Skip to content

Commit

Permalink
[feat] respack fit slater for p shell
Browse files Browse the repository at this point in the history 
allow to use the respack fit slater routine for l=1 (p-shells)
rename fit_slater_fulld -> fit_slater
  • Loading branch information
@the-hampel
the-hampel committed Jan 26, 2024
1 parent 38bbb90 commit 76a268c
Show file tree
Hide file tree
Showing 2 changed files with 39 additions and 23 deletions.
25 changes: 15 additions & 10 deletions python/solid_dmft/postprocessing/eval_U_cRPA_RESPACK.py
View file
Original file line number Diff line number Diff line change
Expand Up @@ -219,16 +219,16 @@ def construct_Uijkl(Uijij, Uiijj):
return Uijkl


def fit_slater_fulld(u_ijij_crpa, u_ijji_crpa, U_init, J_init, fixed_F4_F2=True):
def fit_slater(u_ijij_crpa, u_ijji_crpa, U_init, J_init, fixed_F4_F2=True):
'''
finds best Slater parameters U, J for given Uijij and Uijji matrices
using the triqs U_matrix operator routine assumes F4/F2=0.625
Parameters:
-----------
u_ijij_crpa: np.ndarray of shape (5, 5)
u_ijij_crpa: np.ndarray of shape (3,3) or (5, 5)
Uijij matrix
u_ijji_crpa: np.ndarray of shape (5, 5)
u_ijji_crpa: np.ndarray of shape (3,3) or (5, 5)
Uijji matrix
U_init: float
inital value of U for optimization
Expand All @@ -248,29 +248,34 @@ def fit_slater_fulld(u_ijij_crpa, u_ijji_crpa, U_init, J_init, fixed_F4_F2=True)
from scipy.optimize import minimize

# input checks
assert u_ijij_crpa.shape == (5, 5), 'fit slater only implemented for full d shell (5 orbitals)'
assert u_ijji_crpa.shape == (5, 5), 'fit slater only implemented for full d shell (5 orbitals)'
if u_ijij_crpa.shape == (3,3):
l=1
# for p shell there are only 2 parameters
fixed_F4_F2 = True
elif u_ijij_crpa.shape == (5,5):
l=2
else:
raise ValueError('fit slater only implemented for full p or d shell')

def minimizer(parameters):
U_int, J_hund = parameters
Umat_full = U_matrix_slater(l=2, U_int=U_int, J_hund=J_hund, basis='spherical')
Umat_full = U_matrix_slater(l=l, U_int=U_int, J_hund=J_hund, basis='spherical')
Umat_full = transform_U_matrix(Umat_full, T)

Umat, u_ijij_slater = reduce_4index_to_2index(Umat_full)
u_iijj_slater = u_ijij_slater - Umat
return np.sum((u_ijji_crpa - u_iijj_slater)**2 + (u_ijij_crpa - u_ijij_slater)**2)

def minimizer_radial(parameters):
F0, F2, F4 = parameters
Umat_full = U_matrix_slater(l=2, radial_integrals=[F0, F2, F4], basis='spherical')
Umat_full = U_matrix_slater(l=l, radial_integrals=parameters, basis='spherical')
Umat_full = transform_U_matrix(Umat_full, T)

Umat, u_ijij_slater = reduce_4index_to_2index(Umat_full)
u_iijj_slater = u_ijij_slater - Umat
return np.sum((u_ijji_crpa - u_iijj_slater)**2 + (u_ijij_crpa - u_ijij_slater)**2)

# transformation matrix from spherical to w90 basis
T = spherical_to_cubic(l=2, convention='wannier90')
T = spherical_to_cubic(l=l, convention='wannier90')

if fixed_F4_F2:
result = minimize(minimizer, (U_init, J_init))
Expand All @@ -284,7 +289,7 @@ def minimizer_radial(parameters):
F2 = J_init * 14.0 / (1.0 + 0.63)
F4 = 0.630 * F2

initial_guess = (F0, F2, F4)
initial_guess = [F0, F2, F4]

print('Initial guess: F0 = {0[0]:.3f} eV, F2 = {0[1]:.3f} eV, F4 = {0[2]:.3f} eV'.format(initial_guess))

Expand Down
37 changes: 24 additions & 13 deletions test/python/test_respack_sfo.py
View file
Original file line number Diff line number Diff line change
Expand Up @@ -19,7 +19,7 @@
from itertools import product

from h5 import HDFArchive
from solid_dmft.postprocessing.eval_U_cRPA_RESPACK import read_interaction, fit_slater_fulld
from solid_dmft.postprocessing.eval_U_cRPA_RESPACK import read_interaction, fit_slater
from solid_dmft.postprocessing.eval_U_cRPA_Vasp import fit_slater_fulld as fit_slater_vasp

from triqs.operators.util.U_matrix import transform_U_matrix
Expand All @@ -38,10 +38,10 @@ def setUp(self):
def test_U_J_fit(self):
print('------------')
print('Fitting screened interaction with fixed F4/F2 ratio')
U_int, J_int = fit_slater_fulld(self.res.Uijij.real,
self.res.Uijji.real,
U_init=2, J_init=1,
fixed_F4_F2=True)
U_int, J_int = fit_slater(self.res.Uijij.real,
self.res.Uijji.real,
U_init=2, J_init=1,
fixed_F4_F2=True)

assert abs(U_int - 1.6087813069026353) < 1e-4
assert abs(J_int - 0.6085825226244702) < 1e-4
Expand All @@ -55,23 +55,34 @@ def test_U_J_fit(self):

print('------------')
print('Fitting bare interaction with fixed F4/F2 ratio')
U_int, J_int = fit_slater_fulld(self.res.Vijij.real,
self.res.Vijji.real,
U_init=1.7, J_init=0.7,
fixed_F4_F2=True)
U_int, J_int = fit_slater(self.res.Vijij.real,
self.res.Vijji.real,
U_init=1.7, J_init=0.7,
fixed_F4_F2=True)

assert abs(U_int - 13.169980952573283) < 1e-4
assert abs(J_int - 0.7852793988793887) < 1e-4

return

def test_U_J_fit_p(self):
print('------------')
print('Fitting screened interaction for p-shell with fixed F4/F2 ratio')
print(self.res.Uijij.real[:3,:3])
U_int, J_int = fit_slater(self.res.Uijij.real[:3,:3],
self.res.Uijji.real[:3,:3],
U_init=2, J_init=1,
fixed_F4_F2=True)
assert abs(U_int - 1.7803822) < 1e-4
assert abs(J_int - 0.6158827) < 1e-4

def test_F0_F2_F4_fit(self):
print('------------')
print('Fitting screened interaction to F0, F2, F4')
U_int, J_int = fit_slater_fulld(self.res.U_R[(0, 0, 0)].real,
self.res.J_R[(0, 0, 0)].real,
U_init=13, J_init=1,
fixed_F4_F2=False)
U_int, J_int = fit_slater(self.res.U_R[(0, 0, 0)].real,
self.res.J_R[(0, 0, 0)].real,
U_init=13, J_init=1,
fixed_F4_F2=False)

assert abs(U_int - 1.6072376926602756) < 1e-4
assert abs(J_int - 0.6166868032423679) < 1e-4
Expand Down

0 comments on commit 76a268c

Please sign in to comment.