Source code for gpaw.lcao.dipoletransition

import numpy as np

from gpaw.mpi import world
from gpaw.typing import ArrayND

# NOTE: This routine is not specific to Raman per se. Maybe it should go
#       somewhere else?
def get_dipole_transitions(wfs) -> ArrayND:
r"""
Finds dipole transition matrix elements based on the velocity form.

Dipole and momentum matrix elements are related by the expression:
<nk|r|mk> = -i hbar/m <nk|p|mk> / (E_nk-E_mk)

For n=m this is ill defined, and element will be set to zero.

Parameters
----------
wfs
LCAO WaveFunctions object
"""
p_skvnm = get_momentum_transitions(wfs, False)
r_skvnm = np.zeros_like(p_skvnm)
for kpt in wfs.kpt_u:
# NOTE: Check whether it's this way or other way around.
deltaE = kpt.eps_n[:, None] - kpt.eps_n[None, :]
np.fill_diagonal(deltaE, np.inf)
r_skvnm[kpt.s, kpt.k, :] = -1j * p_skvnm[kpt.s, kpt.k, :] / deltaE
wfs.kd.comm.sum(r_skvnm)
return r_skvnm

[docs]def get_momentum_transitions(wfs, savetofile: bool = True) -> ArrayND:
r"""
Finds the momentum matrix elements:
<nk|p|mk> = k \delta_nm - i <nk|\nabla|mk>

Parameters
----------
wfs
LCAO WaveFunctions object
savetofile: bool
Determines whether matrix is written to the
file mom_skvnm.npy (default=True)
"""
assert wfs.bd.comm.size == 1
assert wfs.mode == 'lcao'
nbands = wfs.bd.nbands
nspins = wfs.nspins
nk = wfs.kd.nibzkpts
gd = wfs.gd
dtype = wfs.dtype
ksl = wfs.ksl

# print(wfs.kd.comm.size, wfs.gd.comm.size, wfs.bd.comm.size)

mom_skvnm = np.zeros((nspins, nk, 3, nbands, nbands), dtype=complex)

ksl.Mstop, False,
derivative=True)

mome_skvnm = np.zeros((nspins, nk, 3, nbands, nbands), dtype=dtype)
momd_skvnm = np.zeros((nspins, nk, 3, nbands, nbands), dtype=dtype)
moma_skvnm = np.zeros((nspins, nk, 3, nbands, nbands), dtype=dtype)

B_cv = 2.0 * np.pi * gd.icell_cv
for kpt in wfs.kpt_u:
C_nM = kpt.C_nM
for v in range(3):
nabla_nn = -(C_nM.conj() @ dThetadRv_MM.conj() @ C_nM.T)
gd.comm.sum(nabla_nn)
mome_skvnm[kpt.s, kpt.k, v] = nabla_nn

# augmentation part
moma_vnm = np.zeros((3, nbands, nbands), dtype=dtype)
for a, P_ni in kpt.P_ani.items():
nabla_iiv = wfs.setups[a].nabla_iiv
moma_vnm += np.einsum('ni,ijv,mj->vnm',
P_ni.conj(), nabla_iiv, P_ni)
gd.comm.sum(moma_vnm)
moma_skvnm[kpt.s, kpt.k] = moma_vnm

# diagonal term
k_v = np.dot(wfs.kd.ibzk_kc[kpt.k], B_cv)
momd_skvnm[kpt.s, kpt.k] = np.einsum("k,nm->knm",
k_v, np.identity(nbands))

mom_skvnm = momd_skvnm - 1j * (mome_skvnm + moma_skvnm)
wfs.kd.comm.sum(mom_skvnm)

if world.rank == 0 and savetofile:
np.save('mom_skvnm.npy', mom_skvnm)
return mom_skvnm