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cp_ddapc_methods.F
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cp_ddapc_methods.F
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!--------------------------------------------------------------------------------------------------!
! CP2K: A general program to perform molecular dynamics simulations !
! Copyright 2000-2024 CP2K developers group <https://cp2k.org> !
! !
! SPDX-License-Identifier: GPL-2.0-or-later !
!--------------------------------------------------------------------------------------------------!
! **************************************************************************************************
!> \brief contains information regarding the decoupling/recoupling method of Bloechl
!> \author Teodoro Laino
! **************************************************************************************************
MODULE cp_ddapc_methods
USE cell_types, ONLY: cell_type
USE cp_log_handling, ONLY: cp_logger_get_default_io_unit
USE input_constants, ONLY: weight_type_mass,&
weight_type_unit
USE input_section_types, ONLY: section_vals_type,&
section_vals_val_get,&
section_vals_val_set
USE kahan_sum, ONLY: accurate_sum
USE kinds, ONLY: dp
USE mathconstants, ONLY: fourpi,&
oorootpi,&
pi,&
twopi
USE mathlib, ONLY: diamat_all,&
invert_matrix
USE message_passing, ONLY: mp_para_env_type
USE particle_types, ONLY: particle_type
USE pw_spline_utils, ONLY: Eval_Interp_Spl3_pbc
USE pw_types, ONLY: pw_type
USE spherical_harmonics, ONLY: legendre
#include "./base/base_uses.f90"
IMPLICIT NONE
PRIVATE
LOGICAL, PRIVATE, PARAMETER :: debug_this_module = .FALSE.
CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'cp_ddapc_methods'
PUBLIC :: ddapc_eval_gfunc, &
build_b_vector, &
build_der_b_vector, &
build_A_matrix, &
build_der_A_matrix_rows, &
prep_g_dot_rvec_sin_cos, &
cleanup_g_dot_rvec_sin_cos, &
ddapc_eval_AmI, &
ewald_ddapc_pot, &
solvation_ddapc_pot
CONTAINS
! **************************************************************************************************
!> \brief ...
!> \param gfunc ...
!> \param w ...
!> \param gcut ...
!> \param rho_tot_g ...
!> \param radii ...
! **************************************************************************************************
SUBROUTINE ddapc_eval_gfunc(gfunc, w, gcut, rho_tot_g, radii)
REAL(KIND=dp), DIMENSION(:, :), POINTER :: gfunc
REAL(kind=dp), DIMENSION(:), POINTER :: w
REAL(KIND=dp), INTENT(IN) :: gcut
TYPE(pw_type), INTENT(IN) :: rho_tot_g
REAL(kind=dp), DIMENSION(:), POINTER :: radii
CHARACTER(len=*), PARAMETER :: routineN = 'ddapc_eval_gfunc'
INTEGER :: e_dim, handle, ig, igauss, s_dim
REAL(KIND=dp) :: g2, gcut2, rc, rc2
CALL timeset(routineN, handle)
gcut2 = gcut*gcut
!
s_dim = rho_tot_g%pw_grid%first_gne0
e_dim = rho_tot_g%pw_grid%ngpts_cut_local
ALLOCATE (gfunc(s_dim:e_dim, SIZE(radii)))
ALLOCATE (w(s_dim:e_dim))
gfunc = 0.0_dp
w = 0.0_dp
DO igauss = 1, SIZE(radii)
rc = radii(igauss)
rc2 = rc*rc
DO ig = s_dim, e_dim
g2 = rho_tot_g%pw_grid%gsq(ig)
IF (g2 > gcut2) EXIT
gfunc(ig, igauss) = EXP(-g2*rc2/4.0_dp)
END DO
END DO
DO ig = s_dim, e_dim
g2 = rho_tot_g%pw_grid%gsq(ig)
IF (g2 > gcut2) EXIT
w(ig) = fourpi*(g2 - gcut2)**2/(g2*gcut2)
END DO
CALL timestop(handle)
END SUBROUTINE ddapc_eval_gfunc
! **************************************************************************************************
!> \brief Computes the B vector for the solution of the linear system
!> \param bv ...
!> \param gfunc ...
!> \param w ...
!> \param particle_set ...
!> \param radii ...
!> \param rho_tot_g ...
!> \param gcut ...
!> \par History
!> 08.2005 created [tlaino]
!> \author Teodoro Laino
! **************************************************************************************************
SUBROUTINE build_b_vector(bv, gfunc, w, particle_set, radii, rho_tot_g, gcut)
REAL(KIND=dp), DIMENSION(:), INTENT(INOUT) :: bv
REAL(KIND=dp), DIMENSION(:, :), POINTER :: gfunc
REAL(KIND=dp), DIMENSION(:), POINTER :: w
TYPE(particle_type), DIMENSION(:), POINTER :: particle_set
REAL(KIND=dp), DIMENSION(:), POINTER :: radii
TYPE(pw_type), INTENT(IN) :: rho_tot_g
REAL(KIND=dp), INTENT(IN) :: gcut
CHARACTER(len=*), PARAMETER :: routineN = 'build_b_vector'
COMPLEX(KIND=dp) :: phase
INTEGER :: e_dim, handle, idim, ig, igauss, igmax, &
iparticle, s_dim
REAL(KIND=dp) :: arg, g2, gcut2, gvec(3), rvec(3)
REAL(KIND=dp), DIMENSION(:), POINTER :: my_bv, my_bvw
CALL timeset(routineN, handle)
NULLIFY (my_bv, my_bvw)
gcut2 = gcut*gcut
s_dim = rho_tot_g%pw_grid%first_gne0
e_dim = rho_tot_g%pw_grid%ngpts_cut_local
igmax = 0
DO ig = s_dim, e_dim
g2 = rho_tot_g%pw_grid%gsq(ig)
IF (g2 > gcut2) EXIT
igmax = ig
END DO
IF (igmax .GE. s_dim) THEN
ALLOCATE (my_bv(s_dim:igmax))
ALLOCATE (my_bvw(s_dim:igmax))
!
DO iparticle = 1, SIZE(particle_set)
rvec = particle_set(iparticle)%r
my_bv = 0.0_dp
DO ig = s_dim, igmax
gvec = rho_tot_g%pw_grid%g(:, ig)
arg = DOT_PRODUCT(gvec, rvec)
phase = CMPLX(COS(arg), -SIN(arg), KIND=dp)
my_bv(ig) = w(ig)*REAL(CONJG(rho_tot_g%cc(ig))*phase, KIND=dp)
END DO
DO igauss = 1, SIZE(radii)
idim = (iparticle - 1)*SIZE(radii) + igauss
DO ig = s_dim, igmax
my_bvw(ig) = my_bv(ig)*gfunc(ig, igauss)
END DO
bv(idim) = accurate_sum(my_bvw)
END DO
END DO
DEALLOCATE (my_bvw)
DEALLOCATE (my_bv)
ELSE
DO iparticle = 1, SIZE(particle_set)
DO igauss = 1, SIZE(radii)
idim = (iparticle - 1)*SIZE(radii) + igauss
bv(idim) = 0.0_dp
END DO
END DO
END IF
CALL timestop(handle)
END SUBROUTINE build_b_vector
! **************************************************************************************************
!> \brief Computes the A matrix for the solution of the linear system
!> \param Am ...
!> \param gfunc ...
!> \param w ...
!> \param particle_set ...
!> \param radii ...
!> \param rho_tot_g ...
!> \param gcut ...
!> \param g_dot_rvec_sin ...
!> \param g_dot_rvec_cos ...
!> \par History
!> 08.2005 created [tlaino]
!> \author Teodoro Laino
!> \note NB accept g_dot_rvec_* arrays
! **************************************************************************************************
SUBROUTINE build_A_matrix(Am, gfunc, w, particle_set, radii, rho_tot_g, gcut, g_dot_rvec_sin, g_dot_rvec_cos)
REAL(KIND=dp), DIMENSION(:, :), INTENT(INOUT) :: Am
REAL(KIND=dp), DIMENSION(:, :), POINTER :: gfunc
REAL(KIND=dp), DIMENSION(:), POINTER :: w
TYPE(particle_type), DIMENSION(:), POINTER :: particle_set
REAL(KIND=dp), DIMENSION(:), POINTER :: radii
TYPE(pw_type), INTENT(IN) :: rho_tot_g
REAL(KIND=dp), INTENT(IN) :: gcut
REAL(KIND=dp), DIMENSION(:, :), INTENT(IN) :: g_dot_rvec_sin, g_dot_rvec_cos
CHARACTER(len=*), PARAMETER :: routineN = 'build_A_matrix'
INTEGER :: e_dim, handle, idim1, idim2, ig, &
igauss1, igauss2, igmax, iparticle1, &
iparticle2, istart_g, s_dim
REAL(KIND=dp) :: g2, gcut2, tmp
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: my_Am, my_Amw
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :) :: gfunc_sq(:, :, :)
!NB precalculate as many things outside of the innermost loop as possible, in particular w(ig)*gfunc(ig,igauus1)*gfunc(ig,igauss2)
CALL timeset(routineN, handle)
gcut2 = gcut*gcut
s_dim = rho_tot_g%pw_grid%first_gne0
e_dim = rho_tot_g%pw_grid%ngpts_cut_local
igmax = 0
DO ig = s_dim, e_dim
g2 = rho_tot_g%pw_grid%gsq(ig)
IF (g2 > gcut2) EXIT
igmax = ig
END DO
IF (igmax .GE. s_dim) THEN
ALLOCATE (my_Am(s_dim:igmax))
ALLOCATE (my_Amw(s_dim:igmax))
ALLOCATE (gfunc_sq(s_dim:igmax, SIZE(radii), SIZE(radii)))
DO igauss1 = 1, SIZE(radii)
DO igauss2 = 1, SIZE(radii)
gfunc_sq(s_dim:igmax, igauss1, igauss2) = w(s_dim:igmax)*gfunc(s_dim:igmax, igauss1)*gfunc(s_dim:igmax, igauss2)
END DO
END DO
DO iparticle1 = 1, SIZE(particle_set)
DO iparticle2 = iparticle1, SIZE(particle_set)
DO ig = s_dim, igmax
!NB replace explicit dot product and cosine with cos(A+B) formula - much faster
my_Am(ig) = (g_dot_rvec_cos(ig - s_dim + 1, iparticle1)*g_dot_rvec_cos(ig - s_dim + 1, iparticle2) + &
g_dot_rvec_sin(ig - s_dim + 1, iparticle1)*g_dot_rvec_sin(ig - s_dim + 1, iparticle2))
END DO
DO igauss1 = 1, SIZE(radii)
idim1 = (iparticle1 - 1)*SIZE(radii) + igauss1
istart_g = 1
IF (iparticle2 == iparticle1) istart_g = igauss1
DO igauss2 = istart_g, SIZE(radii)
idim2 = (iparticle2 - 1)*SIZE(radii) + igauss2
my_Amw(s_dim:igmax) = my_Am(s_dim:igmax)*gfunc_sq(s_dim:igmax, igauss1, igauss2)
!NB no loss of accuracy in my test cases
!tmp = accurate_sum(my_Amw)
tmp = SUM(my_Amw)
Am(idim2, idim1) = tmp
Am(idim1, idim2) = tmp
END DO
END DO
END DO
END DO
DEALLOCATE (gfunc_sq)
DEALLOCATE (my_Amw)
DEALLOCATE (my_Am)
END IF
CALL timestop(handle)
END SUBROUTINE build_A_matrix
! **************************************************************************************************
!> \brief Computes the derivative of B vector for the evaluation of the Pulay forces
!> \param dbv ...
!> \param gfunc ...
!> \param w ...
!> \param particle_set ...
!> \param radii ...
!> \param rho_tot_g ...
!> \param gcut ...
!> \param iparticle0 ...
!> \par History
!> 08.2005 created [tlaino]
!> \author Teodoro Laino
! **************************************************************************************************
SUBROUTINE build_der_b_vector(dbv, gfunc, w, particle_set, radii, rho_tot_g, gcut, iparticle0)
REAL(KIND=dp), DIMENSION(:, :), INTENT(INOUT) :: dbv
REAL(KIND=dp), DIMENSION(:, :), POINTER :: gfunc
REAL(KIND=dp), DIMENSION(:), POINTER :: w
TYPE(particle_type), DIMENSION(:), POINTER :: particle_set
REAL(KIND=dp), DIMENSION(:), INTENT(IN) :: radii
TYPE(pw_type), INTENT(IN) :: rho_tot_g
REAL(KIND=dp), INTENT(IN) :: gcut
INTEGER, INTENT(IN) :: iparticle0
CHARACTER(len=*), PARAMETER :: routineN = 'build_der_b_vector'
COMPLEX(KIND=dp) :: dphase
INTEGER :: e_dim, handle, idim, ig, igauss, igmax, &
iparticle, s_dim
REAL(KIND=dp) :: arg, g2, gcut2
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: my_dbvw
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :) :: my_dbv
REAL(KIND=dp), DIMENSION(3) :: gvec, rvec
CALL timeset(routineN, handle)
gcut2 = gcut*gcut
s_dim = rho_tot_g%pw_grid%first_gne0
e_dim = rho_tot_g%pw_grid%ngpts_cut_local
igmax = 0
DO ig = s_dim, e_dim
g2 = rho_tot_g%pw_grid%gsq(ig)
IF (g2 > gcut2) EXIT
igmax = ig
END DO
IF (igmax .GE. s_dim) THEN
ALLOCATE (my_dbv(3, s_dim:igmax))
ALLOCATE (my_dbvw(s_dim:igmax))
DO iparticle = 1, SIZE(particle_set)
IF (iparticle /= iparticle0) CYCLE
rvec = particle_set(iparticle)%r
DO ig = s_dim, igmax
gvec = rho_tot_g%pw_grid%g(:, ig)
arg = DOT_PRODUCT(gvec, rvec)
dphase = -CMPLX(SIN(arg), COS(arg), KIND=dp)
my_dbv(:, ig) = w(ig)*REAL(CONJG(rho_tot_g%cc(ig))*dphase, KIND=dp)*gvec(:)
END DO
DO igauss = 1, SIZE(radii)
idim = (iparticle - 1)*SIZE(radii) + igauss
DO ig = s_dim, igmax
my_dbvw(ig) = my_dbv(1, ig)*gfunc(ig, igauss)
END DO
dbv(idim, 1) = accurate_sum(my_dbvw)
DO ig = s_dim, igmax
my_dbvw(ig) = my_dbv(2, ig)*gfunc(ig, igauss)
END DO
dbv(idim, 2) = accurate_sum(my_dbvw)
DO ig = s_dim, igmax
my_dbvw(ig) = my_dbv(3, ig)*gfunc(ig, igauss)
END DO
dbv(idim, 3) = accurate_sum(my_dbvw)
END DO
END DO
DEALLOCATE (my_dbvw)
DEALLOCATE (my_dbv)
ELSE
DO iparticle = 1, SIZE(particle_set)
IF (iparticle /= iparticle0) CYCLE
DO igauss = 1, SIZE(radii)
idim = (iparticle - 1)*SIZE(radii) + igauss
dbv(idim, 1:3) = 0.0_dp
END DO
END DO
END IF
CALL timestop(handle)
END SUBROUTINE build_der_b_vector
! **************************************************************************************************
!> \brief Computes the derivative of the A matrix for the evaluation of the
!> Pulay forces
!> \param dAm ...
!> \param gfunc ...
!> \param w ...
!> \param particle_set ...
!> \param radii ...
!> \param rho_tot_g ...
!> \param gcut ...
!> \param iparticle0 ...
!> \param nparticles ...
!> \param g_dot_rvec_sin ...
!> \param g_dot_rvec_cos ...
!> \par History
!> 08.2005 created [tlaino]
!> \author Teodoro Laino
!> \note NB accept g_dot_rvec_* arrays
! **************************************************************************************************
SUBROUTINE build_der_A_matrix_rows(dAm, gfunc, w, particle_set, radii, &
rho_tot_g, gcut, iparticle0, nparticles, g_dot_rvec_sin, g_dot_rvec_cos)
REAL(KIND=dp), DIMENSION(:, :, :), INTENT(INOUT) :: dAm
REAL(KIND=dp), DIMENSION(:, :), POINTER :: gfunc
REAL(KIND=dp), DIMENSION(:), POINTER :: w
TYPE(particle_type), DIMENSION(:), POINTER :: particle_set
REAL(KIND=dp), DIMENSION(:), POINTER :: radii
TYPE(pw_type), INTENT(IN) :: rho_tot_g
REAL(KIND=dp), INTENT(IN) :: gcut
INTEGER, INTENT(IN) :: iparticle0, nparticles
REAL(KIND=dp), DIMENSION(:, :), INTENT(IN) :: g_dot_rvec_sin, g_dot_rvec_cos
CHARACTER(len=*), PARAMETER :: routineN = 'build_der_A_matrix_rows'
INTEGER :: e_dim, handle, ig, igauss2, igmax, &
iparticle1, iparticle2, s_dim
REAL(KIND=dp) :: g2, gcut2
!NB calculate derivatives for a block of particles, just the row parts (since derivative matrix is symmetric)
!NB Use DGEMM to speed up calculation, can't do accurate_sum() anymore because dgemm does the sum over g
EXTERNAL DGEMM
REAL(KIND=dp), ALLOCATABLE :: lhs(:, :), rhs(:, :)
INTEGER :: Nr, Np, Ng, icomp, ipp
CALL timeset(routineN, handle)
gcut2 = gcut*gcut
s_dim = rho_tot_g%pw_grid%first_gne0
e_dim = rho_tot_g%pw_grid%ngpts_cut_local
igmax = 0
DO ig = s_dim, e_dim
g2 = rho_tot_g%pw_grid%gsq(ig)
IF (g2 > gcut2) EXIT
igmax = ig
END DO
Nr = SIZE(radii)
Np = SIZE(particle_set)
Ng = igmax - s_dim + 1
IF (igmax .GE. s_dim) THEN
ALLOCATE (lhs(nparticles*Nr, Ng))
ALLOCATE (rhs(Ng, Np*Nr))
! rhs with first term of sin(g.(rvec1-rvec2))
! rhs has all parts that depend on iparticle2
DO iparticle2 = 1, Np
DO igauss2 = 1, Nr
rhs(1:Ng, (iparticle2 - 1)*Nr + igauss2) = g_dot_rvec_sin(1:Ng, iparticle2)*gfunc(s_dim:igmax, igauss2)
END DO
END DO
DO icomp = 1, 3
! create lhs, which has all parts that depend on iparticle1
DO ipp = 1, nparticles
iparticle1 = iparticle0 + ipp - 1
DO ig = s_dim, igmax
lhs((ipp - 1)*Nr + 1:(ipp - 1)*Nr + Nr, ig - s_dim + 1) = w(ig)*rho_tot_g%pw_grid%g(icomp, ig)* &
gfunc(ig, 1:Nr)*g_dot_rvec_cos(ig - s_dim + 1, iparticle1)
END DO
END DO ! ipp
! do main multiply
CALL DGEMM('N', 'N', nparticles*Nr, Np*Nr, Ng, 1.0D0, lhs(1, 1), nparticles*Nr, rhs(1, 1), &
Ng, 0.0D0, dAm((iparticle0 - 1)*Nr + 1, 1, icomp), Np*Nr)
! do extra multiplies to compensate for missing factor of 2
DO ipp = 1, nparticles
iparticle1 = iparticle0 + ipp - 1
CALL DGEMM('N', 'N', Nr, Nr, Ng, 1.0D0, lhs((ipp - 1)*Nr + 1, 1), nparticles*Nr, rhs(1, (iparticle1 - 1)*Nr + 1), &
Ng, 1.0D0, dAm((iparticle1 - 1)*Nr + 1, (iparticle1 - 1)*Nr + 1, icomp), Np*Nr)
END DO
! now extra columns to account for factor of 2 in some rhs columns
END DO ! icomp
! rhs with second term of sin(g.(rvec1-rvec2))
! rhs has all parts that depend on iparticle2
DO iparticle2 = 1, Np
DO igauss2 = 1, Nr
rhs(1:Ng, (iparticle2 - 1)*Nr + igauss2) = -g_dot_rvec_cos(1:Ng, iparticle2)*gfunc(s_dim:igmax, igauss2)
END DO
END DO
DO icomp = 1, 3
! create lhs, which has all parts that depend on iparticle1
DO ipp = 1, nparticles
iparticle1 = iparticle0 + ipp - 1
DO ig = s_dim, igmax
lhs((ipp - 1)*Nr + 1:(ipp - 1)*Nr + Nr, ig - s_dim + 1) = w(ig)*rho_tot_g%pw_grid%g(icomp, ig)*gfunc(ig, 1:Nr)* &
g_dot_rvec_sin(ig - s_dim + 1, iparticle1)
END DO
END DO
! do main multiply
CALL DGEMM('N', 'N', nparticles*Nr, Np*Nr, Ng, 1.0D0, lhs(1, 1), nparticles*Nr, rhs(1, 1), &
Ng, 1.0D0, dAm((iparticle0 - 1)*Nr + 1, 1, icomp), Np*Nr)
! do extra multiples to compensate for missing factor of 2
DO ipp = 1, nparticles
iparticle1 = iparticle0 + ipp - 1
CALL DGEMM('N', 'N', Nr, Nr, Ng, 1.0D0, lhs((ipp - 1)*Nr + 1, 1), nparticles*Nr, rhs(1, (iparticle1 - 1)*Nr + 1), &
Ng, 1.0D0, dAm((iparticle1 - 1)*Nr + 1, (iparticle1 - 1)*Nr + 1, icomp), Np*Nr)
END DO
END DO
DEALLOCATE (rhs)
DEALLOCATE (lhs)
END IF
CALL timestop(handle)
END SUBROUTINE build_der_A_matrix_rows
! **************************************************************************************************
!> \brief deallocate g_dot_rvec_* arrays
!> \param g_dot_rvec_sin ...
!> \param g_dot_rvec_cos ...
! **************************************************************************************************
SUBROUTINE cleanup_g_dot_rvec_sin_cos(g_dot_rvec_sin, g_dot_rvec_cos)
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :) :: g_dot_rvec_sin, g_dot_rvec_cos
IF (ALLOCATED(g_dot_rvec_sin)) DEALLOCATE (g_dot_rvec_sin)
IF (ALLOCATED(g_dot_rvec_cos)) DEALLOCATE (g_dot_rvec_cos)
END SUBROUTINE cleanup_g_dot_rvec_sin_cos
! **************************************************************************************************
!> \brief precompute sin(g.r) and cos(g.r) for quicker evaluations of sin(g.(r1-r2)) and cos(g.(r1-r2))
!> \param rho_tot_g ...
!> \param particle_set ...
!> \param gcut ...
!> \param g_dot_rvec_sin ...
!> \param g_dot_rvec_cos ...
! **************************************************************************************************
SUBROUTINE prep_g_dot_rvec_sin_cos(rho_tot_g, particle_set, gcut, g_dot_rvec_sin, g_dot_rvec_cos)
TYPE(pw_type), INTENT(IN) :: rho_tot_g
TYPE(particle_type), DIMENSION(:), POINTER :: particle_set
REAL(KIND=dp), INTENT(IN) :: gcut
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :) :: g_dot_rvec_sin, g_dot_rvec_cos
INTEGER :: e_dim, ig, igmax, iparticle, s_dim
REAL(KIND=dp) :: g2, g_dot_rvec, gcut2, rvec(3)
gcut2 = gcut*gcut
s_dim = rho_tot_g%pw_grid%first_gne0
e_dim = rho_tot_g%pw_grid%ngpts_cut_local
igmax = 0
DO ig = s_dim, e_dim
g2 = rho_tot_g%pw_grid%gsq(ig)
IF (g2 > gcut2) EXIT
igmax = ig
END DO
IF (igmax .GE. s_dim) THEN
ALLOCATE (g_dot_rvec_sin(1:igmax - s_dim + 1, SIZE(particle_set)))
ALLOCATE (g_dot_rvec_cos(1:igmax - s_dim + 1, SIZE(particle_set)))
DO iparticle = 1, SIZE(particle_set)
rvec = particle_set(iparticle)%r
DO ig = s_dim, igmax
g_dot_rvec = DOT_PRODUCT(rho_tot_g%pw_grid%g(:, ig), rvec)
g_dot_rvec_sin(ig - s_dim + 1, iparticle) = SIN(g_dot_rvec)
g_dot_rvec_cos(ig - s_dim + 1, iparticle) = COS(g_dot_rvec)
END DO
END DO
END IF
END SUBROUTINE prep_g_dot_rvec_sin_cos
! **************************************************************************************************
!> \brief Computes the inverse AmI of the Am matrix
!> \param GAmI ...
!> \param c0 ...
!> \param gfunc ...
!> \param w ...
!> \param particle_set ...
!> \param gcut ...
!> \param rho_tot_g ...
!> \param radii ...
!> \param iw ...
!> \param Vol ...
!> \par History
!> 12.2005 created [tlaino]
!> \author Teodoro Laino
! **************************************************************************************************
SUBROUTINE ddapc_eval_AmI(GAmI, c0, gfunc, w, particle_set, gcut, &
rho_tot_g, radii, iw, Vol)
REAL(KIND=dp), DIMENSION(:, :), POINTER :: GAmI
REAL(KIND=dp), INTENT(OUT) :: c0
REAL(KIND=dp), DIMENSION(:, :), POINTER :: gfunc
REAL(KIND=dp), DIMENSION(:), POINTER :: w
TYPE(particle_type), DIMENSION(:), POINTER :: particle_set
REAL(KIND=dp), INTENT(IN) :: gcut
TYPE(pw_type), INTENT(IN) :: rho_tot_g
REAL(KIND=dp), DIMENSION(:), POINTER :: radii
INTEGER, INTENT(IN) :: iw
REAL(KIND=dp), INTENT(IN) :: Vol
CHARACTER(len=*), PARAMETER :: routineN = 'ddapc_eval_AmI'
INTEGER :: handle, ndim
REAL(KIND=dp) :: condition_number, inv_error
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: AmE, cv
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :) :: Am, AmI, Amw, g_dot_rvec_cos, &
g_dot_rvec_sin
!NB for precomputation of sin(g.r) and cos(g.r)
CALL timeset(routineN, handle)
ndim = SIZE(particle_set)*SIZE(radii)
ALLOCATE (Am(ndim, ndim))
ALLOCATE (AmI(ndim, ndim))
ALLOCATE (GAmI(ndim, ndim))
ALLOCATE (cv(ndim))
Am = 0.0_dp
AmI = 0.0_dp
cv = 1.0_dp/Vol
!NB precompute sin(g.r) and cos(g.r) for faster evaluation of cos(g.(r1-r2)) in build_A_matrix()
CALL prep_g_dot_rvec_sin_cos(rho_tot_g, particle_set, gcut, g_dot_rvec_sin, g_dot_rvec_cos)
CALL build_A_matrix(Am, gfunc, w, particle_set, radii, rho_tot_g, gcut, g_dot_rvec_sin, g_dot_rvec_cos)
CALL cleanup_g_dot_rvec_sin_cos(g_dot_rvec_sin, g_dot_rvec_cos)
Am(:, :) = Am(:, :)/(Vol*Vol)
CALL rho_tot_g%pw_grid%para%group%sum(Am)
IF (iw > 0) THEN
! Checking conditions numbers and eigenvalues
ALLOCATE (Amw(ndim, ndim))
ALLOCATE (AmE(ndim))
Amw(:, :) = Am
CALL diamat_all(Amw, AmE)
condition_number = MAXVAL(ABS(AmE))/MINVAL(ABS(AmE))
WRITE (iw, '(T3,A)') " Eigenvalues of Matrix A:"
WRITE (iw, '(T3,4E15.8)') AmE
WRITE (iw, '(T3,A,1E15.9)') " Condition number:", condition_number
IF (condition_number > 1.0E12_dp) THEN
WRITE (iw, FMT="(/,T2,A)") &
"WARNING: high condition number => possibly ill-conditioned matrix"
END IF
DEALLOCATE (Amw)
DEALLOCATE (AmE)
END IF
CALL invert_matrix(Am, AmI, inv_error, "N", improve=.FALSE.)
IF (iw > 0) THEN
WRITE (iw, '(T3,A,F15.9)') " Error inverting the A matrix: ", inv_error
END IF
c0 = DOT_PRODUCT(cv, MATMUL(AmI, cv))
DEALLOCATE (Am)
DEALLOCATE (cv)
GAmI = AmI
DEALLOCATE (AmI)
CALL timestop(handle)
END SUBROUTINE ddapc_eval_AmI
! **************************************************************************************************
!> \brief Evaluates the Ewald term E2 and E3 energy term for the decoupling/coupling
!> of periodic images
!> \param cp_para_env ...
!> \param coeff ...
!> \param factor ...
!> \param cell ...
!> \param multipole_section ...
!> \param particle_set ...
!> \param M ...
!> \param radii ...
!> \par History
!> 08.2005 created [tlaino]
!> \author Teodoro Laino
!> \note NB receive cp_para_env for parallelization
! **************************************************************************************************
RECURSIVE SUBROUTINE ewald_ddapc_pot(cp_para_env, coeff, factor, cell, multipole_section, &
particle_set, M, radii)
TYPE(mp_para_env_type), INTENT(IN) :: cp_para_env
TYPE(pw_type), INTENT(IN), POINTER :: coeff
REAL(KIND=dp), INTENT(IN) :: factor
TYPE(cell_type), POINTER :: cell
TYPE(section_vals_type), POINTER :: multipole_section
TYPE(particle_type), DIMENSION(:), POINTER :: particle_set
REAL(KIND=dp), DIMENSION(:, :), POINTER :: M
REAL(KIND=dp), DIMENSION(:), POINTER :: radii
CHARACTER(len=*), PARAMETER :: routineN = 'ewald_ddapc_pot'
INTEGER :: ewmdim, handle, idim, idim1, idim2, idimo, igauss1, igauss2, ip1, ip2, &
iparticle1, iparticle2, istart_g, k1, k2, k3, n_rep, ndim, nmax1, nmax2, nmax3, r1, r2, &
r3, rmax1, rmax2, rmax3
LOGICAL :: analyt
REAL(KIND=dp) :: alpha, eps, ew_neut, fac, fac3, fs, g_ewald, galpha, gsq, gsqi, ij_fac, &
my_val, r, r2tmp, r_ewald, rc1, rc12, rc2, rc22, rcut, rcut2, t1, tol, tol1
REAL(KIND=dp), DIMENSION(3) :: fvec, gvec, ra, rvec
REAL(KIND=dp), DIMENSION(:), POINTER :: EwM
NULLIFY (EwM)
CALL timeset(routineN, handle)
CPASSERT(.NOT. ASSOCIATED(M))
CPASSERT(ASSOCIATED(radii))
CPASSERT(cell%orthorhombic)
rcut = MIN(cell%hmat(1, 1), cell%hmat(2, 2), cell%hmat(3, 3))/2.0_dp
CALL section_vals_val_get(multipole_section, "RCUT", n_rep_val=n_rep)
IF (n_rep == 1) CALL section_vals_val_get(multipole_section, "RCUT", r_val=rcut)
CALL section_vals_val_get(multipole_section, "EWALD_PRECISION", r_val=eps)
CALL section_vals_val_get(multipole_section, "ANALYTICAL_GTERM", l_val=analyt)
rcut2 = rcut**2
!
! Setting-up parameters for Ewald summation
!
eps = MIN(ABS(eps), 0.5_dp)
tol = SQRT(ABS(LOG(eps*rcut)))
alpha = SQRT(ABS(LOG(eps*rcut*tol)))/rcut
galpha = 1.0_dp/(4.0_dp*alpha*alpha)
tol1 = SQRT(-LOG(eps*rcut*(2.0_dp*tol*alpha)**2))
nmax1 = NINT(0.25_dp + cell%hmat(1, 1)*alpha*tol1/pi)
nmax2 = NINT(0.25_dp + cell%hmat(2, 2)*alpha*tol1/pi)
nmax3 = NINT(0.25_dp + cell%hmat(3, 3)*alpha*tol1/pi)
rmax1 = CEILING(rcut/cell%hmat(1, 1))
rmax2 = CEILING(rcut/cell%hmat(2, 2))
rmax3 = CEILING(rcut/cell%hmat(3, 3))
fac = 1.e0_dp/cell%deth
fac3 = fac*pi
fvec = twopi/(/cell%hmat(1, 1), cell%hmat(2, 2), cell%hmat(3, 3)/)
ew_neut = -fac*pi/alpha**2
!
ewmdim = SIZE(particle_set)*(SIZE(particle_set) + 1)/2
ndim = SIZE(particle_set)*SIZE(radii)
ALLOCATE (EwM(ewmdim))
ALLOCATE (M(ndim, ndim))
M = 0.0_dp
!
idim = 0
EwM = 0.0_dp
DO iparticle1 = 1, SIZE(particle_set)
ip1 = (iparticle1 - 1)*SIZE(radii)
DO iparticle2 = 1, iparticle1
ij_fac = 1.0_dp
IF (iparticle1 == iparticle2) ij_fac = 0.5_dp
ip2 = (iparticle2 - 1)*SIZE(radii)
idim = idim + 1
!NB parallelization, done here so indexing is right
IF (MOD(iparticle1, cp_para_env%num_pe) /= cp_para_env%mepos) CYCLE
!
! Real-Space Contribution
!
my_val = 0.0_dp
rvec = particle_set(iparticle1)%r - particle_set(iparticle2)%r
r_ewald = 0.0_dp
IF (iparticle1 /= iparticle2) THEN
ra = rvec
r2tmp = DOT_PRODUCT(ra, ra)
IF (r2tmp <= rcut2) THEN
r = SQRT(r2tmp)
t1 = erfc(alpha*r)/r
r_ewald = t1
END IF
END IF
DO r1 = -rmax1, rmax1
DO r2 = -rmax2, rmax2
DO r3 = -rmax3, rmax3
IF ((r1 == 0) .AND. (r2 == 0) .AND. (r3 == 0)) CYCLE
ra(1) = rvec(1) + cell%hmat(1, 1)*r1
ra(2) = rvec(2) + cell%hmat(2, 2)*r2
ra(3) = rvec(3) + cell%hmat(3, 3)*r3
r2tmp = DOT_PRODUCT(ra, ra)
IF (r2tmp <= rcut2) THEN
r = SQRT(r2tmp)
t1 = erfc(alpha*r)/r
r_ewald = r_ewald + t1*ij_fac
END IF
END DO
END DO
END DO
!
! G-space Contribution
!
IF (analyt) THEN
g_ewald = 0.0_dp
DO k1 = 0, nmax1
DO k2 = -nmax2, nmax2
DO k3 = -nmax3, nmax3
IF (k1 == 0 .AND. k2 == 0 .AND. k3 == 0) CYCLE
fs = 2.0_dp; IF (k1 == 0) fs = 1.0_dp
gvec = fvec*(/REAL(k1, KIND=dp), REAL(k2, KIND=dp), REAL(k3, KIND=dp)/)
gsq = DOT_PRODUCT(gvec, gvec)
gsqi = fs/gsq
t1 = fac*gsqi*EXP(-galpha*gsq)
g_ewald = g_ewald + t1*COS(DOT_PRODUCT(gvec, rvec))
END DO
END DO
END DO
ELSE
g_ewald = Eval_Interp_Spl3_pbc(rvec, coeff)
END IF
!
! G-EWALD, R-EWALD
!
g_ewald = r_ewald + fourpi*g_ewald
!
! Self Contribution
!
IF (iparticle1 == iparticle2) THEN
g_ewald = g_ewald - 2.0_dp*alpha*oorootpi
END IF
!
IF (iparticle1 /= iparticle2) THEN
ra = rvec
r = SQRT(DOT_PRODUCT(ra, ra))
my_val = factor/r
END IF
EwM(idim) = my_val - factor*g_ewald
END DO ! iparticle2
END DO ! iparticle1
!NB sum over parallelized contributions of different nodes
CALL cp_para_env%sum(EwM)
idim = 0
DO iparticle2 = 1, SIZE(particle_set)
ip2 = (iparticle2 - 1)*SIZE(radii)
idimo = (iparticle2 - 1)
idimo = idimo*(idimo + 1)/2
DO igauss2 = 1, SIZE(radii)
idim2 = ip2 + igauss2
rc2 = radii(igauss2)
rc22 = rc2*rc2
DO iparticle1 = 1, iparticle2
ip1 = (iparticle1 - 1)*SIZE(radii)
idim = idimo + iparticle1
istart_g = 1
IF (iparticle1 == iparticle2) istart_g = igauss2
DO igauss1 = istart_g, SIZE(radii)
idim1 = ip1 + igauss1
rc1 = radii(igauss1)
rc12 = rc1*rc1
M(idim1, idim2) = EwM(idim) - factor*ew_neut - factor*fac3*(rc12 + rc22)
M(idim2, idim1) = M(idim1, idim2)
END DO
END DO
END DO ! iparticle2
END DO ! iparticle1
DEALLOCATE (EwM)
CALL timestop(handle)
END SUBROUTINE ewald_ddapc_pot
! **************************************************************************************************
!> \brief Evaluates the electrostatic potential due to a simple solvation model
!> Spherical cavity in a dieletric medium
!> \param solvation_section ...
!> \param particle_set ...
!> \param M ...
!> \param radii ...
!> \par History
!> 08.2006 created [tlaino]
!> \author Teodoro Laino
! **************************************************************************************************
SUBROUTINE solvation_ddapc_pot(solvation_section, particle_set, M, radii)
TYPE(section_vals_type), POINTER :: solvation_section
TYPE(particle_type), DIMENSION(:), POINTER :: particle_set
REAL(KIND=dp), DIMENSION(:, :), POINTER :: M
REAL(KIND=dp), DIMENSION(:), POINTER :: radii
INTEGER :: i, idim, idim1, idim2, igauss1, igauss2, ip1, ip2, iparticle1, iparticle2, &
istart_g, j, l, lmax, n_rep1, n_rep2, ndim, output_unit, weight
INTEGER, DIMENSION(:), POINTER :: list
LOGICAL :: fixed_center
REAL(KIND=dp) :: center(3), eps_in, eps_out, factor, &
mass, mycos, r1, r2, Rs, rvec(3)
REAL(KIND=dp), DIMENSION(:), POINTER :: pos, R0
REAL(KIND=dp), DIMENSION(:, :), POINTER :: cost, LocP
fixed_center = .FALSE.
output_unit = cp_logger_get_default_io_unit()
ndim = SIZE(particle_set)*SIZE(radii)
ALLOCATE (M(ndim, ndim))
M = 0.0_dp
eps_in = 1.0_dp
CALL section_vals_val_get(solvation_section, "EPS_OUT", r_val=eps_out)
CALL section_vals_val_get(solvation_section, "LMAX", i_val=lmax)
CALL section_vals_val_get(solvation_section, "SPHERE%RADIUS", r_val=Rs)
CALL section_vals_val_get(solvation_section, "SPHERE%CENTER%XYZ", n_rep_val=n_rep1)
IF (n_rep1 /= 0) THEN
CALL section_vals_val_get(solvation_section, "SPHERE%CENTER%XYZ", r_vals=R0)
center = R0
ELSE
CALL section_vals_val_get(solvation_section, "SPHERE%CENTER%ATOM_LIST", &
n_rep_val=n_rep2)
IF (n_rep2 /= 0) THEN
CALL section_vals_val_get(solvation_section, "SPHERE%CENTER%ATOM_LIST", i_vals=list)
CALL section_vals_val_get(solvation_section, "SPHERE%CENTER%WEIGHT_TYPE", i_val=weight)
ALLOCATE (R0(3))
SELECT CASE (weight)
CASE (weight_type_unit)
R0 = 0.0_dp
DO i = 1, SIZE(list)
R0 = R0 + particle_set(list(i))%r
END DO
R0 = R0/REAL(SIZE(list), KIND=dp)
CASE (weight_type_mass)
R0 = 0.0_dp
mass = 0.0_dp
DO i = 1, SIZE(list)
R0 = R0 + particle_set(list(i))%r*particle_set(list(i))%atomic_kind%mass
mass = mass + particle_set(list(i))%atomic_kind%mass
END DO
R0 = R0/mass
END SELECT
center = R0
CALL section_vals_val_get(solvation_section, "SPHERE%CENTER%FIXED", l_val=fixed_center)
IF (fixed_center) THEN
CALL section_vals_val_set(solvation_section, "SPHERE%CENTER%XYZ", &
r_vals_ptr=R0)
ELSE
DEALLOCATE (R0)
END IF
END IF
END IF
CPASSERT(n_rep1 /= 0 .OR. n_rep2 /= 0)
! Potential calculation
ALLOCATE (LocP(0:lmax, SIZE(particle_set)))
ALLOCATE (pos(SIZE(particle_set)))
ALLOCATE (cost(SIZE(particle_set), SIZE(particle_set)))
! Determining the single atomic contribution to the dielectric dipole
DO i = 1, SIZE(particle_set)
rvec = particle_set(i)%r - center
r2 = DOT_PRODUCT(rvec, rvec)
r1 = SQRT(r2)
IF (r1 >= Rs) THEN
IF (output_unit > 0) THEN
WRITE (output_unit, '(A,I6,A)') "Atom number :: ", i, " is out of the solvation sphere"
WRITE (output_unit, '(2(A,F12.6))') "Distance from the center::", r1, " Radius of the sphere::", rs
END IF
CPABORT("")
END IF
LocP(:, i) = 0.0_dp
IF (r1 /= 0.0_dp) THEN
DO l = 0, lmax
LocP(l, i) = (r1**l*REAL(l + 1, KIND=dp)*(eps_in - eps_out))/ &
(Rs**(2*l + 1)*eps_in*(REAL(l, KIND=dp)*eps_in + REAL(l + 1, KIND=dp)*eps_out))
END DO
ELSE
! limit for r->0
LocP(0, i) = (eps_in - eps_out)/(Rs*eps_in*eps_out)
END IF
pos(i) = r1
END DO
! Particle-Particle potential energy matrix
cost = 0.0_dp
DO i = 1, SIZE(particle_set)
DO j = 1, i
factor = 0.0_dp
IF (pos(i)*pos(j) /= 0.0_dp) THEN
mycos = DOT_PRODUCT(particle_set(i)%r - center, particle_set(j)%r - center)/(pos(i)*pos(j))
IF (ABS(mycos) > 1.0_dp) mycos = SIGN(1.0_dp, mycos)
DO l = 0, lmax
factor = factor + LocP(l, i)*pos(j)**l*legendre(mycos, l, 0)
END DO
ELSE
factor = LocP(0, i)
END IF
cost(i, j) = factor
cost(j, i) = factor
END DO
END DO
! Computes the full potential energy matrix
idim = 0
DO iparticle2 = 1, SIZE(particle_set)
ip2 = (iparticle2 - 1)*SIZE(radii)
DO igauss2 = 1, SIZE(radii)
idim2 = ip2 + igauss2
DO iparticle1 = 1, iparticle2
ip1 = (iparticle1 - 1)*SIZE(radii)
istart_g = 1
IF (iparticle1 == iparticle2) istart_g = igauss2
DO igauss1 = istart_g, SIZE(radii)
idim1 = ip1 + igauss1
M(idim1, idim2) = cost(iparticle1, iparticle2)
M(idim2, idim1) = M(idim1, idim2)
END DO
END DO
END DO
END DO
DEALLOCATE (cost)
DEALLOCATE (pos)
DEALLOCATE (LocP)
END SUBROUTINE solvation_ddapc_pot
END MODULE cp_ddapc_methods