q in the domain of fit
+ max_q = 100;
+ %mpower = 2; % The power used in the fit
+ %a0 = 0.25; % parameters of the preconditioner
+ %ktf = 1; % parameters of the preconditioner
+ %q0 = 1.36; % parameters of the preconditioner
+ %Rs = 2.76; % parameters of the preconditioner
+ mpower = S.precond_fitpow;
+ ktf = S.precond_kTF;
+ a0 = S.precond_thresh;
+ q0 = S.precond_resta_q0;
+ Rs = S.precond_resta_Rs;
+ e0 = sinh(q0*Rs)/(q0*Rs); % parameters of the preconditioner
+ [a_temp, lambda_TF_temp, const_temp] = fit_mixing_preconditioner(...
+ max_q, q0, e0, Rs, a0, ktf, mpower, 1);
+ S.precondcoeff_a = a_temp;
+ S.precondcoeff_lambda_TF = lambda_TF_temp;
+ S.precondcoeff_k = const_temp;
+end
+
+if S.nspin == 1
+ S.occfac = 2;
+else
+ S.occfac = 1;
+end
+
+% Name of the relax file
+% if S.RelaxFlag == 1
+% S.relaxfname = strcat(filename,'.geopt');
+% i = 1;
+% while exist(S.relaxfname,'file')
+% S.relaxfname = sprintf('%s.geopt_%d',filename,i);
+% i = i + 1;
+% end
+%
+% % if there are already 100 files, then start using .geopt only
+% OUT_MAX = 100;
+% if i > OUT_MAX
+% S.relaxfname = strcat(filename,'.geopt');
+% end
+% end
+
+% Name of the MD file
+% if S.MDFlag == 1
+% S.mdfname = strcat(filename,'.aimd');
+% i = 1;
+% while exist(S.mdfname,'file')
+% S.mdfname = sprintf('%s.aimd_%d',filename,i);
+% i = i + 1;
+% end
+%
+% % if there are already 100 files, then start using .geopt only
+% OUT_MAX = 100;
+% if i > OUT_MAX
+% S.mdfname = strcat(filename,'.aimd');
+% end
+% end
+
+
+if (S.RelaxFlag || S.MDFlag)
+ % Name of the restart file
+ S.restartfname = strcat(filename,'.restart');
+ % charge difference histories for charge extrapolation
+ S.delta_rho_tm2 = zeros(S.N,1);
+ S.delta_rho_tm1 = zeros(S.N,1);
+ S.delta_rho_t = zeros(S.N,1);
+ S.delta_rho_in_tp1 = zeros(S.N,1);
+ % S.dV_tm2 = S.dV;
+ % S.dV_tm1 = S.dV;
+ % S.dV_t = S.dV;
+ % S.dV_tp1 = S.dV;
+ S.atom_pos_tm2 = S.Atoms_init;
+ S.atom_pos_tm1 = S.Atoms_init;
+ S.atom_pos_t = S.Atoms_init;
+ S.atom_pos_tp1 = S.Atoms_init;
+ S.Atoms_old = S.Atoms_init;
+end
+
+S.Relax_iter = 1;
+S.ForceCount = 1;
+S.amu2au = 1822.888485332371; % 1 au = 9.10938356e-31 Kg; 1 amu = 1.660539040e-27 Kg;
+S.fs2atu = 41.34137333649300; %1atu = 2.418884326509e-17 s;
+
+fprintf(' Creating differentiation matrices ...\n');
+t1 = tic;
+
+% Calculate discrete laplacian (1D) and discrete gradient indices' values
+S = lapIndicesValues_1d(S);
+S = gradIndicesValues(S);
+
+% Calculate discrete laplacian
+[DL11,DL22,DL33,DG1,DG2,DG3] = blochLaplacian_1d(S,[0 0 0]);
+if S.cell_typ < 3
+ S.Lap_std = S.lapc_T(1,1) * kron(speye(S.Nz),kron(speye(S.Ny),DL11)) + S.lapc_T(2,2) * kron(speye(S.Nz),kron(DL22,speye(S.Nx))) + ...
+ S.lapc_T(3,3) * kron(DL33,kron(speye(S.Ny),speye(S.Nx))) ;
+ if (S.cell_typ == 2)
+ MDL = S.lapc_T(1,2) * kron(speye(S.Nz),kron(DG2,DG1)) + S.lapc_T(2,3) * kron(DG3,kron(DG2,speye(S.Nx))) + ...
+ S.lapc_T(1,3) * kron(DG3,kron(speye(S.Ny),DG1)) ;
+ S.Lap_std = S.Lap_std + MDL;
+ end
+elseif (S.cell_typ == 3 || S.cell_typ == 4 || S.cell_typ == 5)
+ S.Lap_std = kron(speye(S.Nz),kron(speye(S.Ny),(DL11+DG1))) + kron(DL33,kron(speye(S.Ny),speye(S.Nx))) + ...
+ kron(speye(S.Nz),kron(DL22,S.R2inv));
+ if (S.cell_typ == 4 || S.cell_typ == 5)
+ MDL = kron(speye(S.Nz),kron(DL22,speye(S.Nx))) + kron(DG3,kron(DG2,speye(S.Nx)));
+ S.Lap_std = S.Lap_std + MDL;
+ end
+end
+
+% Calculate discrete gradient
+S.grad_1 = blochGradient(S,[0 0 0],1);
+S.grad_2 = blochGradient(S,[0 0 0],2);
+S.grad_3 = blochGradient(S,[0 0 0],3);
+
+% Calculate preconditioners for negative discrete laplacian
+[S.LapPreconL, S.LapPreconU] = ilu(S.Lap_std,struct('droptol',1e-5));
+
+fprintf(' Done. (%.3f sec)\n', toc(t1));
+
+% Estimate memory usage
+S.memory_usage = estimate_memory(S);
+
+end
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+function memory_usage = estimate_memory(S)
+% estimate the memory required for the simulation
+size_double = 8;
+
+fd_order = S.FDn * 2;
+
+N_ex = (S.Nx+fd_order) * (S.Ny+fd_order) * (S.Nz+fd_order);
+
+% orbitals (dominant)
+ncpy_orbitals = 4; % 4 copies required during chebyshev filtering
+if S.nspin ~= 1, ncpy_orbitals = ncpy_orbitals * 2; end
+% for kpoints, the factor 2 is for complex entries
+if S.tnkpt ~= 1, ncpy_orbitals = ncpy_orbitals * 2 * S.tnkpt; end
+memory_orbitals = S.N * S.Nev * size_double * ncpy_orbitals;
+
+% sparse matrices
+% Lap_std, grad_i, {GIi, GJi, GVi}
+% (nnz * 2 + ncol + 1) * size_double
+nnz_sparse = (2 * (3*fd_order+1) + 3 * fd_order) * S.N;
+memory_sparse = (2*nnz_sparse + S.N + 1) * size_double ...
+ + 9*fd_order*S.N * size_double + (S.BC ~= 1) * 6*fd_order*S.N;
+
+% vectors, rho, phi, Veff, ...; isIn, RR_AUG, RR_AUG_3D
+memory_vectors = 14 * S.N * size_double + ...
+ + (S.BC == 1) * 3 * N_ex * size_double ...
+ + (S.RelaxFlag || S.MDFlag) * 4 * S.N * size_double;
+
+% spherical harmonics
+if S.BC == 1
+ memory_SH = (6+1)^2 * (S.N + N_ex) * size_double;
+else
+ memory_SH = 0;
+end
+
+% history matrix
+memory_hist = 2 * S.MixingHistory * S.N * size_double;
+
+% total
+memory_usage = memory_orbitals + memory_sparse + memory_vectors ...
+ + memory_SH + memory_hist;
+
+fprintf('\n');
+fprintf(' Estimated memory usage:\n');
+fprintf(' Total: %s\n', print_mem(memory_usage));
+fprintf(' orbitals : %s\n', print_mem(memory_orbitals));
+fprintf(' sparse matrices : %s\n', print_mem(memory_sparse));
+fprintf(' global-size vectors : %s\n', print_mem(memory_vectors));
+if S.BC == 1
+ fprintf(' spherical harmonics : %s\n', print_mem(memory_SH));
+end
+fprintf(' mixing histories : %s\n', print_mem(memory_hist));
+fprintf('\n');
+
+end
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+function [mem_str, nXB, XB] = print_mem(nBytes)
+% given memory size in Bytes, print in appropriate units
+
+if nBytes < 0
+ error('Memory size must be non-negative!');
+end
+scale = floor(log(nBytes)/log(1024));
+if nBytes == 0, scale = 0; end
+switch scale
+ case 0
+ nXB = nBytes; XB = 'B';
+ case 1
+ nXB = nBytes/(1024); XB = 'kB';
+ case 2
+ nXB = nBytes/(1024^2); XB = 'MB';
+ case 3
+ nXB = nBytes/(1024^3); XB = 'GB';
+ case 4
+ nXB = nBytes/(1024^4); XB = 'TB';
+ case 5
+ nXB = nBytes/(1024^5); XB = 'PB';
+ otherwise
+ % use PB for all larger mem size
+ nXB = nBytes/(1024^5); XB = 'PB';
+end
+
+if scale == 0
+ mem_str = sprintf('%7.0f %s',nXB,XB);
+else
+ mem_str = sprintf('%7.2f %s',nXB,XB);
+end
+
+end
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+function npl = Mesh2ChebDegree(h)
+ % the relation between h and npl is fit with a cubic polynomial
+ % p(x) = p3 * x^3 + p2 * x^2 + p1 * x + p0.
+ p3 = -700. / 3.;
+ p2 = 1240. / 3.;
+ p1 = -773. / 3.;
+ p0 = 1078. / 15.;
+ if (h > 0.7)
+ npl = 14;
+ else
+ npl = ((p3 * h + p2) * h + p1) * h + p0;
+ end
+ npl = round(npl);
+end
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+function S = inpt_defaults()
+% SET_DEFAULTS sets up the default parameters
+
+% cell_typ: 1 - orthogonal unit cell or 2 - non-orthogonal unit cell
+cell_typ = 1; % default is orthogonal
+
+% lat_vec: Lattice unit vectors
+lat_vec = eye(3);
+% corresponding metric_T, grad_T, lapc_T and Jacb
+metric_T = eye(3);
+grad_T = eye(3);
+lapc_T = eye(3);
+Jacb = 1;
+
+% L1, L2, L3: domain size in each direction
+% no defaults
+L1 = 0.0;
+L2 = 0.0;
+L3 = 0.0;
+
+% Nx, Ny, Nz: number of finite-difference grids in each direction
+% no defaults
+Nx = 0;
+Ny = 0;
+Nz = 0;
+% N: N = Nx * Ny * Nz
+N = 0;
+
+% Ecut
+ecut = -1.0;
+
+% mesh spacing
+mesh_spacing = -1.0;
+
+% kptgrid: k-point grid
+kptgrid = [0.0 0.0 0.0]; % default is Gamma-point
+
+% shift in k-point grid
+kptshift = [0.0 0.0 0.0];
+
+% nkpt: number of k-points
+nkpt = [1 1 1];
+
+% tnkpt: number of Time-Reversal Symmetry reduced k-points
+tnkpt = 1;
+
+% wkpt: weights for k-points
+wkpt = 1;
+
+% BC: boundary conditions.
+% 1 - Zero Dirichlet, 2 - Periodic,
+% 3 - surface in x-y, 4 - wire along z-direction
+BC = -1; % will be set up later after reading user inputs
+BCx = -1; BCy = -1; BCz = -1;
+
+% isBS: flag for band structure calculation
+isBS = 0; % Default is off
+
+% lattice: lattice type, for band structure calculation
+lattice = 'undefined';
+
+% SCF_tol: SCF tolerance
+SCF_tol = -1.0; % default will be set after inpt is read
+
+% Nev: Number of states/bands
+Nev = -1; % default will be set after inpt is read
+
+% poisson_tol: Poisson tolerance
+poisson_tol = -1; % default will be set after inpt is read
+
+% pseudocharge_tol: Pseudocharge (rb) tolerance
+pseudocharge_tol = -1;
+
+% Cst: Factor for conversion from Ha to eV
+Cst = 27.21138602;
+
+% Temp: Electronic temperature, beta := 1/ (kB * Temp)
+%Temp = 315.7751307269723;
+kB = (8.6173303e-5)/Cst;
+%bet = 1.0 / (kB * Temp); % beta = 1 / smearing
+elec_T_type = 1; % gaussian smearing
+bet = -1;
+Temp = -1;
+
+% npl: Degree of Chebyshev polynomial
+npl = -1; % default will be set after inpt is read
+
+% conditioner: mixing type and preconditioner
+% 1 - Potential mixing , 2 - Density + Kerker, 3 - Density mixing
+% conditioner = 1;
+
+% FDn: half of finite difference order
+FDn = 6;
+
+% rc_ref: rc reference
+rc_ref = 0.5;
+
+% max_relax_it: Maximun number of relaxations
+max_relax_it = 0;
+
+% dbg_switch: debug switch
+dbg_switch = 0;
+
+% xc: Exchange-correlation functional
+% 0 - LDA_PW, 1 - LDA_PZ, 2 - PBE(GGA)
+xc = 0;
+
+% Nelectron: number of electrons
+% no default
+Nelectron = 0;
+
+% n_typ: number of atom types
+n_typ = 0;
+
+S = struct(...
+ 'cell_typ',cell_typ,'lat_vec',lat_vec,'metric_T',metric_T,...
+ 'grad_T',grad_T, 'lapc_T',lapc_T,'Jacb',Jacb,'L1',L1,'L2',L2,'L3',L3,...
+ 'Nx',Nx,'Ny',Ny,'Nz',Nz,'N',N,'ecut',ecut,'mesh_spacing',mesh_spacing,'kptgrid',kptgrid,...
+ 'kptshift',kptshift,'nkpt',nkpt,'tnkpt',tnkpt,'wkpt',wkpt,'BC',BC,'BCx',BCx,'BCy',BCy,'BCz',BCz,...
+ 'isBS',isBS,'lattice',lattice,'SCF_tol',SCF_tol,'Nev',Nev,'poisson_tol',poisson_tol,...
+ 'pseudocharge_tol',pseudocharge_tol, 'Cst',Cst,'kB',kB,'elec_T_type',elec_T_type,...
+ 'Temp',Temp,'bet',bet,'npl',npl,'FDn',FDn,...
+ 'rc_ref',rc_ref,'max_relax_it',max_relax_it,...
+ 'dbg_switch',dbg_switch,'xc',xc,...
+ 'Nelectron',Nelectron,'n_typ',n_typ);
+
+S.TimeRevSym = 1;
+
+S.spin_typ = 0;
+S.nspin = 1; % spin
+
+% EXTRA variables from SPARC
+S.CheFSI_Optmz = 0;
+S.chefsibound_flag = 0;
+S.FixRandSeed = 0;
+S.rhoTrigger = 4;
+S.NetCharge = 0;
+S.MAXIT_SCF = 100;
+S.MINIT_SCF = 3;
+S.MAXIT_POISSON = 1000;
+S.accuracy_level = -1;
+S.target_force_accuracy = -1.0;
+S.target_energy_accuracy = -1.0;
+S.TOL_RELAX = 5e-4;
+S.TOL_LANCZOS = 1e-2;
+% S.kerker_tol = -1;
+S.precond_tol = -1;
+
+S.precond_kTF = 1;
+S.precond_thresh = 0.25;
+S.precond_fitpow = 2;
+S.precond_resta_q0 = 1.36;
+S.precond_resta_Rs = 2.76;
+
+% set back to -1
+S.MixingVariable = 1;
+S.MixingPrecond = 0;
+S.Pf_guess = [];
+
+S.MixingHistory = 7;
+S.MixingParameter = 0.3;
+S.MixingParameterSimple = -1.0; % for simple mixing, set up later
+S.PulayFrequency = 1;
+S.PulayRestartFreq = 0;
+S.TWtime = 1000000000;
+S.RelaxFlag = 0;
+S.RelaxMeth = 'LBFGS';
+S.max_relax_it = 100;
+S.max_dilatation = 1.2;
+S.TOL_RELAX_CELL = 0.01; % in GPa (max pressure)
+S.MDFlag = 0;
+S.RestartFlag = 0;
+S.MDMeth = 'NVE';
+S.MD_dt = 1.0;
+S.MD_Nstep = 0;
+S.ion_T = -1.0;
+S.thermos_TF = -1.0;
+S.ion_elec_eqT = 1;
+S.ion_vel_dstr = 2;
+S.NLCG_sigma = 0.5;
+S.qmass = 1;
+S.L_history = 20;
+S.L_finit_stp = 5e-3;
+S.L_maxmov = 0.2;
+S.L_autoscale = 1;
+S.L_lineopt = 1;
+S.L_icurv = 1.0;
+S.FIRE_dt = 1.0;
+S.FIRE_mass = 1.0;
+S.FIRE_maxmov = 0.2;
+S.Calc_stress = 0;
+S.Calc_pres = 0;
+S.PrintForceFlag = 1; % flag for printing forces
+S.PrintAtomPosFlag = 1; % flag for printing atomic positions
+S.PrintAtomVelFlag = 1; % flag for printing atomic velocities
+S.PrintElecDensFlag = 0; % flag for printing final electron density
+S.PrintEigenFlag = 0; % Flag for printing final eigenvalues and occupations
+S.PrintMDout = 1; % Flag for printing MD output in a .aimd file
+S.PrintRelaxout = 1; % Flag for printing relax output in a .relax file
+S.Printrestart = 1; % Flag for printing output needed for restarting a simulation
+S.Printrestart_fq = 1; % Steps after which the output is written in the restart file
+
+% Origin of the unit cell wrt some global origin
+S.xin = 0;
+S.yin = 0;
+S.zin = 0;
+
+% Cychel
+S.alph = 0.0;
+end
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+function S = Write_output_init(S, filename)
+
+% open .out file
+outfname = strcat(filename,'.out');
+i = 1;
+while exist(outfname,'file')
+ outfname = sprintf('%s.out_%d',filename,i);
+ i = i + 1;
+end
+
+suffixNum = i-1; % save suffix number, only used if suffixNum > 0
+
+% if there are already 100 files, then start using .out only
+OUT_MAX = 100;
+if i > OUT_MAX
+ outfname = strcat(filename,'.out');
+ suffixNum = -1;
+end
+
+% create an output file and write initial variables
+fileID = fopen(outfname,'w');
+if (fileID == -1)
+ error('\n Cannot open file "%s"\n',outfname);
+end
+
+start_time = fix(clock);
+fprintf(fileID,'***************************************************************************\n');
+fprintf(fileID,'* M-SPARC (Dec 17, 2019) *\n');
+fprintf(fileID,'* Copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech *\n');
+fprintf(fileID,'* Distributed under GNU General Public License 3 (GPL) *\n');
+fprintf(fileID,'* Date: %s Start time: %02d:%02d:%02d *\n',date,start_time(4),start_time(5),start_time(6));
+fprintf(fileID,'***************************************************************************\n');
+fprintf(fileID,' Input parameters \n');
+fprintf(fileID,'***************************************************************************\n');
+
+fprintf(fileID,'CELL: %f %f %f \n',S.L1,S.L2,S.L3);
+if max(max(abs(S.lat_vec - eye(3)))) > 1e-14
+ fprintf(fileID,'LATVEC:\n');
+ fprintf(fileID,'%.15f %.15f %.15f \n',S.lat_vec(1,:));
+ fprintf(fileID,'%.15f %.15f %.15f \n',S.lat_vec(2,:));
+ fprintf(fileID,'%.15f %.15f %.15f \n',S.lat_vec(3,:));
+end
+fprintf(fileID,'FD_GRID: %d %d %d\n',S.Nx-S.BCx,S.Ny-S.BCy,S.Nz-S.BCz);
+fprintf(fileID,'FD_ORDER: %d\n',S.FDn*2);
+fprintf(fileID,'BOUNDARY_CONDITION: %d\n',S.BC);
+if (S.BC==2 || S.BC==3 || S.BC==4)
+ fprintf(fileID,'KPOINT_GRID: %d %d %d\n',S.nkpt);
+ fprintf(fileID,'KPOINT_SHIFT: %d %d %d\n',S.kptshift);
+end
+
+if (S.spin_typ ~= 0)
+ fprintf(fileID,'SPIN_TYP: %d\n', S.spin_typ);
+end
+
+if (S.elec_T_type == 0)
+ fprintf(fileID,'ELEC_TEMP_TYPE: fermi-dirac\n');
+elseif (S.elec_T_type == 1)
+ fprintf(fileID,'ELEC_TEMP_TYPE: gaussian\n');
+end
+%fprintf(fileID,'ELEC_TEMP: %lf\n',S.elec_T);
+
+fprintf(fileID,'SMEARING: %.9f\n',1/S.bet);
+fprintf(fileID,'CHEB_DEGREE: %d\n',S.npl);
+fprintf(fileID,'NSTATES: %d\n',S.Nev);
+%fprintf(fileID,'NTYPES: %d\n',S.Ntypes);
+fprintf(fileID,'EXCHANGE_CORRELATION: %s\n',S.XC);
+fprintf(fileID,'CALC_STRESS: %d\n',S.Calc_stress);
+if(S.Calc_stress == 0)
+ fprintf(fileID,'CALC_PRES: %d\n',S.Calc_pres);
+end
+%if (S.MDFlag == 1 || S.RelaxFlag == 1)
+% fprintf(fileID,'TWTIME: %f\n',S.TWtime);
+%end
+
+if (S.CheFSI_Optmz == 1)
+ fprintf(fileID,'CHEFSI_OPTMZ: %d\n',S.CheFSI_Optmz);
+end
+if (S.chefsibound_flag == 1)
+ fprintf(fileID,'CHEFSI_BOUND_FLAG: %d\n',S.chefsibound_flag);
+end
+if (S.NetCharge ~= 0)
+ fprintf(fileID,'NET_CHARGE: %d\n',S.NetCharge);
+end
+fprintf(fileID,'MAXIT_SCF: %d\n',S.MAXIT_SCF);
+if (S.MDFlag == 1)
+ fprintf(fileID,'MD_FLAG: %d\n',S.MDFlag);
+ fprintf(fileID,'MD_METHOD: %s\n',S.MDMeth);
+ fprintf(fileID,'MD_TIMESTEP: %.2f\n',S.MD_dt);
+ %fprintf(fileID,'ATOMIC_MASS:');
+ %for (i = 0; i < S.Ntypes; i++)
+ % fprintf(fileID,' %.15f', S.Mass[i]);
+ %end
+ fprintf(fileID,'MD_NSTEP: %d\n',S.MD_Nstep);
+ fprintf(fileID,'ION_ELEC_EQT: %d\n',S.ion_elec_eqT);
+ % fprintf(fileID,'ION_VEL_DSTR: %d\n',S.ion_vel_dstr);
+ fprintf(fileID,'ION_TEMP: %f\n',S.ion_T);
+ % if(strcmp(S.MDMeth,'NVT_NH'))
+ % fprintf(fileID,'ION_TEMP_END: %lf\n',S.thermos_Tf);
+ % fprintf(fileID,'QMASS: %lf\n',S.qmass);
+ % end
+end
+if (S.RelaxFlag==1)
+ fprintf(fileID,'RELAX_FLAG: %d\n',S.RelaxFlag);
+ fprintf(fileID,'RELAX_METHOD: %s\n',S.RelaxMeth);
+ fprintf(fileID,'RELAX_NITER: %d\n',S.max_relax_it);
+ if(strcmp(S.RelaxMeth,'LBFGS'))
+ fprintf(fileID,'L_HISTORY: %d\n',S.L_history);
+ fprintf(fileID,'L_FINIT_STP: %f\n',S.L_finit_stp);
+ fprintf(fileID,'L_MAXMOV: %f\n',S.L_maxmov);
+ fprintf(fileID,'L_AUTOSCALE: %d\n',S.L_autoscale);
+ fprintf(fileID,'L_LINEOPT: %d\n',S.L_lineopt);
+ fprintf(fileID,'L_ICURV: %f\n',S.L_icurv);
+ elseif (strcmp(S.RelaxMeth,'NLCG'))
+ fprintf(fileID,'NLCG_SIGMA: %f\n',S.NLCG_sigma);
+ elseif (strcmp(S.RelaxMeth,'FIRE'))
+ fprintf(fileID,'FIRE_dt: %f\n',S.FIRE_dt);
+ fprintf(fileID,'FIRE_mass: %f\n',S.FIRE_mass);
+ fprintf(fileID,'FIRE_maxmov: %f\n',S.FIRE_maxmov);
+ end
+ fprintf(fileID,'TOL_RELAX: %.2E\n',S.TOL_RELAX);
+elseif (S.RelaxFlag==2)
+ fprintf(fileID,'RELAX_FLAG: %d\n',S.RelaxFlag);
+ fprintf(fileID,'RELAX_NITER: %d\n',S.max_relax_it);
+ fprintf(fileID,'TOL_RELAX_CELL: %.2E\n',S.TOL_RELAX_CELL);
+ fprintf(fileID,'RELAX_MAXDILAT: %f\n',S.max_dilatation);
+end
+fprintf(fileID,'TOL_SCF: %.2E\n',S.SCF_tol);
+fprintf(fileID,'TOL_POISSON: %.2E\n',S.poisson_tol);
+fprintf(fileID,'TOL_LANCZOS: %.2E\n',S.TOL_LANCZOS);
+fprintf(fileID,'TOL_PSEUDOCHARGE: %.2E\n',S.pseudocharge_tol);
+if (S.MixingVariable == 0)
+ fprintf(fileID,'MIXING_VARIABLE: density\n');
+elseif (S.MixingVariable == 1)
+ fprintf(fileID,'MIXING_VARIABLE: potential\n');
+end
+if (S.MixingPrecond == 0)
+ fprintf(fileID,'MIXING_PRECOND: none\n');
+elseif (S.MixingPrecond == 1)
+ fprintf(fileID,'MIXING_PRECOND: kerker\n');
+elseif (S.MixingPrecond == 2)
+ fprintf(fileID,'MIXING_PRECOND: resta\n');
+elseif (S.MixingPrecond == 3)
+ fprintf(fileID,'MIXING_PRECOND: truncated_kerker\n');
+end
+if (S.MixingPrecond ~= 0)
+ fprintf(fileID,'TOL_PRECOND: %.2E\n',S.precond_tol);
+end
+if (S.MixingPrecond == 1) % kerker
+ %fprintf(fileID,'TOL_KERKER: %.2E\n',S.kerker_tol);
+ fprintf(fileID,'PRECOND_KERKER_KTF: %.2f\n',S.precond_kTF);
+elseif (S.MixingPrecond == 2) % resta
+ %fprintf(fileID,'TOL_PRECOND: %.2E\n',S.precond_tol);
+ fprintf(fileID,'PRECOND_RESTA_Q0: %.3f\n',S.precond_resta_q0);
+ fprintf(fileID,'PRECOND_RESTA_RS: %.3f\n',S.precond_resta_Rs);
+ fprintf(fileID,'PRECOND_FITPOW: %d\n',S.precond_fitpow);
+elseif (S.MixingPrecond == 3) % truncated kerker
+ fprintf(fileID,'PRECOND_KERKER_KTF: %.2f\n',S.precond_kTF);
+ fprintf(fileID,'PRECOND_KERKER_THRESH: %.2f\n',S.precond_thresh);
+ fprintf(fileID,'PRECOND_FITPOW: %d\n',S.precond_fitpow);
+end
+
+fprintf(fileID,'MIXING_PARAMETER: %.2f\n',S.MixingParameter);
+if S.MixingParameter ~= S.MixingParameterSimple
+ fprintf(fileID,'MIXING_PARAMETER_SIMPLE: %.2f\n',S.MixingParameterSimple);
+end
+fprintf(fileID,'MIXING_HISTORY: %d\n',S.MixingHistory);
+fprintf(fileID,'PULAY_FREQUENCY: %d\n',S.PulayFrequency);
+fprintf(fileID,'PULAY_RESTART_FREQ: %d\n',S.PulayRestartFreq);
+fprintf(fileID,'REFERENCE_CUTOFF: %.2f\n',S.rc_ref);
+fprintf(fileID,'RHO_TRIGGER: %d\n',S.rhoTrigger);
+fprintf(fileID,'FIX_RAND: %d\n',S.FixRandSeed);
+fprintf(fileID,'PRINT_FORCES: %d\n',S.PrintForceFlag);
+fprintf(fileID,'PRINT_ATOMS: %d\n',S.PrintAtomPosFlag);
+fprintf(fileID,'PRINT_EIGEN: %d\n',S.PrintEigenFlag);
+fprintf(fileID,'PRINT_DENSITY: %d\n',S.PrintElecDensFlag);
+if(S.MDFlag == 1)
+ fprintf(fileID,'PRINT_MDOUT: %d\n',S.PrintMDout);
+end
+if(S.MDFlag == 1 || S.RelaxFlag == 1)
+ fprintf(fileID,'PRINT_VELS: %d\n',S.PrintAtomVelFlag);
+ fprintf(fileID,'PRINT_RESTART: %d\n',S.Printrestart);
+ if(S.Printrestart == 1)
+ fprintf(fileID,'PRINT_RESTART_FQ: %d\n',S.Printrestart_fq);
+ end
+end
+
+if(S.RelaxFlag == 1)
+ fprintf(fileID,'PRINT_RELAXOUT: %d\n',S.PrintRelaxout);
+end
+
+fprintf(fileID,'OUTPUT_FILE: %s\n',outfname);
+if (S.RestartFlag == 1)
+ fprintf(fileID,'RESTART_FLAG: %d\n',S.RestartFlag);
+end
+
+% fprintf(fileID,'***************************************************************************\n');
+% fprintf(fileID,' Parallelization \n');
+% fprintf(fileID,'***************************************************************************\n');
+% fprintf(fileID,'NP_KPOINT_PARAL: %d\n',S.npkpt);
+% fprintf(fileID,'NP_BAND_PARAL: %d\n',S.npband);
+% fprintf(fileID,'NP_DOMAIN_PARAL: %d %d %d\n',S.npNdx,S.npNdy,S.npNdz);
+% fprintf(fileID,'NP_DOMAIN_PHI_PARAL: %d %d %d\n',S.npNdx_phi,S.npNdy_phi,S.npNdz_phi);
+
+fprintf(fileID,'***************************************************************************\n');
+fprintf(fileID,' Initialization \n');
+fprintf(fileID,'***************************************************************************\n');
+% fprintf(fileID,'Number of processors : %d\n',nproc);
+
+if ( (abs(S.dx-S.dy) <=1e-12) && (abs(S.dx-S.dz) <=1e-12) ...
+ && (abs(S.dy-S.dz) <=1e-12) )
+ fprintf(fileID,'Mesh spacing : % f (Bohr)\n',S.dx);
+else
+ fprintf(fileID,'Mesh spacing in x-direction : % f (Bohr)\n',S.dx);
+ fprintf(fileID,'Mesh spacing in y-direction : % f (Bohr)\n',S.dy);
+ fprintf(fileID,'Mesh spacing in z direction : % f (Bohr)\n',S.dz);
+end
+
+if (S.BC==2 || S.BC==3 || S.BC==4)
+ fprintf(fileID,'Number of symmetry adapted k-points: %d\n',S.tnkpt);
+end
+
+fprintf(fileID,'Output printed to : %s\n',outfname);
+
+%if (S.PrintAtomPosFlag==1)
+% fprintf(fileID,'Atom positions printed to : %s\n',S.AtomFilename);
+%end
+
+%if (S.PrintForceFlag==1)
+% fprintf(fileID,'Forces printed to : %s\n',S.ForceFilename);
+%end
+
+% if (S.PrintEigenFlag==1)
+% fprintf(fileID,'Final eigenvalues printed to : %s\n',S.EigenFilename);
+% end
+
+% if (S.MDFlag == 1 && S.PrintMDout == 1)
+% fprintf(fileID,'MD output printed to : %s\n',S.MDFilename);
+% end
+
+% if (S.RelaxFlag == 1 && S.PrintRelaxout == 1)
+% fprintf(fileID,'Relax output printed to : %s\n',S.RelaxFilename);
+% end
+
+fprintf(fileID,'Total number of atom types : %d\n',S.n_typ);
+fprintf(fileID,'Total number of atoms : %d\n',S.n_atm);
+fprintf(fileID,'Total number of electrons : %d\n',S.Nelectron);
+
+for ityp = 1:S.n_typ
+ fprintf(fileID,'Atom type %-2d (valence electrons) : %s %d\n',ityp,S.Atm(ityp).typ, S.Atm(ityp).Z);
+ fprintf(fileID,'Pseudopotential : %s\n',S.Atm(ityp).psdfname);
+ fprintf(fileID,'lloc : %d\n',S.Atm(ityp).lloc);
+ if (S.MDFlag == 1)
+ fprintf(fileID,'Atomic mass : %.15f\n',S.Atm(ityp).Mass);
+ end
+ fprintf(fileID,'Pseudocharge radii of atom type %-2d : %.2f %.2f %.2f\n',ityp,S.Atm(ityp).rb_x,S.Atm(ityp).rb_y,S.Atm(ityp).rb_z);
+ fprintf(fileID,'Number of atoms of type %-2d : %d\n',ityp,S.Atm(ityp).n_atm_typ);
+ % if (S.PrintAtomPosFlag == 1 && S.MDFlag == 0 && S.RelaxFlag == 0)
+ % fprintf(fileID,'Fractional coordinates of atoms of type %-2d :\n',ityp);
+ % for j = 1:S.Atm(ityp).n_atm_typ
+ % fprintf(fileID,'%18.10f %18.10f %18.10f\n',S.Atm(ityp).coords(j,:)./[S.L1, S.L2, S.L3]);
+ % end
+ % end
+end
+
+[~, mem_num, mem_unit] = print_mem(S.memory_usage);
+fprintf(fileID, 'Estimated total memory usage : %-.2f %s\n', mem_num, mem_unit);
+
+fclose(fileID);
+
+
+
+%-----------------------------------------
+% Write atom positions to .static file
+%-----------------------------------------
+if ((S.PrintAtomPosFlag == 1 || S.PrintForceFlag == 1) && S.MDFlag == 0 && S.RelaxFlag == 0)
+ staticfname = strcat(filename,'.static');
+ if suffixNum > 0
+ staticfname = sprintf('%s.static_%d',filename,suffixNum);
+ end
+ % open file
+ fid = fopen(staticfname,'w') ;
+ assert(fid~=-1,'Error: Cannot open .static file %s',staticfname);
+
+ if(S.PrintAtomPosFlag == 1)
+ fprintf(fid,'***************************************************************************\n');
+ fprintf(fid,' Atom positions \n');
+ fprintf(fid,'***************************************************************************\n');
+
+ nFracCoord = sum(S.IsFrac);
+
+ if nFracCoord == S.n_typ
+ fprintf(fileID,'Fractional coordinates of atoms:\n');
+ for j = 1:S.n_atm
+ fprintf(fileID,'%18.10f %18.10f %18.10f\n',S.Atoms(j,:)./[S.L1, S.L2, S.L3]);
+ end
+ elseif nFracCoord == 0
+ fprintf(fileID,'Cartesian coordinates of atoms (Bohr):\n');
+ for j = 1:S.n_atm
+ fprintf(fileID,'%18.10f %18.10f %18.10f\n',S.Atoms(j,:));
+ end
+ else
+ for ityp = 1:S.n_typ
+ if S.IsFrac(ityp)
+ fprintf(fileID,'Fractional coordinates of %s:\n',S.Atm(ityp).typ);
+ for j = 1:S.Atm(ityp).n_atm_typ
+ fprintf(fileID,'%18.10f %18.10f %18.10f\n',S.Atm(ityp).coords(j,:)./[S.L1, S.L2, S.L3]);
+ end
+ else
+ fprintf(fileID,'Cartesian coordinates of %s (Bohr):\n',S.Atm(ityp).typ);
+ for j = 1:S.Atm(ityp).n_atm_typ
+ fprintf(fileID,'%18.10f %18.10f %18.10f\n',S.Atm(ityp).coords(j,:));
+ end
+ end
+ end
+ end
+ end
+
+ % close file
+ fclose(fid);
+
+ S.staticfname = staticfname; % save to structure;
+end
+
+
+% save to structure
+S.suffixNum = suffixNum;
+S.outfname = outfname;
+
+end
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+function h = Ecut2h(Ecut, FDn)
+% Find mesh size h (Bohr) in finite-difference corresponding to a Ecut (Ha)
+% in plane-wave codes.
+% FDn: half of finite difference order
+
+% this can be tuned to make the correspondence between h and Ecut more
+% accurate
+epsilon = 1e-1; % tolerance threshold for FD 2nd derivative approx.
+
+% finite difference weights
+w2 = zeros(1,FDn+1);
+for k=1:FDn
+ w2(k+1) = (2*(-1)^(k+1))*(factorial(FDn)^2)/...
+ (k*k*factorial(FDn-k)*factorial(FDn+k));
+ w2(1) = w2(1)-2*(1/(k*k));
+end
+
+kk = linspace(0,pi,1001);
+y_cos = -w2(1) + (-2*w2(2:end)) * cos((1:FDn)' * kk);
+freq_err = abs(y_cos - kk.^2);
+kc = kk(find(freq_err < epsilon,1,'last'));
+
+h = kc / sqrt(2*Ecut);
+
+end
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+function [r4, p4, constant1] = fit_mixing_preconditioner(max_q, q0, e0, Rs, a0, ktf, m, choose_method)
+% inputs (Defaults mentioned whenever available)
+% max_q: max value of q on domain
+% q0, e0, Rs: parmeters to Resta preconditioner
+% m: power of polynomial used in the fit
+% a0 = 0.25; % Threshold for Vasp preconditioner (AMIN in VASP code)
+% ktf = 1; % Thomas fermi length in Bohr
+% choose_method = 1 for VASP-fit
+% = 2 for Resta-fit
+% Use following values as default:
+% q0 = 1.36, e0 = 5.7, Rs = 2.76 for diamond
+% q0 = 1.10, e0 = 11.94, Rs = 4.28 for silicon
+% q0 = 1.08, e0 = 16, Rs = 4.71 for germanium
+% values taken from https://journals.aps.org/prb/pdf/10.1103/PhysRevB.16.2717
+Initial_guess_vasp{4} = [0.750005180027774 -0.612656341946256 0.176651619589811 -0.021091066193744 0.000902462058248 -0.000006309747662 0.520408099139247 -0.445424309904542 0.149745485915738 -0.061220832540094 0.013655050447764];
+Initial_guess_vasp{3} = [ 0.749987658778237 -0.456416789370834 0.086223230682159 -0.005203450251595 0.000048194773012 0.716134813320535 -0.189056786409910 -0.071804972002278 0.039024958313563];
+Initial_guess_vasp{2} = [ 0.750032410760875 -0.311559965943014 0.030528791849734 -0.000423605614679 0.938408853848147 -0.178908923603946 0.114299964666429];
+Initial_guess_vasp{1} = [0.7499 -0.1849 0.0039 1.0273 0.3241];
+Initial_guess_resta{4} = [0.824617865719867 -1.666939600095733 8.091267716160914 -7.570624248069551 1.103843271821802 -0.003945029200409 0.294295330483791 3.949649251298832 24.616714373390433 -30.280192648230070 4.491018917223143];
+Initial_guess_resta{3} = [0.824427620366807 -1.323851625012163 -1.073719366292704 0.645483368849621 0.012403487988262 0.518438754779273 -2.408422023505795 -7.781456187967437 3.879228313224187];
+Initial_guess_resta{2} = [0.824420567940696 0.390846073880153 -0.319378926237595 -0.006040724645454 2.592804423707606 2.985494672065439 -1.906590310047641];
+Initial_guess_resta{1} = [0.8244 0.8065 0.0150 3.0937 4.5164];
+N = 1000; % Number of Data points
+q = (1e-10:max_q/N: max_q)';
+if choose_method == 1
+ precond_value = max(a0,(q.^2)./(q.^2 + ktf^2)); % expression for VASP preconditioner
+ f_rational = fit(q.^2, (precond_value-a0), strcat('rat',num2str(m),num2str(m)),'StartPoint',Initial_guess_vasp{m-1}); % Fitting of rational polynomial with origin shift
+elseif choose_method == 2
+ precond_value = ((q0^2.*sin(q*Rs)./(e0*q*Rs) + q.^2))./(q0^2 + q.^2); % expression for resta precnditioner
+ f_rational = fit(q.^2, (precond_value-(1/e0)), strcat('rat',num2str(m),num2str(m)),'StartPoint',Initial_guess_resta{m-1}); % Fitting of rational polynomial with origin shift
+end
+coef_rational = coeffvalues(f_rational); % coefficients of the fit
+
+a = [1 coef_rational(1,m+2:end)]; % coefficents in denominator (increasing powers)
+b = coef_rational(1,1:m) - coef_rational(m+1)*a(1,1:end-1)/a(1,end); % coefficients in numerator (decreasing powers)
+%[r,p,k1] = residue(b,a); % partial fraction function
+[r,p,~] = residue(b,a); % partial fraction function
+
+% Only slecting the real and one of the complex numbers in r and p
+r1 = r(imag(r)==0);
+r2 = 2*r(imag(r)~=0);
+r2 = sort(r2);
+p1 = p(imag(p)==0);
+p2 = p(imag(p)~=0);
+p2 = sort(p2);
+
+if isempty(r2) == 0
+ p3 = zeros(floor(length(r2)/2),1);
+ r3 = p3;
+ for i = 1:length(r2)/2
+ p3(i,1) = p2(2*i-1);
+ r3(i,1) = r2(2*i-1);
+ end
+ p4 = [p1;p3];
+ r4 = [r1;r3];
+else
+ p4 = p1;
+ r4 = r1;
+end
+p4 = -p4; % here we make it consistent with kerker preconditioner
+
+if choose_method ==1
+ constant1 = a0+coef_rational(m+1)/a(1,end); % it is the constant which is added to the expansion
+elseif choose_method == 2
+ constant1 = 1/e0+coef_rational(m+1)/a(1,end); % it is the constant which is added to the expansion
+end
+%%% run this section only for printing the error
+% if choose_method == 1
+% error_fit = max(abs(precond_value - f_rational(q.^2) - 1/e0));
+% elseif choose_method == 2
+% error_fit = max(abs(precond_value - f_rational(q.^2) - a0));
+% end
+% display(error_fit)
+%%% checking if the fit is correct
+% part_f = zeros(length(q),1)+constant1;
+% for i = 1:length(q)
+% for j = 1: length(r4)
+% if imag(r4(j)) ==0
+% part_f(i) = part_f(i)+r4(j)*((q(i))^2/((q(i))^2+p4(j)));
+% else
+% part_f(i) = part_f(i)+real(r4(j)*((q(i))^2/((q(i))^2+p4(j))));
+% end
+% end
+% end
+% plot(q, precond_value,'-*',q,part_f,'-*')
+% xlim([0 10])
+end
+
+function [W] = IntgWts(Nx,Ny,Nz,BCx,BCy,BCz,xin,S)
+ if S.cell_typ == 1 || S.cell_typ == 2
+ W_x = ones(Nx,1)*S.dx;
+ W_x(1) = W_x(1) * (1-BCx*0.5);
+ W_x(Nx) = W_x(Nx) * (1-BCx*0.5);
+
+ W_y = ones(Ny,1)*S.dy;
+ W_y(1) = W_y(1) * (1-BCy*0.5);
+ W_y(Ny) = W_y(Ny) * (1-BCy*0.5);
+
+ W_z = ones(Nz,1)*S.dz;
+ W_z(1) = W_z(1) * (1-BCz*0.5);
+ W_z(Nz) = W_z(Nz) * (1-BCz*0.5);
+
+ W = kron(W_z,kron(W_y,W_x)) * S.Jacb;
+ elseif (S.cell_typ == 3 || S.cell_typ == 4 || S.cell_typ == 5)
+ W = IntgWts_cychel(Nx,Ny,Nz,BCx,BCy,BCz,xin,S);
+ end
+end
+
+
+function [S] = Generate_kpts(S)
+ nkpt = S.nkpt;
+ if (S.BCx == 1 && nkpt(1) > 1)
+ error(' nkpt cannot be greater than 1 in Dirichlet boundary direction (x)');
+ end
+ if (S.BCy == 1 && nkpt(2) > 1)
+ error(' nkpt cannot be greater than 1 in Dirichlet boundary direction (y)');
+ end
+ if (S.BCz == 1 && nkpt(3) > 1)
+ error(' nkpt cannot be greater than 1 in Dirichlet boundary direction (z)');
+ end
+
+ % Monkhorst-pack grid for Brillouin zone sampling
+ MPG_typ1 = @(nkpt) (2*(1:nkpt) - nkpt - 1)/2; % MP grid points for infinite group order
+ MPG_typ2 = @(nkpt) (0:nkpt-1); % MP grid points for finite group order
+
+ if S.cell_typ < 3
+ kptgrid_x = (1/nkpt(1)) * MPG_typ1(nkpt(1));
+ kptgrid_y = (1/nkpt(2)) * MPG_typ1(nkpt(2));
+ kptgrid_z = (1/nkpt(3)) * MPG_typ1(nkpt(3));
+ sumx = 0;
+ sumy = 0;
+ sumz = 0;
+ % shift kpoint grid
+ kptgrid_x = kptgrid_x + S.kptshift(1) * (1/nkpt(1));
+ kptgrid_y = kptgrid_y + S.kptshift(2) * (1/nkpt(2));
+ kptgrid_z = kptgrid_z + S.kptshift(3) * (1/nkpt(3));
+
+ % map k-points back to BZ
+ temp_epsilon = eps; % include the right boundary k-points instead of left
+ kptgrid_x = mod(kptgrid_x + 0.5 - temp_epsilon, 1) - 0.5 + temp_epsilon;
+ kptgrid_y = mod(kptgrid_y + 0.5 - temp_epsilon, 1) - 0.5 + temp_epsilon;
+ kptgrid_z = mod(kptgrid_z + 0.5 - temp_epsilon, 1) - 0.5 + temp_epsilon;
+ elseif (S.cell_typ == 3 || S.cell_typ == 4 || S.cell_typ == 5)
+ kptgrid_x = (1/nkpt(1)) * MPG_typ1(nkpt(1));
+ kptgrid_y = (1/nkpt(2)) * MPG_typ2(nkpt(2));
+ kptgrid_z = (1/nkpt(3)) * MPG_typ1(nkpt(3));
+ sumx = 0;
+ sumy = nkpt(2);
+ sumz = 0;
+ end
+
+ % Scale kpoints
+ kptgrid_x = (2*pi/S.L1) * kptgrid_x;
+ kptgrid_y = (2*pi/S.L2) * kptgrid_y;
+ kptgrid_z = (2*pi/S.L3) * kptgrid_z;
+
+ [kptgrid_X, kptgrid_Y, kptgrid_Z] = ndgrid(kptgrid_x,kptgrid_y,kptgrid_z);
+ kptgrid = [reshape(kptgrid_X,[],1),reshape(kptgrid_Y,[],1),reshape(kptgrid_Z,[],1)];
+ disp(' kpoint grid before symmetry:');
+ disp(kptgrid);
+
+ tnkpt = prod(nkpt);
+ wkpt = ones(tnkpt,1)/tnkpt;% weights for k-points
+ TOL = 1e-8;
+ % Time-Reversal Symmetry to reduce k-points
+ if S.TimeRevSym == 1
+ Ikpt = zeros(tnkpt,1);
+ Ikpt_rev = zeros(tnkpt,1);
+ for ii = 1:tnkpt
+ for jj = ii+1:tnkpt
+ if (abs(kptgrid(ii,1) + kptgrid(jj,1) - sumx) < TOL) && (abs(kptgrid(ii,2) + kptgrid(jj,2) - sumy) < TOL) && (abs(kptgrid(ii,3) + kptgrid(jj,3) - sumz) < TOL)
+ Ikpt(ii) = 1;
+ Ikpt_rev(jj) = 1;
+ end
+ end
+ end
+ Ikpt = Ikpt>0.5;
+ Ikpt_rev = Ikpt_rev>0.5;
+ wkpt(Ikpt_rev) = 2*wkpt(Ikpt_rev);
+ kptgrid = kptgrid(~Ikpt,:);
+ wkpt = wkpt(~Ikpt);
+ tnkpt = size(wkpt,1);
+ end
+
+ disp(' kpoint grid after symmetry:');
+ disp(kptgrid);
+ % Store into the structure
+ S.kptgrid = kptgrid;
+ S.tnkpt = tnkpt;
+ S.wkpt = wkpt;
+end
diff --git a/src/lapIndicesValues_1d.m b/src/lapIndicesValues_1d.m
new file mode 100644
index 00000000..66befde2
--- /dev/null
+++ b/src/lapIndicesValues_1d.m
@@ -0,0 +1,264 @@
+function S = lapIndicesValues_1d(S)
+% @ brief Calculates laplacian and gradient (in 1D) indices' values without Bloch factor
+% @ authors
+% Abhiraj Sharma
+% Qimen Xu
+% Phanish Suryanarayana
+%
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+%============================================================================
+if S.cell_typ < 3
+ Nx = S.Nx; Ny = S.Ny; Nz = S.Nz;
+ n0 = S.FDn;
+ w1 = S.w1;
+ w2 = S.w2;
+ dx = S.dx;
+ dy = S.dy;
+ dz = S.dz;
+
+ % D_xx laplacian in 1D
+ %-----------------------
+
+ % Initial number of non-zeros: including ghost nodes
+ nnzCount = (2 * n0 + 1) * Nx;
+
+ % Row and column indices and the corresponding non-zero values
+ % used to generate sparse matrix DL11 s.t. DL11(I(k),II(k)) = V(k)
+ I = zeros(nnzCount,1);
+ V = zeros(nnzCount,1);
+ II = zeros(nnzCount,1);
+ rowCount = 1;
+ count = 1;
+ coef_dxx = 1/dx^2;
+
+ % Find non-zero entries that use forward difference
+ for ii = 1:Nx
+ % diagonal element
+ I(count) = rowCount; II(count) = ii;
+ V(count) = w2(1)*coef_dxx ;
+ count = count + 1;
+ % off-diagonal elements
+ for q = 1:n0
+ % ii + q
+ I(count) = rowCount; II(count) = ii+q;
+ V(count) = w2(q+1)*coef_dxx;
+ count = count + 1;
+ % ii - q
+ I(count) = rowCount; II(count) = ii-q;
+ V(count) = w2(q+1)*coef_dxx;
+ count = count + 1;
+
+ end
+ rowCount = rowCount + 1;
+ end
+
+ if S.BCx == 1
+ % Removing outside domain entries (for periodic code this is unnecessary)
+ isIn = (II >= 1) & (II <= Nx);
+ S.I_11 = I(isIn); S.II_11 = II(isIn); S.V_11 = V(isIn);
+ elseif S.BCx == 0
+ S.isOutl_11 = (II<1); S.isOutr_11 = (II>Nx); % Warning: Assumed influence of only neighboring cells
+ S.I_11 = I; S.II_11 = mod(II+(Nx-1),Nx)+1; S.V_11 = V;
+ end
+
+ % D_yy laplacian in 1D
+ %-----------------------
+
+ % Initial number of non-zeros: including ghost nodes
+ nnzCount = (2 * n0 + 1) * Ny;
+
+ % Row and column indices and the corresponding non-zero values
+ % used to generate sparse matrix DL22 s.t. DL22(I(k),II(k)) = V(k)
+ I = zeros(nnzCount,1);
+ V = zeros(nnzCount,1);
+ II = zeros(nnzCount,1);
+ rowCount = 1;
+ count = 1;
+ coef_dyy = 1/dy^2;
+
+ % Find non-zero entries that use forward difference
+ for ii = 1:Ny
+ % diagonal element
+ I(count) = rowCount; II(count) = ii;
+ V(count) = w2(1)*coef_dyy;
+ count = count + 1;
+ % off-diagonal elements
+ for q = 1:n0
+ % ii + q
+ I(count) = rowCount; II(count) = ii+q;
+ V(count) = w2(q+1)*coef_dyy;
+ count = count + 1;
+ % ii - q
+ I(count) = rowCount; II(count) = ii-q;
+ V(count) = w2(q+1)*coef_dyy;
+ count = count + 1;
+
+ end
+ rowCount = rowCount + 1;
+ end
+
+ if S.BCy == 1
+ % Removing outside domain entries (for periodic code this is unnecessary)
+ isIn = (II >= 1) & (II <= Ny);
+ S.I_22 = I(isIn); S.II_22 = II(isIn); S.V_22 = V(isIn);
+ elseif S.BCy == 0
+ S.isOutl_22 = (II<1); S.isOutr_22 = (II>Ny); % Warning: Assumed influence of only neighboring cells
+ S.I_22 = I; S.II_22 = mod(II+(Ny-1),Ny)+1; S.V_22 = V;
+ end
+
+ % D_zz laplacian in 1D
+ %-----------------------
+
+ % Initial number of non-zeros: including ghost nodes
+ nnzCount = (2 * n0 + 1) * Nz;
+
+ % Row and column indices and the corresponding non-zero values
+ % used to generate sparse matrix DL33 s.t. DL33(I(k),II(k)) = V(k)
+ I = zeros(nnzCount,1);
+ V = zeros(nnzCount,1);
+ II = zeros(nnzCount,1);
+ rowCount = 1;
+ count = 1;
+ coef_dzz = 1/dz^2;
+
+ % Find non-zero entries that use forward difference
+ for ii = 1:Nz
+ % diagonal element
+ I(count) = rowCount; II(count) = ii;
+ V(count) = w2(1)*coef_dzz ;
+ count = count + 1;
+ % off-diagonal elements
+ for q = 1:n0
+ % ii + q
+ I(count) = rowCount; II(count) = ii+q;
+ V(count) = w2(q+1)*coef_dzz;
+ count = count + 1;
+ % ii - q
+ I(count) = rowCount; II(count) = ii-q;
+ V(count) = w2(q+1)*coef_dzz;
+ count = count + 1;
+
+ end
+ rowCount = rowCount + 1;
+ end
+
+ if S.BCz == 1
+ % Removing outside domain entries (for periodic code this is unnecessary)
+ isIn = (II >= 1) & (II <= Nz);
+ S.I_33 = I(isIn); S.II_33 = II(isIn); S.V_33 = V(isIn);
+ elseif S.BCz == 0
+ S.isOutl_33 = (II<1); S.isOutr_33 = (II>Nz); % Warning: Assumed influence of only neighboring cells
+ S.I_33 = I; S.II_33 = mod(II+(Nz-1),Nz)+1; S.V_33 = V;
+ end
+
+ if S.cell_typ == 2
+ % Create 1D gradient in all directions
+ %---------------------------------------
+
+ % x-direction
+ %-------------
+ nnz_x = 2*n0*Nx;
+ G = zeros(nnz_x,1);
+ R = zeros(nnz_x,1);
+ A = zeros(nnz_x,1);
+ rowCount = 1;
+ count = 1;
+ coef_dx = 1/dx;
+
+ for ii = 1:Nx
+ for q = 1:n0
+ % ii + q
+ G(count) = rowCount; R(count) = ii+q;
+ A(count) = w1(q+1)*coef_dx;
+ count = count + 1;
+ % ii - q
+ G(count) = rowCount; R(count) = ii-q;
+ A(count) = -w1(q+1)*coef_dx;
+ count = count + 1;
+ end
+ rowCount = rowCount + 1;
+ end
+
+ if S.BCx == 1
+ % Removing outside domain entries (for periodic code this is unnecessary)
+ isIn = (R >= 1) & (R <= Nx);
+ S.I_1 = G(isIn); S.II_1 = R(isIn); S.V_1 = A(isIn);
+ elseif S.BCx == 0
+ S.isOutl_1 = (R<1); S.isOutr_1 = (R>Nx); % Warning: Assumed influence of only neighboring cells
+ S.I_1 = G; S.II_1 = mod(R+(Nx-1),Nx)+1; S.V_1 = A;
+ end
+
+ % y-direction
+ %-------------
+
+ nnz_y = 2*n0*Ny;
+ G = zeros(nnz_y,1);
+ R = zeros(nnz_y,1);
+ A = zeros(nnz_y,1);
+ count =1;
+ rowCount =1;
+ coef_dy = 1/dy;
+
+ for jj = 1:Ny
+ for q = 1:n0
+ % jj + q
+ G(count) = rowCount; R(count) = jj+q;
+ A(count) = w1(q+1)*coef_dy;
+ count = count + 1;
+ % jj - q
+ G(count) = rowCount; R(count) = jj-q;
+ A(count) = -w1(q+1)*coef_dy;
+ count = count + 1;
+ end
+ rowCount = rowCount + 1;
+ end
+
+ if S.BCy == 1
+ % Removing outside domain entries (for periodic code this is unnecessary)
+ isIn = (R >= 1) & (R <= Ny);
+ S.I_2 = G(isIn); S.II_2 = R(isIn); S.V_2 = A(isIn);
+ elseif S.BCy == 0
+ S.isOutl_2 = (R<1); S.isOutr_2 = (R>Ny);
+ S.I_2 = G; S.II_2 = mod(R+(Ny-1),Ny)+1; S.V_2 = A;
+ end
+
+
+ % z-direction
+ %-------------
+
+ nnz_z = 2*n0*Nz;
+ G = zeros(nnz_z,1);
+ R = zeros(nnz_z,1);
+ A = zeros(nnz_z,1);
+ count =1;
+ rowCount =1;
+ coef_dz = 1/dz;
+
+ for kk = 1:Nz
+ for q = 1:n0
+ % kk + q
+ G(count) = rowCount; R(count) = kk+q;
+ A(count) = w1(q+1)*coef_dz;
+ count = count + 1;
+ % kk - q
+ G(count) = rowCount; R(count) = kk-q;
+ A(count) = -w1(q+1)*coef_dz;
+ count = count + 1;
+ end
+ rowCount = rowCount + 1;
+ end
+
+ if S.BCz == 1
+ % Removing outside domain entries (for periodic code this is unnecessary)
+ isIn = (R >= 1) & (R <= Nz);
+ S.I_3 = G(isIn); S.II_3 = R(isIn); S.V_3 = A(isIn);
+ elseif S.BCz == 0
+ S.isOutl_3 = (R<1); S.isOutr_3 = (R>Nz);
+ S.I_3 = G; S.II_3 = mod(R+(Nz-1),Nz)+1; S.V_3 = A;
+ end
+ end
+
+elseif (S.cell_typ == 3 || S.cell_typ == 4 || S.cell_typ == 5)
+ S = lapIndicesValues_1d_cychel(S);
+
+end
\ No newline at end of file
diff --git a/src/lapVec.m b/src/lapVec.m
new file mode 100644
index 00000000..94eb8a65
--- /dev/null
+++ b/src/lapVec.m
@@ -0,0 +1,64 @@
+function DLX = lapVec(DL11,DL22,DL33,DG1,DG2,DG3,X,S)
+% @ brief Calculates laplacian vector product using
+% Kronecker product method
+% @ authors
+% Abhiraj Sharma
+% Qimen Xu
+% Phanish Suryanarayana
+%
+% @param DLii Discrete laplacian component in 1D along ith direction
+% @param DGi Discrete gradient component in 1D along ith direction
+% @param X N x Ns matrix of eigenfunctions of Hamiltonian
+% @param DLX Discrete laplacian times X
+%
+% @ references
+% "On real-space Density Functional Theory for
+% non-orthogonal crystal systems: Kronecker product
+% formulation of the kinetic energy operator (Sharma et. al. 2018)"
+%
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+%=====================================================================================
+Nx = S.Nx;Ny = S.Ny;Nz = S.Nz;
+if S.cell_typ == 1 % orthogonal systems
+ X1 = reshape(X,Nx,Ny,[]);
+ l_zs = size(X1,3);
+ Hlx1 = zeros(Nx,Ny,l_zs);
+ for i=1:l_zs
+ Hlx1(:,:,i) = DL11*X1(:,:,i) + X1(:,:,i)*DL22.';
+ end
+ Hlx1 = reshape(Hlx1,Nx*Ny,Nz,[]) ;
+ X2 = reshape(X,Nx*Ny,Nz,[]);
+ l_s = size(X2,3);
+ Hlx2 = zeros(Nx*Ny,Nz,l_s);
+ for i=1:l_s
+ Hlx2(:,:,i) = X2(:,:,i)*DL33.';
+ end
+ DLX = reshape((Hlx1 + Hlx2),[],l_s);
+elseif S.cell_typ == 2
+ T11 = S.lapc_T(1,1);T22 = S.lapc_T(2,2);T33 = S.lapc_T(3,3);T12 = S.lapc_T(1,2);
+ T23 = S.lapc_T(2,3);T13 = S.lapc_T(1,3);
+
+ X1 = reshape(X,Nx,Ny,[]);
+ l_zs = size(X1,3);
+ Hlx1 = zeros(Nx,Ny,l_zs);
+ Hlx2 = zeros(Nx,Ny,l_zs);
+ for i=1:l_zs
+ Hlx1(:,:,i) = T11*DL11*X1(:,:,i) + T22*X1(:,:,i)*DL22.' + T12*DG1*X1(:,:,i)*DG2.' ;
+ Hlx2(:,:,i) = T13*DG1*X1(:,:,i) + T23*X1(:,:,i)*DG2.' ;
+ end
+ Hlx1 = reshape(Hlx1,Nx*Ny,Nz,[]);
+ Hlx2 = reshape(Hlx2,Nx*Ny,Nz,[]);
+
+ X2 = reshape(X,Nx*Ny,Nz,[]);
+ l_s = size(X2,3);
+ for i=1:l_s
+ Hlx2(:,:,i) = T33*X2(:,:,i)*DL33.' + Hlx2(:,:,i)*DG3.';
+ end
+
+ DLX = reshape((Hlx1 + Hlx2),[],l_s);
+elseif (S.cell_typ == 3 || S.cell_typ == 4 || S.cell_typ == 5)
+ DLX = lapVec_cychel(DL11,DL22,DL33,DG1,DG2,DG3,X,S);
+end
+
+
+
diff --git a/src/md.m b/src/md.m
new file mode 100644
index 00000000..054a7d69
--- /dev/null
+++ b/src/md.m
@@ -0,0 +1,242 @@
+function S = md(S)
+% @ brief Function to perform molecular dynamics
+% @ authors
+% Abhiraj Sharma
+% Phanish Suryanarayana
+%
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ % Read the .restart file if MD is restarted
+ if S.RestartFlag == 1
+ S = RestartMD(S);
+ end
+
+ % set up MD output filenames
+ S.mdfname = strcat(S.filename,'.aimd');
+ if S.suffixNum > 0
+ S.mdfname = sprintf('%s.aimd_%d',S.filename,S.suffixNum);
+ end
+
+ % Different MD methods
+ if strcmp(S.MDMeth,'NVE')
+ S = MD_NVE(S);
+ else
+ error('Currently only NVE is implemented in this code!');
+ end
+end
+
+
+
+
+function S = MD_NVE(S)
+% @ brief Molecular dynamics of a canonical ensemble is performed
+% using velocity verlet algorithm
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+ % MD parameters
+ MD_dt = S.MD_dt; % in femto-seconds
+ MD_dt = MD_dt * S.fs2atu; % in atu
+ kB = S.kB;
+
+ % Atomic mass
+ S.atomM = zeros(S.n_atm,1);
+ count_typ = 1;
+ count_typ_atms = 1;
+ for JJ_a = 1:S.n_atm % loop over all the atoms
+ S.atomM(JJ_a) = S.Atm(count_typ).Mass;
+ if count_typ_atms == S.Atm(count_typ).n_atm_typ
+ count_typ_atms = 1;
+ count_typ = count_typ + 1;
+ else
+ count_typ_atms = count_typ_atms + 1;
+ end
+ end
+
+ S.atomM = S.atomM * S.amu2au; % in au
+
+ % Degree of freedom in the system
+ dof = 3*S.n_atm - 3;
+
+ % MD initialization
+ if ~S.RestartFlag
+ %x = transpose(S.lat_uvec) * S.Atoms';
+ %x = reshape(x,[],1);
+ x = coordinateTransformation(S, S.Atoms, 'noncart2cart_dis');
+ x = reshape(x',[],1);
+ % 1 - S.MD_velocity initialization (Maxwell-Boltzmann distr.)
+ S.MD_vel = zeros(S.n_atm,3);
+ rng('default');
+ S.MD_vel(:,1) = sqrt(kB * S.ion_T./S.atomM) .* cos(2 * pi * rand(S.n_atm,1)) .* sqrt(-2.0 * log(rand(S.n_atm,1)));
+ S.MD_vel(:,2) = sqrt(kB * S.ion_T./S.atomM) .* cos(2 * pi * rand(S.n_atm,1)) .* sqrt(-2.0 * log(rand(S.n_atm,1)));
+ S.MD_vel(:,3) = sqrt(kB * S.ion_T./S.atomM) .* cos(2 * pi * rand(S.n_atm,1)) .* sqrt(-2.0 * log(rand(S.n_atm,1)));
+ mvsum = sum(S.atomM' * S.MD_vel,1);
+
+ % Remove translation
+ S.MD_vel = S.MD_vel - repmat(mvsum/sum(S.atomM),S.n_atm,1);
+ KE = 0.5 * sum(S.atomM' * (S.MD_vel .* S.MD_vel));
+
+ % Rescale and reshape S.MD_velocities
+ S.MD_vel = S.MD_vel * sqrt(dof * kB * S.ion_T/(2*KE));
+ else
+ x = reshape(S.Atoms',[],1);
+ end
+
+ % 2 - acceleration initialization
+ [x,f,S] = electronicGroundStateAtomicForce(x,S); f = -f;
+ S.ForceCount = S.ForceCount + 1;
+
+ f = transpose(reshape(f,3,[]));
+ acc = f./repmat(S.atomM,1,3);
+ acc = reshape(acc',[],1);
+
+ % Initial MD quantities
+ KE = 0.5 * sum(S.atomM' * (S.MD_vel .* S.MD_vel));
+ S.MD_vel = reshape(S.MD_vel',[],1);
+
+ TE = (S.Etotal + KE)./S.n_atm;
+
+ fprintf('Totalenergy/atom and temperature in MD step %d are: %.15f %.15f\n\n',1,TE, S.ion_T);
+
+ % Print the output in .aimd file
+ if (S.PrintMDout == 1 && ~S.RestartFlag)
+ PrintMD(S,transpose(reshape(x,3,[])),transpose(reshape(S.MD_vel,3,[])),TE);
+ end
+ S.Relax_iter = S.Relax_iter + 1;
+
+
+ for i = 1:S.MD_Nstep+S.RestartFlag-1
+ % Leapfrog step - I
+ S.MD_vel = S.MD_vel + 0.5 * MD_dt * acc;
+ x = x + MD_dt * S.MD_vel;
+
+ % Calculate force
+ [x,f,S] = electronicGroundStateAtomicForce(x,S); f = -f;
+ S.ForceCount = S.ForceCount + 1;
+
+ % Leapfrog step - II
+ f = transpose(reshape(f,3,[]));
+ acc = f./repmat(S.atomM,1,3);
+ acc = reshape(acc',[],1);
+ S.MD_vel = S.MD_vel + 0.5 * MD_dt * acc;
+ S.MD_vel = transpose(reshape(S.MD_vel,3,[]));
+ KE = 0.5 * sum(S.atomM' * (S.MD_vel .* S.MD_vel));
+ S.MD_vel = reshape(S.MD_vel',[],1);
+ TE = (S.Etotal + KE)/S.n_atm;
+ S.ion_T = 2 * KE /(kB * dof);
+ if(S.ion_elec_eqT == 1)
+ S.Temp = S.ion_T;
+ S.bet = 1 / (S.kB * S.Temp);
+ end
+ fprintf('Totalenergy/atom and temperature in MD step %d are: %.15f %.15f\n\n',i+1,TE, S.ion_T);
+
+ % print MD output in .aimd file
+ if S.PrintMDout == 1
+ PrintMD(S,transpose(reshape(x,3,[])),transpose(reshape(S.MD_vel,3,[])),TE);
+ end
+ % print relevant quantities for MD restart in .restart file
+ if (S.Printrestart == 1 && rem(S.Relax_iter, S.Printrestart_fq) == 0)
+ PrintRestartMD(S,transpose(reshape(x,3,[])),transpose(reshape(S.MD_vel,3,[])));
+ end
+
+ S.Relax_iter = S.Relax_iter + 1;
+ end
+
+ if (S.Printrestart == 1)
+ S.Relax_iter = S.Relax_iter - 1;
+ PrintRestartMD(S,transpose(reshape(x,3,[])),transpose(reshape(S.MD_vel,3,[])));
+ end
+end
+
+
+
+
+function [] = PrintMD(S,atom_pos,atom_vel,TE)
+% @ brief Function to write MD output in .aimd file
+%========================================================
+ if S.Relax_iter == 1
+ fileID = fopen(S.mdfname,'w');
+ else
+ fileID = fopen(S.mdfname,'a');
+ end
+ fprintf(fileID,':MDSTEP: %d\n',S.Relax_iter);
+ if (S.PrintAtomPosFlag == 1)
+ fprintf(fileID,':R:\n');
+ fprintf(fileID, '%18.10E %18.10E %18.10E\n', atom_pos');
+ end
+ if (S.PrintAtomVelFlag == 1)
+ fprintf(fileID,':V:\n');
+ fprintf(fileID, '%18.10E %18.10E %18.10E\n', atom_vel');
+ end
+ if (S.PrintForceFlag == 1)
+ fprintf(fileID,':F:\n');
+ fprintf(fileID, '%18.10E %18.10E %18.10E\n', S.force');
+ end
+ fprintf(fileID,':TEL: %18.10E\n',S.Temp);
+ fprintf(fileID,':TIO: %18.10E\n',S.ion_T);
+ fprintf(fileID,':TE: %18.10E\n',TE);
+ fclose(fileID);
+end
+
+
+
+
+function [] = PrintRestartMD(S,atom_pos,atom_vel)
+% @ brief Function to write relevant quantities for MD restart in .restart file
+%===================================================================================
+ fileID = fopen(S.restartfname,'w');
+ fprintf(fileID,':MDSTEP: %d\n',S.Relax_iter);
+ fprintf(fileID,':R:\n');
+ fprintf(fileID, '%18.10E %18.10E %18.10E\n', atom_pos');
+ fprintf(fileID,':V:\n');
+ fprintf(fileID, '%18.10E %18.10E %18.10E\n', atom_vel');
+ fprintf(fileID,':TEL: %18.10E\n',S.Temp);
+ fprintf(fileID,':TIO: %18.10E\n',S.ion_T);
+ fclose(fileID);
+end
+
+
+
+function S = RestartMD(S)
+% @ brief Function to read .restart file of MD
+% ====================================================
+ fprintf(' Reading .restart file ...\n');
+ fid = fopen(S.restartfname,'r');
+ if (fid == -1)
+ error('\n Cannot open file "%s"\n',S.restartfname);
+ end
+
+ while(~feof(fid))
+ C_inpt = textscan(fid,'%s',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ str = char(C_inpt{:});
+ if (strcmp(str,':MDSTEP:'))
+ C_param = textscan(fid,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.Relax_iter = C_param{1};
+ textscan(fid,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,':R:'))
+ textscan(fid,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ for i = 1:S.n_atm
+ C_param = textscan(fid,'%f %f %f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ textscan(fid,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ S.Atoms(i,:) = cell2mat(C_param);
+ end
+ elseif (strcmp(str,':V:'))
+ S.MD_vel = zeros(S.n_atm,3);
+ textscan(fid,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ for i = 1:S.n_atm
+ C_param = textscan(fid,'%f %f %f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ textscan(fid,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ S.MD_vel(i,:) = cell2mat(C_param);
+ end
+ elseif (strcmp(str,':TEL:'))
+ C_param = textscan(fid,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.Temp = C_param{1};
+ textscan(fid,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,':TIO:'))
+ C_param = textscan(fid,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.ion_T = C_param{1};
+ textscan(fid,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ end
+ end
+ S.bet = 1 / (S.kB * S.Temp);
+ fclose(fid);
+end
diff --git a/src/mixing.m b/src/mixing.m
new file mode 100644
index 00000000..eb9db4f0
--- /dev/null
+++ b/src/mixing.m
@@ -0,0 +1,183 @@
+function [S,x_kp1] = mixing(S, g_k, x_k, iter)
+% @brief MIXING performs mixing of the previous SCF iterates to
+% accelerate SCF convergence.
+%
+% @param g_k Current output mixing iterate.
+% @param x_in Current input mixing iterate.
+% @param iter Iteration number.
+%
+% @authors Qimen Xu
+% Abhiraj Sharma
+% Phanish Suryanarayana
+%
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+
+[S,x_kp1] = Periodic_Pulay(S, g_k, x_k, iter);
+
+end
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+function [S,x_kp1] = Periodic_Pulay(S, g_k, x_k, iter)
+% periodic pulay mixing
+% Ref: A Banerjee et al, Chemical Physics Letters 647 (2016) 31-35.
+% http://dx.doi.org/10.1016/j.cplett.2016.01.033
+mix_hist = S.MixingHistory;
+mix_p_pulay = S.PulayFrequency;
+mix_param = S.MixingParameter; % beta
+omega = S.MixingParameterSimple; % mixing parameter for simple mixing step
+
+f_k = g_k - x_k;
+if iter > 1
+ f_km1 = S.mixing_hist_fkm1;
+ x_km1 = S.mixing_hist_xkm1;
+end
+
+% store residual & iteration history
+if iter > 1
+ i_hist = mod(iter-2,mix_hist)+1;
+ if (S.PulayRestartFreq > 0 && mod(iter, S.PulayRestartFreq) == 0)
+ S.X = zeros(size(S.X)); S.F = zeros(size(S.F));
+ S.X(:,1) = x_k - x_km1;
+ S.F(:,1) = f_k - f_km1;
+ else
+ S.X(:,i_hist) = x_k - x_km1;
+ S.F(:,i_hist) = f_k - f_km1;
+ end
+end
+
+% apply Anderson extrapolation every p iters
+if rem(iter,mix_p_pulay) == 0 && iter > 1
+ % find weighted averages x_wavg, f_wavg
+ [x_wavg, f_wavg] = andersonWtdAvg(x_k, f_k, S.X, S.F);
+else
+ % simple mixing
+ x_wavg = x_k; f_wavg = f_k;
+end
+
+% apply preconditioner to the weighted residual
+if S.MixingPrecond > 0
+ if S.nspin == 1
+ % precondition total density
+ if S.MixingPrecond == 1 % kerker precond
+ S.Pf_guess = zeros(size(f_wavg)); % similar to using previous guess
+ f_wavg = Kerker_Precond(S, f_wavg, S.precond_tol, 1000, S.Pf_guess);
+ % S.Pf_guess = f_wavg; % update guess vector
+ elseif S.MixingPrecond == 2 % resta precond
+ S.Pf_guess = 1e-6*rand(length(f_wavg),length(S.precondcoeff_a));
+ %S.precondcoeff_lambda_TF
+ f_wavg = Resta_Precond(S, f_wavg, S.precond_tol, 1000, S.Pf_guess);
+ %S.Pf_guess = repmat(f_wavg,1,length(S.precondcoeff_a)); % update guess vector
+ elseif S.MixingPrecond == 3 % truncated kerker precond
+ S.Pf_guess = 1e-6*rand(length(f_wavg),length(S.precondcoeff_a));
+ %S.precondcoeff_lambda_TF
+ f_wavg = TruncatedKerker_Precond(S, f_wavg, S.precond_tol, 1000, S.Pf_guess);
+ %S.Pf_guess = repmat(f_wavg,1,length(S.precondcoeff_a)); % update guess vector
+ end
+ else
+ f_Rho = f_wavg(1:S.N) + f_wavg(S.N+1:end);
+ f_M = f_wavg(1:S.N) - f_wavg(S.N+1:end);
+ % precondition total density
+ if S.MixingPrecond == 1 % kerker precond
+ Pf_Rho = Kerker_Precond(S, f_Rho, S.precond_tol, 1000, S.Pf_guess);
+ S.Pf_guess = Pf_Rho; % update guess vector
+ elseif S.MixingPrecond == 2 % resta precond
+ S.Pf_guess = 1e-6*rand(length(f_Rho),length(S.precondcoeff_a));
+ Pf_Rho = Resta_Precond(S, f_Rho, S.precond_tol, 1000, S.Pf_guess);
+ %S.Pf_guess = repmat(Pf_Rho,1,length(S.precondcoeff_a)); % update guess vector
+ elseif S.MixingPrecond == 3 % truncated kerker precond
+ S.Pf_guess = 1e-6*rand(length(f_Rho),length(S.precondcoeff_a));
+ Pf_Rho = TruncatedKerker_Precond(S, f_Rho, S.precond_tol, 1000, S.Pf_guess);
+ %S.Pf_guess = repmat(Pf_Rho,1,length(S.precondcoeff_a)); % update guess vector
+ end
+ f_wavg = vertcat(Pf_Rho + f_M, Pf_Rho - f_M)/2;
+ end
+end
+
+% update new input iterate
+if (rem(iter,mix_p_pulay) == 0)
+ x_kp1 = x_wavg + mix_param * f_wavg;
+else
+ x_kp1 = x_wavg + omega * f_wavg;
+end
+
+if S.MixingVariable == 0
+ % due to inaccurate kerker solver, the density might have
+ % slightly inaccuate integral
+ if S.MixingPrecond ~= 0
+ % scale the density
+ x_kp1 = x_kp1 * (-S.NegCharge/sum(S.W'*reshape(x_kp1,S.N,S.nspin),2));
+ end
+end
+
+% update the history vectors
+S.mixing_hist_fkm1 = f_k;
+S.mixing_hist_xkm1 = x_k;
+
+end
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+function Pf = Kerker_Precond(S, f, tol, maxit, Pf_guess)
+% KERKER_PRECOND applies kerker preconditioner.
+% KERKER_PRECOND effectively applies (Lap - k_TF^2)^-1 * Lap to f
+% by solving the linear system (Lap - k_TF^2) s = Lap*f.
+
+% lambda_sqr = lambda_TF * lambda_TF;
+%
+% % these are fixed, so it should be possible to store them
+% B = S.Lap_std - spdiags(lambda_sqr * ones(S.N,1),0,S.N,S.N);
+%
+% Df = S.Lap_std * f;
+%
+% Pf = aar(B,Df,Pf_guess,tol,maxit,[],[],[],[],[]);
+
+Pf = RSfit_Precond(S,f,S.precondcoeff_a,S.precondcoeff_lambda_TF,...
+ S.precondcoeff_k,tol,maxit,Pf_guess);
+
+end
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+function Pf = Resta_Precond(S, f, tol, maxit, Pf_guess)
+% RESTA_PRECOND applies real-space resta preconditioner.
+
+Pf = RSfit_Precond(S,f,S.precondcoeff_a,S.precondcoeff_lambda_TF,...
+ S.precondcoeff_k,tol,maxit,Pf_guess);
+
+end
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+function Pf = TruncatedKerker_Precond(S, f, tol, maxit, Pf_guess)
+% TRUNCATEDKERKER_PRECOND applies real-space truncated-Kerker preconditioner.
+
+Pf = RSfit_Precond(S,f,S.precondcoeff_a,S.precondcoeff_lambda_TF,...
+ S.precondcoeff_k,tol,maxit,Pf_guess);
+
+end
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+function Pf = RSfit_Precond(S, f, a, lambda_sqr, k, tol, maxit, Pf_guess)
+% RSFIT_PRECOND applies real-space preconditioner with any rational fit
+% coefficients.
+% RSFIT_PRECOND effectively applies sum_i (a_i*(Lap - k_TF2_i)^-1 * Lap + k*I)
+% to f by solving the linear systems a_i*(Lap - k_TF2_i) s = Lap*f and
+% summing the sols. To apply any preconditioner, simply perform a
+% rational curve fit to the preconditioner in fourier space and provide
+% the fit coeffs a(i), lambda_TF(i) and a constant k.
+
+m = length(a); % number of terms
+
+Df = S.Lap_std * f;
+
+Pf = k * f;
+
+isguess = size(Pf_guess,2) >= m;
+for i = 1:m
+ B = S.Lap_std - spdiags(lambda_sqr(i) * ones(S.N,1),0,S.N,S.N);
+ guess = []; if isguess, guess = Pf_guess(:,i); end
+ Pf = Pf + a(i) * aar(B,Df,guess,tol,maxit,0.6,0.6,7,6,S.LapPreconL,S.LapPreconU);
+ %[f1,~,~,~] = gmres(B,Df,50,tol,maxit,S.LapPreconL,S.LapPreconU,guess);
+ %Pf = Pf + a(i) * f1;
+end
+
+Pf = real(Pf);
+end
+
diff --git a/src/msparc.m b/src/msparc.m
new file mode 100644
index 00000000..03f8b30d
--- /dev/null
+++ b/src/msparc.m
@@ -0,0 +1,116 @@
+function S = msparc(fname,varargin)
+% @brief M-SPARC implements DFT calculation
+%
+% @param fname The input filename.
+% @param parallel_switch (optional) 1: turn on parallelization
+% 0: turn off parallelization
+%
+% @authors Qimen Xu
+% Abhiraj Sharma
+% Phanish Suryanarayana
+%
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+%
+
+format long;
+fprintf('\n');
+
+% Start timer
+total_time = tic;
+
+% check input arguments
+if isempty(fname)
+ error('Please provide input file name (excluding extension)!');
+end
+
+parallel_switch = 0; % default is off
+if nargin == 2
+ parallel_switch = varargin{1};
+elseif nargin > 2
+ error('Too many input arguments.');
+end
+
+% Read initial data and create a structure S to store the data
+S = initialization(fname);
+
+S.parallel = parallel_switch; %0 - N0 && 1 - Yes
+if S.parallel == 1
+ % Set up the parallel environment
+ warning('off','MATLAB:maxNumCompThreads:Deprecated');
+ max_threads = 12; % Experiment with this
+ max_threads_default = maxNumCompThreads;
+ if(max_threads > max_threads_default)
+ max_threads = max_threads_default;
+ end
+ LASTN_all_comp = maxNumCompThreads(max_threads);
+ fprintf('\n \n Starting the Matlab pool ... \n');
+ tic_pool = tic;
+ num_worker_heuristic = S.tnkpt;
+
+ % Get the default size as a safeguard
+ myCluster = parcluster();
+ if(myCluster.NumWorkers < num_worker_heuristic)
+ num_worker_heuristic = myCluster.NumWorkers;
+ end
+
+ % Clean up older pools
+ delete(gcp('nocreate'));
+
+ % Launch new pool
+ poolobj = parpool(num_worker_heuristic) ;
+ S.num_worker_heuristic = num_worker_heuristic;
+ fprintf('\n \n Pool set up in %f s. \n', toc(tic_pool));
+end
+
+% Perform relaxation/MD/Single point calculation
+if S.RelaxFlag
+ S = relax(S);
+elseif S.MDFlag
+ S = md(S);
+else
+ [~,~,S] = electronicGroundStateAtomicForce(S.Atoms,S);
+end
+
+% Print results (Final atom positions)
+fprintf(' Final atomic positions (Cartesian) are as follows:\n');
+for k = 1:S.n_atm
+ fprintf(' %9.6f \t %9.6f \t %9.6f \n', S.Atoms(k,1),S.Atoms(k,2),S.Atoms(k,3));
+end
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+if S.parallel == 1
+ fprintf('\n \n Closing the Matlab pool ... \n');
+ tic_pool = tic;
+ delete(poolobj);
+ fprintf('\n \n Pool closed in %f s. \n', toc(tic_pool));
+end
+
+% write to output file
+outfname = S.outfname;
+fileID = fopen(outfname,'a');
+if (fileID == -1)
+ error('\n Cannot open file "%s"\n',outfname);
+end
+
+t_wall = toc(total_time);
+fprintf(fileID,'***************************************************************************\n');
+fprintf(fileID,' Timing info \n');
+fprintf(fileID,'***************************************************************************\n');
+fprintf(fileID,'Total walltime : %.3f sec\n', t_wall);
+fprintf(fileID,'___________________________________________________________________________\n');
+fprintf(fileID,'\n');
+fprintf(fileID,'***************************************************************************\n');
+fprintf(fileID,'* Material Physics & Mechanics Group, Georgia Tech *\n');
+fprintf(fileID,'* PI: Phanish Suryanarayana *\n');
+fprintf(fileID,'* Main Developers: Qimen Xu, Abhiraj Sharma *\n');
+fprintf(fileID,'* Acknowledgements: U.S. DOE (DE-SC0019410); NSF (1333500,1553212) *\n');
+fprintf(fileID,'***************************************************************************\n');
+fprintf(fileID,' \n');
+fclose(fileID);
+
+% Program run-time
+fprintf('\n Run-time of the program: %f seconds\n', t_wall);
+
+if S.parallel == 1
+ LASTN_reset = maxNumCompThreads(LASTN_all_comp);
+end
diff --git a/src/occupations.m b/src/occupations.m
new file mode 100644
index 00000000..13893984
--- /dev/null
+++ b/src/occupations.m
@@ -0,0 +1,36 @@
+function S = occupations(S)
+
+FermiEnergyEvaluator = @(lambda_f_g) fermiCalc(lambda_f_g,S);
+
+S.lambda_f = fzero(FermiEnergyEvaluator,0);
+
+%fprintf(2,' ------------------\n');
+fprintf(' Fermi energy = %f\n',S.lambda_f);
+
+% Calculate occupations
+if S.elec_T_type == 0 % fermi-dirac smearing
+ S.occ = 1./(1+exp(S.bet*(S.EigVal-S.lambda_f)));
+elseif S.elec_T_type == 1 % gaussian smearing
+ S.occ = 0.5 * (1.0 - erf(S.bet*(S.EigVal-S.lambda_f)));
+end
+
+end
+
+
+
+function f = fermiCalc(lambda_f_g, S)
+ f = 0;
+ ks = 1;
+ for spin = 1:S.nspin
+ for kpt = 1:S.tnkpt
+ if S.elec_T_type == 0 % fermi-dirac smearing
+ f = f + S.occfac * sum(S.wkpt(kpt)./(1+exp(S.bet*(S.EigVal(:,ks)-lambda_f_g)))) ;
+ else
+ f = f + S.occfac * sum(S.wkpt(kpt)*0.5*(1.0-erf(S.bet*(S.EigVal(:,ks)-lambda_f_g)))) ;
+ end
+ ks = ks + 1;
+ end
+ end
+ %f = f - S.Nelectron;
+ f = f + S.NegCharge;
+end
\ No newline at end of file
diff --git a/src/poissonSolve.m b/src/poissonSolve.m
new file mode 100644
index 00000000..71644300
--- /dev/null
+++ b/src/poissonSolve.m
@@ -0,0 +1,294 @@
+function [S] = poissonSolve(S, poisson_tol, Isguess)
+% @brief POISSONSOLVE solves the poisson equation for the
+% electrostatic potential.
+%
+% @param poisson_tol Tolerance for solving the poisson equation
+% using iterative method AAR.
+% @param Isguess 1: guess vector provided,
+% 0: no guess vector available.
+%
+% @authors Qimen Xu
+% Abhiraj Sharma
+% Phanish Suryanarayana
+%
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+%
+
+t1 = tic;
+
+if S.cell_typ < 3
+ f = poisson_RHS(S);
+else
+ f = -4*pi*(S.rho(:,1)+S.b);
+end
+
+%fprintf(' Time taken for poisson_RHS: %f s\n',toc(t1));
+
+% solve the poisson equation using a linear solver (AAR or gmres)
+% AAR reference: see AAR.m
+if Isguess
+ phi_guess = S.phi;
+else
+ phi_guess = [];
+end
+
+%[S.phi,conv_flag, relres, iter] = gmres(S.Lap_std,f,50,poisson_tol,50,S.LapPreconL,S.LapPreconU,phi_guess);
+S.phi = aar(S.Lap_std,f,phi_guess,poisson_tol,S.MAXIT_POISSON,0.6,0.6,7,6,S.LapPreconL,S.LapPreconU);
+
+if(S.BC == 2)
+ % To make sure integral phi is 0 (this removes the arbitariness of the
+ % constant in phi calculation)
+ S.phi = S.phi - dot(S.W,S.phi)/sum(S.W);
+end
+
+% [phi,conv_flag] = pcg(S.Lap,f,S.poisson_tol,50,S.LapPreconL,S.LapPreconU);
+% fprintf('\n Poisson problem took %fs and %d iterations\n',toc(t1),iter(1)*iter(2));
+% assert(conv_flag==0,'Electrostatic Poisson solve did not converge')
+% S_Debug.relax(S.Relax_iter).poisson_flag_init = conv_flag;
+
+fprintf(' Poisson problem took %fs\n',toc(t1));
+
+end
+
+
+function f = poisson_RHS(S)
+% @brief Poisson_RHS evaluates the right hand side of the poisson equation,
+% including the boundary condtions, i.e. f = -4 * pi * ( rho + b - d)
+% for cluster system, while for periodic system it's just
+% f = -4 * pi * (rho + b).
+rho = S.rho(:,1);
+f = -4 * pi * (rho + S.b);
+
+% for charged systems, add a uniform background charge so that total charge
+% is 0
+if S.NetCharge ~= 0
+ unif_bkgd_chrg = S.NetCharge / (S.L1*S.L2*S.L3);
+ f = f + (-4 * pi) * unif_bkgd_chrg;
+ % fprintf(2,'total charge + background charge = %d\n',dot(S.W,rho+S.b+unif_bkgd_chrg));
+end
+
+if(S.BC == 1)
+ % For cluster systems, we need to include boundary conditions d
+ % RR = S.RR_AUG(S.isIn);
+ for l = 0:S.l_cut
+ multipole_moment(l+1).Qlm = sum(repmat(S.RR.^l .* (rho + S.b) .* S.W,1,2*l+1).* S.SH(l+1).Ylm )';
+ end
+
+ % Calculate phi using multipole expansion
+ phi = zeros(size(S.RR_AUG_3D));
+ for l = 0 : S.l_cut
+ denom = (2*l+1)*S.RR_AUG_3D.^(l+1);
+ for m = -l : l
+ Ylm_AUG_3D = reshape(S.SH(l+1).Ylm_AUG(:,m+l+1),size(phi));
+ phi = phi + Ylm_AUG_3D .* multipole_moment(l+1).Qlm(m+l+1) ./ denom;
+ end
+ end
+ phi = 4 * pi * phi;
+ phi(S.isIn) = 0;
+elseif S.BC == 2
+ return;
+elseif S.BC == 3
+ % find boundary conditions for periodic in 2D, dirichlet in 1D
+ % Calculate phi
+ phi = zeros(S.Nx+2*S.FDn, S.Ny+2*S.FDn, S.Nz+2*S.FDn);
+
+ cellsize = [S.L1, S.L2, S.L3];
+ gridsizes = [S.Nx, S.Ny, S.Nz];
+ meshsizes = [S.dx, S.dy, S.dz];
+ bcs = [S.BCx,S.BCy,S.BCz];
+
+ % find which direction has Dirichlet BC
+ dir_Z = find(bcs == 1);
+ dir_X = mod(dir_Z, 3) + 1;
+ dir_Y = mod(dir_X, 3) + 1;
+
+ % once we find the direction, we assume that direction is the Z
+ % direction, the other two directions are then called X, Y
+ NX = gridsizes(dir_X); NY = gridsizes(dir_Y); NZ = gridsizes(dir_Z);
+ LX = cellsize(dir_X); LY = cellsize(dir_Y); LZ = cellsize(dir_Z);
+ dX = meshsizes(dir_X); dY = meshsizes(dir_Y); dZ = meshsizes(dir_Z);
+ A_XY = LX * LY; % area of (x',y') surface
+
+ % reshape rho to 3D
+ rho = reshape(rho+S.b, S.Nx, S.Ny, S.Nz); % note here after rho = rho + b
+
+ % permute rho so that the new z' direction has Dirichlet BC
+ new_order = [dir_X, dir_Y, dir_Z]; % a permutation of [1,2,3]
+ [~, reverse_order] = sort(new_order); % reverse order to get back
+ rho = permute(rho,new_order);
+ phi = permute(phi,new_order);
+ % rho = permute(rho,reverse_order); % this will recover original
+
+ % find fft of rho in the new X, Y directions
+ % rho is a 3D matrix, this applies 2D fft to each dim higher than 2
+ rho_hat = fft2(rho);
+ rho_hat(1,1,:) = 0; % remove the 0 frequency term (constant term in real-space)
+
+ % rho_zp_bar = zeros(Nzp,1);
+ % sum over x' and y' directions, \int (\rho) dxdy
+ %rho_zp_bar = sum(sum(rho, dir_xp), dir_yp) * dxp * dyp;
+ rho_Z_av = sum(sum(rho, 1), 2) * dX * dY;
+ rho_Z_av = rho_Z_av(:);
+ Z = (0 : NZ-1) * dZ;
+ Z_bc = [-S.FDn:-1,NZ:NZ+S.FDn-1] * dZ;
+
+ % a matrix of size Nz' x Nz', a(i,j) = z_i - z_j
+ %ZZp = abs(Z_bc.' - Z);
+ ZZp = abs(colminusrow(Z_bc.', Z));
+
+ % V_av(Z) = int (rho_Z_av * |Z - Z'|) dZ', note this can be simplified
+ % for charge neutrual systems to int (rho_Z_av * Z') dZ', indep of Z
+ V_Z_av = (-2*pi/A_XY*dZ) * sum(bsxfun(@times, rho_Z_av', ZZp),2);
+
+ % wave vectors
+ GX = ifftshift( -floor(NX/2) : ceil(NX/2)-1 ) * (2*pi/NX);
+ GY = ifftshift( -floor(NY/2) : ceil(NY/2)-1 ) * (2*pi/NY);
+ [GX3D, GY3D, Z3D] = ndgrid(GX, GY, Z);
+ GR3D = sqrt(GX3D.^2 + GY3D.^2);
+ V_hat = zeros(NX,NY,2*S.FDn);
+ for k = 1:length(Z_bc) % in fact, no need to calculate for all Z values
+ V_hat(:,:,k) = V_hat(:,:,k) + (2*pi*dZ) * ...
+ sum(rho_hat ./ GR3D .* exp(-abs(Z3D - Z_bc(k)) .* GR3D) , 3);
+ end
+ V_hat(1,1,:) = 0; % remove the 0 frequency term (constant term in real-space)
+
+ II = (1+S.FDn):(NX+S.FDn);
+ JJ = (1+S.FDn):(NY+S.FDn);
+
+ % put phi back to the 3D matrix
+ ind_z = [1:S.FDn,NZ+S.FDn+1:NZ+2*S.FDn];
+ phi(II,JJ,ind_z) = reshape(kron(V_Z_av', ones(NX,NY)),NX,NY,length(Z_bc));
+
+ % remove 0 before ifft2 to include more terms
+ phi(II,JJ,ind_z) = phi(II,JJ,ind_z) + 0*ifft2(V_hat);
+ % phi(S.isIn) = 0; % any value inside the fd-grid will be set to 0
+
+ % permute phi back to original directions
+ phi = real(phi);
+ phi = permute(phi,reverse_order);
+elseif S.BC == 4
+ % find boundary conditions for periodic in 1D, dirichlet in 2D
+ % Calculate phi
+ phi = zeros(S.Nx+2*S.FDn, S.Ny+2*S.FDn, S.Nz+2*S.FDn);
+
+ cellsize = [S.L1, S.L2, S.L3];
+ gridsizes = [S.Nx, S.Ny, S.Nz];
+ meshsizes = [S.dx, S.dy, S.dz];
+ bcs = [S.BCx,S.BCy,S.BCz];
+
+ % find which direction has Periodic BC
+ dir_Z = find(bcs == 0);
+ dir_X = mod(dir_Z, 3) + 1;
+ dir_Y = mod(dir_X, 3) + 1;
+
+ % once we find the direction, we assume that direction is the Z
+ % direction, the other two directions are then called X, Y
+ NX = gridsizes(dir_X); NY = gridsizes(dir_Y); NZ = gridsizes(dir_Z);
+ LX = cellsize(dir_X); LY = cellsize(dir_Y); LZ = cellsize(dir_Z);
+ dX = meshsizes(dir_X); dY = meshsizes(dir_Y); dZ = meshsizes(dir_Z);
+ % A_XY = LX * LY; % area of (x',y') surface
+
+ % reshape rho to 3D
+ rho = reshape(rho+S.b, S.Nx, S.Ny, S.Nz); % note here after rho = rho + b
+
+ % permute rho so that the new Z direction has Periodic BC
+ new_order = [dir_X, dir_Y, dir_Z]; % a permutation of [1,2,3]
+ [~, reverse_order] = sort(new_order); % reverse order to get back
+ rho = permute(rho,new_order);
+ phi = permute(phi,new_order);
+ % rho = permute(rho,reverse_order); % this will recover original
+
+ % sum over Z direction, \int (\rho) dz / LZ
+ rho_XY_av = sum(rho,3) * (dZ/LZ); % NX * NY
+ rho_XY_av = rho_XY_av(:);
+ X = (0 : NX-1) * dX;
+ Y = (0 : NY-1) * dY;
+
+ [XX,YY] = ndgrid(X,Y);
+
+ I_ex = 1:NX+2*S.FDn;
+ J_ex = 1:NY+2*S.FDn;
+ [II_ex,JJ_ex] = ndgrid(I_ex,J_ex);
+
+ % flag for points inside the domain
+ % isIn = ones(NX+2*S.FDn,NY+2*S.FDn);
+ % isIn(1:S.FDn,:) = 0;
+ % isIn(:,1:S.FDn) = 0;
+ % isIn(S.FDn+NX+1:end,:) = 0;
+ % isIn(:,S.FDn+NY+1:end) = 0;
+ isIn = zeros(NX+2*S.FDn,NY+2*S.FDn);
+ isIn(S.FDn+1:NX+S.FDn, S.FDn+1:NY+S.FDn) = 1;
+
+ % positions of nodes outside the domain
+ isbc = find(~isIn);
+
+ XX_bc = (II_ex(isbc)-1-S.FDn) * dX;
+ YY_bc = (JJ_ex(isbc)-1-S.FDn) * dY;
+
+ % ln((X-X')^2 + (Y-Y')^2)
+ % ln_RRp = log((XX_bc - XX(:)').^2 + (YY_bc - YY(:)').^2 );
+ ln_RRp = log(colminusrow(XX_bc,XX(:)').^2 + colminusrow(YY_bc,YY(:)').^2);
+
+ % V_XY_av = int (-ln((X-X')^2 + (Y-Y')^2) * rho_XY_av) dX'dY'
+ V_XY_av = (-dX*dY) * sum(bsxfun(@times, rho_XY_av', ln_RRp),2);
+
+ V_XY_av_full = zeros(NX+2*S.FDn,NY+2*S.FDn);
+ V_XY_av_full(isbc) = V_XY_av;
+
+ phi = bsxfun(@plus, phi, V_XY_av_full);
+
+ % permute phi back to original directions
+ phi = real(phi);
+ phi = permute(phi,reverse_order);
+end
+
+% Calculate boundary conditions, this part can be combined for 2D
+% periodic, 1D periodic and all Dirichlet BC
+dx2 = S.dx * S.dx;
+dy2 = S.dy * S.dy;
+dz2 = S.dz * S.dz;
+d = zeros(S.Nx,S.Ny,S.Nz);
+
+II = (1+S.FDn):(S.Nx+S.FDn);
+JJ = (1+S.FDn):(S.Ny+S.FDn);
+KK = (1+S.FDn):(S.Nz+S.FDn);
+
+% only add charge correction on Dirichlet boundaries
+if S.BCx == 1
+ for p = 1:S.FDn
+ d = d - S.w2(p+1)/dx2 * (phi(II+p,JJ,KK) + phi(II-p,JJ,KK));
+ end
+end
+if S.BCy == 1
+ for p = 1:S.FDn
+ d = d - S.w2(p+1)/dy2 * (phi(II,JJ+p,KK) + phi(II,JJ-p,KK));
+ end
+end
+if S.BCz == 1
+ for p = 1:S.FDn
+ d = d - S.w2(p+1)/dz2 * (phi(II,JJ,KK+p) + phi(II,JJ,KK-p));
+ end
+end
+d = d(:);
+f = f + d;
+
+end
+
+
+
+% tool function colminusrow
+function xmy = colminusrow(x,y)
+% A column vector x minus a row vector.
+% In Matlab versions after R2018b, it's just x - y
+if (size(x,2) ~= 1)
+ error('Error: the first vector must be a column vector');
+end
+if (size(y,1) ~= 1)
+ error('Error: the second vector must be a row vector');
+end
+
+[xx,yy] = ndgrid(x,y);
+xmy = xx - yy;
+
+end
+
diff --git a/src/pseudochargeDensity_atom.m b/src/pseudochargeDensity_atom.m
new file mode 100644
index 00000000..d9761f52
--- /dev/null
+++ b/src/pseudochargeDensity_atom.m
@@ -0,0 +1,56 @@
+function b = pseudochargeDensity_atom(V,II,JJ,KK,xin,S)
+% @ brief Calculate lap * V = b (in this function)
+% @ authors
+% Abhiraj Sharma
+% Qimen Xu
+% Phanish Suryanarayana
+%
+% @param V potential at FD nodes
+% @param II Node indices in X direction
+% @param JJ Node indices in Y direction
+% @param KK Node indices in Z direction
+% @param xin Reference x-coordinate
+% @param b laplacian of the potential
+%
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+%======================================================================
+ if S.cell_typ == 1
+ b = zeros(size(V));
+ dx2 = S.dx*S.dx;
+ dy2 = S.dy*S.dy;
+ dz2 = S.dz*S.dz;
+ coeff = S.w2(1) * (1/dx2 + 1/dy2 + 1/dz2);
+ b(II,JJ,KK) = coeff * V(II,JJ,KK);
+ for p = 1:S.FDn
+ b(II,JJ,KK) = b(II,JJ,KK) + S.w2(p+1)/dx2 * (V(II+p,JJ,KK) + V(II-p,JJ,KK)) + ...
+ S.w2(p+1)/dy2 * (V(II,JJ+p,KK) + V(II,JJ-p,KK)) + ...
+ S.w2(p+1)/dz2 * (V(II,JJ,KK+p) + V(II,JJ,KK-p));
+ end
+ elseif S.cell_typ == 2
+ b = zeros(size(V));
+ dx2 = S.dx*S.dx;
+ dy2 = S.dy*S.dy;
+ dz2 = S.dz*S.dz;
+ dxdy = S.dx*S.dy;
+ dydz = S.dy*S.dz;
+ dzdx = S.dz*S.dx;
+ coeff = S.w2(1) * (S.lapc_T(1,1)/dx2 + S.lapc_T(2,2)/dy2 + S.lapc_T(3,3)/dz2);
+ b(II,JJ,KK) = coeff * V(II,JJ,KK);
+ for p = 1:S.FDn
+ b(II,JJ,KK) = b(II,JJ,KK) + S.w2(p+1)*S.lapc_T(1,1)/dx2 * (V(II+p,JJ,KK) + V(II-p,JJ,KK)) + ...
+ S.w2(p+1)*S.lapc_T(2,2)/dy2 * (V(II,JJ+p,KK) + V(II,JJ-p,KK)) + ...
+ S.w2(p+1)*S.lapc_T(3,3)/dz2 * (V(II,JJ,KK+p) + V(II,JJ,KK-p));
+ for q = 1:S.FDn
+ b(II,JJ,KK) = b(II,JJ,KK) + S.w1(p+1)*S.w1(q+1)*S.lapc_T(1,2)/dxdy * ( V(II+q,JJ+p,KK) - ...
+ V(II-q,JJ+p,KK) - V(II+q,JJ-p,KK) + V(II-q,JJ-p,KK) ) + ...
+ S.w1(p+1)*S.w1(q+1)*S.lapc_T(2,3)/dydz * ( V(II,JJ+q,KK+p) - ...
+ V(II,JJ-q,KK+p) - V(II,JJ+q,KK-p) + V(II,JJ-q,KK-p) ) + ...
+ S.w1(p+1)*S.w1(q+1)*S.lapc_T(1,3)/dzdx * ( V(II+q,JJ,KK+p) - ...
+ V(II-q,JJ,KK+p) - V(II+q,JJ,KK-p) + V(II-q,JJ,KK-p) ) ;
+ end
+ end
+
+ elseif (S.cell_typ == 3 || S.cell_typ == 4 || S.cell_typ == 5)
+ b = pseudochargeDensity_atom_cychel(V,II,JJ,KK,xin,S);
+ end
+end
\ No newline at end of file
diff --git a/src/readPseudopot.m b/src/readPseudopot.m
new file mode 100644
index 00000000..3de3ac8f
--- /dev/null
+++ b/src/readPseudopot.m
@@ -0,0 +1,98 @@
+function S = readPseudopot(S, ityp, psdfname, element)
+% @brief READPSEUDOPOT reads the pseudopotential file (psp8 format).
+%
+% @param ityp Element type index.
+% @param psdfname The pseudopotential filename, with suffix.
+% @param element Element type.
+%
+% @authors Qimen Xu
+% Abhiraj Sharma
+% Phanish Suryanarayana
+%
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+%
+
+%filename = sprintf('%s/%s',S.inputfile_path, psdfname);
+filename = fullfile(S.inputfile_path, psdfname);
+
+fid = fopen(filename,'r') ;
+
+assert(fid~=-1,'Error: Cannot open pseudopotential file %s',filename);
+
+textscan(fid,'%s',1,'delimiter','\n') ;
+fscanf(fid,'%s',1);
+Z = fscanf(fid,'%f',1);
+textscan(fid,'%s',1,'delimiter','\n');
+A = textscan(fid,'%f %f %f %f %f %f') ;
+
+lmax = A{1,3};
+lloc = A{1,4}; lloc = 4; % forcing nonlocal component to 4!
+mmax = A{1,5};
+
+textscan(fid,'%s',2,'delimiter','\n') ;
+A = textscan(fid,'%f %f %f %f %f');
+nproj = ones(lmax+1,1);
+for i = 0:lmax
+ nproj(i+1) = A{1,i+1};
+end
+textscan(fid,'%s',2,'delimiter','\n') ;
+
+Pot = repmat(struct([]), lmax+1, 1);
+l = 0;
+while l<=lmax
+ fscanf(fid,'%f',1) ;
+ if l ~= lloc
+ A = fscanf(fid,'%f',nproj(l+1)) ;
+ Pot(l+1).gamma_Jl = A(:);
+ sz = [2+nproj(l+1),mmax];
+ A = fscanf(fid,'%g',sz) ;
+ r = A(2,:)' ;
+ Pot(l+1).proj = A(3:end,:)';
+ Pot(l+1).proj(2:end,:) = Pot(l+1).proj(2:end,:)./repmat(r(2:end),1,nproj(l+1));
+ Pot(l+1).proj(1,:) = Pot(l+1).proj(2,:);
+ else
+ A = fscanf(fid,'%g',[3,mmax]);
+ r = A(2,:)' ;
+ Vloc = A(3,:)';
+ end
+ l = l+1;
+end
+
+if lloc > lmax
+ fscanf(fid,'%f',1) ;
+ A = fscanf(fid,'%g',[3,mmax]) ;
+ r = A(2,:)';
+ Vloc = A(3,:)';
+end
+
+uu = zeros(mmax,1);
+size = [5,mmax];
+A = fscanf(fid,'%d %g %g %g %g',size);
+uu(1:end,1) = A(3,:)/(4*pi);
+rho_isolated_guess = uu;
+
+frewind(fid);
+fscanf(fid,'%s',3);
+rc = 0 ;
+for i=1:lmax+1
+ a = fscanf(fid,'%g',1) ;
+ if a > rc
+ rc = a ;
+ end
+end
+
+r_grid_vloc = r;
+r_grid_rho = r;
+
+S.Atm(ityp).Z = Z;
+S.Atm(ityp).Vloc = Vloc;
+S.Atm(ityp).r_grid_vloc = r_grid_vloc;
+S.Atm(ityp).rc = rc;
+S.Atm(ityp).Pot = Pot;
+S.Atm(ityp).lmax = lmax;
+S.Atm(ityp).lloc = lloc;
+S.Atm(ityp).nproj = nproj;
+S.Atm(ityp).r_grid_rho = r_grid_rho;
+S.Atm(ityp).rho_isolated_guess = rho_isolated_guess;
+
+end
diff --git a/src/read_inpt.m b/src/read_inpt.m
new file mode 100644
index 00000000..1a92f005
--- /dev/null
+++ b/src/read_inpt.m
@@ -0,0 +1,617 @@
+function S = read_inpt(S, filename)
+% @brief READ_INPT reads the filename.inpt file.
+%
+% @param fname The input filename, without suffix.
+%
+% @authors Qimen Xu
+% Abhiraj Sharma
+% Phanish Suryanarayana
+%
+% @copyright (c) 2019 Material Physics % @2016-2019 (c) Georgia Institute of Technology. Mechanics Group, Georgia Tech
+%
+
+fprintf(' Reading .inpt file ...\n');
+
+S.filename = filename;
+
+[inputfile_path,~,~] = fileparts(filename);
+
+if isempty(inputfile_path)
+ S.inputfile_path = '.';
+else
+ S.inputfile_path = inputfile_path;
+end
+
+fid1=fopen(strcat(filename,'.inpt'),'r');
+if (fid1 == -1)
+ error('\nCannot open file "%s.inpt"\n',filename);
+end
+
+% print out the .inpt file on screen for debug
+fprintf('\n\n\n');
+fprintf('# $ cat %s.inpt',filename);
+type(strcat(filename,'.inpt'));
+fprintf('<\\INPT>\n\n');
+
+Flag_smear_typ = 0;
+Flag_Temp = 0;
+Flag_elecT = 0;
+Flag_accuracy = 0;
+Flag_ionT = 0;
+Flag_eqT = 0;
+%Flag_ionT_end = 0;
+
+while(~feof(fid1))
+ C_inpt = textscan(fid1,'%s',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ str = char(C_inpt{:}); % for R2016b and later, can use string()
+ % skip commented lines starting by '#'
+ %if (isempty(str) || str(1) == '#' || strcmp(str,'undefined'))
+ if (isempty(str) || str(1) == '#')
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ %fprintf('skipping current line!\n');
+ continue;
+ end
+ % check variable name and assign value
+ if (strcmp(str,'NP_SPIN_PARAL:'))
+ msparc_neglect_warning(str);
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'NP_KPOINT_PARAL:'))
+ msparc_neglect_warning(str);
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'NP_BAND_PARAL:'))
+ msparc_neglect_warning(str);
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'NP_DOMAIN_PARAL:'))
+ msparc_neglect_warning(str);
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'NP_DOMAIN_PHI_PARAL:'))
+ msparc_neglect_warning(str);
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'CELL:'))
+ C_param = textscan(fid1,'%f %f %f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.L1 = C_param{1};
+ S.L2 = C_param{2};
+ S.L3 = C_param{3};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'TWIST_ANGLE:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.alph = C_param{1}; % in radian/Bohr
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'LATVEC:'))
+ C_param = textscan(fid1,'%f %f %f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ S.lat_vec(1,:) = cell2mat(C_param);
+ C_param = textscan(fid1,'%f %f %f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ S.lat_vec(2,:) = cell2mat(C_param);
+ C_param = textscan(fid1,'%f %f %f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ S.lat_vec(3,:) = cell2mat(C_param);
+ elseif (strcmp(str,'BOUNDARY_CONDITION:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.BC = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ fprintf('Warning: "BOUNDARY_CONDITION" is obsolete, use "BC" instead!\n');
+ elseif (strcmp(str,'BC:'))
+ C_param = textscan(fid1,'%s %s %s',1,'delimiter',' ','MultipleDelimsAsOne',1); % read smearing type
+ bcx = char(C_param{1});
+ bcy = char(C_param{2});
+ bcz = char(C_param{3});
+ if bcx == 'p' || bcx == 'P'
+ S.BCx = 0;
+ elseif bcx == 'd' || bcx == 'D'
+ S.BCx = 1;
+ end
+
+ if bcy == 'p' || bcy == 'P'
+ S.BCy = 0;
+ elseif bcy == 'd' || bcy == 'D'
+ S.BCy = 1;
+ elseif bcy == 'c' || bcy == 'C'
+ S.BCy = 0;
+ S.cell_typ = 3;
+ end
+
+ if bcz == 'p' || bcz == 'P'
+ S.BCz = 0;
+ elseif bcz == 'd' || bcz == 'D'
+ S.BCz = 1;
+ elseif bcz == 'h' || bcz == 'H'
+ S.BCz = 0;
+ if(S.cell_typ == 3)
+ S.cell_typ = 5;
+ else
+ S.cell_typ = 4;
+ end
+ end
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'SPIN_TYP:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.spin_typ = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'FD_ORDER:'))
+ %fscanf(fid1,'%f',S.order);
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.FDn = C_param{1};
+ S.FDn = S.FDn / 2; % FDn is half the order
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'FD_GRID:'))
+ C_param = textscan(fid1,'%f %f %f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.Nx = C_param{1};
+ S.Ny = C_param{2};
+ S.Nz = C_param{3};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'ECUT:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.ecut = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'MESH_SPACING:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.mesh_spacing = C_param{1}; % mesh spacing
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'KPOINT_GRID:'))
+ C_param = textscan(fid1,'%f %f %f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.nkpt = cell2mat(C_param);
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'KPOINT_SHIFT:'))
+ C_param = textscan(fid1,'%f %f %f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.kptshift = cell2mat(C_param);
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'ELEC_TEMP_TYPE:'))
+ Flag_smear_typ = Flag_smear_typ + 1;
+ C_param = textscan(fid1,'%s',1,'delimiter',' ','MultipleDelimsAsOne',1); % read smearing type
+ temp = char(C_param{:});
+ if (strcmp(temp,'fd') || strcmp(temp,'fermi-dirac'))
+ % currently only fermi-dirac is implemented in M-SPARC
+ %fprintf('Fermi-Dirac smearing\n');
+ S.elec_T_type = 0;
+ elseif (strcmp(temp,'gaussian'))
+ % currently only fermi-dirac is implemented in M-SPARC
+ %error('Gaussian smearing is not implemented in M-SPARC!\n');
+ S.elec_T_type = 1;
+ else
+ error(['\nCannot recognize electronic temperature (smearing) type: "%s"\n',...
+ 'Available options: "fd" (or "fermi-dirac"), "gaussian" \n'], temp);
+ %fprintf('Available options: "fd" (or "fermi-dirac"), "gaussian" \n');
+ end
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'SMEARING:'))
+ Flag_Temp = Flag_Temp + 1;
+ Flag_elecT = Flag_elecT + 1;
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ smearing = C_param{1};
+ S.bet = 1 / smearing;
+ S.Temp = smearing / S.kB;
+ %str = 'undefined'; % initialize str
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'BETA:'))
+ Flag_Temp = Flag_Temp + 1;
+ Flag_elecT = Flag_elecT + 1;
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.bet = C_param{1};
+ S.Temp = 1 / (S.kB * S.bet);
+ str = 'undefined'; % initialize str
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'ELEC_TEMP:'))
+ Flag_Temp = Flag_Temp + 1;
+ Flag_elecT = Flag_elecT + 1;
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.Temp = C_param{1};
+ S.bet = 1 / (S.kB * S.Temp);
+ str = 'undefined'; % initialize str
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'CHEB_DEGREE:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.npl = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'CHEFSI_OPTMZ:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.CheFSI_Optmz = C_param{1};
+ fprintf('Neglecting option "%s", which is not supported in M-SPARC\n',str);
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'CHEFSI_BOUND_FLAG:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.chefsibound_flag = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'FIX_RAND:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.FixRandSeed = C_param{1};
+ fprintf('Neglecting option "%s", which is not supported in M-SPARC\n',str);
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'RHO_TRIGGER:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.rhoTrigger = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'NSTATES:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.Nev = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'NET_CHARGE:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.NetCharge = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ % error exit
+ %msparc_error_exit(str);
+ elseif (strcmp(str,'MAXIT_SCF:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.MAXIT_SCF = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'MINIT_SCF:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.MINIT_SCF = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'MAXIT_POISSON:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.MAXIT_POISSON = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'RELAX_NITER:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.max_relax_it = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'RELAX_MAXDILAT:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.max_dilatation = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'TOL_RELAX_CELL:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.TOL_RELAX_CELL = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'ACCURACY:'))
+ C_param = textscan(fid1,'%s',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ temp = char(C_param{:});
+ if (strcmp(temp,'minimal'))
+ S.accuracy_level = 0;
+ elseif (strcmp(temp,'low'))
+ S.accuracy_level = 1;
+ elseif (strcmp(temp,'medium'))
+ S.accuracy_level = 2;
+ elseif (strcmp(temp,'high'))
+ S.accuracy_level = 3;
+ elseif (strcmp(temp,'extreme'))
+ S.accuracy_level = 4;
+ else
+ error('\nCannot recognize accuracy level: "%s"\n',temp);
+ end
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'SCF_FORCE_ACC:'))
+ Flag_accuracy = Flag_accuracy + 1;
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.target_force_accuracy = C_param{1};
+ %str = 'undefined'; % initialize str
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'SCF_ENERGY_ACC:'))
+ Flag_accuracy = Flag_accuracy + 1;
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.target_energy_accuracy = C_param{1};
+ %str = 'undefined'; % initialize str
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'TOL_SCF:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.SCF_tol = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'TOL_POISSON:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.poisson_tol = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'TOL_RELAX:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.TOL_RELAX = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'TOL_LANCZOS:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.TOL_LANCZOS = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'TOL_PSEUDOCHARGE:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.pseudocharge_tol = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'TOL_KERKER:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ %S.kerker_tol = C_param{1};
+ fprintf('Warning: TOL_KERKER is obsolete, use TOL_PRECOND instead!\n')
+ S.precond_tol = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'TOL_PRECOND:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.precond_tol = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'PRECOND_KERKER_KTF:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.precond_kTF = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'PRECOND_KERKER_THRESH:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.precond_thresh = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'PRECOND_RESTA_Q0:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.precond_resta_q0 = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'PRECOND_RESTA_RS:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.precond_resta_Rs = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'PRECOND_FITPOW:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.precond_fitpow = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'REFERENCE_CUTOFF:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.rc_ref = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'MIXING_VARIABLE:'))
+ C_param = textscan(fid1,'%s',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ temp = char(C_param{:});
+ if (strcmp(temp,'density'))
+ S.MixingVariable = 0;
+ elseif (strcmp(temp,'potential'))
+ S.MixingVariable = 1;
+ else
+ fprintf('\nCannot recognize mixing variable: "%s"\n',temp);
+ fprintf('Available options: "density", "potential" \n');
+ error('exiting');
+ end
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'MIXING_PRECOND:'))
+ C_param = textscan(fid1,'%s',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ temp = char(C_param{:});
+ if (strcmp(temp,'none'))
+ S.MixingPrecond = 0;
+ elseif (strcmp(temp,'kerker'))
+ S.MixingPrecond = 1;
+ elseif (strcmp(temp,'resta'))
+ S.MixingPrecond = 2;
+ elseif (strcmp(temp,'truncated_kerker'))
+ S.MixingPrecond = 3;
+ else
+ fprintf('\nCannot recognize mixing preconditioner: "%s"\n',temp);
+ fprintf('Available options: "none", "kerker" \n');
+ error('exiting');
+ end
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'MIXING_HISTORY:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.MixingHistory = C_param{1};
+ %fscanf(fid1,'%f',S.MixingHistory);
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'MIXING_PARAMETER:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.MixingParameter = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'MIXING_PARAMETER_SIMPLE:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.MixingParameterSimple = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'PULAY_FREQUENCY:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.PulayFrequency = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'PULAY_RESTART:'))
+ % C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ % S.PulayRestartFlag = C_param{1};
+ % textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ error('"PULAY_RESTART" is obsolete, please provide PULAY_RESTART_FREQ instead!\n');
+ elseif (strcmp(str,'PULAY_RESTART_FREQ:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.PulayRestartFreq = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'TWTIME:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.TWtime = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'MD_FLAG:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.MDFlag = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'MD_METHOD:'))
+ C_param = textscan(fid1,'%s',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.MDMeth = char(C_param{:});
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'MD_TIMESTEP:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.MD_dt = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'MD_NSTEP:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.MD_Nstep = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'ION_TEMP:'))
+ Flag_ionT = Flag_ionT + 1;
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.ion_T = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'ION_TEMP_END:'))
+ %Flag_ionT_end = Flag_ionT_end + 1;
+ %C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ %S.thermos_Tf = C_param{1};
+ msparc_neglect_warning(str);
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'ION_ELEC_EQT:'))
+ Flag_eqT = Flag_eqT + 1;
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.ion_elec_eqT = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'ION_VEL_DSTR:'))
+ %C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ %S.ion_vel_dstr = C_param{1};
+ msparc_neglect_warning(str);
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'QMASS:'))
+ %C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ %S.qmass = C_param{1};
+ msparc_neglect_warning(str);
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'PRINT_MDOUT:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.PrintMDout = C_param{1};
+ %fscanf(fid1,'%f',S.PrintMDout);
+ %msparc_neglect_warning(str);
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'RELAX_FLAG:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.RelaxFlag = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'RELAX_METHOD:'))
+ C_param = textscan(fid1,'%s',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.RelaxMeth = char(C_param{:});
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'NLCG_SIGMA:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.NLCG_sigma = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'L_HISTORY:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.L_history = C_param{:};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'L_FINIT_STP:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.L_finit_stp = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'L_MAXMOV:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.L_maxmov = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'L_AUTOSCALE:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.L_autoscale = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'L_LINEOPT:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.L_lineopt = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'L_ICURV:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.L_icurv = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'FIRE_dt:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.FIRE_dt = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'FIRE_mass:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.FIRE_mass = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'FIRE_maxmov:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.FIRE_maxmov = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'PRINT_RELAXOUT:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.PrintRelaxout = C_param{1};
+ %msparc_neglect_warning(str);
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'RESTART_FLAG:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.RestartFlag = C_param{1};
+ %msparc_neglect_warning(str);
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'PRINT_RESTART:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.Printrestart = C_param{1};
+ %msparc_neglect_warning(str);
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'PRINT_RESTART_FQ:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.Printrestart_fq = C_param{1};
+ %msparc_neglect_warning(str);
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'EXCHANGE_CORRELATION:'))
+ C_param = textscan(fid1,'%s',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.XC = char(C_param{:});
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'CALC_STRESS:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.Calc_stress = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'CALC_PRES:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.Calc_pres = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'NTYPES:'))
+ fprintf('Warning: NTYPES is no longer needed, skipping this option ...\n');
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'ATOMIC_MASS:'))
+ fprintf('Warning: ATOMIC_MASS is now moved to .ion file, skipping this option ...\n');
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'PSEUDOPOTENTIAL_LOCAL:'))
+ fprintf('Warning: PSEUDOPOTENTIAL_LOCAL is no longer needed, skipping this option ...\n');
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line% remove this, and this if cond
+ elseif(strcmp(str,'PSEUDOPOTENTIAL_FILE:'))
+ fprintf('Warning: PSEUDOPOTENTIAL_FILE is now moved to .ion file, skipping this option ...\n');
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif(strcmp(str,'PRINT_FORCES:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.PrintForceFlag = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif(strcmp(str,'PRINT_ATOMS:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.PrintAtomPosFlag = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif(strcmp(str,'PRINT_VELS:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.PrintAtomVelFlag = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif(strcmp(str,'PRINT_EIGEN:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.PrintEigenFlag = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif(strcmp(str,'PRINT_DENSITY:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.PrintElecDensFlag = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,'OUTPUT_FILE:'))
+ C_param = textscan(fid1,'%s',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.filename_out = char(C_param{:});
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ else
+ error('\nCannot recognize input variable identifier: "%s"\n',str);
+ %fprintf('\nCannot recognize input flag in .inpt file: "%s"\n',str);
+ end
+end
+
+fclose(fid1);
+
+% check if the inpt options have conflict
+
+if (S.Nx > 0 && S.Ny > 0 && S.Nz > 0) + (S.ecut > 0) + (S.mesh_spacing > 0) > 1
+ error('"FD_GRID", "ECUT" and "MESH_SPACING" cannot be specified simultaneously!');
+end
+
+% check if non-orthogonal unit cell is used for Dirichlet BC
+% if (S.BC == 1 && S.cell_typ == 2)
+% error('\nOnly orthogonal cells permitted for isolated clusters\n');
+% end
+n_Dirichlet = S.BCx + S.BCy + S.BCz;
+if (S.BC >= 0) && (S.BCx >= 0 && S.BCy >= 0 && S.BCz >= 0)
+ error('"BOUNDARY_CONDITION" and "BC" cannot be specified together!');
+end
+
+% % Boundary condition type: 1--isolated cluster; 2--periodic system
+% if (S.cell_typ == 2) && (((S.BC == 1) || (S.BC == 4)) || (n_Dirichlet == 3 || n_Dirichlet == 2))
+% error('Non-orthogonal option allowed only for boundary conditions 2 & 3');
+% end
+
+% check if MD and Relaxation are turned on simultaneously
+if (S.MDFlag ~= 0 && S.RelaxFlag ~= 0)
+ fprintf('\nStructural relaxations and MD cannot be turned on simultaneously!\n');
+end
+
+if(S.MDFlag == 1 && Flag_ionT == 0)
+ error('\nIonic temperature must be specified for MD!\n');
+end
+
+if(S.MDFlag == 1 && S.ion_elec_eqT == 1)
+ S.Temp = S.ion_T;
+ S.bet = 1 / (S.kB * S.Temp);
+end
+
+end
+
+function msparc_neglect_warning(str)
+ fprintf('Neglecting option "%s", which is not supported in M-SPARC\n',str);
+end
+
+function msparc_error_exit(str)
+ error('The option "%s" is not supported in M-SPARC\n',str);
+end
+
diff --git a/src/read_ion.m b/src/read_ion.m
new file mode 100644
index 00000000..fd8b9057
--- /dev/null
+++ b/src/read_ion.m
@@ -0,0 +1,216 @@
+function S = read_ion(S, filename)
+% @brief READ_ION reads the filename.ion file.
+%
+% @param fname The ion filename, without suffix.
+%
+% @authors Qimen Xu
+% Abhiraj Sharma
+% Phanish Suryanarayana
+%
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+%
+
+fprintf(' Reading .ion file ...\n');
+
+% open .ion file
+fid1=fopen(strcat(filename,'.ion'),'r');
+if (fid1 == -1)
+ error('\n Cannot open file "%s.ion"\n',filename);
+end
+
+% first identify total number of atom types
+typcnt = 0;
+while (~feof(fid1))
+ %fscanf(fid1,"%s",str);
+ C_inpt = textscan(fid1,'%s',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ str = char(C_inpt{:});
+ if (strcmp(str, 'ATOM_TYPE:'))
+ typcnt = typcnt + 1;
+ end
+ % skip current line
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0);
+end
+
+fprintf(' Number of atom types : %d\n',typcnt);
+
+if (typcnt < 1)
+ error('\n Please provide at least one type of atoms!\n');
+end
+
+S.n_typ = typcnt;
+
+% reset file pointer to the start of the file
+fseek(fid1, 0, 'bof'); % equivalent ot frewind(fid1)
+
+% find total number of atoms
+n_atom = 0; % totoal num of atoms
+typcnt = 0; % atom type count
+atmcnt_cum = zeros(S.n_typ+1,1);
+
+S.Atm = repmat(struct([]), S.n_typ, 1);
+while (~feof(fid1))
+ C_inpt = textscan(fid1,'%s',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ str = char(C_inpt{:}); % for R2016b and later, can use string()
+ if (strcmp(str, 'ATOM_TYPE:'))
+ typcnt = typcnt + 1;
+ C_param = textscan(fid1,'%s',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.Atm(typcnt).typ = char(C_param{:});
+ elseif (strcmp(str, 'N_TYPE_ATOM:'))
+ C_inpt = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.Atm(typcnt).n_atm_typ = C_inpt{1};
+ S.Atm(typcnt).coords = zeros(S.Atm(typcnt).n_atm_typ, 3);
+ S.Atm(typcnt).psdfname = 'undefined';
+ S.Atm(typcnt).Mass = 1e9; % set the default later
+ S.Atm(typcnt).lloc = 4; % default is 4 for oncv
+ S.Atm(typcnt).psptyp = 1; % default is psp8 format
+ S.Atm(typcnt).mag = zeros(S.Atm(typcnt).n_atm_typ,1);
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0);
+ n_atom = n_atom + S.Atm(typcnt).n_atm_typ ;
+ atmcnt_cum(typcnt+1) = n_atom;
+ else
+ % skip current line
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0);
+ end
+end
+
+fprintf(' Total number of atoms: %d\n',n_atom);
+
+if (n_atom < 1)
+ error('\n Please provide at least one atom!\n');
+end
+
+S.n_atm = n_atom;
+
+S.Atoms = zeros(n_atom,3);
+
+% set default atom relax constraints to be all on (move in all DOFs)
+S.mvAtmConstraint = ones(n_atom,3);
+
+% set default atomic masses based on atom types (for MD)
+if (1) % atomic mass is only needed for MD
+ for ityp = 1:S.n_typ
+ % first identify element type
+ elemType = S.Atm(ityp).typ;
+ % remove the number appending the element type name if any
+ elemType = elemType(isstrprop(elemType, 'alpha')); % e.g., Si2 -> Si
+ % S.Atm(ityp).element = elemType;
+ % find default atomic mass
+ S.Atm(ityp).Mass = atomdata_mass(elemType);
+ fprintf(' Default atomic mass for %s is %f\n',elemType,S.Atm(ityp).Mass);
+ end
+end
+
+% reset temp var
+typcnt = 0;
+atmcnt_coord = 0;
+
+% allocate the size of the Isfrac vector which stores the coordinate type of each atom type
+S.IsFrac = zeros(S.n_typ,1);
+S.IsSpin = zeros(S.n_typ,1);
+
+% reset file pointer to the start of the file
+fseek(fid1, 0, 'bof'); % equivalent ot frewind(fid1)
+
+while (~feof(fid1))
+ C_inpt = textscan(fid1,'%s',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ str = char(C_inpt{:}); % for R2016b and later, can use string()
+
+ % enable commenting with '#'
+ if (isempty(str) || str(1) == '#')
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ continue;
+ end
+
+ if (strcmp(str, 'ATOM_TYPE:'))
+ typcnt = typcnt + 1;
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str, 'N_TYPE_ATOM:'))
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str, 'COORD:'))
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ %fprintf(' typcnt = %d, \n',typcnt);
+ typ_atm_count = 0; % atom count for this type
+ S.Atm(typcnt).coords = zeros(S.Atm(typcnt).n_atm_typ,3);
+ for i = 1:S.Atm(typcnt).n_atm_typ
+ typ_atm_count = typ_atm_count + 1;
+ atmcnt_coord = atmcnt_coord + 1;
+ C_param = textscan(fid1,'%f %f %f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.Atm(typcnt).coords(typ_atm_count,1) = C_param{1};
+ S.Atm(typcnt).coords(typ_atm_count,2) = C_param{2};
+ S.Atm(typcnt).coords(typ_atm_count,3) = C_param{3};
+ S.Atoms(atmcnt_coord,:) = S.Atm(typcnt).coords(typ_atm_count,:);
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ end
+ elseif (strcmp(str, 'COORD_FRAC:'))
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ %fprintf(' typcnt = %d, \n',typcnt);
+ typ_atm_count = 0; % atom count for this type
+ for i = 1:S.Atm(typcnt).n_atm_typ
+ typ_atm_count = typ_atm_count + 1;
+ atmcnt_coord = atmcnt_coord + 1;
+ C_param = textscan(fid1,'%f %f %f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.Atm(typcnt).coords(typ_atm_count,1) = C_param{1} * S.L1;
+ S.Atm(typcnt).coords(typ_atm_count,2) = C_param{2} * S.L2;
+ S.Atm(typcnt).coords(typ_atm_count,3) = C_param{3} * S.L3;
+ S.Atoms(atmcnt_coord,:) = S.Atm(typcnt).coords(typ_atm_count,:);
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ end
+ S.IsFrac(typcnt) = 1;
+ elseif (strcmp(str, 'SPIN:'))
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ %fprintf(' typcnt = %d, \n',typcnt);
+ typ_atm_count = 0; % atom count for this type
+ for i = 1:S.Atm(typcnt).n_atm_typ
+ typ_atm_count = typ_atm_count + 1;
+ C_param = textscan(fid1,'%f %f %f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.Atm(typcnt).mag(typ_atm_count) = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ end
+ S.IsSpin(typcnt) = 1;
+ elseif (strcmp(str, 'RELAX:'))
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ atmcnt_relax = atmcnt_cum(typcnt);
+ %typ_atm_count = 0; % atom count for this type
+ for i = 1:S.Atm(typcnt).n_atm_typ
+ % typ_atm_count = typ_atm_count + 1;
+ atmcnt_relax = atmcnt_relax + 1;
+ C_param = textscan(fid1,'%d %d %d',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.mvAtmConstraint(atmcnt_relax,1) = C_param{1,1};
+ S.mvAtmConstraint(atmcnt_relax,2) = C_param{1,2};
+ S.mvAtmConstraint(atmcnt_relax,3) = C_param{1,3};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ end
+ fprintf('Warning: All atoms will be forced to relax\n');
+ elseif (strcmp(str, 'PSEUDO_POT:'))
+ C_param = textscan(fid1,'%s',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.Atm(typcnt).psdfname = char(C_param{:});
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ S.is_default_psd = 0; % switch off default psedopots
+ fprintf(' pseudo_dir # %d = %s\n',typcnt,S.Atm(typcnt).psdfname);
+ elseif (strcmp(str, 'ATOMIC_MASS:'))
+ C_param = textscan(fid1,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.Atm(typcnt).Mass = C_param{1};
+ textscan(fid1,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif ( isnumeric(str(1)) )
+ error(['\nPlease specify the identifier before numbers!\n', ...
+ 'Reminder: check if the number of atoms specified is inconsistent\n' ...
+ ' with the number of coordinates provided\n']);
+ else
+ fprintf('\nCannot recognize input flag: "%s"',str);
+ end
+end
+
+if (atmcnt_coord ~= n_atom)
+ error(['The number of coordinates provided is inconsistent '...
+ 'with the given number of atoms!']);
+end
+
+fprintf('\n COORD:\n');
+disp(S.Atoms);
+
+%fprintf(' RELAX:\n');
+%disp(S.mvAtmConstraint);
+
+fclose(fid1);
+end
+
diff --git a/src/relax.m b/src/relax.m
new file mode 100644
index 00000000..68c13aa4
--- /dev/null
+++ b/src/relax.m
@@ -0,0 +1,711 @@
+function S = relax(S)
+% @ brief Function to perform structural relaxation
+% @ authors
+% Abhiraj Sharma
+% Qimen Xu
+% Phanish Suryanarayana
+%
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+%======================================================================
+
+ % Read .restart file if relaxation is restarted
+ if S.RestartFlag == 1
+ S = RestartRelax(S);
+ end
+
+ % set up relaxation output filename
+ if S.RelaxFlag == 1
+ S.relaxfname = strcat(S.filename,'.geopt');
+ if S.suffixNum > 0
+ S.relaxfname = sprintf('%s.geopt_%d',S.filename,S.suffixNum);
+ end
+ elseif S.RelaxFlag == 2
+ S.relaxfname = strcat(S.filename,'.cellopt');
+ if S.suffixNum > 0
+ S.relaxfname = sprintf('%s.cellopt_%d',S.filename,S.suffixNum);
+ end
+ end
+
+ % Different relaxation methods
+ if S.RelaxFlag == 1
+ if strcmp(S.RelaxMeth,'NLCG')
+ S = NLCG(S);
+ elseif strcmp(S.RelaxMeth,'LBFGS')
+ S = LBFGS(S);
+ elseif strcmp(S.RelaxMeth,'FIRE')
+ S = FIRE(S);
+ else
+ error('Invalid relaxation method option! Current version only has NLCG, LBFGS, and FIRE algorithms.');
+ end
+ elseif S.RelaxFlag == 2
+ S = cell_relax(S);
+ end
+end
+
+
+
+
+function S = NLCG(S)
+% @ brief Function to perform structural relaxation using NON-LINEAR CONJUGATE GRADIENT method
+% @ reference: "An introduction to the conjugate gradient method without the agonizing pain"
+%===================================================================================================
+ % Obtain cartesian coordinates and reshape into a vector
+ if ~S.RestartFlag
+ %x = transpose(S.lat_uvec) * S.Atoms';
+ x = coordinateTransformation(S, S.Atoms, 'noncart2cart_dis');
+ x = reshape(x',[],1);
+ else
+ x = reshape(S.Atoms',[],1);
+ end
+
+ imax = S.max_relax_it;
+ jmax = 6;
+ n = 30;
+ tol1 = S.TOL_RELAX;
+ tol2 = tol1*1e-2;
+ sigma_0 = S.NLCG_sigma;
+ i = 1;
+
+ % Residual is same as atomic force (but the function returns dE/dR)
+ [x,r,S] = electronicGroundStateAtomicForce(x,S); r = -r;
+ S.ForceCount = S.ForceCount + 1;
+
+ % Print the output in .geopt file
+ if (S.PrintRelaxout == 1 && ~S.RestartFlag)
+ PrintRelax(S,transpose(reshape(x,3,[])));
+ end
+
+ S.Relax_iter = S.Relax_iter + 1;
+ k = S.Relax_iter;
+
+ M = ones(size(x)); % TODO: Need to set REAL PRECONDITIONER
+ s = r./M;
+ delta_new = dot(r,s);
+ % Search direction
+ if ~S.RestartFlag
+ S.NLCG_d = s;
+ end
+ % Error is defined as the supremum norm of the residual vector
+ err = max(abs(r));
+
+ while (itol1)
+ delta_d = max(abs(S.NLCG_d));
+ [~,r_temp,S] = electronicGroundStateAtomicForce(x+sigma_0*S.NLCG_d,S);
+ S.ForceCount = S.ForceCount + 1;
+ eta_prev = dot(r_temp,S.NLCG_d);
+ j = 0 ;
+ alph = -sigma_0;
+ r_temp = -r;
+ % Find the step length (alph) using secant method
+ while ((j < jmax) && (abs(alph)*delta_d > tol2))
+ eta = dot(r_temp,S.NLCG_d);
+ alph = alph * (eta / (eta_prev - eta));
+ x = x + alph * S.NLCG_d;
+ [x,r_temp,S] = electronicGroundStateAtomicForce(x,S);
+ S.ForceCount = S.ForceCount + 1;
+ eta_prev = eta;
+ j = j + 1;
+ fprintf('\n Secant step no. %d completed. \n',j);
+ end
+ delta_old = delta_new;
+ r = -r_temp;
+ delta_mid = dot(r,s);
+ M = ones(size(x)); %TODO: Need to set REAL PRECONDITIONER
+ s = r./M;
+ delta_new = dot(r,s);
+ err = max(abs(r));
+ bet = (delta_new-delta_mid)/delta_old;
+ if (k==n || bet <=0)
+ S.NLCG_d = s;
+ k = 0;
+ else
+ S.NLCG_d = s + bet*S.NLCG_d;
+ end
+
+ % print the result in .geopt file
+ if S.PrintRelaxout == 1
+ PrintRelax(S,transpose(reshape(x,3,[])));
+ end
+ %print relevant quanties for restart in .restart file
+ if (S.Printrestart == 1 && rem(S.Relax_iter, S.Printrestart_fq) == 0)
+ PrintRestart(S,transpose(reshape(x,3,[])));
+ end
+
+ k = k + 1;
+ i = i + 1;
+ S.Relax_iter = S.Relax_iter + 1;
+ fprintf('\n Outer CG iteration no. %d completed. \n',i);
+ fprintf('\n error in CG relaxation = %.9f\n',delta_new);
+ end
+
+ if (S.Printrestart == 1)
+ S.Relax_iter = S.Relax_iter - 1;
+ PrintRestart(S,transpose(reshape(x,3,[])));
+ end
+ fprintf('\n Total no. of outer CG iterations = %d. ',i);
+
+end
+
+
+
+
+function S = LBFGS(S)
+% @ brief Function to perform relaxation using LIMITED-MEMORY BFGS
+% (Broyden–Fletcher–Goldfarb–Shanno) method
+%@ reference: "Based on the implementation in VTST(VASP Transition State Tools)"
+%================================================================================
+ imax = S.max_relax_it;
+ lbfgs_tol = S.TOL_RELAX;
+ N = 3 * S.n_atm;
+
+ % User input
+ M = S.L_history;
+ FINIT_STP = S.L_finit_stp;
+ MAXMOV = S.L_maxmov;
+ AUTOSCALE = S.L_autoscale;
+ LINEOPT = S.L_lineopt; % needed only if AUTOSCALE = 0
+ ICURV = S.L_icurv; % needed only if AUTOSCALE = 0;
+
+ DAMPING = 2.0; % Don't change
+ if ~S.RestartFlag
+ S.LBFGS_ISFD = 1; % Don't change
+ S.LBFGS_ISRESET = 1; % Don't change
+ S.LBFGS_STEP = 0; % Don't change
+
+ S.LBFGS_DELTAX = zeros(N,M);
+ S.LBFGS_DELTAG = zeros(N,M);
+ S.LBFGS_IYS = zeros(M,1);
+ S.LBFGS_FOLD = zeros(N,1);
+ end
+ ALPHA = zeros(M,1);
+
+ % Obtain atomic positions in cartesian coordinates in a vector form
+ if ~S.RestartFlag
+ %X = transpose(S.lat_uvec) * S.Atoms';
+ X = coordinateTransformation(S, S.Atoms, 'noncart2cart_dis');
+ X = reshape(X',[],1);
+ else
+ X = reshape(S.Atoms',[],1);
+ end
+
+ % Residual (F) is equal to atomic force (function returns dE/dR)
+ [X,G,S] = electronicGroundStateAtomicForce(X,S); F = -G;
+ S.ForceCount = S.ForceCount + 1;
+
+ % Print the relaxation output
+ if (S.PrintRelaxout == 1 && ~S.RestartFlag)
+ PrintRelax(S,transpose(reshape(X,3,[])));
+ end
+
+ S.Relax_iter = S.Relax_iter + 1;
+ err = max(abs(F));
+ i = 1;
+
+ while(i < imax && err > lbfgs_tol)
+ MAXMOV_FLAG = 0;
+ if(AUTOSCALE == 1)
+ if(S.LBFGS_ISFD == 1)
+ DIR = F/norm(F);
+ XOLD = X;
+ S.LBFGS_FOLD = F;
+ X = X + DIR * FINIT_STP;
+ S.LBFGS_ISFD = 0;
+ else
+ % Compute inverse curvature
+ DIR = S.LBFGS_ATOMDISP;
+ %disp(DIR);
+ DIR_NRM = norm(DIR);
+ %disp(DIR_NRM);
+ FP1 = dot(S.LBFGS_FOLD, DIR)/DIR_NRM;
+ FP2 = dot(F, DIR)/DIR_NRM;
+ CURV = (FP1 - FP2)/DIR_NRM;
+ %disp(CURV);
+ ICURV = 1/CURV/DAMPING; % must be positive-definite
+ if(ICURV < 0)
+ S.LBFGS_ISRESET = 1;
+ MAXMOV_FLAG = 1;
+ end
+ if(S.LBFGS_ISRESET == 1)
+ S.LBFGS_STEP = 0;
+ S.LBFGS_ISRESET = 0;
+ else
+ S.LBFGS_STEP = S.LBFGS_STEP + 1;
+ if(S.LBFGS_STEP <= M)
+ S.LBFGS_DELTAX(:,S.LBFGS_STEP) = S.LBFGS_ATOMDISP;
+ S.LBFGS_DELTAG(:,S.LBFGS_STEP) = -(F - S.LBFGS_FOLD);
+ S.LBFGS_IYS(S.LBFGS_STEP) = 1/dot(S.LBFGS_DELTAX(:,S.LBFGS_STEP),S.LBFGS_DELTAG(:,S.LBFGS_STEP));
+ else
+ S.LBFGS_DELTAX(:,1:M-1) = S.LBFGS_DELTAX(:,2:M);
+ S.LBFGS_DELTAG(:,1:M-1) = S.LBFGS_DELTAG(:,2:M);
+ S.LBFGS_IYS(1:M-1) = S.LBFGS_IYS(2:M);
+ S.LBFGS_DELTAX(:,M) = S.LBFGS_ATOMDISP;
+ S.LBFGS_DELTAG(:,M) = -(F - S.LBFGS_FOLD);
+ S.LBFGS_IYS(M) = 1/dot(S.LBFGS_DELTAX(:,M),S.LBFGS_DELTAG(:,M));
+ end
+ end
+ XOLD = X;
+ S.LBFGS_FOLD = F;
+ % Compute H0*g
+ if(S.LBFGS_STEP <= M)
+ BOUND = S.LBFGS_STEP;
+ else
+ BOUND = M;
+ end
+ DIR = -F;
+
+ for IM = 1:BOUND
+ JM = BOUND + 1 - IM;
+ ALPHA(JM) = S.LBFGS_IYS(JM) * dot(S.LBFGS_DELTAX(:,JM),DIR);
+ DIR = DIR - ALPHA(JM) * S.LBFGS_DELTAG(:,JM);
+ end
+ DIR = ICURV * DIR;
+ for IM = 1:BOUND
+ BETA = S.LBFGS_IYS(IM) * dot(S.LBFGS_DELTAG(:,IM), DIR);
+ DIR = DIR + S.LBFGS_DELTAX(:,IM) * (ALPHA(IM) - BETA);
+ end
+ DIR = -DIR;
+ %disp(DIR);
+ STP_SIZ = norm(DIR);
+ %disp(STP_SIZ);
+ if(STP_SIZ > MAXMOV)
+ S.LBFGS_ISRESET = 1;
+ STP_SIZ = MAXMOV;
+ DIR = STP_SIZ * F/norm(F);
+ end
+ if(MAXMOV_FLAG == 1)
+ DIR = F/norm(F);
+ X = X + MAXMOV * DIR;
+ MAXMOV_FLAG = 0;
+ else
+ X = X + DIR;
+ end
+ % disp(X);
+ end
+ else
+ if(S.LBFGS_ISFD == 1)
+ S.LBFGS_ISFD = 0;
+ OPTFLAG = 1;
+ a1 = abs(dot(F,S.LBFGS_FOLD));
+ a2 = dot(S.LBFGS_FOLD,S.LBFGS_FOLD);
+ if(a1 > 0.5 * a2 || a2 == 0)
+ S.LBFGS_ISRESET = 1;
+ end
+ if(LINEOPT == 0)
+ S.LBFGS_ISRESET = 0;
+ end
+ if(a2 == 0)
+ S.LBFGS_ISRESET = 1;
+ end
+ if(S.LBFGS_ISRESET == 1)
+ S.LBFGS_STEP = 0;
+ S.LBFGS_ISRESET = 0;
+ else
+ S.LBFGS_STEP = S.LBFGS_STEP + 1;
+ if(S.LBFGS_STEP <= M)
+ S.LBFGS_DELTAX(:,S.LBFGS_STEP) = S.LBFGS_ATOMDISP;
+ S.LBFGS_DELTAG(:,S.LBFGS_STEP) = -(F - S.LBFGS_FOLD);
+ S.LBFGS_IYS(S.LBFGS_STEP) = 1/dot(S.LBFGS_DELTAX(:,S.LBFGS_STEP),S.LBFGS_DELTAG(:,S.LBFGS_STEP));
+ else
+ S.LBFGS_DELTAX(:,1:M-1) = S.LBFGS_DELTAX(:,2:M);
+ S.LBFGS_DELTAG(:,1:M-1) = S.LBFGS_DELTAG(:,2:M);
+ S.LBFGS_IYS(1:M-1) = S.LBFGS_IYS(2:M);
+ S.LBFGS_DELTAX(:,M) = S.LBFGS_ATOMDISP;
+ S.LBFGS_DELTAG(:,M) = -(F - S.LBFGS_FOLD);
+ S.LBFGS_IYS(M) = 1/dot(S.LBFGS_DELTAX(:,M),S.LBFGS_DELTAG(:,M));
+ end
+ end
+ XOLD = X;
+ S.LBFGS_FOLD = F;
+ % Compute H0*g
+ if(S.LBFGS_STEP <= M)
+ BOUND = S.LBFGS_STEP;
+ else
+ BOUND = M;
+ end
+ DIR = -F;
+ for IM = 1:BOUND
+ JM = BOUND + 1 - IM;
+ ALPHA(JM) = S.LBFGS_IYS(JM) * dot(S.LBFGS_DELTAX(:,JM),DIR);
+ DIR = DIR - ALPHA(JM) * S.LBFGS_DELTAG(:,JM);
+ end
+ DIR = ICURV * DIR;
+ for IM = 1:BOUND
+ BETA = S.LBFGS_IYS(IM) * dot(S.LBFGS_DELTAG(:,IM), DIR);
+ DIR = DIR + S.LBFGS_DELTAX(:,IM) * (ALPHA(IM) - BETA);
+ end
+ DIR = -DIR;
+ if(LINEOPT == 1)
+ DIR = DIR/norm(DIR);
+ X = X + DIR * FINIT_STP;
+ else
+ STP_SIZ = norm(DIR);
+ if(STP_SIZ > MAXMOV)
+ STP_SIZ = MAXMOV;
+ DIR = STP_SIZ * DIR /norm(DIR);
+ end
+ X = X + DIR;
+ S.LBFGS_ISFD = 1;
+ OPTFLAG = 0;
+ end
+ else
+ S.LBFGS_ISFD = 1;
+ OPTFLAG = 0;
+ FP1 = dot(S.LBFGS_FOLD,DIR);
+ FP2 = dot(F,DIR);
+ CURV = (FP1 - FP2)/FINIT_STP;
+ if(CURV < 0)
+ STP_SIZ = MAXMOV;
+ else
+ FAVG = 0.5 * (FP1 + FP2);
+ STP_SIZ = FAVG/CURV;
+ if(abs(STP_SIZ) > MAXMOV)
+ if(STP_SIZ >= 0)
+ STP_SIZ = abs(MAXMOV) - abs(FINIT_STP);
+ else
+ STP_SIZ = -abs(MAXMOV) + abs(FINIT_STP);
+ end
+ else
+ STP_SIZ = STP_SIZ - 0.5 * FINIT_STP;
+ end
+ end
+ X = X + DIR * STP_SIZ;
+ end
+ end
+ %X(1:3) = Y(1:3);
+ S.LBFGS_ATOMDISP = X - XOLD;
+ [X,G,S] = electronicGroundStateAtomicForce(X,S); F = -G;
+ S.ForceCount = S.ForceCount + 1;
+ err = max(abs(F));
+
+ % print the relaxed configuration in .geopt file
+ if S.PrintRelaxout == 1
+ PrintRelax(S,transpose(reshape(X,3,[])));
+ end
+ % print the relevant quantities needed for restart in .restart file
+ if (S.Printrestart == 1 && rem(S.Relax_iter, S.Printrestart_fq) == 0)
+ PrintRestart(S,transpose(reshape(X,3,[])));
+ end
+
+ i = i + 1;
+ S.Relax_iter = S.Relax_iter + 1;
+ end
+
+ if (S.Printrestart == 1)
+ S.Relax_iter = S.Relax_iter - 1;
+ PrintRestart(S,transpose(reshape(X,3,[])));
+ end
+end
+
+
+
+
+
+function S = FIRE(S)
+% @ brief Function to perform relaxation using FAST INERTIAL RELAXATION ENGINE method
+% @ reference: "Structural Relaxation Made Simple (Bitzek et. al., 2006)"
+%==========================================================================================
+ % Obtain atomic positions in cartesian coordinates and as a vector
+ if ~S.RestartFlag
+ %x_var = transpose(S.lat_uvec) * S.Atoms';
+ x_var = coordinateTransformation(S, S.Atoms, 'noncart2cart_dis');
+ x_var = reshape(x_var',[],1);
+ else
+ x_var = reshape(S.Atoms',[],1);
+ end
+
+ % FIRE related variables : user modifiable
+ S.FIRE_dt = S.FIRE_dt * S.fs2atu;
+ FIRE_Mass = S.FIRE_mass * S.amu2au;
+ FIRE_Tol = S.TOL_RELAX;
+ Max_FIRE_Iter = S.max_relax_it;
+ dx_Max = S.FIRE_maxmov;
+
+ % FIRE related variables : internal
+ fDec = 0.5;
+ fInc = 1.1;
+ nMin = 5;
+ alphaStart = 0.1;
+ fAlpha = 0.99;
+ dt_Max = 10.0 * S.FIRE_dt;
+
+ % Do a static calculation first
+ %fprintf('\n\n Starting single shot static calculation: \n\n')
+ [x_var,force_fun,S] = electronicGroundStateAtomicForce(x_var,S); Force_var = -force_fun;
+ S.ForceCount = S.ForceCount + 1;
+
+ % print atomic configuration in .geopt file
+ if (S.PrintRelaxout == 1 && ~S.RestartFlag)
+ PrintRelax(S,transpose(reshape(x_var,3,[])));
+ end
+
+ S.Relax_iter = S.Relax_iter + 1;
+
+ if ~S.RestartFlag
+ S.FIRE_resetIter = 0;
+ S.FIRE_alpha = alphaStart;
+ S.FIRE_dtNow = S.FIRE_dt;
+ S.FIRE_vel = 0.0 * Force_var; % Set zero initial velocities
+ end
+
+ err = max(abs(Force_var));
+ FIRE_iter = S.Relax_iter;
+ iter = 1;
+
+ while (iter < Max_FIRE_Iter && err > FIRE_Tol)
+
+ % Verlet step
+ S.FIRE_vel = S.FIRE_vel + 0.5 * S.FIRE_dtNow * (Force_var/FIRE_Mass);
+ delta_x = S.FIRE_vel * S.FIRE_dtNow;
+
+ % Apply a "trust region"
+ ind = (delta_x > dx_Max);
+ delta_x(ind) = dx_Max;
+
+ ind = (delta_x < -dx_Max);
+ delta_x(ind) = -dx_Max;
+
+ x_var = x_var + delta_x;
+ [x_var,force_fun,S] = electronicGroundStateAtomicForce(x_var,S); Force_var = -force_fun;
+ S.ForceCount = S.ForceCount + 1;
+
+ S.FIRE_vel = S.FIRE_vel + 0.5 * S.FIRE_dtNow * (Force_var/FIRE_Mass);
+
+ % Check power
+ P = dot(Force_var, S.FIRE_vel);
+
+ if(P < 0.0)
+
+ S.FIRE_vel = 0.0 * S.FIRE_vel; % Reset velosity to 0
+ S.FIRE_resetIter = FIRE_iter; % S.FIRE_resetIter <-- iter #
+ S.FIRE_dtNow = S.FIRE_dtNow*fDec; % decrease dt
+ S.FIRE_alpha = alphaStart; % reset alpha to alpha_start
+
+ elseif ((P >= 0.0) && (( FIRE_iter - S.FIRE_resetIter) > nMin))
+
+ S.FIRE_dtNow = min(S.FIRE_dtNow*fInc, dt_Max); % Update dt
+ S.FIRE_alpha = fAlpha*S.FIRE_alpha; % update alpha
+
+ end
+
+ % Adjust velocities
+ hatF = Force_var / norm(Force_var); % the unit vector
+ S.FIRE_vel = (1.0 - S.FIRE_alpha)*S.FIRE_vel + (S.FIRE_alpha * norm(S.FIRE_vel)) * hatF ;
+
+ % print atomic configuration in .geopt file
+ if S.PrintRelaxout == 1
+ PrintRelax(S,transpose(reshape(x_var,3,[])));
+ end
+ % print relevant quantities needed for restart in .restart file
+ if (S.Printrestart == 1 && rem(S.Relax_iter, S.Printrestart_fq) == 0)
+ PrintRestart(S,transpose(reshape(x_var,3,[])));
+ end
+
+ err = max(abs(Force_var));
+
+ FIRE_iter = FIRE_iter + 1;
+ iter = iter + 1;
+ S.Relax_iter = S.Relax_iter + 1;
+ end
+
+ if (S.Printrestart == 1)
+ S.Relax_iter = S.Relax_iter - 1;
+ PrintRestart(S,transpose(reshape(x_var,3,[])));
+ end
+
+end
+
+
+
+
+function [] = PrintRelax(S,atom_pos)
+% @ brief Function to write relaxation output in .geopt file
+%================================================================
+ if S.Relax_iter == 1
+ fileID = fopen(S.relaxfname,'w');
+ else
+ fileID = fopen(S.relaxfname,'a');
+ end
+ fprintf(fileID,':RELAXSTEP: %d\n',S.Relax_iter);
+ if (S.PrintAtomPosFlag == 1)
+ fprintf(fileID,':R:\n');
+ fprintf(fileID, '%18.10E %18.10E %18.10E\n', atom_pos');
+ end
+ if (S.PrintForceFlag == 1)
+ fprintf(fileID,':F:\n');
+ fprintf(fileID, '%18.10E %18.10E %18.10E\n', S.force');
+ end
+ fclose(fileID);
+end
+
+
+
+
+function [] = PrintRestart(S,atom_pos)
+% brief Function to write relevant quantities needed for restart of relaxation
+%==================================================================================
+ fileID = fopen(S.restartfname,'w');
+ fprintf(fileID,':RELAXSTEP: %d\n',S.Relax_iter);
+ fprintf(fileID,':R:\n');
+ fprintf(fileID, '%18.10E %18.10E %18.10E\n', atom_pos');
+
+ if (strcmp(S.RelaxMeth,'NLCG'))
+ % Print search direction
+ fprintf(fileID,':D:\n');
+ fprintf(fileID,'%18.10E\n', S.NLCG_d);
+ elseif (strcmp(S.RelaxMeth,'LBFGS'))
+ fprintf(fileID,':ISFD: %d\n', S.LBFGS_ISFD);
+ fprintf(fileID,':ISRESET: %d\n', S.LBFGS_ISRESET);
+ fprintf(fileID,':STEP: %d\n', S.LBFGS_STEP);
+ fprintf(fileID,':DX:\n');
+ DX = reshape(S.LBFGS_DELTAX,[],1);
+ fprintf(fileID,'%18.10E\n', DX);
+ fprintf(fileID,':DG:\n');
+ DG = reshape(S.LBFGS_DELTAG,[],1);
+ fprintf(fileID,'%18.10E\n', DG);
+ fprintf(fileID,':IYS:\n');
+ fprintf(fileID,'%18.10E\n', S.LBFGS_IYS);
+ fprintf(fileID,':FOLD:\n');
+ fprintf(fileID,'%18.10E\n', S.LBFGS_FOLD);
+ fprintf(fileID,':RDISP:\n');
+ fprintf(fileID,'%18.10E\n', S.LBFGS_ATOMDISP);
+ elseif(strcmp(S.RelaxMeth,'FIRE'))
+ fprintf(fileID,':FIRE_alpha: %18.10E\n', S.FIRE_alpha);
+ fprintf(fileID,':FIRE_dtNow: %18.10E\n', S.FIRE_dtNow);
+ fprintf(fileID,':FIRE_resetIter: %d\n', S.FIRE_resetIter);
+ fprintf(fileID,':FIRE_V:\n');
+ fprintf(fileID,'%18.10E\n', S.FIRE_vel);
+ end
+
+ fclose(fileID);
+end
+
+
+
+
+function S = RestartRelax(S)
+% @ brief Function to read the .restart file of relaxation
+%================================================================
+ fprintf(' Reading .restart file ...\n');
+ fid = fopen(S.restartfname,'r');
+ if (fid == -1)
+ error('\n Cannot open file "%s"\n',S.restartfname);
+ end
+
+ while(~feof(fid))
+ C_inpt = textscan(fid,'%s',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ str = char(C_inpt{:});
+ if (strcmp(str,':RELAXSTEP:'))
+ C_param = textscan(fid,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.Relax_iter = C_param{1};
+ textscan(fid,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,':R:'))
+ textscan(fid,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ for i = 1:S.n_atm
+ C_param = textscan(fid,'%f %f %f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ textscan(fid,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ S.Atoms(i,:) = cell2mat(C_param);
+ end
+ elseif (strcmp(str,':D:'))
+ S.NLCG_d = zeros(3*S.n_atm,1);
+ textscan(fid,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ for i = 1:3*S.n_atm
+ C_param = textscan(fid,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ textscan(fid,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ S.NLCG_d(i) = C_param{1};
+ end
+ elseif (strcmp(str,':ISFD:'))
+ C_param = textscan(fid,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.LBFGS_ISFD = C_param{1};
+ textscan(fid,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,':ISRESET:'))
+ C_param = textscan(fid,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.LBFGS_ISRESET = C_param{1};
+ textscan(fid,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,':STEP:'))
+ C_param = textscan(fid,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.LBFGS_STEP = C_param{1};
+ textscan(fid,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,':DX:'))
+ S.LBFGS_DELTAX = zeros(3*S.n_atm,S.L_history);
+ textscan(fid,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ for j = 1:S.L_history
+ for i = 1:3*S.n_atm
+ C_param = textscan(fid,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ textscan(fid,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ S.LBFGS_DELTAX(i,j) = C_param{1};
+ end
+ end
+ elseif (strcmp(str,':DG:'))
+ S.LBFGS_DELTAG = zeros(3*S.n_atm,S.L_history);
+ textscan(fid,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ for j = 1:S.L_history
+ for i = 1:3*S.n_atm
+ C_param = textscan(fid,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ textscan(fid,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ S.LBFGS_DELTAG(i,j) = C_param{1};
+ end
+ end
+ elseif (strcmp(str,':IYS:'))
+ S.LBFGS_IYS = zeros(S.L_history,1);
+ textscan(fid,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ for i = 1:S.L_history
+ C_param = textscan(fid,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ textscan(fid,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ S.LBFGS_IYS(i) = C_param{1};
+ end
+ elseif (strcmp(str,':FOLD:'))
+ S.LBFGS_FOLD = zeros(3*S.n_atm,1);
+ textscan(fid,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ for i = 1:3*S.n_atm
+ C_param = textscan(fid,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ textscan(fid,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ S.LBFGS_FOLD(i) = C_param{1};
+ end
+ elseif (strcmp(str,':RDISP:'))
+ S.LBFGS_ATOMDISP = zeros(3*S.n_atm,1);
+ textscan(fid,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ for i = 1:3*S.n_atm
+ C_param = textscan(fid,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ textscan(fid,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ S.LBFGS_ATOMDISP(i) = C_param{1};
+ end
+ elseif (strcmp(str,':FIRE_alpha:'))
+ C_param = textscan(fid,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.FIRE_alpha = C_param{1};
+ textscan(fid,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,':FIRE_dtNow:'))
+ C_param = textscan(fid,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.FIRE_dtNow = C_param{1};
+ textscan(fid,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,':FIRE_resetIter:'))
+ C_param = textscan(fid,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ S.FIRE_resetIter = C_param{1};
+ textscan(fid,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ elseif (strcmp(str,':FIRE_V:'))
+ S.FIRE_vel = zeros(3*S.n_atm,1);
+ textscan(fid,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ for i = 1:3*S.n_atm
+ C_param = textscan(fid,'%f',1,'delimiter',' ','MultipleDelimsAsOne',1);
+ textscan(fid,'%s',1,'delimiter','\n','MultipleDelimsAsOne',0); % skip current line
+ S.FIRE_vel(i) = C_param{1};
+ end
+ end
+ end
+
+ fclose(fid);
+end
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/src/scf.m b/src/scf.m
new file mode 100644
index 00000000..eb3ffb71
--- /dev/null
+++ b/src/scf.m
@@ -0,0 +1,325 @@
+function [S] = scf(S)
+% @brief SCF(S) implements the self consistent field calculation.
+%
+% @authors Qimen Xu
+% Abhiraj Sharma
+% Phanish Suryanarayana
+%
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+%
+
+fprintf('\n ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \n');
+fprintf(' Starting SCF iteration...\n');
+
+outfname = S.outfname;
+fileID = fopen(outfname,'a');
+if (fileID == -1)
+ error('\n Cannot open file "%s"\n',outfname);
+end
+if(S.nspin == 1)
+ fprintf(fileID,'=====================================================================\n');
+ fprintf(fileID,' Self Consistent Field (SCF#%d) \n',S.Relax_iter);
+ fprintf(fileID,'=====================================================================\n');
+ fprintf(fileID,'Iteration Free Energy (Ha/atom) SCF Error Timing (sec)\n');
+else
+ fprintf(fileID,'========================================================================================\n');
+ fprintf(fileID,' Self Consistent Field (SCF#%d) \n',S.Relax_iter);
+ fprintf(fileID,'========================================================================================\n');
+ fprintf(fileID,'Iteration Free Energy (Ha/atom) Magnetization SCF Error Timing (sec)\n');
+end
+fclose(fileID);
+
+% Electrostatic potential
+S = poissonSolve(S, S.poisson_tol, 0);
+
+% Exchange-correlation potential
+S = exchangeCorrelationPotential(S);
+
+% Effective potential
+S.Veff = real(bsxfun(@plus,S.phi,S.Vxc));
+
+% Initialize the mixing history vectors
+S.X = zeros(S.N*S.nspin,S.MixingHistory);
+S.F = zeros(S.N*S.nspin,S.MixingHistory);
+S.mixing_hist_fkm1 = zeros(S.N*S.nspin,1);
+
+if S.nspin == 1
+ if S.MixingVariable == 0
+ S.mixing_hist_xkm1 = S.rho;
+ rho_temp = S.rho;
+ else
+ % for potential mixing, we store the mean-0 part only
+ if S.BC == 2
+ Veff_mean = mean(S.Veff);
+ else
+ Veff_mean = 0.0;
+ end
+ S.mixing_hist_xkm1 = S.Veff - Veff_mean;
+ Veff_temp = S.Veff;
+ end
+else
+ if S.MixingVariable == 0
+ RHO_temp = vertcat(S.rho(:,2),S.rho(:,3));
+ S.mixing_hist_xkm1 = RHO_temp;
+ rho_temp = S.rho;
+ else
+ VEFF_temp = vertcat(S.Veff(:,1),S.Veff(:,2));
+ % for potential mixing, we store the mean-0 part only
+ VEFF_temp_mean = mean(VEFF_temp);
+ S.mixing_hist_xkm1 = VEFF_temp - VEFF_temp_mean;
+ Veff_temp = S.Veff;
+ end
+end
+
+% update charges
+% S.PosCharge = abs(dot(S.W, S.b));
+% S.NegCharge = -S.PosCharge + S.NetCharge;
+
+% Generate guess psi WARNING: psi is an internal matlab function
+if(S.ForceCount == 1)
+ rng('default'); % Initialize random number generator
+ rng(1); % Specify the seed to be 1
+ S.psi = rand(S.N,S.Nev,S.tnkpt*S.nspin)-0.5;
+ S.upper_bound_guess_vecs = zeros(S.N,S.tnkpt*S.nspin);
+ S.EigVal = zeros(S.Nev,S.tnkpt*S.nspin);
+end
+% S.EigVal = zeros(S.Nev,S.tnkpt*S.nspin);
+
+
+% SCF LOOP
+count = 1;
+count_SCF = 1;
+err = 100;
+max_count_first_relax = S.rhoTrigger;
+max_count_gen_relax = 1;
+max_scf_iter = S.MAXIT_SCF;
+min_scf_iter = S.MINIT_SCF;
+if max_scf_iter < min_scf_iter
+ min_scf_iter = max_scf_iter;
+end
+S.lambda_f = 0.0;
+
+% Spectrum bounds and filter cutoff for Chebyshev filtering
+bup = zeros(S.tnkpt*S.nspin,1);
+a0 = zeros(S.tnkpt*S.nspin,1);
+lambda_cutoff = zeros(S.tnkpt*S.nspin,1);
+
+% time for one scf
+t_SCF = 0;
+
+% start scf loop
+while (err > S.SCF_tol && count_SCF <= max_scf_iter || count_SCF <= min_scf_iter)
+ tic_cheb = tic;
+ if(count_SCF > 1)
+ fprintf(' ========================= \n');
+ fprintf(' Relaxation iteration: %2d \n SCF iteration number: %2d \n',S.Relax_iter,count_SCF);
+ fprintf(' ========================= \n');
+ else
+ fprintf(' ============================================= \n');
+ fprintf(' Relaxation iteration: %2d\n SCF iteration number: 1, Chebyshev cycle: %d \n',S.Relax_iter,count);
+ fprintf(' ============================================= \n');
+ end
+
+ [S.upper_bound_guess_vecs,S.psi,S.EigVal,a0,bup,lambda_cutoff] = ...
+ eigSolver(S,count,S.upper_bound_guess_vecs,S.psi,S.EigVal,a0,bup,lambda_cutoff);
+
+ % Solve for Fermi energy S.lambda_f and occupations
+ S = occupations(S);
+
+ if (((S.ForceCount == 1) && (count >= max_count_first_relax)) ...
+ || ((S.ForceCount > 1) && (count >= max_count_gen_relax)))
+ % for density mixing, can estimate energy based on input rho and
+ % input veff, will recalculate energy once scf is converged
+ if S.MixingVariable == 0
+ [S.Etotal,S.Eband,S.Exc,S.Exc_dc,S.Eelec_dc,S.Eent] = evaluateTotalEnergy(S);
+ end
+
+ % Electron density
+ S = electronDensity(S);
+
+ if S.MixingVariable == 1
+ % update Veff before calculating the energy %
+ % Electrostatic potential
+ S = poissonSolve(S, S.poisson_tol, 1);
+ % Exchange-correlation potential
+ S = exchangeCorrelationPotential(S);
+ % Effective potential
+ S.Veff = real(bsxfun(@plus,S.phi,S.Vxc));
+ % Calculate energy
+ [S.Etotal,S.Eband,S.Exc,S.Exc_dc,S.Eelec_dc,S.Eent] = evaluateTotalEnergy(S);
+ % Calculate Self Consistency Correction to energy
+ if S.nspin == 1
+ S.Escc = sum((S.Veff-Veff_temp) .* S.rho .* S.W);
+ else
+ S.Escc = sum(sum((S.Veff-Veff_temp) .* S.rho(:,2:3),2) .* S.W);
+ end
+ fprintf(' Escc = %.8f\n', S.Escc);
+ S.Etotal = S.Etotal + S.Escc;
+ end
+ fprintf(' Etot = %.8f\n', S.Etotal);
+ fprintf(' Eatom = %.8f\n', S.Etotal/S.n_atm);
+
+ % fprintf('\n Time for total energy calculation = %f s.',toc(t1));
+ % fprintf('\n Total energy (Ha/atom): %1.9f \n',Etotal/S.n_atm) ;
+ S_Debug.relax(S.Relax_iter).fermi_energy(count_SCF,1) = S.lambda_f;
+ S_Debug.relax(S.Relax_iter).Etotal(count_SCF,1) = S.Etotal;
+ S_Debug.relax(S.Relax_iter).Eband(count_SCF,1) = S.Eband;
+ S_Debug.relax(S.Relax_iter).Exc(count_SCF,1) = S.Exc;
+ S_Debug.relax(S.Relax_iter).Exc_dc(count_SCF,1) = S.Exc_dc;
+ S_Debug.relax(S.Relax_iter).Eelec_dc(count_SCF,1) = S.Eelec_dc;
+ S_Debug.relax(S.Relax_iter).Eent(count_SCF,1) = S.Eent;
+ if S.MixingVariable == 1
+ S_Debug.relax(S.Relax_iter).Escc(count_SCF,1) = S.Escc;
+ end
+ % Error in SCF fixed-point iteration
+ if S.nspin == 1
+ if S.MixingVariable == 1
+ err = (norm(S.Veff - Veff_temp))/(norm(S.Veff));
+ else
+ err = (norm(S.rho - rho_temp))/(norm(S.rho));
+ end
+ else
+ S.netM = dot(S.W,S.rho(:,2)) - dot(S.W,S.rho(:,3));
+ fprintf('======================================\n');
+ fprintf('Net magnetization in this iteration is: % .15f \n', S.netM);
+ fprintf('======================================\n');
+ if S.MixingVariable == 1
+ VEFF = vertcat(S.Veff(:,1), S.Veff(:,2));
+ err = norm(VEFF - VEFF_temp)/norm(VEFF);
+ else
+ RHO = vertcat(S.rho(:,2), S.rho(:,3));
+ err = norm(RHO - RHO_temp)/norm(RHO);
+ end
+ end
+
+ fprintf(' Error in SCF iteration: %.4e \n',err) ;
+
+ % Mixing to accelerate SCF convergence
+ if (err > S.SCF_tol || count_SCF < S.MINIT_SCF)
+ if S.nspin == 1
+ if S.MixingVariable == 1 % potential mixing
+ % shift Veff and Veff_temp so they have mean 0
+ if S.BC == 2
+ Veff_mean = mean(S.Veff); Veff_temp_mean = mean(Veff_temp);
+ else
+ Veff_mean = 0; Veff_temp_mean = 0;
+ end
+ S.Veff = S.Veff - Veff_mean;
+ Veff_temp = Veff_temp - Veff_temp_mean;
+ % enter mixing
+ [S,S.Veff] = mixing(S,S.Veff,Veff_temp,count_SCF);
+ % shift the mean back
+ S.Veff = S.Veff + Veff_mean; % the new veff for next input
+ % note we add Veff_mean not Veff_temp_mean, since the one
+ % used for the next input is S.Veff
+ Veff_temp = S.Veff;
+ else % density mixing
+ [S, S.rho] = mixing(S,S.rho,rho_temp,count_SCF);
+ rho_temp = S.rho;
+ % at this point rho_temp = S.rho, i.e., new input density
+ % update Veff
+ S = poissonSolve(S, S.poisson_tol, 1);
+
+ % Exchange-correlation potential
+ S = exchangeCorrelationPotential(S);
+
+ % Effective potential
+ S.Veff = real(bsxfun(@plus,S.phi,S.Vxc));
+ end
+ else
+ if S.MixingVariable == 1 % potential mixing
+ % shift Veff and Veff_temp so they have mean 0
+ if S.BC == 2
+ VEFF_mean = mean(VEFF); VEFF_temp_mean = mean(VEFF_temp);
+ else
+ VEFF_mean = 0; VEFF_temp_mean = 0;
+ end
+ VEFF = VEFF - VEFF_mean;
+ VEFF_temp = VEFF_temp - VEFF_temp_mean;
+ % enter mixing
+ [S,VEFF] = mixing(S,VEFF,VEFF_temp,count_SCF);
+ % shift the mean back
+ VEFF = VEFF + VEFF_mean; % the new veff for next input
+ % note we add Veff_mean not Veff_temp_mean, since the one
+ % used for the next input is S.Veff
+ S.Veff(:,1) = VEFF(1:S.N);
+ S.Veff(:,2) = VEFF(S.N+1:end);
+ Veff_temp = S.Veff;
+ VEFF_temp = VEFF;
+ else % density mixing
+ [S, RHO] = mixing(S,RHO,RHO_temp,count_SCF);
+ negrho_count = sum(RHO < 0);
+ if (negrho_count > 0)
+ fprintf('\nDensity got negative\n\n');
+ RHO(RHO < 0) = 0;
+ end
+
+ S.rho(:,2) = RHO(1:S.N);
+ S.rho(:,3) = RHO(S.N+1:end);
+ S.rho(:,1) = S.rho(:,2) + S.rho(:,3);
+ if (negrho_count > 0)
+ scal = (-S.NegCharge/dot(S.W,S.rho(:,1)));
+ S.rho = scal*S.rho;
+ end
+ rho_temp = S.rho;
+ RHO_temp = vertcat(rho_temp(:,2),rho_temp(:,3));
+ % at this point rho_temp = S.rho, i.e., new input density
+ % update Veff
+ S = poissonSolve(S, S.poisson_tol, 1);
+
+ % Exchange-correlation potential
+ S = exchangeCorrelationPotential(S);
+
+ % Effective potential
+ S.Veff = real(bsxfun(@plus,S.phi,S.Vxc));
+ end
+ end
+ end
+
+ % write to output file
+ fileID = fopen(S.outfname,'a');
+ if (fileID == -1)
+ error('\n Cannot open file "%s"\n',S.outfname);
+ end
+ if t_SCF == 0
+ t_SCF = toc(tic_cheb);
+ end
+
+ if S.nspin == 1
+ fprintf(fileID,'%-6d %18.10E %.3E %.3f\n', ...
+ count_SCF, S.Etotal/S.n_atm, err, t_SCF);
+ else
+ fprintf(fileID,'%-6d %18.10E %11.4E %.3E %.3f\n', ...
+ count_SCF, S.Etotal/S.n_atm, S.netM, err, t_SCF);
+ end
+ t_SCF = 0; % reset SCF timer
+ fclose(fileID);
+ count_SCF = count_SCF + 1 ;
+ end
+ scf_runtime = toc(tic_cheb);
+ t_SCF = t_SCF + scf_runtime; % add chebyshev filtering time to SCF time
+ S_Debug.relax(S.Relax_iter).scf_runtime(count_SCF,1) = scf_runtime;
+ fprintf(' This SCF iteration took %.3f s.\n\n', scf_runtime);
+ count = count + 1;
+end
+
+S_Debug.relax(S.Relax_iter).scf_flag = 0; % scf_flag being 0 means it's converged
+if (count_SCF == max_scf_iter + 1)
+ disp(' SCF did not converge. Maximum iterations reached!')
+ S_Debug.relax(S.Relax_iter).scf_flag = 1; % scf_flag being 1 means it's not converged
+end
+
+S_Debug.relax(S.Relax_iter).count_SCF = count_SCF - 1;
+fprintf('\n Finished SCF iteration in %d steps!\n', (count_SCF - 1));
+fprintf(' ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \n');
+
+% write to output file
+fileID = fopen(S.outfname,'a');
+if (fileID == -1)
+ error('\n Cannot open file "%s"\n',S.outfname);
+end
+fprintf(fileID,'Total number of SCF: %-6d\n',count_SCF-1);
+fclose(fileID);
+
+end
+
diff --git a/src/sphericalHarmonics.m b/src/sphericalHarmonics.m
new file mode 100644
index 00000000..c5a884ca
--- /dev/null
+++ b/src/sphericalHarmonics.m
@@ -0,0 +1,397 @@
+function Ylm = sphericalHarmonics(X,Y,Z,l,m,kind)
+% @brief sphericalHarmonics(X,Y,Z,l,m,kind) calculates the sperical harmonics
+% Ylm (real or complex) at the given positions (X,Y,Z)
+%
+% @param X The x coordinates of the positions
+% @param Y The y coordinates of the positions
+% @param Z The z coordinates of the positions
+% @param l The azimuthal quantum number
+% @param m The magnetic quantum number
+% @param kind Optional arguments: 'real' - Compute real spherical harmonics
+% 'complex' - Compute complex spherical harmonics
+%
+% @authors Qimen Xu
+% Abhiraj Sharma
+% Phanish Suryanarayana
+%
+% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech
+%============================================================================================
+
+szX = size(X); szY = size(Y); szZ = size(Z);
+if ~isequal(szX,szY,szZ)
+ error('sphericalHarmonics(X,Y,Z,l,m,kind): dimensions of must match');
+end
+
+isInt = l - round(l);
+if (isInt ~= 0)||(l < 0)
+ error('sphericalHarmonics(X,Y,Z,l,m,kind): must be a nonnegative integer');
+end
+
+isInt = m - round(m);
+if (isInt ~= 0)||(m < -l)||(m > l)
+ error('sphericalHarmonics(X,Y,Z,l,m,kind): must be a integer between [-l,l]');
+end
+
+if strcmp(kind,'real')
+ isRealSH = true;
+elseif strcmp(kind,'complex')
+ isRealSH = false;
+else
+ error('sphericalHarmonics(X,Y,Z,l,m,kind): must be either ''real'' or ''complex''');
+end
+
+if (isRealSH)
+ Ylm = RealSphericalHarmonics(X,Y,Z,l,m);
+else
+ Ylm = ComplexSphericalHarmonics(X,Y,Z,l,m);
+end
+
+end
+
+
+
+
+% ------------- Calculator for Real Spherical Harmonics
+function Ylm = RealSphericalHarmonics(X,Y,Z,l,m)
+% RealSphericalHarmonics calculates real spherical harmonics
+
+if (l > 6)
+ error('Only less than or equal to 6 supported.');
+end
+
+r = sqrt(X.^2 + Y.^2 + Z.^2) ;
+
+if (l == 0)
+ % l=0
+ C00 = 0.282094791773878; % 0.5*sqrt(1/pi)
+ Ylm = C00 * ones(size(X));
+elseif (l == 1)
+ % l=1
+ C1m1 = 0.488602511902920; % sqrt(3/(4*pi))
+ C10 = 0.488602511902920; % sqrt(3/(4*pi))
+ C1p1 = 0.488602511902920; % sqrt(3/(4*pi))
+ if(m==-1)
+ Ylm = C1m1 * (Y ./ r);
+ elseif(m==0)
+ Ylm = C10 * (Z ./ r);
+ elseif(m==1)
+ Ylm = C1p1 * (X ./ r);
+ end
+elseif(l == 2)
+ % l=2
+ C2m2 = 1.092548430592079; % 0.5*sqrt(15/pi)
+ C2m1 = 1.092548430592079; % 0.5*sqrt(15/pi)
+ C20 = 0.315391565252520; % 0.25*sqrt(5/pi)
+ C2p1 = 1.092548430592079; % 0.5*sqrt(15/pi)
+ C2p2 = 0.546274215296040; % 0.25*sqrt(15/pi)
+ if(m==-2)
+ Ylm = C2m2*(X.*Y)./(r.*r);
+ elseif(m==-1)
+ Ylm = C2m1*(Y.*Z)./(r.*r);
+ elseif(m==0)
+ Ylm = C20*(-X.*X - Y.*Y + 2*Z.*Z)./(r.*r);
+ elseif(m==1)
+ Ylm = C2p1*(Z.*X)./(r.*r);
+ elseif(m==2)
+ Ylm = C2p2*(X.*X - Y.*Y)./(r.*r);
+ end
+elseif(l == 3)
+ % l=3
+ C3m3 = 0.590043589926644; % 0.25*sqrt(35/(2*pi))
+ C3m2 = 2.890611442640554; % 0.5*sqrt(105/(pi))
+ C3m1 = 0.457045799464466; % 0.25*sqrt(21/(2*pi))
+ C30 = 0.373176332590115; % 0.25*sqrt(7/pi)
+ C3p1 = 0.457045799464466; % 0.25*sqrt(21/(2*pi))
+ C3p2 = 1.445305721320277; % 0.25*sqrt(105/(pi))
+ C3p3 = 0.590043589926644; % 0.25*sqrt(35/(2*pi))
+ if(m==-3)
+ Ylm = C3m3*(3*X.*X - Y.*Y).*Y./(r.*r.*r);
+ elseif(m==-2)
+ Ylm = C3m2*(X.*Y.*Z)./(r.*r.*r);
+ elseif(m==-1)
+ Ylm = C3m1*Y.*(4*Z.*Z - X.*X - Y.*Y)./(r.*r.*r);
+ elseif(m==0)
+ Ylm = C30*Z.*(2*Z.*Z-3*X.*X-3*Y.*Y)./(r.*r.*r);
+ elseif(m==1)
+ Ylm = C3p1*X.*(4*Z.*Z - X.*X - Y.*Y)./(r.*r.*r);
+ elseif(m==2)
+ Ylm = C3p2*Z.*(X.*X - Y.*Y)./(r.*r.*r);
+ elseif(m==3)
+ Ylm = C3p3*X.*(X.*X-3*Y.*Y)./(r.*r.*r);
+ end
+elseif(l == 4)
+ if(m==-4)
+ Ylm=(3.0/4.0)*sqrt(35.0/pi)*(X.*Y.*(X.*X-Y.*Y))./(r.^4);
+ elseif(m==-3)
+ Ylm=(3.0/4.0)*sqrt(35.0/(2.0*pi))*(3.0*X.*X-Y.*Y).*Y.*Z./(r.^4);
+ elseif(m==-2)
+ Ylm=(3.0/4.0)*sqrt(5.0/pi)*X.*Y.*(7.0*Z.*Z-r.*r)./(r.^4);
+ elseif(m==-1)
+ Ylm=(3.0/4.0)*sqrt(5.0/(2.0*pi))*Y.*Z.*(7.0*Z.*Z-3.0*r.*r)./(r.^4);
+ elseif(m==0)
+ Ylm=(3.0/16.0)*sqrt(1.0/pi)*(35.0*Z.^4-30.0*Z.*Z.*r.*r+3.0*r.^4)./(r.^4);
+ elseif(m==1)
+ Ylm=(3.0/4.0)*sqrt(5.0/(2.0*pi))*X.*Z.*(7.0*Z.*Z-3.0*r.*r)./(r.^4);
+ elseif(m==2)
+ Ylm=(3.0/8.0)*sqrt(5.0/(pi))*(X.*X-Y.*Y).*(7.0*Z.*Z-r.*r)./(r.^4);
+ elseif(m==3)
+ Ylm=(3.0/4.0)*sqrt(35.0/(2.0*pi))*(X.*X-3.0*Y.*Y).*X.*Z./(r.^4);
+ elseif(m==4)
+ Ylm=(3.0/16.0)*sqrt(35.0/pi)*(X.*X.*(X.*X-3.0*Y.*Y) - Y.*Y.*(3.0*X.*X-Y.*Y))./(r.^4);
+ end
+elseif(l == 5)
+ p = sqrt(X.*X+Y.*Y);
+ if(m==-5)
+ Ylm = (3.0*sqrt(2*77/pi)/32.0)*(8.0*X.^4.*Y-4.0*X.*X.*Y.^3 + 4.0*Y.^5-3.0*Y.*p.^4)./(r.^5);
+ elseif(m==-4)
+ Ylm = (3.0/16.0)*sqrt(385.0/pi)*(4.0*X.^3.*Y - 4.0*X.*Y.^3).*Z./(r.^5);
+ elseif(m==-3)
+ Ylm = (sqrt(2.0*385.0/pi)/32.0)*(3.0*Y.*p.*p - 4.0*Y.^3).*(9*Z.*Z-r.*r)./(r.^5);
+ elseif(m==-2)
+ Ylm = (1.0/8.0)*sqrt(1155.0/pi)*2.0*X.*Y.*(3.0*Z.^3-Z.*r.*r)./(r.^5);
+ elseif(m==-1)
+ Ylm = (1.0/16.0)*sqrt(165.0/pi)*Y.*(21.0*Z.^4 - 14.0*r.*r.*Z.*Z+r.^4)./(r.^5);
+ elseif(m==0)
+ Ylm = (1.0/16.0)*sqrt(11.0/pi)*(63.0*Z.^5 -70.0*Z.^3.*r.*r + 15.0*Z.*r.^4)./(r.^5);
+ elseif(m==1)
+ Ylm = (1.0/16.0)*sqrt(165.0/pi)*X.*(21.0*Z.^4 - 14.0*r.*r.*Z.*Z+r.^4)./(r.^5);
+ elseif(m==2)
+ Ylm = (1.0/8.0)*sqrt(1155.0/pi)*(X.*X-Y.*Y).*(3.0*Z.^3 - r.*r.*Z)./(r.^5);
+ elseif(m==3)
+ Ylm = (sqrt(2.0*385.0/pi)/32.0)*(4.0*X.^3-3.0*p.*p.*X).*(9.0*Z.*Z-r.*r)./(r.^5);
+ elseif(m==4)
+ Ylm = (3.0/16.0)*sqrt(385.0/pi)*(4.0*(X.^4+Y.^4)-3.0*p.^4).*Z./(r.^5);
+ %Ylm = (3.0/16.0)*sqrt(385.0/pi)*(X.^4+Y.^4-6*X.^2.*Y.^2).*Z./(r.^5);
+ elseif(m==5)
+ Ylm = (3.0*sqrt(2.0)/32.0)*sqrt(77.0/pi)*(4.0*X.^5 + 8.0*X.*Y.^4 -4.0*X.^3.*Y.*Y -3.0*X.*p.^4)./(r.^5);
+ end
+elseif(l == 6)
+ p = sqrt(X.*X+Y.*Y);
+ if(m==-6)
+ Ylm = (sqrt(2.0*3003.0/pi)/64.0)*(12.0*X.^5.*Y+12.0*X.*Y.^5 - 8.0*X.^3.*Y.^3-6.0*X.*Y.*p.^4)./(r.^6);
+ elseif(m==-5)
+ Ylm = (3.0/32.0)*sqrt(2.0*1001.0/pi)*(8.0*X.^4.*Y - 4.0*X.*X.*Y.^3 + 4.0*Y.^5 -3.0*Y.*p.^4).*Z./(r.^6);
+ elseif(m==-4)
+ Ylm = (3.0/32.0)*sqrt(91.0/pi)*(4.0*X.^3.*Y -4.0*X.*Y.^3).*(11.0*Z.*Z-r.*r)./(r.^6);
+ elseif(m==-3)
+ Ylm = (sqrt(2.0*1365.0/pi)/32.0)*(-4.0*Y.^3 + 3.0*Y.*p.*p).*(11.0*Z.^3 - 3.0*Z.*r.*r)./(r.^6);
+ elseif(m==-2)
+ Ylm = (sqrt(2.0*1365/pi)/64.0)*(2.0*X.*Y).*(33.0*Z.^4-18.0*Z.*Z.*r.*r + r.^4)./(r.^6);
+ elseif(m==-1)
+ Ylm = (sqrt(273.0/pi)/16.0)*Y.*(33.0*Z.^5-30.0*Z.^3.*r.*r +5.0*Z.*r.^4)./(r.^6);
+ elseif(m==0)
+ Ylm = (sqrt(13.0/pi)/32.0)*(231.0*Z.^6-315*Z.^4.*r.*r + 105.0*Z.*Z.*r.^4 -5.0*r.^6)./(r.^6);
+ elseif(m==1)
+ Ylm = (sqrt(273.0/pi)/16.0)*X.*(33.0*Z.^5-30.0*Z.^3.*r.*r +5*Z.*r.^4)./(r.^6);
+ elseif(m==2)
+ Ylm = (sqrt(2.0*1365/pi)/64.0)*(X.*X-Y.*Y).*(33.0*Z.^4 - 18.0*Z.*Z.*r.*r + r.^4)./(r.^6);
+ elseif(m==3)
+ Ylm = (sqrt(2.0*1365.0/pi)/32.0)*(4.0*X.^3 -3.0*X.*p.*p).*(11.0*Z.^3 - 3.0*Z.*r.*r)./(r.^6);
+ elseif(m==4)
+ Ylm = (3.0/32.0)*sqrt(91.0/pi)*(4.0*X.^4+4.0*Y.^4 -3.0*p.^4).*(11.0*Z.*Z -r.*r)./(r.^6);
+ elseif(m==5)
+ Ylm = (3.0/32.0)*sqrt(2.0*1001.0/pi)*(4.0*X.^5 + 8.0*X.*Y.^4-4.0*X.^3.*Y.*Y-3.0*X.*p.^4).*Z./(r.^6);
+ elseif(m==6)
+ Ylm = (sqrt(2.0*3003.0/pi)/64.0)*(4.0*X.^6-4.0*Y.^6 +12.0*X.*X.*Y.^4-12.0*X.^4.*Y.*Y + 3.0*Y.*Y.*p.^4-3.0*X.*X.*p.^4)./(r.^6);
+ end
+else
+ error(' must be an integer between [0,6]');
+end
+
+
+if (l > 0)
+ Ylm(abs(r) < 1e-10) = 0;
+end
+
+end
+
+
+
+% ------------- Calculator for Complex Spherical Harmonics
+function Ylm = ComplexSphericalHarmonics(X,Y,Z,l,m)
+% ComplexSphericalHarmonics calculates complex spherical harmonics
+
+
+%fprintf('In Complex spherical harmonics\n');
+
+r = sqrt(X.*X + Y.*Y + Z.*Z);
+iota = sqrt(-1);
+
+if l == 0
+
+ C00 = 0.282094791773878; % 0.5*sqrt(1/pi)
+ Ylm = C00*ones(size(X));
+elseif l == 1
+%fprintf('In Complex spherical harmonics with l = %d \n',l);
+ C11 = 0.345494149471335; % 0.5 * sqrt(3/(2*pi))
+ C10 = 0.488602511902920; % sqrt(3/(4*pi))
+
+ if m==-1
+ Ylm = C11 * ((X-iota*Y)./r);
+ elseif m==0
+ Ylm = C10*(Z./r);
+ elseif m==1
+ Ylm = -C11 * ((X+iota*Y)./r);
+ else
+ error('Error:incorrect l: %d,m: %d \n',l,m);
+ end
+elseif l == 2
+%fprintf('In Complex spherical harmonics with l = %d \n',l);
+ C22 = 0.386274202023190;
+ C21 = 0.772548404046379;
+ C20 = 0.315391565252520;
+
+ r2 = r.^2;
+
+ if m==-2
+ Ylm = C22 * ((X-iota*Y).^2)./r2;
+ elseif m==-1
+ Ylm = C21 * ((X-iota*Y).*Z)./r2;
+ elseif m==0
+ Ylm = C20 * (2*Z.*Z - X.*X - Y.*Y)./r2;
+ elseif m==1
+ Ylm = -C21 * ((X+iota*Y).*Z)./r2;
+ elseif m==2
+ Ylm = C22 * ((X+iota*Y).^2)./r2;
+ else
+ error('Error: incorrect l: %d, m: %d \n',l,m);
+ end
+elseif l == 3
+ C33 = 0.417223823632784;
+ C32 = 1.021985476433282;
+ C31 = 0.323180184114151;
+ C30 = 0.373176332590115;
+
+ r3 = r.^3;
+
+ if m==-3
+ Ylm = C33 * ((X-iota*Y).^3)./r3;
+ elseif m==-2
+ Ylm = C32 * (((X-iota*Y).^2).*Z)./r3;
+ elseif m==-1
+ Ylm = C31 * (X-iota*Y).*(4*Z.*Z - X.*X - Y.*Y)./r3;
+ elseif m==0
+ Ylm = C30 * Z.*(2*Z.*Z - 3*X.*X - 3*Y.*Y)./r3;
+ elseif m==1
+ Ylm = -C31 * (X+iota*Y).*(4*Z.*Z - X.*X - Y.*Y)./r3;
+ elseif m==2
+ Ylm = C32 * (((X+iota*Y).^2).*Z)./r3;
+ elseif m==3
+ Ylm = -C33 * ((X+iota*Y).^3)./r3;
+ else
+ error('Error: incorrect l: %d, m: %d \n',l,m);
+ end
+elseif l == 4
+ C44 = 0.442532692444983;
+ C43 = 1.251671470898352;
+ C42 = 0.334523271778645;
+ C41 = 0.473087347878780;
+ C40 = 0.105785546915204;
+
+ r4 = r.^4;
+
+ if m==-4
+ Ylm = C44 * ((X-iota*Y).^4)./r4;
+ elseif m==-3
+ Ylm = C43 * (((X-iota*Y).^3).*Z)./r4;
+ elseif m==-2
+ Ylm = C42 * (((X-iota*Y).^2).*(7*Z.^2 - r.^2))./r4;
+ elseif m==-1
+ Ylm = C41 * ((X-iota*Y).*Z.*(7*Z.^2 - 3*r.^2))./r4;
+ elseif m==0
+ Ylm = C40 * (35*Z.^4 - 30*(Z.^2).*(r.^2) + 3*r.^4)/r4;
+ elseif m==1
+ Ylm = -C41 * ((X+iota*Y).*Z.*(7*Z.^2 - 3*r.^2))./r4;
+ elseif m==2
+ Ylm = C42 * (((X+iota*Y).^2).*(7*Z.^2 - r.^2))./r4;
+ elseif m==3
+ Ylm = -C43 * (((X+iota*Y).^3).*Z)./r4;
+ elseif m==4
+ Ylm = C44 * ((X+iota*Y).^4)./r4;
+ else
+ error('Error: incorrect l: %d, m: %d \n',l,m);
+ end
+elseif l == 5
+ C55 = 0.464132203440858;
+ C54 = 1.467714898305751;
+ C53 = 0.345943719146840;
+ C52 = 1.694771183260899;
+ C51 = 0.320281648576215;
+ C50 = 0.116950322453424;
+
+ r5 = r.^5;
+
+ if m==-5
+ Ylm = C55 * ((X-iota*Y).^5)./r5;
+ elseif m==-4
+ Ylm = C54 * (((X-iota*Y).^4).*Z)./r5;
+ elseif m==-3
+ Ylm = C53 * (((X-iota*Y).^3).*(9*Z.^2 - r.^2))./r5;
+ elseif m==-2
+ Ylm = C52 * (((X-iota*Y).^2).*(3*Z.^3 - Z.*(r.^2)))./r5;
+ elseif m==-1
+ Ylm = C51 * ((X-iota*Y).*(21*Z.^4 - 14*Z.*Z.*r.*r + r.^4))./r5;
+ elseif m==0
+ Ylm = C50 * (63*Z.^5 - 70*(Z.^3).*(r.^2) + 15*Z.*(r.^4))./r5;
+ elseif m==1
+ Ylm = -C51 * ((X+iota*Y).*(21*Z.^4 - 14*Z.*Z.*r.*r + r.^4))./r5;
+ elseif m==2
+ Ylm = C52 * (((X+iota*Y).^2).*(3*Z.^3 - Z.*(r.^2)))./r5;
+ elseif m==3
+ Ylm = -C53 * (((X+iota*Y).^3).*(9*Z.^2 - r.^2))./r5;
+ elseif m==4
+ Ylm = C54 * (((X+iota*Y).^4).*Z)./r5;
+ elseif m==-5
+ Ylm = -C55 * ((X+iota*Y).^5)./r5;
+ else
+ error('Error: incorrect l: %d, m: %d \n',l,m);
+ end
+elseif l == 6
+ C66 = 0.483084113580066;
+ C65 = 1.673452458100098;
+ C64 = 0.356781262853998;
+ C63 = 0.651390485867716;
+ C62 = 0.325695242933858;
+ C61 = 0.411975516301141;
+ C60 = 0.063569202267628;
+
+ r6 = r.^6;
+
+ if m==-6
+ Ylm = C66 * ((X-iota*Y).^6)./r6;
+ elseif m==-5
+ Ylm = C65 * (((X-iota*Y).^5).*Z)./r6;
+ elseif m==-4
+ Ylm = C64 * (((X-iota*Y).^4).*(11*Z.^2 - r.^2))./r6;
+ elseif m==-3
+ Ylm = C63 * (((X-iota*Y).^3).*(11*Z.^3 - 3*Z.*(r.^2)))./r6;
+ elseif m==-2
+ Ylm = C62 * (((X-iota*Y).^2).*(33*Z.^4 - 18*(Z.^2).*(r.^2) + r.^4))./r6;
+ elseif m==-1
+ Ylm = C61 * ((X-iota*Y).*(33*Z.^5 - 30*(Z.^3).*(r.^2) + 5*Z.*(r.^4)))./r6;
+ elseif m==0
+ Ylm = C60 * (231*Z.^6 - 315*(Z.^4).*(r.^2) + 105*(Z.^2).*(r.^4) - 5*r6)./r6;
+ elseif m==1
+ Ylm = -C61 * ((X+iota*Y).*(33*Z.^5 - 30*(Z.^3).*(r.^2) + 5*Z.*(r.^4)))./r6;
+ elseif m==2
+ Ylm = C62 * (((X+iota*Y).^2).*(33*Z.^4 - 18*(Z.^2).*(r.^2) + r.^4))./r6;
+ elseif m==3
+ Ylm = -C63 * (((X+iota*Y).^3).*(11*Z.^3 - 3*Z.*(r.^2)))./r6;
+ elseif m==4
+ Ylm = C64 * (((X+iota*Y).^4).*(11*Z.^2 - r.^2))./r6;
+ elseif m==5
+ Ylm = -C65 * (((X+iota*Y).^5).*Z)./r6;
+ elseif m==6
+ Ylm = C66 * ((X+iota*Y).^6)./r6;
+ else
+ error('Error: incorrect l: %d, m: %d \n',l,m);
+ end
+else
+ error('Only l=0,1,supported. Input l:%d\n',l);
+end
+
+if l > 0
+ Ylm(abs(r)<(1e-10))=0;
+end
+
+end
diff --git a/tests/BC/H2O_sheet/H.psp8 b/tests/BC/H2O_sheet/H.psp8
new file mode 100644
index 00000000..8cfcd218
--- /dev/null
+++ b/tests/BC/H2O_sheet/H.psp8
@@ -0,0 +1,1859 @@
+H ONCVPSP-3.3.1 r_core= 1.15113
+ 1.0000 1.0000 190128 zatom,zion,pspd
+ 8 2 0 4 600 0 pspcod,pspxc,lmax,lloc,mmax,r2well
+ 5.99000000 0.00000000 0.00000000 rchrg fchrg qchrg
+ 2 0 0 0 0 nproj
+ 1 1 extension_switch
+ 0 -1.2539437611788E+00 -4.0727290034061E-01
+ 1 0.0000000000000E+00 4.6168487866094E-08 -3.4318619543394E-08
+ 2 1.0000000000000E-02 3.0205697226572E-02 1.2138998345020E-02
+ 3 2.0000000000000E-02 6.1520920405994E-02 2.3897417609999E-02
+ 4 3.0000000000000E-02 9.5025730951330E-02 3.4910538706878E-02
+ 5 4.0000000000000E-02 1.3174187672572E-01 4.4844951510226E-02
+ 6 5.0000000000000E-02 1.7260516197975E-01 5.3413190813061E-02
+ 7 6.0000000000000E-02 2.1843961566096E-01 6.0387175148664E-02
+ 8 7.0000000000000E-02 2.6993400210192E-01 6.5610090721067E-02
+ 9 8.0000000000000E-02 3.2762117192434E-01 6.9006397005503E-02
+ 10 9.0000000000000E-02 3.9186069495896E-01 7.0589672163570E-02
+ 11 1.0000000000000E-01 4.6282515214355E-01 7.0468064425559E-02
+ 12 1.1000000000000E-01 5.4049039096860E-01 6.8847169050086E-02
+ 13 1.2000000000000E-01 6.2462997048174E-01 6.6030208290916E-02
+ 14 1.3000000000000E-01 7.1481393865217E-01 6.2415452799431E-02
+ 15 1.4000000000000E-01 8.1041199864468E-01 5.8490885815360E-02
+ 16 1.5000000000000E-01 9.1060103293295E-01 5.4826175046603E-02
+ 17 1.6000000000000E-01 1.0143768669036E+00 5.2062079989264E-02
+ 18 1.7000000000000E-01 1.1205700683707E+00 5.0897483274831E-02
+ 19 1.8000000000000E-01 1.2278654979137E+00 5.2074292166079E-02
+ 20 1.9000000000000E-01 1.3348252487822E+00 5.6360509332163E-02
+ 21 2.0000000000000E-01 1.4399145457774E+00 6.4531819373226E-02
+ 22 2.1000000000000E-01 1.5415301114230E+00 7.7352078203955E-02
+ 23 2.2000000000000E-01 1.6380304560807E+00 9.5553125443707E-02
+ 24 2.3000000000000E-01 1.7277675074917E+00 1.1981436465341E-01
+ 25 2.4000000000000E-01 1.8091189653642E+00 1.5074257202906E-01
+ 26 2.5000000000000E-01 1.8805207486677E+00 1.8885240062404E-01
+ 27 2.6000000000000E-01 1.9404988975903E+00 2.3454804413616E-01
+ 28 2.7000000000000E-01 1.9877002987715E+00 2.8810651177510E-01
+ 29 2.8000000000000E-01 2.0209216212596E+00 3.4966294394966E-01
+ 30 2.9000000000000E-01 2.0391358812465E+00 4.1919836790960E-01
+ 31 3.0000000000000E-01 2.0415160953157E+00 4.9653025368045E-01
+ 32 3.1000000000000E-01 2.0274555337767E+00 5.8130618446229E-01
+ 33 3.2000000000000E-01 1.9965841464944E+00 6.7300090312771E-01
+ 34 3.3000000000000E-01 1.9487808021003E+00 7.7091693870154E-01
+ 35 3.4000000000000E-01 1.8841810560430E+00 8.7418895503063E-01
+ 36 3.5000000000000E-01 1.8031802419298E+00 9.8179189964031E-01
+ 37 3.6000000000000E-01 1.7064317622069E+00 1.0925529655063E+00
+ 38 3.7000000000000E-01 1.5948405365795E+00 1.2051673136500E+00
+ 39 3.8000000000000E-01 1.4695516477561E+00 1.3182174416188E+00
+ 40 3.9000000000000E-01 1.3319343022465E+00 1.4301960235301E+00
+ 41 4.0000000000000E-01 1.1835612971973E+00 1.5395319928785E+00
+ 42 4.1000000000000E-01 1.0261842508881E+00 1.6446195910524E+00
+ 43 4.2000000000000E-01 8.6170491293297E-01 1.7438500636981E+00
+ 44 4.3000000000000E-01 6.9214291901632E-01 1.8356456547336E+00
+ 45 4.4000000000000E-01 5.1960039294361E-01 1.9184955248183E+00
+ 46 4.5000000000000E-01 3.4622382493654E-01 1.9909932080609E+00
+ 47 4.6000000000000E-01 1.7416366877261E-01 2.0518752181090E+00
+ 48 4.7000000000000E-01 5.5321011530228E-03 2.1000604226777E+00
+ 49 4.8000000000000E-01 -1.5764062602878E-01 2.1346898261811E+00
+ 50 4.9000000000000E-01 -3.1345081552600E-01 2.1551663452840E+00
+ 51 5.0000000000000E-01 -4.6016629543791E-01 2.1611931266703E+00
+ 52 5.1000000000000E-01 -5.9625591382369E-01 2.1527492051407E+00
+ 53 5.2000000000000E-01 -7.2039020551646E-01 2.1299809285899E+00
+ 54 5.3000000000000E-01 -8.3145156671353E-01 2.0931786295933E+00
+ 55 5.4000000000000E-01 -9.2854644314640E-01 2.0427796661406E+00
+ 56 5.5000000000000E-01 -1.0110135002025E+00 1.9793685275495E+00
+ 57 5.6000000000000E-01 -1.0784276622659E+00 1.9036739069728E+00
+ 58 5.7000000000000E-01 -1.1306000028775E+00 1.8165627714535E+00
+ 59 5.8000000000000E-01 -1.1675735516025E+00 1.7190315364398E+00
+ 60 5.9000000000000E-01 -1.1896151633225E+00 1.6121945129425E+00
+ 61 6.0000000000000E-01 -1.1972036715439E+00 1.4972698545252E+00
+ 62 6.1000000000000E-01 -1.1910146184165E+00 1.3755632856545E+00
+ 63 6.2000000000000E-01 -1.1719019177280E+00 1.2484499404645E+00
+ 64 6.3000000000000E-01 -1.1408768631985E+00 1.1173546816199E+00
+ 65 6.4000000000000E-01 -1.0990849406935E+00 9.8373130101749E-01
+ 66 6.5000000000000E-01 -1.0477809393453E+00 8.4904102739180E-01
+ 67 6.6000000000000E-01 -9.8830288208610E-01 7.1473077979955E-01
+ 68 6.7000000000000E-01 -9.2204531021757E-01 5.8221161013853E-01
+ 69 6.8000000000000E-01 -8.5043245945698E-01 4.5283777243431E-01
+ 70 6.9000000000000E-01 -7.7489185622061E-01 3.2788684153140E-01
+ 71 7.0000000000000E-01 -6.9682884319454E-01 2.0854127961249E-01
+ 72 7.1000000000000E-01 -6.1760251307944E-01 9.5871816179689E-02
+ 73 7.2000000000000E-01 -5.3850348952091E-01 -9.1770334863580E-03
+ 74 7.3000000000000E-01 -4.6073394549446E-01 -1.0579903402106E-01
+ 75 7.4000000000000E-01 -3.8539019335151E-01 -1.9333565568679E-01
+ 76 7.5000000000000E-01 -3.1344811832926E-01 -2.7128269390988E-01
+ 77 7.6000000000000E-01 -2.4575166010267E-01 -3.3929397771982E-01
+ 78 7.7000000000000E-01 -1.8300447683449E-01 -3.9718212505127E-01
+ 79 7.8000000000000E-01 -1.2576485400750E-01 -4.4491636661792E-01
+ 80 7.9000000000000E-01 -7.4443848481754E-02 -4.8261752258148E-01
+ 81 8.0000000000000E-01 -2.9306587934977E-02 -5.1055027646917E-01
+ 82 8.1000000000000E-01 9.5234213352451E-03 -5.2911294739721E-01
+ 83 8.2000000000000E-01 4.2057187778858E-02 -5.3882501330273E-01
+ 84 8.3000000000000E-01 6.8430595211134E-02 -5.4031268348692E-01
+ 85 8.4000000000000E-01 8.8892546156295E-02 -5.3429285733880E-01
+ 86 8.5000000000000E-01 1.0379124461401E-01 -5.2155583681517E-01
+ 87 8.6000000000000E-01 1.1355900718061E-01 -5.0294718246246E-01
+ 88 8.7000000000000E-01 1.1869601410271E-01 -4.7934911603272E-01
+ 89 8.8000000000000E-01 1.1975342452176E-01 -4.5166187683298E-01
+ 90 8.9000000000000E-01 1.1731628274177E-01 -4.2078543382192E-01
+ 91 9.0000000000000E-01 1.1198663491228E-01 -3.8760194131348E-01
+ 92 9.1000000000000E-01 1.0436725838658E-01 -3.5295930334722E-01
+ 93 9.2000000000000E-01 9.5046379736144E-02 -3.1765618092019E-01
+ 94 9.3000000000000E-01 8.4583722727618E-02 -2.8242873810788E-01
+ 95 9.4000000000000E-01 7.3498185436239E-02 -2.4793937855562E-01
+ 96 9.5000000000000E-01 6.2257397299766E-02 -2.1476767407560E-01
+ 97 9.6000000000000E-01 5.1269352663974E-02 -1.8340363246289E-01
+ 98 9.7000000000000E-01 4.0876261523102E-02 -1.5424339627659E-01
+ 99 9.8000000000000E-01 3.1350696703618E-02 -1.2758740424202E-01
+ 100 9.9000000000000E-01 2.2894057248927E-02 -1.0364098946937E-01
+ 101 1.0000000000000E+00 1.5637307525408E-02 -8.2517331081607E-02
+ 102 1.0100000000000E+00 9.6438936463982E-03 -6.4242621034729E-02
+ 103 1.0200000000000E+00 4.9146844802597E-03 -4.8763257028532E-02
+ 104 1.0300000000000E+00 1.3947339219019E-03 -3.5954825615378E-02
+ 105 1.0400000000000E+00 -1.0183804994297E-03 -2.5632601579407E-02
+ 106 1.0500000000000E+00 -2.4649274533108E-03 -1.7563253889733E-02
+ 107 1.0600000000000E+00 -3.1124122136799E-03 -1.1477424750032E-02
+ 108 1.0700000000000E+00 -3.1443210681285E-03 -7.0828305063728E-03
+ 109 1.0800000000000E+00 -2.7485647612221E-03 -4.0775249483192E-03
+ 110 1.0900000000000E+00 -2.1059689795922E-03 -2.1629653325217E-03
+ 111 1.1000000000000E+00 -1.3791546993888E-03 -1.0565294459653E-03
+ 112 1.1100000000000E+00 -7.0213474614291E-04 -5.0315069161267E-04
+ 113 1.1200000000000E+00 -1.7026588248527E-04 -2.8619369259804E-04
+ 114 1.1300000000000E+00 1.5899018601691E-04 -2.3044526457756E-04
+ 115 1.1400000000000E+00 3.1850760277554E-04 -2.4126877567936E-04
+ 116 1.1500000000000E+00 3.2692318632233E-04 -2.3270406202876E-04
+ 117 1.1600000000000E+00 1.0651941562221E-04 -7.6574581943587E-05
+ 118 1.1700000000000E+00 -3.2613375353914E-05 2.3224491253795E-05
+ 119 1.1800000000000E+00 2.2400537080203E-06 -1.5742515839512E-06
+ 120 1.1900000000000E+00 4.3601331455045E-06 -3.0598591619301E-06
+ 121 1.2000000000000E+00 -8.8898250383997E-07 6.3357959206729E-07
+ 122 1.2100000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 123 1.2200000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 124 1.2300000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 125 1.2400000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 126 1.2500000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 127 1.2600000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 128 1.2700000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 129 1.2800000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 130 1.2900000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 131 1.3000000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 132 1.3100000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 133 1.3200000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 134 1.3300000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 135 1.3400000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 136 1.3500000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 137 1.3600000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 138 1.3700000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 139 1.3800000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 140 1.3900000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 141 1.4000000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 142 1.4100000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 143 1.4200000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 144 1.4300000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 145 1.4400000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 146 1.4500000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 147 1.4600000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 148 1.4700000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 149 1.4800000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 150 1.4900000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 151 1.5000000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 152 1.5100000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 153 1.5200000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 154 1.5300000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 155 1.5400000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 156 1.5500000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 157 1.5600000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 158 1.5700000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 159 1.5800000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 160 1.5900000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 161 1.6000000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 162 1.6100000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 163 1.6200000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 164 1.6300000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 165 1.6400000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 166 1.6500000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 167 1.6600000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 168 1.6700000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 169 1.6800000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 170 1.6900000000000E+00 0.0000000000000E+00 0.0000000000000E+00
+ 171 1.7000000000000E+00 0.0000000000000E+00 0.0000000000000E+00
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+ 585 5.8400000000000E+00 1.1105775566562E-04 1.1106293714343E-04 0.0000000000000E+00
+ 586 5.8500000000000E+00 1.0924901612333E-04 1.0925412313628E-04 0.0000000000000E+00
+ 587 5.8600000000000E+00 1.0746999656356E-04 1.0747503017938E-04 0.0000000000000E+00
+ 588 5.8700000000000E+00 1.0572020417793E-04 1.0572516544906E-04 0.0000000000000E+00
+ 589 5.8800000000000E+00 1.0399915440669E-04 1.0400404437056E-04 0.0000000000000E+00
+ 590 5.8900000000000E+00 1.0230637079932E-04 1.0231119047851E-04 0.0000000000000E+00
+ 591 5.9000000000000E+00 1.0064138487750E-04 1.0064613527999E-04 0.0000000000000E+00
+ 592 5.9100000000000E+00 9.9003735996281E-05 9.9008418115630E-05 0.0000000000000E+00
+ 593 5.9200000000000E+00 9.7392971224773E-05 9.7397586040348E-05 0.0000000000000E+00
+ 594 5.9300000000000E+00 9.5808645202972E-05 9.5813193680135E-05 0.0000000000000E+00
+ 595 5.9400000000000E+00 9.4250320017889E-05 9.4254803108201E-05 0.0000000000000E+00
+ 596 5.9500000000000E+00 9.2717565077799E-05 9.2721983719215E-05 0.0000000000000E+00
+ 597 5.9600000000000E+00 9.1209956988643E-05 9.1214312105707E-05 0.0000000000000E+00
+ 598 5.9700000000000E+00 8.9727079432550E-05 8.9731371936586E-05 0.0000000000000E+00
+ 599 5.9800000000000E+00 8.8268523044768E-05 8.8272753834068E-05 0.0000000000000E+00
+ 600 5.9900000000000E+00 8.6833885307547E-05 8.6838055267556E-05 0.0000000000000E+00
+
+#
+#ONCVPSP (Optimized Norm-Conservinng Vanderbilt PSeudopotential)
+#scalar-relativistic version 3.3.1 12/12/2017
+#
+#While it is not required under the terms of the GNU GPL, it is
+#suggested that you cite D. R. Hamann, Phys. Rev. B 88, 085117 (2013)
+#in any publication utilizing these pseudopotentials.
+#
+# ATOM AND REFERENCE CONFIGURATION
+# atsym z nc nv iexc psfile
+ H 1.00 0 1 3 psp8
+#
+# n l f
+ 1 0 1.00
+#
+# PSEUDOPOTENTIAL AND OPTIMIZATION
+# lmax
+ 0
+#
+# l, rc, ep, ncon, nbas, qcut
+ 0 1.13748 -0.23366 5 8 9.72141
+#
+# LOCAL POTENTIAL
+# lloc, lpopt, rc(5), dvloc0
+ 4 5 0.49352 0.00000
+#
+# VANDERBILT-KLEINMAN-BYLANDER PROJECTORs
+# l, nproj, debl
+ 0 2 1.27464
+#
+# MODEL CORE CHARGE
+# icmod, fcfact, rcfact
+ 0 0.00000 0.00000
+#
+# LOG DERIVATIVE ANALYSIS
+# epsh1, epsh2, depsh
+ -5.00 3.00 0.02
+#
+# OUTPUT GRID
+# rlmax, drl
+ 6.00 0.01
+#
+# TEST CONFIGURATIONS
+# ncnf
+ 0
+# nvcnf
+# n l f
+
+
+END_PSP
diff --git a/tests/BC/H2O_sheet/H2O_Nx_28.inpt b/tests/BC/H2O_sheet/H2O_Nx_28.inpt
new file mode 100644
index 00000000..c082a088
--- /dev/null
+++ b/tests/BC/H2O_sheet/H2O_Nx_28.inpt
@@ -0,0 +1,19 @@
+# Test: H2O sheet in x,y plane #
+CELL: 5.669178374980770 5.669178374980770 22.676713499923078
+FD_GRID: 28 28 112
+FD_ORDER: 12
+BOUNDARY_CONDITION: 3
+#CHEB_DEGREE: 32
+#RHO_TRIGGER: 5
+EXCHANGE_CORRELATION: LDA_PZ
+#MAXIT_SCF: 30
+ELEC_TEMP_TYPE: fd
+SMEARING: 0.001
+TOL_SCF: 1e-6
+TOL_PSEUDOCHARGE: 1e-8
+#TOL_POISSON: 1e-7
+NSTATES: 8
+PRINT_FORCES: 1
+PRINT_ATOMS: 1
+
+
diff --git a/tests/BC/H2O_sheet/H2O_Nx_28.ion b/tests/BC/H2O_sheet/H2O_Nx_28.ion
new file mode 100644
index 00000000..75d036e2
--- /dev/null
+++ b/tests/BC/H2O_sheet/H2O_Nx_28.ion
@@ -0,0 +1,29 @@
+#=========================
+# format of ion file
+#=========================
+# ATOM_TYPE:
+# PSEUDO_POT:
+# N_TYPE_ATOM:
+# COORD:
+#
+# ...
+# RELAX:
+#
+# ...
+
+# Reminder: when changing number of atoms, change the RELAX flags accordingly
+# as well.
+
+ATOM_TYPE: H # atom type
+PSEUDO_POT: H.psp8
+N_TYPE_ATOM: 2 # number of atoms of this type
+COORD: # coordinates follows
+ 4.265111864110533 2.834589187490385 12.445736259207782
+ 1.404066510870237 2.834589187490385 12.445736259207782
+
+ATOM_TYPE: O # atom type
+PSEUDO_POT: O.psp8
+N_TYPE_ATOM: 1 # number of atoms of this type
+COORD: # coordinates follows
+ 2.834589187490385 2.834589187490385 11.338356749961539
+
diff --git a/tests/BC/H2O_sheet/H2O_Nx_28.refout b/tests/BC/H2O_sheet/H2O_Nx_28.refout
new file mode 100644
index 00000000..d65b920c
--- /dev/null
+++ b/tests/BC/H2O_sheet/H2O_Nx_28.refout
@@ -0,0 +1,105 @@
+***************************************************************************
+* M-SPARC (Dec 17, 2019) *
+* Copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech *
+* Distributed under GNU General Public License 3 (GPL) *
+* Date: 17-Dec-2019 Start time: 16:41:08 *
+***************************************************************************
+ Input parameters
+***************************************************************************
+CELL: 5.669178 5.669178 22.676713
+FD_GRID: 28 28 112
+FD_ORDER: 12
+BOUNDARY_CONDITION: 3
+KPOINT_GRID: 1 1 1
+KPOINT_SHIFT: 0 0 0
+ELEC_TEMP_TYPE: fermi-dirac
+SMEARING: 0.001000000
+CHEB_DEGREE: 35
+NSTATES: 8
+EXCHANGE_CORRELATION: LDA_PZ
+CALC_STRESS: 0
+CALC_PRES: 0
+MAXIT_SCF: 100
+TOL_SCF: 1.00E-06
+TOL_POISSON: 1.00E-08
+TOL_LANCZOS: 1.00E-02
+TOL_PSEUDOCHARGE: 1.00E-08
+MIXING_VARIABLE: potential
+MIXING_PRECOND: none
+MIXING_PARAMETER: 0.30
+MIXING_HISTORY: 7
+PULAY_FREQUENCY: 1
+PULAY_RESTART_FREQ: 0
+REFERENCE_CUTOFF: 0.50
+RHO_TRIGGER: 4
+FIX_RAND: 0
+PRINT_FORCES: 1
+PRINT_ATOMS: 1
+PRINT_EIGEN: 0
+PRINT_DENSITY: 0
+OUTPUT_FILE: ../tests/BC/H2O_sheet/H2O_Nx_28.out
+***************************************************************************
+ Initialization
+***************************************************************************
+Mesh spacing : 0.202471 (Bohr)
+Number of symmetry adapted k-points: 1
+Output printed to : ../tests/BC/H2O_sheet/H2O_Nx_28.out
+Total number of atom types : 2
+Total number of atoms : 3
+Total number of electrons : 8
+Atom type 1 (valence electrons) : H 1
+Pseudopotential : H.psp8
+lloc : 4
+Pseudocharge radii of atom type 1 : 6.68 6.68 6.68
+Number of atoms of type 1 : 2
+Atom type 2 (valence electrons) : O 6
+Pseudopotential : O.psp8
+lloc : 4
+Pseudocharge radii of atom type 2 : 6.68 6.68 6.68
+Number of atoms of type 2 : 1
+Estimated total memory usage : 269.01 MB
+=====================================================================
+ Self Consistent Field (SCF#1)
+=====================================================================
+Iteration Free Energy (Ha/atom) SCF Error Timing (sec)
+1 -5.6231916849E+00 5.313E-01 3.077
+2 -5.6727655238E+00 1.008E-01 3.003
+3 -5.6741003009E+00 2.591E-02 2.959
+4 -5.6741757619E+00 3.185E-02 2.726
+5 -5.6742566340E+00 6.540E-03 2.703
+6 -5.6742638473E+00 1.094E-03 2.329
+7 -5.6742642641E+00 3.816E-03 2.329
+8 -5.6742649714E+00 8.866E-04 2.239
+9 -5.6742650100E+00 2.584E-04 2.094
+10 -5.6742650317E+00 3.233E-05 1.983
+11 -5.6742650293E+00 7.606E-06 1.854
+12 -5.6742650212E+00 2.944E-06 1.379
+13 -5.6742650102E+00 1.482E-06 1.262
+14 -5.6742650192E+00 4.900E-07 1.076
+Total number of SCF: 14
+====================================================================
+ Energy
+====================================================================
+Free energy per atom : -5.6742650192E+00 (Ha/atom)
+Total free energy : -1.7022795057E+01 (Ha)
+Band structure energy : -4.1002774979E+00 (Ha)
+Exchange correlation energy : -4.1627063761E+00 (Ha)
+Self and correction energy : -3.5341201837E+01 (Ha)
+Entropy*kb*T : -9.8840325431E-11 (Ha)
+Fermi level : -1.7067741068E-01 (Ha)
+Average force : 1.8531933032E-02 (Ha/Bohr)
+Maximum force : 2.2454697551E-02 (Ha/Bohr)
+Time for force calculation : 0.735 (sec)
+***************************************************************************
+ Timing info
+***************************************************************************
+Total walltime : 36.436 sec
+___________________________________________________________________________
+
+***************************************************************************
+* Material Physics & Mechanics Group, Georgia Tech *
+* PI: Phanish Suryanarayana *
+* Main Developers: Qimen Xu, Abhiraj Sharma *
+* Acknowledgements: U.S. DOE (DE-SC0019410); NSF (1333500,1553212) *
+***************************************************************************
+
diff --git a/tests/BC/H2O_sheet/H2O_Nx_28.refstatic b/tests/BC/H2O_sheet/H2O_Nx_28.refstatic
new file mode 100644
index 00000000..5234ad92
--- /dev/null
+++ b/tests/BC/H2O_sheet/H2O_Nx_28.refstatic
@@ -0,0 +1,11 @@
+***************************************************************************
+ Atom positions
+***************************************************************************
+Cartesian coordinates of atoms (Bohr):
+ 4.2651118641 2.8345891875 12.4457362592
+ 1.4040665109 2.8345891875 12.4457362592
+ 2.8345891875 2.8345891875 11.3383567500
+Atomic forces (Ha/Bohr):
+ -0.0218097129 0.0000000020 -0.0053432021
+ 0.0218097139 0.0000000018 -0.0053432032
+ -0.0000000011 -0.0000000038 0.0106864053
diff --git a/tests/BC/H2O_sheet/O.psp8 b/tests/BC/H2O_sheet/O.psp8
new file mode 100644
index 00000000..58f5aa79
--- /dev/null
+++ b/tests/BC/H2O_sheet/O.psp8
@@ -0,0 +1,2464 @@
+O ONCVPSP-3.3.1 r_core= 1.29195 1.47310
+ 8.0000 6.0000 190128 zatom,zion,pspd
+ 8 2 1 4 600 0 pspcod,pspxc,lmax,lloc,mmax,r2well
+ 5.99000000 0.00000000 0.00000000 rchrg fchrg qchrg
+ 2 2 0 0 0 nproj
+ 1 1 extension_switch
+ 0 9.8039458648062E+00 1.3940968705798E+00
+ 1 0.0000000000000E+00 2.8163213983134E-09 -9.8156246741699E-09
+ 2 1.0000000000000E-02 8.9663020185480E-02 -6.4027817020632E-03
+ 3 2.0000000000000E-02 1.7918092483447E-01 -1.3049427776932E-02
+ 4 3.0000000000000E-02 2.6840691548778E-01 -2.0176041044928E-02
+ 5 4.0000000000000E-02 3.5719087019612E-01 -2.8003350708319E-02
+ 6 5.0000000000000E-02 4.4537778693024E-01 -3.6729396702763E-02
+ 7 6.0000000000000E-02 5.3280635113698E-01 -4.6522652323702E-02
+ 8 7.0000000000000E-02 6.1930766545706E-01 -5.7515719480801E-02
+ 9 8.0000000000000E-02 7.0470417680425E-01 -6.9799721117865E-02
+ 10 9.0000000000000E-02 7.8880883257007E-01 -8.3419503369501E-02
+ 11 1.0000000000000E-01 8.7142449371820E-01 -9.8369746103570E-02
+ 12 1.1000000000000E-01 9.5234362803191E-01 -1.1459206484851E-01
+ 13 1.2000000000000E-01 1.0313483018487E+00 -1.3197316998196E-01
+ 14 1.3000000000000E-01 1.1082104833363E+00 -1.5034413074331E-01
+ 15 1.4000000000000E-01 1.1826926648206E+00 -1.6948077242832E-01
+ 16 1.5000000000000E-01 1.2545488059549E+00 -1.8910521534537E-01
+ 17 1.6000000000000E-01 1.3235255937164E+00 -2.0888854408794E-01
+ 18 1.7000000000000E-01 1.3893640094233E+00 -2.2845457573710E-01
+ 19 1.8000000000000E-01 1.4518011872782E+00 -2.4738467608605E-01
+ 20 1.9000000000000E-01 1.5105725434525E+00 -2.6522355420045E-01
+ 21 2.0000000000000E-01 1.5654141495302E+00 -2.8148594791135E-01
+ 22 2.1000000000000E-01 1.6160653192987E+00 -2.9566409648191E-01
+ 23 2.2000000000000E-01 1.6622713735128E+00 -3.0723588197458E-01
+ 24 2.3000000000000E-01 1.7037865434127E+00 -3.1567350802539E-01
+ 25 2.4000000000000E-01 1.7403769705430E+00 -3.2045257403308E-01
+ 26 2.5000000000000E-01 1.7718237578249E+00 -3.2106139438034E-01
+ 27 2.6000000000000E-01 1.7979260249536E+00 -3.1701040638094E-01
+ 28 2.7000000000000E-01 1.8185039200367E+00 -3.0784150729913E-01
+ 29 2.8000000000000E-01 1.8334015390070E+00 -2.9313716009328E-01
+ 30 2.9000000000000E-01 1.8424897047222E+00 -2.7252910951996E-01
+ 31 3.0000000000000E-01 1.8456685588283E+00 -2.4570655488315E-01
+ 32 3.1000000000000E-01 1.8428699213827E+00 -2.1242363296860E-01
+ 33 3.2000000000000E-01 1.8340593758926E+00 -1.7250607445688E-01
+ 34 3.3000000000000E-01 1.8192380407870E+00 -1.2585690922174E-01
+ 35 3.4000000000000E-01 1.7984439923520E+00 -7.2461110200767E-02
+ 36 3.5000000000000E-01 1.7717533087712E+00 -1.2389081754199E-02
+ 37 3.6000000000000E-01 1.7392807100478E+00 5.4201083654791E-02
+ 38 3.7000000000000E-01 1.7011797741681E+00 1.2706263730575E-01
+ 39 3.8000000000000E-01 1.6576427158184E+00 2.0586053103016E-01
+ 40 3.9000000000000E-01 1.6088997201830E+00 2.9017311425879E-01
+ 41 4.0000000000000E-01 1.5552178307505E+00 3.7949516500803E-01
+ 42 4.1000000000000E-01 1.4968993965271E+00 4.7324222688455E-01
+ 43 4.2000000000000E-01 1.4342800904993E+00 5.7075620287486E-01
+ 44 4.3000000000000E-01 1.3677265175103E+00 6.7131213604299E-01
+ 45 4.4000000000000E-01 1.2976334358012E+00 7.7412608763087E-01
+ 46 4.5000000000000E-01 1.2244206222349E+00 8.7836400477956E-01
+ 47 4.6000000000000E-01 1.1485294165692E+00 9.8315145347463E-01
+ 48 4.7000000000000E-01 1.0704189849879E+00 1.0875840776525E+00
+ 49 4.8000000000000E-01 9.9056234736461E-01 1.1907386329432E+00
+ 50 4.9000000000000E-01 9.0944221634647E-01 1.2916844334840E+00
+ 51 5.0000000000000E-01 8.2754669925025E-01 1.3894950427966E+00
+ 52 5.1000000000000E-01 7.4536491591358E-01 1.4832600350140E+00
+ 53 5.2000000000000E-01 6.6338258700389E-01 1.5720966508584E+00
+ 54 5.3000000000000E-01 5.8207764783533E-01 1.6551611737456E+00
+ 55 5.4000000000000E-01 5.0191594247190E-01 1.7316598552200E+00
+ 56 5.5000000000000E-01 4.2334705180743E-01 1.8008592255438E+00
+ 57 5.6000000000000E-01 3.4680030742678E-01 1.8620956345750E+00
+ 58 5.7000000000000E-01 2.7268104040715E-01 1.9147838798867E+00
+ 59 5.8000000000000E-01 2.0136711083962E-01 1.9584247932796E+00
+ 60 5.9000000000000E-01 1.3320575982831E-01 1.9926116730468E+00
+ 61 6.0000000000000E-01 6.8510821077059E-02 2.0170354674760E+00
+ 62 6.1000000000000E-01 7.5603240377331E-03 2.0314886345831E+00
+ 63 6.2000000000000E-01 -4.9405485002878E-02 2.0358676238454E+00
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+ 82 8.1000000000000E-01 -3.3865193545650E-01 7.3292061624420E-01
+ 83 8.2000000000000E-01 -3.2270702258437E-01 6.4170383417866E-01
+ 84 8.3000000000000E-01 -3.0548984962164E-01 5.5380579325456E-01
+ 85 8.4000000000000E-01 -2.8729332618298E-01 4.6984596488037E-01
+ 86 8.5000000000000E-01 -2.6840007037643E-01 3.9037122136373E-01
+ 87 8.6000000000000E-01 -2.4907941486696E-01 3.1585005817557E-01
+ 88 8.7000000000000E-01 -2.2958461096574E-01 2.4666777742580E-01
+ 89 8.8000000000000E-01 -2.1015024382297E-01 1.8312263334043E-01
+ 90 8.9000000000000E-01 -1.9098986604052E-01 1.2542291736528E-01
+ 91 9.0000000000000E-01 -1.7229385204689E-01 7.3684943059780E-02
+ 92 9.1000000000000E-01 -1.5422752046992E-01 2.7932091868699E-02
+ 93 9.2000000000000E-01 -1.3692925731967E-01 -1.1906333602932E-02
+ 94 9.3000000000000E-01 -1.2051120556809E-01 -4.5984728023036E-02
+ 95 9.4000000000000E-01 -1.0506238348155E-01 -7.4521342541395E-02
+ 96 9.5000000000000E-01 -9.0650808367554E-02 -9.7785102012969E-02
+ 97 9.6000000000000E-01 -7.7324230892534E-02 -1.1608984051460E-01
+ 98 9.7000000000000E-01 -6.5111318011866E-02 -1.2978696626768E-01
+ 99 9.8000000000000E-01 -5.4022977350497E-02 -1.3925807122376E-01
+ 100 9.9000000000000E-01 -4.4053835327051E-02 -1.4490739731465E-01
+ 101 1.0000000000000E+00 -3.5183837768318E-02 -1.4715429253531E-01
+ 102 1.0100000000000E+00 -2.7379939303828E-02 -1.4642579456299E-01
+ 103 1.0200000000000E+00 -2.0597849087741E-02 -1.4314946901638E-01
+ 104 1.0300000000000E+00 -1.4783801251513E-02 -1.3774662112109E-01
+ 105 1.0400000000000E+00 -9.8763198789799E-03 -1.3062598929987E-01
+ 106 1.0500000000000E+00 -5.8079503351342E-03 -1.2217801630884E-01
+ 107 1.0600000000000E+00 -2.5069308181172E-03 -1.1276978146107E-01
+ 108 1.0700000000000E+00 1.0121888439697E-04 -1.0274066034687E-01
+ 109 1.0800000000000E+00 2.0922116436211E-03 -9.2398763813596E-02
+ 110 1.0900000000000E+00 3.5416270752912E-03 -8.2018190813498E-02
+ 111 1.1000000000000E+00 4.5236786383715E-03 -7.1837111903564E-02
+ 112 1.1100000000000E+00 5.1102606592498E-03 -6.2057152961654E-02
+ 113 1.1200000000000E+00 5.3692049460931E-03 -5.2840383220207E-02
+ 114 1.1300000000000E+00 5.3641890033145E-03 -4.4312208700560E-02
+ 115 1.1400000000000E+00 5.1654674342127E-03 -3.6601580632664E-02
+ 116 1.1500000000000E+00 4.7833875037664E-03 -2.9616779501490E-02
+ 117 1.1600000000000E+00 4.2543539223793E-03 -2.3344597635714E-02
+ 118 1.1700000000000E+00 3.6953748008237E-03 -1.8041029242800E-02
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+ 596 5.9500000000000E+00 4.4181997925932E-05 4.4186661635686E-05 0.0000000000000E+00
+ 597 5.9600000000000E+00 4.3304241394230E-05 4.3308817460847E-05 0.0000000000000E+00
+ 598 5.9700000000000E+00 4.2444171054593E-05 4.2448661150919E-05 0.0000000000000E+00
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+
+#
+#ONCVPSP (Optimized Norm-Conservinng Vanderbilt PSeudopotential)
+#scalar-relativistic version 3.3.1 12/12/2017
+#
+#While it is not required under the terms of the GNU GPL, it is
+#suggested that you cite D. R. Hamann, Phys. Rev. B 88, 085117 (2013)
+#in any publication utilizing these pseudopotentials.
+#
+# ATOM AND REFERENCE CONFIGURATION
+# atsym z nc nv iexc psfile
+ O 8.00 1 2 3 psp8
+#
+# n l f
+ 1 0 2.00
+ 2 0 2.00
+ 2 1 4.00
+#
+# PSEUDOPOTENTIAL AND OPTIMIZATION
+# lmax
+ 1
+#
+# l, rc, ep, ncon, nbas, qcut
+ 0 1.29195 -0.87291 5 8 8.98916
+ 1 1.47310 -0.33804 5 8 9.14990
+#
+# LOCAL POTENTIAL
+# lloc, lpopt, rc(5), dvloc0
+ 4 5 0.90330 0.00000
+#
+# VANDERBILT-KLEINMAN-BYLANDER PROJECTORs
+# l, nproj, debl
+ 0 2 1.51851
+ 1 2 1.53631
+#
+# MODEL CORE CHARGE
+# icmod, fcfact, rcfact
+ 0 0.00000 0.00000
+#
+# LOG DERIVATIVE ANALYSIS
+# epsh1, epsh2, depsh
+ -5.00 3.00 0.02
+#
+# OUTPUT GRID
+# rlmax, drl
+ 6.00 0.01
+#
+# TEST CONFIGURATIONS
+# ncnf
+ 0
+# nvcnf
+# n l f
+
+
+END_PSP
diff --git a/tests/BC/H2O_wire/H.psp8 b/tests/BC/H2O_wire/H.psp8
new file mode 100644
index 00000000..8cfcd218
--- /dev/null
+++ b/tests/BC/H2O_wire/H.psp8
@@ -0,0 +1,1859 @@
+H ONCVPSP-3.3.1 r_core= 1.15113
+ 1.0000 1.0000 190128 zatom,zion,pspd
+ 8 2 0 4 600 0 pspcod,pspxc,lmax,lloc,mmax,r2well
+ 5.99000000 0.00000000 0.00000000 rchrg fchrg qchrg
+ 2 0 0 0 0 nproj
+ 1 1 extension_switch
+ 0 -1.2539437611788E+00 -4.0727290034061E-01
+ 1 0.0000000000000E+00 4.6168487866094E-08 -3.4318619543394E-08
+ 2 1.0000000000000E-02 3.0205697226572E-02 1.2138998345020E-02
+ 3 2.0000000000000E-02 6.1520920405994E-02 2.3897417609999E-02
+ 4 3.0000000000000E-02 9.5025730951330E-02 3.4910538706878E-02
+ 5 4.0000000000000E-02 1.3174187672572E-01 4.4844951510226E-02
+ 6 5.0000000000000E-02 1.7260516197975E-01 5.3413190813061E-02
+ 7 6.0000000000000E-02 2.1843961566096E-01 6.0387175148664E-02
+ 8 7.0000000000000E-02 2.6993400210192E-01 6.5610090721067E-02
+ 9 8.0000000000000E-02 3.2762117192434E-01 6.9006397005503E-02
+ 10 9.0000000000000E-02 3.9186069495896E-01 7.0589672163570E-02
+ 11 1.0000000000000E-01 4.6282515214355E-01 7.0468064425559E-02
+ 12 1.1000000000000E-01 5.4049039096860E-01 6.8847169050086E-02
+ 13 1.2000000000000E-01 6.2462997048174E-01 6.6030208290916E-02
+ 14 1.3000000000000E-01 7.1481393865217E-01 6.2415452799431E-02
+ 15 1.4000000000000E-01 8.1041199864468E-01 5.8490885815360E-02
+ 16 1.5000000000000E-01 9.1060103293295E-01 5.4826175046603E-02
+ 17 1.6000000000000E-01 1.0143768669036E+00 5.2062079989264E-02
+ 18 1.7000000000000E-01 1.1205700683707E+00 5.0897483274831E-02
+ 19 1.8000000000000E-01 1.2278654979137E+00 5.2074292166079E-02
+ 20 1.9000000000000E-01 1.3348252487822E+00 5.6360509332163E-02
+ 21 2.0000000000000E-01 1.4399145457774E+00 6.4531819373226E-02
+ 22 2.1000000000000E-01 1.5415301114230E+00 7.7352078203955E-02
+ 23 2.2000000000000E-01 1.6380304560807E+00 9.5553125443707E-02
+ 24 2.3000000000000E-01 1.7277675074917E+00 1.1981436465341E-01
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+ 541 5.4000000000000E+00 2.2929386481866E-04 2.2930365607930E-04 0.0000000000000E+00
+ 542 5.4100000000000E+00 2.2553474658292E-04 2.2554439736491E-04 0.0000000000000E+00
+ 543 5.4200000000000E+00 2.2183782137311E-04 2.2184733368612E-04 0.0000000000000E+00
+ 544 5.4300000000000E+00 2.1820205047855E-04 2.1821142630361E-04 0.0000000000000E+00
+ 545 5.4400000000000E+00 2.1462641270693E-04 2.1463565399683E-04 0.0000000000000E+00
+ 546 5.4500000000000E+00 2.1110990409396E-04 2.1111901277366E-04 0.0000000000000E+00
+ 547 5.4600000000000E+00 2.0765153759853E-04 2.0766051556554E-04 0.0000000000000E+00
+ 548 5.4700000000000E+00 2.0425034281824E-04 2.0425919194303E-04 0.0000000000000E+00
+ 549 5.4800000000000E+00 2.0090536570603E-04 2.0091408783239E-04 0.0000000000000E+00
+ 550 5.4900000000000E+00 1.9761566829161E-04 1.9762426523703E-04 0.0000000000000E+00
+ 551 5.5000000000000E+00 1.9438032840380E-04 1.9438880195989E-04 0.0000000000000E+00
+ 552 5.5100000000000E+00 1.9119843941285E-04 1.9120679134565E-04 0.0000000000000E+00
+ 553 5.5200000000000E+00 1.8806910995773E-04 1.8807734200810E-04 0.0000000000000E+00
+ 554 5.5300000000000E+00 1.8499146368589E-04 1.8499957756987E-04 0.0000000000000E+00
+ 555 5.5400000000000E+00 1.8196463899924E-04 1.8197263640837E-04 0.0000000000000E+00
+ 556 5.5500000000000E+00 1.7898778880311E-04 1.7899567140484E-04 0.0000000000000E+00
+ 557 5.5600000000000E+00 1.7606008025884E-04 1.7606784969682E-04 0.0000000000000E+00
+ 558 5.5700000000000E+00 1.7318069453973E-04 1.7318835243415E-04 0.0000000000000E+00
+ 559 5.5800000000000E+00 1.7034882660378E-04 1.7035637455174E-04 0.0000000000000E+00
+ 560 5.5900000000000E+00 1.6756368494680E-04 1.6757112452260E-04 0.0000000000000E+00
+ 561 5.6000000000000E+00 1.6482449137646E-04 1.6483182413194E-04 0.0000000000000E+00
+ 562 5.6100000000000E+00 1.6213048078611E-04 1.6213770825099E-04 0.0000000000000E+00
+ 563 5.6200000000000E+00 1.5948090093251E-04 1.5948802461465E-04 0.0000000000000E+00
+ 564 5.6300000000000E+00 1.5687501221490E-04 1.5688203360068E-04 0.0000000000000E+00
+ 565 5.6400000000000E+00 1.5431208746554E-04 1.5431900802009E-04 0.0000000000000E+00
+ 566 5.6500000000000E+00 1.5179141173901E-04 1.5179823290657E-04 0.0000000000000E+00
+ 567 5.6600000000000E+00 1.4931228209917E-04 1.4931900530338E-04 0.0000000000000E+00
+ 568 5.6700000000000E+00 1.4687400741779E-04 1.4688063406195E-04 0.0000000000000E+00
+ 569 5.6800000000000E+00 1.4447590817417E-04 1.4448243964155E-04 0.0000000000000E+00
+ 570 5.6900000000000E+00 1.4211731625821E-04 1.4212375391236E-04 0.0000000000000E+00
+ 571 5.7000000000000E+00 1.3979757477345E-04 1.3980391995842E-04 0.0000000000000E+00
+ 572 5.7100000000000E+00 1.3751603785665E-04 1.3752229189732E-04 0.0000000000000E+00
+ 573 5.7200000000000E+00 1.3527207048380E-04 1.3527823468613E-04 0.0000000000000E+00
+ 574 5.7300000000000E+00 1.3306504828576E-04 1.3307112393706E-04 0.0000000000000E+00
+ 575 5.7400000000000E+00 1.3089435736894E-04 1.3090034573815E-04 0.0000000000000E+00
+ 576 5.7500000000000E+00 1.2875939413772E-04 1.2876529647565E-04 0.0000000000000E+00
+ 577 5.7600000000000E+00 1.2665956512002E-04 1.2666538265962E-04 0.0000000000000E+00
+ 578 5.7700000000000E+00 1.2459428679171E-04 1.2460002074833E-04 0.0000000000000E+00
+ 579 5.7800000000000E+00 1.2256298542067E-04 1.2256863699228E-04 0.0000000000000E+00
+ 580 5.7900000000000E+00 1.2056509688949E-04 1.2057066725697E-04 0.0000000000000E+00
+ 581 5.8000000000000E+00 1.1860006653534E-04 1.1860555686268E-04 0.0000000000000E+00
+ 582 5.8100000000000E+00 1.1666734899029E-04 1.1667276042488E-04 0.0000000000000E+00
+ 583 5.8200000000000E+00 1.1476640802406E-04 1.1477174169687E-04 0.0000000000000E+00
+ 584 5.8300000000000E+00 1.1289671638935E-04 1.1290197341521E-04 0.0000000000000E+00
+ 585 5.8400000000000E+00 1.1105775566562E-04 1.1106293714343E-04 0.0000000000000E+00
+ 586 5.8500000000000E+00 1.0924901612333E-04 1.0925412313628E-04 0.0000000000000E+00
+ 587 5.8600000000000E+00 1.0746999656356E-04 1.0747503017938E-04 0.0000000000000E+00
+ 588 5.8700000000000E+00 1.0572020417793E-04 1.0572516544906E-04 0.0000000000000E+00
+ 589 5.8800000000000E+00 1.0399915440669E-04 1.0400404437056E-04 0.0000000000000E+00
+ 590 5.8900000000000E+00 1.0230637079932E-04 1.0231119047851E-04 0.0000000000000E+00
+ 591 5.9000000000000E+00 1.0064138487750E-04 1.0064613527999E-04 0.0000000000000E+00
+ 592 5.9100000000000E+00 9.9003735996281E-05 9.9008418115630E-05 0.0000000000000E+00
+ 593 5.9200000000000E+00 9.7392971224773E-05 9.7397586040348E-05 0.0000000000000E+00
+ 594 5.9300000000000E+00 9.5808645202972E-05 9.5813193680135E-05 0.0000000000000E+00
+ 595 5.9400000000000E+00 9.4250320017889E-05 9.4254803108201E-05 0.0000000000000E+00
+ 596 5.9500000000000E+00 9.2717565077799E-05 9.2721983719215E-05 0.0000000000000E+00
+ 597 5.9600000000000E+00 9.1209956988643E-05 9.1214312105707E-05 0.0000000000000E+00
+ 598 5.9700000000000E+00 8.9727079432550E-05 8.9731371936586E-05 0.0000000000000E+00
+ 599 5.9800000000000E+00 8.8268523044768E-05 8.8272753834068E-05 0.0000000000000E+00
+ 600 5.9900000000000E+00 8.6833885307547E-05 8.6838055267556E-05 0.0000000000000E+00
+
+#
+#ONCVPSP (Optimized Norm-Conservinng Vanderbilt PSeudopotential)
+#scalar-relativistic version 3.3.1 12/12/2017
+#
+#While it is not required under the terms of the GNU GPL, it is
+#suggested that you cite D. R. Hamann, Phys. Rev. B 88, 085117 (2013)
+#in any publication utilizing these pseudopotentials.
+#
+# ATOM AND REFERENCE CONFIGURATION
+# atsym z nc nv iexc psfile
+ H 1.00 0 1 3 psp8
+#
+# n l f
+ 1 0 1.00
+#
+# PSEUDOPOTENTIAL AND OPTIMIZATION
+# lmax
+ 0
+#
+# l, rc, ep, ncon, nbas, qcut
+ 0 1.13748 -0.23366 5 8 9.72141
+#
+# LOCAL POTENTIAL
+# lloc, lpopt, rc(5), dvloc0
+ 4 5 0.49352 0.00000
+#
+# VANDERBILT-KLEINMAN-BYLANDER PROJECTORs
+# l, nproj, debl
+ 0 2 1.27464
+#
+# MODEL CORE CHARGE
+# icmod, fcfact, rcfact
+ 0 0.00000 0.00000
+#
+# LOG DERIVATIVE ANALYSIS
+# epsh1, epsh2, depsh
+ -5.00 3.00 0.02
+#
+# OUTPUT GRID
+# rlmax, drl
+ 6.00 0.01
+#
+# TEST CONFIGURATIONS
+# ncnf
+ 0
+# nvcnf
+# n l f
+
+
+END_PSP
diff --git a/tests/BC/H2O_wire/H2O_wire.inpt b/tests/BC/H2O_wire/H2O_wire.inpt
new file mode 100644
index 00000000..a011bd40
--- /dev/null
+++ b/tests/BC/H2O_wire/H2O_wire.inpt
@@ -0,0 +1,18 @@
+# Test: H2O wire in z direction #
+CELL: 14.000000000000000 14.000000000000000 6.000000000000000
+FD_GRID: 70 70 30
+FD_ORDER: 12
+BC: D D P
+#BOUNDARY_CONDITION: 4
+EXCHANGE_CORRELATION: LDA_PZ
+ELEC_TEMP_TYPE: fd
+SMEARING: 0.003674932
+TOL_SCF: 1e-5
+NSTATES: 8
+PRINT_FORCES: 1
+PRINT_ATOMS: 1
+
+KPOINT_GRID: 1 1 2
+
+
+
diff --git a/tests/BC/H2O_wire/H2O_wire.ion b/tests/BC/H2O_wire/H2O_wire.ion
new file mode 100644
index 00000000..c2f692f7
--- /dev/null
+++ b/tests/BC/H2O_wire/H2O_wire.ion
@@ -0,0 +1,29 @@
+#=========================
+# format of ion file
+#=========================
+# ATOM_TYPE:
+# PSEUDO_POT:
+# N_TYPE_ATOM:
+# COORD:
+#
+# ...
+# RELAX:
+#
+# ...
+
+# Reminder: when changing number of atoms, change the RELAX flags accordingly
+# as well.
+
+ATOM_TYPE: H # atom type
+PSEUDO_POT: H.psp8
+N_TYPE_ATOM: 2 # number of atoms of this type
+COORD: # coordinates follows
+ 7.369126503082081 7.000000000000000 4.430522676620148
+ 7.369126503082081 7.000000000000000 1.569477323379852
+
+ATOM_TYPE: O # atom type
+PSEUDO_POT: O.psp8
+N_TYPE_ATOM: 1 # number of atoms of this type
+COORD: # coordinates follows
+ 6.261746993835837 7.000000000000000 3.000000000000000
+
diff --git a/tests/BC/H2O_wire/H2O_wire.refout b/tests/BC/H2O_wire/H2O_wire.refout
new file mode 100644
index 00000000..f2f1e16e
--- /dev/null
+++ b/tests/BC/H2O_wire/H2O_wire.refout
@@ -0,0 +1,101 @@
+***************************************************************************
+* M-SPARC (Dec 17, 2019) *
+* Copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech *
+* Distributed under GNU General Public License 3 (GPL) *
+* Date: 17-Dec-2019 Start time: 16:45:02 *
+***************************************************************************
+ Input parameters
+***************************************************************************
+CELL: 14.000000 14.000000 6.000000
+FD_GRID: 70 70 30
+FD_ORDER: 12
+BOUNDARY_CONDITION: 4
+KPOINT_GRID: 1 1 2
+KPOINT_SHIFT: 0 0 0
+ELEC_TEMP_TYPE: fermi-dirac
+SMEARING: 0.003674932
+CHEB_DEGREE: 35
+NSTATES: 8
+EXCHANGE_CORRELATION: LDA_PZ
+CALC_STRESS: 0
+CALC_PRES: 0
+MAXIT_SCF: 100
+TOL_SCF: 1.00E-05
+TOL_POISSON: 1.00E-07
+TOL_LANCZOS: 1.00E-02
+TOL_PSEUDOCHARGE: 1.00E-07
+MIXING_VARIABLE: potential
+MIXING_PRECOND: none
+MIXING_PARAMETER: 0.30
+MIXING_HISTORY: 7
+PULAY_FREQUENCY: 1
+PULAY_RESTART_FREQ: 0
+REFERENCE_CUTOFF: 0.50
+RHO_TRIGGER: 4
+FIX_RAND: 0
+PRINT_FORCES: 1
+PRINT_ATOMS: 1
+PRINT_EIGEN: 0
+PRINT_DENSITY: 0
+OUTPUT_FILE: ../tests/BC/H2O_wire/H2O_wire.out
+***************************************************************************
+ Initialization
+***************************************************************************
+Mesh spacing : 0.200000 (Bohr)
+Number of symmetry adapted k-points: 1
+Output printed to : ../tests/BC/H2O_wire/H2O_wire.out
+Total number of atom types : 2
+Total number of atoms : 3
+Total number of electrons : 8
+Atom type 1 (valence electrons) : H 1
+Pseudopotential : H.psp8
+lloc : 4
+Pseudocharge radii of atom type 1 : 6.40 6.40 6.40
+Number of atoms of type 1 : 2
+Atom type 2 (valence electrons) : O 6
+Pseudopotential : O.psp8
+lloc : 4
+Pseudocharge radii of atom type 2 : 6.40 6.40 6.40
+Number of atoms of type 2 : 1
+Estimated total memory usage : 459.21 MB
+=====================================================================
+ Self Consistent Field (SCF#1)
+=====================================================================
+Iteration Free Energy (Ha/atom) SCF Error Timing (sec)
+1 -5.6660098682E+00 2.595E-01 14.478
+2 -5.7024408766E+00 7.429E-02 6.053
+3 -5.7037594772E+00 1.935E-02 5.318
+4 -5.7038696681E+00 7.629E-03 5.497
+5 -5.7038973239E+00 4.619E-03 5.042
+6 -5.7039044999E+00 9.016E-04 5.235
+7 -5.7039045554E+00 1.211E-04 4.872
+8 -5.7039045609E+00 3.530E-05 4.500
+9 -5.7039045096E+00 2.927E-05 4.868
+10 -5.7039045220E+00 3.538E-06 4.313
+Total number of SCF: 10
+====================================================================
+ Energy
+====================================================================
+Free energy per atom : -5.7039045220E+00 (Ha/atom)
+Total free energy : -1.7111713566E+01 (Ha)
+Band structure energy : -4.2864617193E+00 (Ha)
+Exchange correlation energy : -4.1163721578E+00 (Ha)
+Self and correction energy : -3.5340948500E+01 (Ha)
+Entropy*kb*T : -4.9204460696E-09 (Ha)
+Fermi level : -1.1690019704E-01 (Ha)
+Average force : 1.4160825352E-02 (Ha/Bohr)
+Maximum force : 1.7693666301E-02 (Ha/Bohr)
+Time for force calculation : 0.848 (sec)
+***************************************************************************
+ Timing info
+***************************************************************************
+Total walltime : 68.804 sec
+___________________________________________________________________________
+
+***************************************************************************
+* Material Physics & Mechanics Group, Georgia Tech *
+* PI: Phanish Suryanarayana *
+* Main Developers: Qimen Xu, Abhiraj Sharma *
+* Acknowledgements: U.S. DOE (DE-SC0019410); NSF (1333500,1553212) *
+***************************************************************************
+
diff --git a/tests/BC/H2O_wire/H2O_wire.refstatic b/tests/BC/H2O_wire/H2O_wire.refstatic
new file mode 100644
index 00000000..f5b22299
--- /dev/null
+++ b/tests/BC/H2O_wire/H2O_wire.refstatic
@@ -0,0 +1,11 @@
+***************************************************************************
+ Atom positions
+***************************************************************************
+Cartesian coordinates of atoms (Bohr):
+ 7.3691265031 7.0000000000 4.4305226766
+ 7.3691265031 7.0000000000 1.5694773234
+ 6.2617469938 7.0000000000 3.0000000000
+Atomic forces (Ha/Bohr):
+ 0.0088467916 0.0000006604 0.0086803334
+ 0.0088468747 0.0000006824 -0.0086810969
+ -0.0176936662 -0.0000013428 0.0000007635
diff --git a/tests/BC/H2O_wire/O.psp8 b/tests/BC/H2O_wire/O.psp8
new file mode 100644
index 00000000..58f5aa79
--- /dev/null
+++ b/tests/BC/H2O_wire/O.psp8
@@ -0,0 +1,2464 @@
+O ONCVPSP-3.3.1 r_core= 1.29195 1.47310
+ 8.0000 6.0000 190128 zatom,zion,pspd
+ 8 2 1 4 600 0 pspcod,pspxc,lmax,lloc,mmax,r2well
+ 5.99000000 0.00000000 0.00000000 rchrg fchrg qchrg
+ 2 2 0 0 0 nproj
+ 1 1 extension_switch
+ 0 9.8039458648062E+00 1.3940968705798E+00
+ 1 0.0000000000000E+00 2.8163213983134E-09 -9.8156246741699E-09
+ 2 1.0000000000000E-02 8.9663020185480E-02 -6.4027817020632E-03
+ 3 2.0000000000000E-02 1.7918092483447E-01 -1.3049427776932E-02
+ 4 3.0000000000000E-02 2.6840691548778E-01 -2.0176041044928E-02
+ 5 4.0000000000000E-02 3.5719087019612E-01 -2.8003350708319E-02
+ 6 5.0000000000000E-02 4.4537778693024E-01 -3.6729396702763E-02
+ 7 6.0000000000000E-02 5.3280635113698E-01 -4.6522652323702E-02
+ 8 7.0000000000000E-02 6.1930766545706E-01 -5.7515719480801E-02
+ 9 8.0000000000000E-02 7.0470417680425E-01 -6.9799721117865E-02
+ 10 9.0000000000000E-02 7.8880883257007E-01 -8.3419503369501E-02
+ 11 1.0000000000000E-01 8.7142449371820E-01 -9.8369746103570E-02
+ 12 1.1000000000000E-01 9.5234362803191E-01 -1.1459206484851E-01
+ 13 1.2000000000000E-01 1.0313483018487E+00 -1.3197316998196E-01
+ 14 1.3000000000000E-01 1.1082104833363E+00 -1.5034413074331E-01
+ 15 1.4000000000000E-01 1.1826926648206E+00 -1.6948077242832E-01
+ 16 1.5000000000000E-01 1.2545488059549E+00 -1.8910521534537E-01
+ 17 1.6000000000000E-01 1.3235255937164E+00 -2.0888854408794E-01
+ 18 1.7000000000000E-01 1.3893640094233E+00 -2.2845457573710E-01
+ 19 1.8000000000000E-01 1.4518011872782E+00 -2.4738467608605E-01
+ 20 1.9000000000000E-01 1.5105725434525E+00 -2.6522355420045E-01
+ 21 2.0000000000000E-01 1.5654141495302E+00 -2.8148594791135E-01
+ 22 2.1000000000000E-01 1.6160653192987E+00 -2.9566409648191E-01
+ 23 2.2000000000000E-01 1.6622713735128E+00 -3.0723588197458E-01
+ 24 2.3000000000000E-01 1.7037865434127E+00 -3.1567350802539E-01
+ 25 2.4000000000000E-01 1.7403769705430E+00 -3.2045257403308E-01
+ 26 2.5000000000000E-01 1.7718237578249E+00 -3.2106139438034E-01
+ 27 2.6000000000000E-01 1.7979260249536E+00 -3.1701040638094E-01
+ 28 2.7000000000000E-01 1.8185039200367E+00 -3.0784150729913E-01
+ 29 2.8000000000000E-01 1.8334015390070E+00 -2.9313716009328E-01
+ 30 2.9000000000000E-01 1.8424897047222E+00 -2.7252910951996E-01
+ 31 3.0000000000000E-01 1.8456685588283E+00 -2.4570655488315E-01
+ 32 3.1000000000000E-01 1.8428699213827E+00 -2.1242363296860E-01
+ 33 3.2000000000000E-01 1.8340593758926E+00 -1.7250607445688E-01
+ 34 3.3000000000000E-01 1.8192380407870E+00 -1.2585690922174E-01
+ 35 3.4000000000000E-01 1.7984439923520E+00 -7.2461110200767E-02
+ 36 3.5000000000000E-01 1.7717533087712E+00 -1.2389081754199E-02
+ 37 3.6000000000000E-01 1.7392807100478E+00 5.4201083654791E-02
+ 38 3.7000000000000E-01 1.7011797741681E+00 1.2706263730575E-01
+ 39 3.8000000000000E-01 1.6576427158184E+00 2.0586053103016E-01
+ 40 3.9000000000000E-01 1.6088997201830E+00 2.9017311425879E-01
+ 41 4.0000000000000E-01 1.5552178307505E+00 3.7949516500803E-01
+ 42 4.1000000000000E-01 1.4968993965271E+00 4.7324222688455E-01
+ 43 4.2000000000000E-01 1.4342800904993E+00 5.7075620287486E-01
+ 44 4.3000000000000E-01 1.3677265175103E+00 6.7131213604299E-01
+ 45 4.4000000000000E-01 1.2976334358012E+00 7.7412608763087E-01
+ 46 4.5000000000000E-01 1.2244206222349E+00 8.7836400477956E-01
+ 47 4.6000000000000E-01 1.1485294165692E+00 9.8315145347463E-01
+ 48 4.7000000000000E-01 1.0704189849879E+00 1.0875840776525E+00
+ 49 4.8000000000000E-01 9.9056234736461E-01 1.1907386329432E+00
+ 50 4.9000000000000E-01 9.0944221634647E-01 1.2916844334840E+00
+ 51 5.0000000000000E-01 8.2754669925025E-01 1.3894950427966E+00
+ 52 5.1000000000000E-01 7.4536491591358E-01 1.4832600350140E+00
+ 53 5.2000000000000E-01 6.6338258700389E-01 1.5720966508584E+00
+ 54 5.3000000000000E-01 5.8207764783533E-01 1.6551611737456E+00
+ 55 5.4000000000000E-01 5.0191594247190E-01 1.7316598552200E+00
+ 56 5.5000000000000E-01 4.2334705180743E-01 1.8008592255438E+00
+ 57 5.6000000000000E-01 3.4680030742678E-01 1.8620956345750E+00
+ 58 5.7000000000000E-01 2.7268104040715E-01 1.9147838798867E+00
+ 59 5.8000000000000E-01 2.0136711083962E-01 1.9584247932796E+00
+ 60 5.9000000000000E-01 1.3320575982831E-01 1.9926116730468E+00
+ 61 6.0000000000000E-01 6.8510821077059E-02 2.0170354674760E+00
+ 62 6.1000000000000E-01 7.5603240377331E-03 2.0314886345831E+00
+ 63 6.2000000000000E-01 -4.9405485002878E-02 2.0358676238454E+00
+ 64 6.3000000000000E-01 -1.0218568344691E-01 2.0301739472341E+00
+ 65 6.4000000000000E-01 -1.5061976022354E-01 2.0145138287603E+00
+ 66 6.5000000000000E-01 -1.9458824297923E-01 1.9890964438486E+00
+ 67 6.6000000000000E-01 -2.3401286298402E-01 1.9542307814575E+00
+ 68 6.7000000000000E-01 -2.6885626239664E-01 1.9103211828402E+00
+ 69 6.8000000000000E-01 -2.9912125465144E-01 1.8578616307671E+00
+ 70 6.9000000000000E-01 -3.2484965455966E-01 1.7974288814605E+00
+ 71 7.0000000000000E-01 -3.4612070017945E-01 1.7296745481842E+00
+ 72 7.1000000000000E-01 -3.6304909355304E-01 1.6553162601687E+00
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+ 492 4.9100000000000E+00 3.6935436800399E-04 3.6938919650191E-04 0.0000000000000E+00
+ 493 4.9200000000000E+00 3.6174679303389E-04 3.6178094023363E-04 0.0000000000000E+00
+ 494 4.9300000000000E+00 3.5429902135973E-04 3.5433250091348E-04 0.0000000000000E+00
+ 495 4.9400000000000E+00 3.4700762013094E-04 3.4704044540945E-04 0.0000000000000E+00
+ 496 4.9500000000000E+00 3.3986923212300E-04 3.3990141622159E-04 0.0000000000000E+00
+ 497 4.9600000000000E+00 3.3288057404123E-04 3.3291212978565E-04 0.0000000000000E+00
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+ 500 4.9900000000000E+00 3.1278122038252E-04 3.1281096540827E-04 0.0000000000000E+00
+ 501 5.0000000000000E+00 3.0636006981933E-04 3.0638923521084E-04 0.0000000000000E+00
+ 502 5.0100000000000E+00 3.0007328440227E-04 3.0010188172088E-04 0.0000000000000E+00
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+ 506 5.0500000000000E+00 2.7621325960250E-04 2.7623969557707E-04 0.0000000000000E+00
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+ 508 5.0700000000000E+00 2.6501765217684E-04 2.6504307091802E-04 0.0000000000000E+00
+ 509 5.0800000000000E+00 2.5959439354641E-04 2.5961931878079E-04 0.0000000000000E+00
+ 510 5.0900000000000E+00 2.5428419828142E-04 2.5430863980862E-04 0.0000000000000E+00
+ 511 5.1000000000000E+00 2.4908465879761E-04 2.4910862621741E-04 0.0000000000000E+00
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+ 513 5.1200000000000E+00 2.3900817839756E-04 2.3903122562347E-04 0.0000000000000E+00
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+ 549 5.4800000000000E+00 1.1425664457214E-04 1.1426810030004E-04 0.0000000000000E+00
+ 550 5.4900000000000E+00 1.1195318171479E-04 1.1196441874338E-04 0.0000000000000E+00
+ 551 5.5000000000000E+00 1.0969691848836E-04 1.0970794107249E-04 0.0000000000000E+00
+ 552 5.5100000000000E+00 1.0748686979324E-04 1.0749768210309E-04 0.0000000000000E+00
+ 553 5.5200000000000E+00 1.0532207152222E-04 1.0533267764506E-04 0.0000000000000E+00
+ 554 5.5300000000000E+00 1.0320158010249E-04 1.0321198404432E-04 0.0000000000000E+00
+ 555 5.5400000000000E+00 1.0112447204133E-04 1.0113467772859E-04 0.0000000000000E+00
+ 556 5.5500000000000E+00 9.9089843494616E-05 9.9099854775781E-05 0.0000000000000E+00
+ 557 5.5600000000000E+00 9.7096809864778E-05 9.7106630511950E-05 0.0000000000000E+00
+ 558 5.5700000000000E+00 9.5144505342366E-05 9.5154139052834E-05 0.0000000000000E+00
+ 559 5.5800000000000E+00 9.3232082511326E-05 9.3241532909089E-05 0.0000000000000E+00
+ 560 5.5900000000000E+00 9.1358711949032E-05 9.1367982586287E-05 0.0000000000000E+00
+ 561 5.6000000000000E+00 8.9523581835313E-05 8.9532676193916E-05 0.0000000000000E+00
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+ 564 5.6300000000000E+00 8.4239772013035E-05 8.4248357744648E-05 0.0000000000000E+00
+ 565 5.6400000000000E+00 8.2549824340142E-05 8.2558247045243E-05 0.0000000000000E+00
+ 566 5.6500000000000E+00 8.0894308981699E-05 8.0902571811281E-05 0.0000000000000E+00
+ 567 5.6600000000000E+00 7.9272512000227E-05 7.9280618043080E-05 0.0000000000000E+00
+ 568 5.6700000000000E+00 7.7683734557044E-05 7.7691686841015E-05 0.0000000000000E+00
+ 569 5.6800000000000E+00 7.6127292569218E-05 7.6135094062439E-05 0.0000000000000E+00
+ 570 5.6900000000000E+00 7.4602516441777E-05 7.4610170053878E-05 0.0000000000000E+00
+ 571 5.7000000000000E+00 7.3108750706584E-05 7.3116259289871E-05 0.0000000000000E+00
+ 572 5.7100000000000E+00 7.1645353729711E-05 7.1652720080326E-05 0.0000000000000E+00
+ 573 5.7200000000000E+00 7.0211697413907E-05 7.0218924272960E-05 0.0000000000000E+00
+ 574 5.7300000000000E+00 6.8807166906621E-05 6.8814256961300E-05 0.0000000000000E+00
+ 575 5.7400000000000E+00 6.7431160312323E-05 6.7438116196978E-05 0.0000000000000E+00
+ 576 5.7500000000000E+00 6.6083088406250E-05 6.6089912703463E-05 0.0000000000000E+00
+ 577 5.7600000000000E+00 6.4762374399298E-05 6.4769069640919E-05 0.0000000000000E+00
+ 578 5.7700000000000E+00 6.3468453628438E-05 6.3475022296613E-05 0.0000000000000E+00
+ 579 5.7800000000000E+00 6.2200773309505E-05 6.2207217837667E-05 0.0000000000000E+00
+ 580 5.7900000000000E+00 6.0958792281771E-05 6.0965115055628E-05 0.0000000000000E+00
+ 581 5.8000000000000E+00 5.9741980758212E-05 5.9748184116696E-05 0.0000000000000E+00
+ 582 5.8100000000000E+00 5.8549820077542E-05 5.8555906313755E-05 0.0000000000000E+00
+ 583 5.8200000000000E+00 5.7381802465969E-05 5.7387773828099E-05 0.0000000000000E+00
+ 584 5.8300000000000E+00 5.6237430827731E-05 5.6243289519954E-05 0.0000000000000E+00
+ 585 5.8400000000000E+00 5.5116218484419E-05 5.5121966667781E-05 0.0000000000000E+00
+ 586 5.8500000000000E+00 5.4017688962681E-05 5.4023328755962E-05 0.0000000000000E+00
+ 587 5.8600000000000E+00 5.2941375775620E-05 5.2946909256178E-05 0.0000000000000E+00
+ 588 5.8700000000000E+00 5.1886822209025E-05 5.1892251413625E-05 0.0000000000000E+00
+ 589 5.8800000000000E+00 5.0853581108450E-05 5.0858908034079E-05 0.0000000000000E+00
+ 590 5.8900000000000E+00 4.9841214677044E-05 4.9846441281700E-05 0.0000000000000E+00
+ 591 5.9000000000000E+00 4.8849294294996E-05 4.8854422498474E-05 0.0000000000000E+00
+ 592 5.9100000000000E+00 4.7877400296114E-05 4.7882431980761E-05 0.0000000000000E+00
+ 593 5.9200000000000E+00 4.6925121786300E-05 4.6930058797768E-05 0.0000000000000E+00
+ 594 5.9300000000000E+00 4.5992056456327E-05 4.5996900604303E-05 0.0000000000000E+00
+ 595 5.9400000000000E+00 4.5077810398747E-05 4.5082563457666E-05 0.0000000000000E+00
+ 596 5.9500000000000E+00 4.4181997925932E-05 4.4186661635686E-05 0.0000000000000E+00
+ 597 5.9600000000000E+00 4.3304241394230E-05 4.3308817460847E-05 0.0000000000000E+00
+ 598 5.9700000000000E+00 4.2444171054593E-05 4.2448661150919E-05 0.0000000000000E+00
+ 599 5.9800000000000E+00 4.1601424856796E-05 4.1605830623150E-05 0.0000000000000E+00
+ 600 5.9900000000000E+00 4.0775648295124E-05 4.0779971339947E-05 0.0000000000000E+00
+
+#
+#ONCVPSP (Optimized Norm-Conservinng Vanderbilt PSeudopotential)
+#scalar-relativistic version 3.3.1 12/12/2017
+#
+#While it is not required under the terms of the GNU GPL, it is
+#suggested that you cite D. R. Hamann, Phys. Rev. B 88, 085117 (2013)
+#in any publication utilizing these pseudopotentials.
+#
+# ATOM AND REFERENCE CONFIGURATION
+# atsym z nc nv iexc psfile
+ O 8.00 1 2 3 psp8
+#
+# n l f
+ 1 0 2.00
+ 2 0 2.00
+ 2 1 4.00
+#
+# PSEUDOPOTENTIAL AND OPTIMIZATION
+# lmax
+ 1
+#
+# l, rc, ep, ncon, nbas, qcut
+ 0 1.29195 -0.87291 5 8 8.98916
+ 1 1.47310 -0.33804 5 8 9.14990
+#
+# LOCAL POTENTIAL
+# lloc, lpopt, rc(5), dvloc0
+ 4 5 0.90330 0.00000
+#
+# VANDERBILT-KLEINMAN-BYLANDER PROJECTORs
+# l, nproj, debl
+ 0 2 1.51851
+ 1 2 1.53631
+#
+# MODEL CORE CHARGE
+# icmod, fcfact, rcfact
+ 0 0.00000 0.00000
+#
+# LOG DERIVATIVE ANALYSIS
+# epsh1, epsh2, depsh
+ -5.00 3.00 0.02
+#
+# OUTPUT GRID
+# rlmax, drl
+ 6.00 0.01
+#
+# TEST CONFIGURATIONS
+# ncnf
+ 0
+# nvcnf
+# n l f
+
+
+END_PSP
diff --git a/tests/IllustrativeExamples/Au_fcc/isolated/Au_iso.inpt b/tests/IllustrativeExamples/Au_fcc/isolated/Au_iso.inpt
new file mode 100644
index 00000000..66e21619
--- /dev/null
+++ b/tests/IllustrativeExamples/Au_fcc/isolated/Au_iso.inpt
@@ -0,0 +1,17 @@
+# Test: Au isolated atom #
+CELL: 20.00 20.00 20.00
+FD_GRID: 67 67 67
+BOUNDARY_CONDITION: 1
+EXCHANGE_CORRELATION: LDA_PZ
+ELEC_TEMP_TYPE: fd
+SMEARING: 0.001
+TOL_SCF: 1e-6
+NSTATES: 20
+PRINT_FORCES: 1
+PRINT_ATOMS: 1
+
+CALC_STRESS: 0
+
+MIXING_VARIABLE: potential
+
+
diff --git a/tests/IllustrativeExamples/Au_fcc/isolated/Au_iso.ion b/tests/IllustrativeExamples/Au_fcc/isolated/Au_iso.ion
new file mode 100644
index 00000000..404d59ff
--- /dev/null
+++ b/tests/IllustrativeExamples/Au_fcc/isolated/Au_iso.ion
@@ -0,0 +1,18 @@
+#=========================
+# format of ion file
+#=========================
+# ATOM_TYPE:
+# N_TYPE_ATOM:
+# COORD:
+#
+# ...
+# RELAX:
+#
+# ...
+
+ATOM_TYPE: Au # atom type followed with valence charge
+PSEUDO_POT: ../psp/Au.psp8 # pseudopotential file
+N_TYPE_ATOM: 1 # number of atoms of this type
+COORD_FRAC: # coordinates follows
+0.5 0.5 0.5
+
diff --git a/tests/IllustrativeExamples/Au_fcc/isolated/Au_iso.refout b/tests/IllustrativeExamples/Au_fcc/isolated/Au_iso.refout
new file mode 100644
index 00000000..c7fb42e4
--- /dev/null
+++ b/tests/IllustrativeExamples/Au_fcc/isolated/Au_iso.refout
@@ -0,0 +1,95 @@
+***************************************************************************
+* M-SPARC (Dec 15, 2019) *
+* Copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech *
+* Distributed under GNU General Public License 3 (GPL) *
+* Date: 16-Dec-2019 Start time: 21:25:15 *
+***************************************************************************
+ Input parameters
+***************************************************************************
+CELL: 20.000000 20.000000 20.000000
+FD_GRID: 67 67 67
+FD_ORDER: 12
+BOUNDARY_CONDITION: 1
+ELEC_TEMP_TYPE: fermi-dirac
+SMEARING: 0.001000000
+CHEB_DEGREE: 26
+NSTATES: 20
+EXCHANGE_CORRELATION: LDA_PZ
+CALC_STRESS: 0
+CALC_PRES: 0
+MAXIT_SCF: 100
+TOL_SCF: 1.00E-06
+TOL_POISSON: 1.00E-08
+TOL_LANCZOS: 1.00E-02
+TOL_PSEUDOCHARGE: 1.00E-08
+MIXING_VARIABLE: potential
+MIXING_PRECOND: none
+MIXING_PARAMETER: 0.30
+MIXING_HISTORY: 7
+PULAY_FREQUENCY: 1
+PULAY_RESTART_FREQ: 0
+REFERENCE_CUTOFF: 0.50
+RHO_TRIGGER: 4
+FIX_RAND: 0
+PRINT_FORCES: 1
+PRINT_ATOMS: 1
+PRINT_EIGEN: 0
+PRINT_DENSITY: 0
+OUTPUT_FILE: Au_iso.out
+***************************************************************************
+ Initialization
+***************************************************************************
+Mesh spacing : 0.298507 (Bohr)
+Output printed to : Au_iso.out
+Total number of atom types : 1
+Total number of atoms : 1
+Total number of electrons : 19
+Atom type 1 (valence electrons) : Au 19
+Pseudopotential : ../psp/Au.psp8
+lloc : 4
+Pseudocharge radii of atom type 1 : 6.87 6.87 6.87
+Number of atoms of type 1 : 1
+Estimated total memory usage : 1.34 GB
+=====================================================================
+ Self Consistent Field (SCF#1)
+=====================================================================
+Iteration Free Energy (Ha/atom) SCF Error Timing (sec)
+1 -1.3728297685E+02 1.045E-01 32.777
+2 -1.3731127691E+02 4.718E-02 20.145
+3 -1.3731365494E+02 2.867E-02 20.142
+4 -1.3731377468E+02 1.265E-02 18.682
+5 -1.3731379314E+02 2.091E-03 17.656
+6 -1.3731380010E+02 8.812E-04 16.832
+7 -1.3731380017E+02 2.664E-04 17.181
+8 -1.3731380023E+02 1.042E-04 15.632
+9 -1.3731380028E+02 3.758E-05 15.090
+10 -1.3731380028E+02 1.083E-05 15.340
+11 -1.3731380026E+02 3.529E-06 13.971
+12 -1.3731380027E+02 5.447E-07 13.588
+Total number of SCF: 12
+====================================================================
+ Energy
+====================================================================
+Free energy per atom : -1.3731380027E+02 (Ha/atom)
+Total free energy : -1.3731380027E+02 (Ha)
+Band structure energy : -2.4093369437E+01 (Ha)
+Exchange correlation energy : -1.2434111610E+01 (Ha)
+Self and correction energy : -1.9038370885E+02 (Ha)
+Entropy*kb*T : -1.3862943611E-03 (Ha)
+Fermi level : -2.2383789175E-01 (Ha)
+Average force : 0.0000000000E+00 (Ha/Bohr)
+Maximum force : 0.0000000000E+00 (Ha/Bohr)
+Time for force calculation : 1.699 (sec)
+***************************************************************************
+ Timing info
+***************************************************************************
+Total walltime : 252.732 sec
+___________________________________________________________________________
+
+***************************************************************************
+* Material Physics & Mechanics Group, Georgia Tech *
+* PI: Phanish Suryanarayana *
+* Main Developers: Qimen Xu, Abhiraj Sharma *
+* Acknowledgements: U.S. DOE (DE-SC0019410); NSF (1333500,1553212) *
+***************************************************************************
+
diff --git a/tests/IllustrativeExamples/Au_fcc/isolated/Au_iso.refstatic b/tests/IllustrativeExamples/Au_fcc/isolated/Au_iso.refstatic
new file mode 100644
index 00000000..9616f547
--- /dev/null
+++ b/tests/IllustrativeExamples/Au_fcc/isolated/Au_iso.refstatic
@@ -0,0 +1,7 @@
+***************************************************************************
+ Atom positions
+***************************************************************************
+Fractional coordinates of atoms:
+ 0.5000000000 0.5000000000 0.5000000000
+Atomic forces (Ha/Bohr):
+ 0.0000000000 0.0000000000 0.0000000000
diff --git a/tests/IllustrativeExamples/Au_fcc/lat7.00/Au_fcc.inpt b/tests/IllustrativeExamples/Au_fcc/lat7.00/Au_fcc.inpt
new file mode 100644
index 00000000..a2d11ef7
--- /dev/null
+++ b/tests/IllustrativeExamples/Au_fcc/lat7.00/Au_fcc.inpt
@@ -0,0 +1,18 @@
+# Test: Au mesh conv #
+CELL: 7.00 7.00 7.00
+FD_GRID: 23 23 23
+BOUNDARY_CONDITION: 2
+KPOINT_GRID: 7 7 7
+EXCHANGE_CORRELATION: LDA_PZ
+ELEC_TEMP_TYPE: fd
+SMEARING: 0.001
+TOL_SCF: 1e-6
+NSTATES: 50
+PRINT_FORCES: 1
+PRINT_ATOMS: 1
+
+CALC_STRESS: 1
+
+MIXING_VARIABLE: potential
+
+
diff --git a/tests/IllustrativeExamples/Au_fcc/lat7.00/Au_fcc.ion b/tests/IllustrativeExamples/Au_fcc/lat7.00/Au_fcc.ion
new file mode 100644
index 00000000..9f81ce27
--- /dev/null
+++ b/tests/IllustrativeExamples/Au_fcc/lat7.00/Au_fcc.ion
@@ -0,0 +1,21 @@
+#=========================
+# format of ion file
+#=========================
+# ATOM_TYPE:
+# N_TYPE_ATOM:
+# COORD:
+#
+# ...
+# RELAX:
+#
+# ...
+
+ATOM_TYPE: Au # atom type followed with valence charge
+PSEUDO_POT: ../psp/Au.psp8 # pseudopotential file
+N_TYPE_ATOM: 4 # number of atoms of this type
+COORD_FRAC: # coordinates follows
+0.0 0.0 0.0
+0.0 0.5 0.5
+0.5 0.0 0.5
+0.5 0.5 0.0
+
diff --git a/tests/IllustrativeExamples/Au_fcc/lat7.00/Au_fcc.refout b/tests/IllustrativeExamples/Au_fcc/lat7.00/Au_fcc.refout
new file mode 100644
index 00000000..17b3dde1
--- /dev/null
+++ b/tests/IllustrativeExamples/Au_fcc/lat7.00/Au_fcc.refout
@@ -0,0 +1,99 @@
+***************************************************************************
+* M-SPARC (Dec 15, 2019) *
+* Copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech *
+* Distributed under GNU General Public License 3 (GPL) *
+* Date: 16-Dec-2019 Start time: 21:31:47 *
+***************************************************************************
+ Input parameters
+***************************************************************************
+CELL: 7.000000 7.000000 7.000000
+FD_GRID: 23 23 23
+FD_ORDER: 12
+BOUNDARY_CONDITION: 2
+KPOINT_GRID: 7 7 7
+KPOINT_SHIFT: 0 0 0
+ELEC_TEMP_TYPE: fermi-dirac
+SMEARING: 0.001000000
+CHEB_DEGREE: 25
+NSTATES: 50
+EXCHANGE_CORRELATION: LDA_PZ
+CALC_STRESS: 1
+MAXIT_SCF: 100
+TOL_SCF: 1.00E-06
+TOL_POISSON: 1.00E-08
+TOL_LANCZOS: 1.00E-02
+TOL_PSEUDOCHARGE: 1.00E-08
+MIXING_VARIABLE: potential
+MIXING_PRECOND: none
+MIXING_PARAMETER: 0.30
+MIXING_HISTORY: 7
+PULAY_FREQUENCY: 1
+PULAY_RESTART_FREQ: 0
+REFERENCE_CUTOFF: 0.50
+RHO_TRIGGER: 4
+FIX_RAND: 0
+PRINT_FORCES: 1
+PRINT_ATOMS: 1
+PRINT_EIGEN: 0
+PRINT_DENSITY: 0
+OUTPUT_FILE: lat7.00/Au_fcc.out
+***************************************************************************
+ Initialization
+***************************************************************************
+Mesh spacing : 0.304348 (Bohr)
+Number of symmetry adapted k-points: 172
+Output printed to : lat7.00/Au_fcc.out
+Total number of atom types : 1
+Total number of atoms : 4
+Total number of electrons : 76
+Atom type 1 (valence electrons) : Au 19
+Pseudopotential : ../psp/Au.psp8
+lloc : 4
+Pseudocharge radii of atom type 1 : 7.30 7.30 7.30
+Number of atoms of type 1 : 4
+Estimated total memory usage : 6.27 GB
+=====================================================================
+ Self Consistent Field (SCF#1)
+=====================================================================
+Iteration Free Energy (Ha/atom) SCF Error Timing (sec)
+1 -1.3744169165E+02 7.176E-04 179.318
+2 -1.3744173846E+02 4.767E-04 64.553
+3 -1.3744174151E+02 6.526E-05 65.781
+4 -1.3744174147E+02 3.492E-05 63.900
+5 -1.3744174155E+02 1.187E-05 64.688
+6 -1.3744174151E+02 3.475E-06 63.098
+7 -1.3744174153E+02 4.487E-07 65.098
+Total number of SCF: 7
+====================================================================
+ Energy
+====================================================================
+Free energy per atom : -1.3744174153E+02 (Ha/atom)
+Total free energy : -5.4976696612E+02 (Ha)
+Band structure energy : -3.7331078687E+01 (Ha)
+Exchange correlation energy : -5.0952838353E+01 (Ha)
+Self and correction energy : -7.6153585680E+02 (Ha)
+Entropy*kb*T : -1.4833224536E-04 (Ha)
+Fermi level : 7.3216795727E-01 (Ha)
+Average force : 1.0605678341E-06 (Ha/Bohr)
+Maximum force : 1.1616552180E-06 (Ha/Bohr)
+Time for force calculation : 27.542 (sec)
+Stress (GPa):
+ -107.3204551503 -0.0000286738 0.0001404321
+ -0.0000286736 -107.3204487083 0.0000878054
+ 0.0001404320 0.0000878050 -107.3204182234
+Pressure : 1.0732044069E+02 (GPa)
+Maximum stress : 1.0732045515E+02 (GPa)
+Time for stress calculation : 69.676 (sec)
+***************************************************************************
+ Timing info
+***************************************************************************
+Total walltime : 770.574 sec
+___________________________________________________________________________
+
+***************************************************************************
+* Material Physics & Mechanics Group, Georgia Tech *
+* PI: Phanish Suryanarayana *
+* Main Developers: Qimen Xu, Abhiraj Sharma *
+* Acknowledgements: U.S. DOE (DE-SC0019410); NSF (1333500,1553212) *
+***************************************************************************
+
diff --git a/tests/IllustrativeExamples/Au_fcc/lat7.00/Au_fcc.refstatic b/tests/IllustrativeExamples/Au_fcc/lat7.00/Au_fcc.refstatic
new file mode 100644
index 00000000..99a53737
--- /dev/null
+++ b/tests/IllustrativeExamples/Au_fcc/lat7.00/Au_fcc.refstatic
@@ -0,0 +1,13 @@
+***************************************************************************
+ Atom positions
+***************************************************************************
+Fractional coordinates of atoms:
+ 0.0000000000 0.0000000000 0.0000000000
+ 0.0000000000 0.5000000000 0.5000000000
+ 0.5000000000 0.0000000000 0.5000000000
+ 0.5000000000 0.5000000000 0.0000000000
+Atomic forces (Ha/Bohr):
+ 0.0000007357 -0.0000005415 -0.0000007177
+ 0.0000005544 0.0000003374 0.0000007789
+ -0.0000007219 0.0000002126 0.0000007590
+ -0.0000005682 -0.0000000085 -0.0000008203
diff --git a/tests/IllustrativeExamples/Au_fcc/lat7.05/Au_fcc.inpt b/tests/IllustrativeExamples/Au_fcc/lat7.05/Au_fcc.inpt
new file mode 100644
index 00000000..aa3e4480
--- /dev/null
+++ b/tests/IllustrativeExamples/Au_fcc/lat7.05/Au_fcc.inpt
@@ -0,0 +1,18 @@
+# Test: Au mesh conv #
+CELL: 7.05 7.05 7.05
+FD_GRID: 24 24 24
+BOUNDARY_CONDITION: 2
+KPOINT_GRID: 7 7 7
+EXCHANGE_CORRELATION: LDA_PZ
+ELEC_TEMP_TYPE: fd
+SMEARING: 0.001
+TOL_SCF: 1e-6
+NSTATES: 50
+PRINT_FORCES: 1
+PRINT_ATOMS: 1
+
+CALC_STRESS: 1
+
+MIXING_VARIABLE: potential
+
+
diff --git a/tests/IllustrativeExamples/Au_fcc/lat7.05/Au_fcc.ion b/tests/IllustrativeExamples/Au_fcc/lat7.05/Au_fcc.ion
new file mode 100644
index 00000000..9f81ce27
--- /dev/null
+++ b/tests/IllustrativeExamples/Au_fcc/lat7.05/Au_fcc.ion
@@ -0,0 +1,21 @@
+#=========================
+# format of ion file
+#=========================
+# ATOM_TYPE:
+# N_TYPE_ATOM:
+# COORD:
+#
+# ...
+# RELAX:
+#
+# ...
+
+ATOM_TYPE: Au # atom type followed with valence charge
+PSEUDO_POT: ../psp/Au.psp8 # pseudopotential file
+N_TYPE_ATOM: 4 # number of atoms of this type
+COORD_FRAC: # coordinates follows
+0.0 0.0 0.0
+0.0 0.5 0.5
+0.5 0.0 0.5
+0.5 0.5 0.0
+
diff --git a/tests/IllustrativeExamples/Au_fcc/lat7.05/Au_fcc.refout b/tests/IllustrativeExamples/Au_fcc/lat7.05/Au_fcc.refout
new file mode 100644
index 00000000..1df3250f
--- /dev/null
+++ b/tests/IllustrativeExamples/Au_fcc/lat7.05/Au_fcc.refout
@@ -0,0 +1,99 @@
+***************************************************************************
+* M-SPARC (Dec 15, 2019) *
+* Copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech *
+* Distributed under GNU General Public License 3 (GPL) *
+* Date: 16-Dec-2019 Start time: 21:44:36 *
+***************************************************************************
+ Input parameters
+***************************************************************************
+CELL: 7.050000 7.050000 7.050000
+FD_GRID: 24 24 24
+FD_ORDER: 12
+BOUNDARY_CONDITION: 2
+KPOINT_GRID: 7 7 7
+KPOINT_SHIFT: 0 0 0
+ELEC_TEMP_TYPE: fermi-dirac
+SMEARING: 0.001000000
+CHEB_DEGREE: 26
+NSTATES: 50
+EXCHANGE_CORRELATION: LDA_PZ
+CALC_STRESS: 1
+MAXIT_SCF: 100
+TOL_SCF: 1.00E-06
+TOL_POISSON: 1.00E-08
+TOL_LANCZOS: 1.00E-02
+TOL_PSEUDOCHARGE: 1.00E-08
+MIXING_VARIABLE: potential
+MIXING_PRECOND: none
+MIXING_PARAMETER: 0.30
+MIXING_HISTORY: 7
+PULAY_FREQUENCY: 1
+PULAY_RESTART_FREQ: 0
+REFERENCE_CUTOFF: 0.50
+RHO_TRIGGER: 4
+FIX_RAND: 0
+PRINT_FORCES: 1
+PRINT_ATOMS: 1
+PRINT_EIGEN: 0
+PRINT_DENSITY: 0
+OUTPUT_FILE: lat7.05/Au_fcc.out
+***************************************************************************
+ Initialization
+***************************************************************************
+Mesh spacing : 0.293750 (Bohr)
+Number of symmetry adapted k-points: 172
+Output printed to : lat7.05/Au_fcc.out
+Total number of atom types : 1
+Total number of atoms : 4
+Total number of electrons : 76
+Atom type 1 (valence electrons) : Au 19
+Pseudopotential : ../psp/Au.psp8
+lloc : 4
+Pseudocharge radii of atom type 1 : 7.05 7.05 7.05
+Number of atoms of type 1 : 4
+Estimated total memory usage : 7.12 GB
+=====================================================================
+ Self Consistent Field (SCF#1)
+=====================================================================
+Iteration Free Energy (Ha/atom) SCF Error Timing (sec)
+1 -1.3744795255E+02 7.435E-04 209.576
+2 -1.3744800484E+02 4.923E-04 76.299
+3 -1.3744800825E+02 5.970E-05 75.178
+4 -1.3744800815E+02 3.528E-05 76.643
+5 -1.3744800828E+02 8.578E-06 74.443
+6 -1.3744800818E+02 1.926E-06 75.364
+7 -1.3744800826E+02 5.828E-07 74.924
+Total number of SCF: 7
+====================================================================
+ Energy
+====================================================================
+Free energy per atom : -1.3744800826E+02 (Ha/atom)
+Total free energy : -5.4979203303E+02 (Ha)
+Band structure energy : -3.8584206633E+01 (Ha)
+Exchange correlation energy : -5.0888138122E+01 (Ha)
+Self and correction energy : -7.6153604567E+02 (Ha)
+Entropy*kb*T : -1.5178020900E-04 (Ha)
+Fermi level : 7.0957535096E-01 (Ha)
+Average force : 2.2427370442E-06 (Ha/Bohr)
+Maximum force : 2.6468277801E-06 (Ha/Bohr)
+Time for force calculation : 31.715 (sec)
+Stress (GPa):
+ -93.2419961810 -0.0000202407 0.0000076354
+ -0.0000202410 -93.2419490605 0.0000004697
+ 0.0000076352 0.0000004699 -93.2419840758
+Pressure : 9.3241976439E+01 (GPa)
+Maximum stress : 9.3241996181E+01 (GPa)
+Time for stress calculation : 80.195 (sec)
+***************************************************************************
+ Timing info
+***************************************************************************
+Total walltime : 869.810 sec
+___________________________________________________________________________
+
+***************************************************************************
+* Material Physics & Mechanics Group, Georgia Tech *
+* PI: Phanish Suryanarayana *
+* Main Developers: Qimen Xu, Abhiraj Sharma *
+* Acknowledgements: U.S. DOE (DE-SC0019410); NSF (1333500,1553212) *
+***************************************************************************
+
diff --git a/tests/IllustrativeExamples/Au_fcc/lat7.05/Au_fcc.refstatic b/tests/IllustrativeExamples/Au_fcc/lat7.05/Au_fcc.refstatic
new file mode 100644
index 00000000..40f8c1ee
--- /dev/null
+++ b/tests/IllustrativeExamples/Au_fcc/lat7.05/Au_fcc.refstatic
@@ -0,0 +1,13 @@
+***************************************************************************
+ Atom positions
+***************************************************************************
+Fractional coordinates of atoms:
+ 0.0000000000 0.0000000000 0.0000000000
+ 0.0000000000 0.5000000000 0.5000000000
+ 0.5000000000 0.0000000000 0.5000000000
+ 0.5000000000 0.5000000000 0.0000000000
+Atomic forces (Ha/Bohr):
+ 0.0000023610 -0.0000010133 -0.0000003281
+ -0.0000022718 -0.0000012216 -0.0000005935
+ -0.0000006158 0.0000014187 -0.0000008121
+ 0.0000005267 0.0000008162 0.0000017337
diff --git a/tests/IllustrativeExamples/Au_fcc/lat7.10/Au_fcc.inpt b/tests/IllustrativeExamples/Au_fcc/lat7.10/Au_fcc.inpt
new file mode 100644
index 00000000..c0233010
--- /dev/null
+++ b/tests/IllustrativeExamples/Au_fcc/lat7.10/Au_fcc.inpt
@@ -0,0 +1,18 @@
+# Test: Au mesh conv #
+CELL: 7.10 7.10 7.10
+FD_GRID: 24 24 24
+BOUNDARY_CONDITION: 2
+KPOINT_GRID: 7 7 7
+EXCHANGE_CORRELATION: LDA_PZ
+ELEC_TEMP_TYPE: fd
+SMEARING: 0.001
+TOL_SCF: 1e-6
+NSTATES: 50
+PRINT_FORCES: 1
+PRINT_ATOMS: 1
+
+CALC_STRESS: 1
+
+MIXING_VARIABLE: potential
+
+
diff --git a/tests/IllustrativeExamples/Au_fcc/lat7.10/Au_fcc.ion b/tests/IllustrativeExamples/Au_fcc/lat7.10/Au_fcc.ion
new file mode 100644
index 00000000..9f81ce27
--- /dev/null
+++ b/tests/IllustrativeExamples/Au_fcc/lat7.10/Au_fcc.ion
@@ -0,0 +1,21 @@
+#=========================
+# format of ion file
+#=========================
+# ATOM_TYPE:
+# N_TYPE_ATOM:
+# COORD:
+#
+# ...
+# RELAX:
+#
+# ...
+
+ATOM_TYPE: Au # atom type followed with valence charge
+PSEUDO_POT: ../psp/Au.psp8 # pseudopotential file
+N_TYPE_ATOM: 4 # number of atoms of this type
+COORD_FRAC: # coordinates follows
+0.0 0.0 0.0
+0.0 0.5 0.5
+0.5 0.0 0.5
+0.5 0.5 0.0
+
diff --git a/tests/IllustrativeExamples/Au_fcc/lat7.10/Au_fcc.refout b/tests/IllustrativeExamples/Au_fcc/lat7.10/Au_fcc.refout
new file mode 100644
index 00000000..b43db88f
--- /dev/null
+++ b/tests/IllustrativeExamples/Au_fcc/lat7.10/Au_fcc.refout
@@ -0,0 +1,99 @@
+***************************************************************************
+* M-SPARC (Dec 15, 2019) *
+* Copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech *
+* Distributed under GNU General Public License 3 (GPL) *
+* Date: 16-Dec-2019 Start time: 21:59:06 *
+***************************************************************************
+ Input parameters
+***************************************************************************
+CELL: 7.100000 7.100000 7.100000
+FD_GRID: 24 24 24
+FD_ORDER: 12
+BOUNDARY_CONDITION: 2
+KPOINT_GRID: 7 7 7
+KPOINT_SHIFT: 0 0 0
+ELEC_TEMP_TYPE: fermi-dirac
+SMEARING: 0.001000000
+CHEB_DEGREE: 26
+NSTATES: 50
+EXCHANGE_CORRELATION: LDA_PZ
+CALC_STRESS: 1
+MAXIT_SCF: 100
+TOL_SCF: 1.00E-06
+TOL_POISSON: 1.00E-08
+TOL_LANCZOS: 1.00E-02
+TOL_PSEUDOCHARGE: 1.00E-08
+MIXING_VARIABLE: potential
+MIXING_PRECOND: none
+MIXING_PARAMETER: 0.30
+MIXING_HISTORY: 7
+PULAY_FREQUENCY: 1
+PULAY_RESTART_FREQ: 0
+REFERENCE_CUTOFF: 0.50
+RHO_TRIGGER: 4
+FIX_RAND: 0
+PRINT_FORCES: 1
+PRINT_ATOMS: 1
+PRINT_EIGEN: 0
+PRINT_DENSITY: 0
+OUTPUT_FILE: lat7.10/Au_fcc.out
+***************************************************************************
+ Initialization
+***************************************************************************
+Mesh spacing : 0.295833 (Bohr)
+Number of symmetry adapted k-points: 172
+Output printed to : lat7.10/Au_fcc.out
+Total number of atom types : 1
+Total number of atoms : 4
+Total number of electrons : 76
+Atom type 1 (valence electrons) : Au 19
+Pseudopotential : ../psp/Au.psp8
+lloc : 4
+Pseudocharge radii of atom type 1 : 7.10 7.10 7.10
+Number of atoms of type 1 : 4
+Estimated total memory usage : 7.12 GB
+=====================================================================
+ Self Consistent Field (SCF#1)
+=====================================================================
+Iteration Free Energy (Ha/atom) SCF Error Timing (sec)
+1 -1.3745347815E+02 7.799E-04 206.505
+2 -1.3745352940E+02 5.093E-04 75.042
+3 -1.3745353315E+02 6.789E-05 74.572
+4 -1.3745353316E+02 3.594E-05 75.424
+5 -1.3745353322E+02 1.703E-05 75.387
+6 -1.3745353317E+02 3.464E-06 75.712
+7 -1.3745353320E+02 5.705E-07 73.929
+Total number of SCF: 7
+====================================================================
+ Energy
+====================================================================
+Free energy per atom : -1.3745353320E+02 (Ha/atom)
+Total free energy : -5.4981413278E+02 (Ha)
+Band structure energy : -3.9807191484E+01 (Ha)
+Exchange correlation energy : -5.0825650726E+01 (Ha)
+Self and correction energy : -7.6153591300E+02 (Ha)
+Entropy*kb*T : -1.4265745033E-04 (Ha)
+Fermi level : 6.8751029676E-01 (Ha)
+Average force : 3.0488342405E-06 (Ha/Bohr)
+Maximum force : 3.4298313012E-06 (Ha/Bohr)
+Time for force calculation : 31.385 (sec)
+Stress (GPa):
+ -80.3333137565 -0.0000231674 0.0000060263
+ -0.0000231675 -80.3332741261 -0.0000043938
+ 0.0000060263 -0.0000043938 -80.3333032073
+Pressure : 8.0333297030E+01 (GPa)
+Maximum stress : 8.0333313756E+01 (GPa)
+Time for stress calculation : 77.162 (sec)
+***************************************************************************
+ Timing info
+***************************************************************************
+Total walltime : 858.758 sec
+___________________________________________________________________________
+
+***************************************************************************
+* Material Physics & Mechanics Group, Georgia Tech *
+* PI: Phanish Suryanarayana *
+* Main Developers: Qimen Xu, Abhiraj Sharma *
+* Acknowledgements: U.S. DOE (DE-SC0019410); NSF (1333500,1553212) *
+***************************************************************************
+
diff --git a/tests/IllustrativeExamples/Au_fcc/lat7.10/Au_fcc.refstatic b/tests/IllustrativeExamples/Au_fcc/lat7.10/Au_fcc.refstatic
new file mode 100644
index 00000000..4e1377d8
--- /dev/null
+++ b/tests/IllustrativeExamples/Au_fcc/lat7.10/Au_fcc.refstatic
@@ -0,0 +1,13 @@
+***************************************************************************
+ Atom positions
+***************************************************************************
+Fractional coordinates of atoms:
+ 0.0000000000 0.0000000000 0.0000000000
+ 0.0000000000 0.5000000000 0.5000000000
+ 0.5000000000 0.0000000000 0.5000000000
+ 0.5000000000 0.5000000000 0.0000000000
+Atomic forces (Ha/Bohr):
+ 0.0000009066 0.0000004205 0.0000021940
+ -0.0000016269 -0.0000016651 -0.0000025188
+ 0.0000001361 0.0000017742 -0.0000026973
+ 0.0000005842 -0.0000005295 0.0000030221
diff --git a/tests/IllustrativeExamples/Au_fcc/lat7.15/Au_fcc.inpt b/tests/IllustrativeExamples/Au_fcc/lat7.15/Au_fcc.inpt
new file mode 100644
index 00000000..ac0649e3
--- /dev/null
+++ b/tests/IllustrativeExamples/Au_fcc/lat7.15/Au_fcc.inpt
@@ -0,0 +1,18 @@
+# Test: Au mesh conv #
+CELL: 7.15 7.15 7.15
+FD_GRID: 24 24 24
+BOUNDARY_CONDITION: 2
+KPOINT_GRID: 7 7 7
+EXCHANGE_CORRELATION: LDA_PZ
+ELEC_TEMP_TYPE: fd
+SMEARING: 0.001
+TOL_SCF: 1e-6
+NSTATES: 50
+PRINT_FORCES: 1
+PRINT_ATOMS: 1
+
+CALC_STRESS: 1
+
+MIXING_VARIABLE: potential
+
+
diff --git a/tests/IllustrativeExamples/Au_fcc/lat7.15/Au_fcc.ion b/tests/IllustrativeExamples/Au_fcc/lat7.15/Au_fcc.ion
new file mode 100644
index 00000000..9f81ce27
--- /dev/null
+++ b/tests/IllustrativeExamples/Au_fcc/lat7.15/Au_fcc.ion
@@ -0,0 +1,21 @@
+#=========================
+# format of ion file
+#=========================
+# ATOM_TYPE:
+# N_TYPE_ATOM:
+# COORD:
+#
+# ...
+# RELAX:
+#
+# ...
+
+ATOM_TYPE: Au # atom type followed with valence charge
+PSEUDO_POT: ../psp/Au.psp8 # pseudopotential file
+N_TYPE_ATOM: 4 # number of atoms of this type
+COORD_FRAC: # coordinates follows
+0.0 0.0 0.0
+0.0 0.5 0.5
+0.5 0.0 0.5
+0.5 0.5 0.0
+
diff --git a/tests/IllustrativeExamples/Au_fcc/lat7.15/Au_fcc.refout b/tests/IllustrativeExamples/Au_fcc/lat7.15/Au_fcc.refout
new file mode 100644
index 00000000..3f344873
--- /dev/null
+++ b/tests/IllustrativeExamples/Au_fcc/lat7.15/Au_fcc.refout
@@ -0,0 +1,99 @@
+***************************************************************************
+* M-SPARC (Dec 15, 2019) *
+* Copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech *
+* Distributed under GNU General Public License 3 (GPL) *
+* Date: 16-Dec-2019 Start time: 22:13:25 *
+***************************************************************************
+ Input parameters
+***************************************************************************
+CELL: 7.150000 7.150000 7.150000
+FD_GRID: 24 24 24
+FD_ORDER: 12
+BOUNDARY_CONDITION: 2
+KPOINT_GRID: 7 7 7
+KPOINT_SHIFT: 0 0 0
+ELEC_TEMP_TYPE: fermi-dirac
+SMEARING: 0.001000000
+CHEB_DEGREE: 26
+NSTATES: 50
+EXCHANGE_CORRELATION: LDA_PZ
+CALC_STRESS: 1
+MAXIT_SCF: 100
+TOL_SCF: 1.00E-06
+TOL_POISSON: 1.00E-08
+TOL_LANCZOS: 1.00E-02
+TOL_PSEUDOCHARGE: 1.00E-08
+MIXING_VARIABLE: potential
+MIXING_PRECOND: none
+MIXING_PARAMETER: 0.30
+MIXING_HISTORY: 7
+PULAY_FREQUENCY: 1
+PULAY_RESTART_FREQ: 0
+REFERENCE_CUTOFF: 0.50
+RHO_TRIGGER: 4
+FIX_RAND: 0
+PRINT_FORCES: 1
+PRINT_ATOMS: 1
+PRINT_EIGEN: 0
+PRINT_DENSITY: 0
+OUTPUT_FILE: lat7.15/Au_fcc.out
+***************************************************************************
+ Initialization
+***************************************************************************
+Mesh spacing : 0.297917 (Bohr)
+Number of symmetry adapted k-points: 172
+Output printed to : lat7.15/Au_fcc.out
+Total number of atom types : 1
+Total number of atoms : 4
+Total number of electrons : 76
+Atom type 1 (valence electrons) : Au 19
+Pseudopotential : ../psp/Au.psp8
+lloc : 4
+Pseudocharge radii of atom type 1 : 6.85 6.85 6.85
+Number of atoms of type 1 : 4
+Estimated total memory usage : 7.12 GB
+=====================================================================
+ Self Consistent Field (SCF#1)
+=====================================================================
+Iteration Free Energy (Ha/atom) SCF Error Timing (sec)
+1 -1.3745831011E+02 8.185E-04 205.754
+2 -1.3745836059E+02 5.266E-04 74.054
+3 -1.3745836454E+02 8.622E-05 74.726
+4 -1.3745836469E+02 3.953E-05 73.811
+5 -1.3745836468E+02 1.909E-05 74.574
+6 -1.3745836468E+02 4.134E-06 74.658
+7 -1.3745836472E+02 5.965E-07 75.452
+Total number of SCF: 7
+====================================================================
+ Energy
+====================================================================
+Free energy per atom : -1.3745836472E+02 (Ha/atom)
+Total free energy : -5.4983345888E+02 (Ha)
+Band structure energy : -4.1001687484E+01 (Ha)
+Exchange correlation energy : -5.0765293474E+01 (Ha)
+Self and correction energy : -7.6153576930E+02 (Ha)
+Entropy*kb*T : -1.4662020080E-04 (Ha)
+Fermi level : 6.6596064451E-01 (Ha)
+Average force : 2.9745828529E-06 (Ha/Bohr)
+Maximum force : 3.4763905566E-06 (Ha/Bohr)
+Time for force calculation : 30.189 (sec)
+Stress (GPa):
+ -68.5764947856 -0.0000245961 0.0000109451
+ -0.0000245962 -68.5764564356 -0.0000087772
+ 0.0000109450 -0.0000087775 -68.5764839822
+Pressure : 6.8576478401E+01 (GPa)
+Maximum stress : 6.8576494786E+01 (GPa)
+Time for stress calculation : 77.045 (sec)
+***************************************************************************
+ Timing info
+***************************************************************************
+Total walltime : 853.195 sec
+___________________________________________________________________________
+
+***************************************************************************
+* Material Physics & Mechanics Group, Georgia Tech *
+* PI: Phanish Suryanarayana *
+* Main Developers: Qimen Xu, Abhiraj Sharma *
+* Acknowledgements: U.S. DOE (DE-SC0019410); NSF (1333500,1553212) *
+***************************************************************************
+
diff --git a/tests/IllustrativeExamples/Au_fcc/lat7.15/Au_fcc.refstatic b/tests/IllustrativeExamples/Au_fcc/lat7.15/Au_fcc.refstatic
new file mode 100644
index 00000000..ed82e272
--- /dev/null
+++ b/tests/IllustrativeExamples/Au_fcc/lat7.15/Au_fcc.refstatic
@@ -0,0 +1,13 @@
+***************************************************************************
+ Atom positions
+***************************************************************************
+Fractional coordinates of atoms:
+ 0.0000000000 0.0000000000 0.0000000000
+ 0.0000000000 0.5000000000 0.5000000000
+ 0.5000000000 0.0000000000 0.5000000000
+ 0.5000000000 0.5000000000 0.0000000000
+Atomic forces (Ha/Bohr):
+ 0.0000005519 0.0000010201 0.0000020217
+ -0.0000017591 -0.0000021310 -0.0000021094
+ 0.0000004863 0.0000021835 -0.0000024042
+ 0.0000007209 -0.0000010726 0.0000024919
diff --git a/tests/IllustrativeExamples/Au_fcc/lat7.20/Au_fcc.inpt b/tests/IllustrativeExamples/Au_fcc/lat7.20/Au_fcc.inpt
new file mode 100644
index 00000000..166e5d75
--- /dev/null
+++ b/tests/IllustrativeExamples/Au_fcc/lat7.20/Au_fcc.inpt
@@ -0,0 +1,18 @@
+# Test: Au mesh conv #
+CELL: 7.20 7.20 7.20
+FD_GRID: 24 24 24
+BOUNDARY_CONDITION: 2
+KPOINT_GRID: 7 7 7
+EXCHANGE_CORRELATION: LDA_PZ
+ELEC_TEMP_TYPE: fd
+SMEARING: 0.001
+TOL_SCF: 1e-6
+NSTATES: 50
+PRINT_FORCES: 1
+PRINT_ATOMS: 1
+
+CALC_STRESS: 1
+
+MIXING_VARIABLE: potential
+
+
diff --git a/tests/IllustrativeExamples/Au_fcc/lat7.20/Au_fcc.ion b/tests/IllustrativeExamples/Au_fcc/lat7.20/Au_fcc.ion
new file mode 100644
index 00000000..9f81ce27
--- /dev/null
+++ b/tests/IllustrativeExamples/Au_fcc/lat7.20/Au_fcc.ion
@@ -0,0 +1,21 @@
+#=========================
+# format of ion file
+#=========================
+# ATOM_TYPE:
+# N_TYPE_ATOM:
+# COORD:
+#
+# ...
+# RELAX:
+#
+# ...
+
+ATOM_TYPE: Au # atom type followed with valence charge
+PSEUDO_POT: ../psp/Au.psp8 # pseudopotential file
+N_TYPE_ATOM: 4 # number of atoms of this type
+COORD_FRAC: # coordinates follows
+0.0 0.0 0.0
+0.0 0.5 0.5
+0.5 0.0 0.5
+0.5 0.5 0.0
+
diff --git a/tests/IllustrativeExamples/Au_fcc/lat7.20/Au_fcc.refout b/tests/IllustrativeExamples/Au_fcc/lat7.20/Au_fcc.refout
new file mode 100644
index 00000000..c6bcf2a2
--- /dev/null
+++ b/tests/IllustrativeExamples/Au_fcc/lat7.20/Au_fcc.refout
@@ -0,0 +1,99 @@
+***************************************************************************
+* M-SPARC (Dec 15, 2019) *
+* Copyright (c) 2019 Material Physics & Mechanics Group, Georgia Tech *
+* Distributed under GNU General Public License 3 (GPL) *
+* Date: 16-Dec-2019 Start time: 22:27:38 *
+***************************************************************************
+ Input parameters
+***************************************************************************
+CELL: 7.200000 7.200000 7.200000
+FD_GRID: 24 24 24
+FD_ORDER: 12
+BOUNDARY_CONDITION: 2
+KPOINT_GRID: 7 7 7
+KPOINT_SHIFT: 0 0 0
+ELEC_TEMP_TYPE: fermi-dirac
+SMEARING: 0.001000000
+CHEB_DEGREE: 25
+NSTATES: 50
+EXCHANGE_CORRELATION: LDA_PZ
+CALC_STRESS: 1
+MAXIT_SCF: 100
+TOL_SCF: 1.00E-06
+TOL_POISSON: 1.00E-08
+TOL_LANCZOS: 1.00E-02
+TOL_PSEUDOCHARGE: 1.00E-08
+MIXING_VARIABLE: potential
+MIXING_PRECOND: none
+MIXING_PARAMETER: 0.30
+MIXING_HISTORY: 7
+PULAY_FREQUENCY: 1
+PULAY_RESTART_FREQ: 0
+REFERENCE_CUTOFF: 0.50
+RHO_TRIGGER: 4
+FIX_RAND: 0
+PRINT_FORCES: 1
+PRINT_ATOMS: 1
+PRINT_EIGEN: 0
+PRINT_DENSITY: 0
+OUTPUT_FILE: lat7.20/Au_fcc.out
+***************************************************************************
+ Initialization
+***************************************************************************
+Mesh spacing : 0.300000 (Bohr)
+Number of symmetry adapted k-points: 172
+Output printed to : lat7.20/Au_fcc.out
+Total number of atom types : 1
+Total number of atoms : 4
+Total number of electrons : 76
+Atom type 1 (valence electrons) : Au 19
+Pseudopotential : ../psp/Au.psp8
+lloc : 4
+Pseudocharge radii of atom type 1 : 7.50 7.50 7.50
+Number of atoms of type 1 : 4
+Estimated total memory usage : 7.12 GB
+=====================================================================
+ Self Consistent Field (SCF#1)
+=====================================================================
+Iteration Free Energy (Ha/atom) SCF Error Timing (sec)
+1 -1.3746243029E+02 8.489E-04 200.723
+2 -1.3746251427E+02 5.439E-04 73.911
+3 -1.3746251881E+02 9.760E-05 73.387
+4 -1.3746251897E+02 4.477E-05 73.352
+5 -1.3746251898E+02 2.084E-05 71.857
+6 -1.3746251896E+02 5.380E-06 72.457
+7 -1.3746251901E+02 7.096E-07 71.629
+Total number of SCF: 7
+====================================================================
+ Energy
+====================================================================
+Free energy per atom : -1.3746251901E+02 (Ha/atom)
+Total free energy : -5.4985007605E+02 (Ha)
+Band structure energy : -4.2164832997E+01 (Ha)
+Exchange correlation energy : -5.0707465873E+01 (Ha)
+Self and correction energy : -7.6153561006E+02 (Ha)
+Entropy*kb*T : -1.5196852417E-04 (Ha)
+Fermi level : 6.4505087859E-01 (Ha)
+Average force : 4.3315044058E-06 (Ha/Bohr)
+Maximum force : 5.4514202775E-06 (Ha/Bohr)
+Time for force calculation : 31.339 (sec)
+Stress (GPa):
+ -57.9297884621 -0.0000216991 0.0000276696
+ -0.0000216994 -57.9297311365 -0.0000022295
+ 0.0000276695 -0.0000022299 -57.9297741568
+Pressure : 5.7929764585E+01 (GPa)
+Maximum stress : 5.7929788462E+01 (GPa)
+Time for stress calculation : 76.863 (sec)
+***************************************************************************
+ Timing info
+***************************************************************************
+Total walltime : 837.163 sec
+___________________________________________________________________________
+
+***************************************************************************
+* Material Physics & Mechanics Group, Georgia Tech *
+* PI: Phanish Suryanarayana *
+* Main Developers: Qimen Xu, Abhiraj Sharma *
+* Acknowledgements: U.S. DOE (DE-SC0019410); NSF (1333500,1553212) *
+***************************************************************************
+
diff --git a/tests/IllustrativeExamples/Au_fcc/lat7.20/Au_fcc.refstatic b/tests/IllustrativeExamples/Au_fcc/lat7.20/Au_fcc.refstatic
new file mode 100644
index 00000000..b8f59fe6
--- /dev/null
+++ b/tests/IllustrativeExamples/Au_fcc/lat7.20/Au_fcc.refstatic
@@ -0,0 +1,13 @@
+***************************************************************************
+ Atom positions
+***************************************************************************
+Fractional coordinates of atoms:
+ 0.0000000000 0.0000000000 0.0000000000
+ 0.0000000000 0.5000000000 0.5000000000
+ 0.5000000000 0.0000000000 0.5000000000
+ 0.5000000000 0.5000000000 0.0000000000
+Atomic forces (Ha/Bohr):
+ -0.0000005381 0.0000021727 0.0000020716
+ -0.0000037355 -0.0000035935 -0.0000016883
+ 0.0000020332 0.0000036175 -0.0000026769
+ 0.0000022404 -0.0000021966 0.0000022937
diff --git a/tests/IllustrativeExamples/Au_fcc/lat7.25/Au_fcc.inpt b/tests/IllustrativeExamples/Au_fcc/lat7.25/Au_fcc.inpt
new file mode 100644
index 00000000..03b54f78
--- /dev/null
+++ b/tests/IllustrativeExamples/Au_fcc/lat7.25/Au_fcc.inpt
@@ -0,0 +1,18 @@
+# Test: Au mesh conv #
+CELL: 7.25 7.25 7.25
+FD_GRID: 24 24 24
+BOUNDARY_CONDITION: 2
+KPOINT_GRID: 7 7 7
+EXCHANGE_CORRELATION: LDA_PZ
+ELEC_TEMP_TYPE: fd
+SMEARING: 0.001
+TOL_SCF: 1e-6
+NSTATES: 50
+PRINT_FORCES: 1
+PRINT_ATOMS: 1
+
+CALC_STRESS: 1
+
+MIXING_VARIABLE: potential
+
+
diff --git a/tests/IllustrativeExamples/Au_fcc/lat7.25/Au_fcc.ion b/tests/IllustrativeExamples/Au_fcc/lat7.25/Au_fcc.ion
new file mode 100644
index 00000000..9f81ce27
--- /dev/null
+++ b/tests/IllustrativeExamples/Au_fcc/lat7.25/Au_fcc.ion
@@ -0,0 +1,21 @@
+#=========================
+# format of ion file
+#=========================
+# ATOM_TYPE:
+# N_TYPE_ATOM:
+# COORD:
+#