Source code for gpaw.raman.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) dThetadR_qvMM, dTdR_qvMM = wfs.manytci.O_qMM_T_qMM(gd.comm, ksl.Mstart, 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) for kpt in wfs.kpt_u: C_nM = kpt.C_nM for v in range(3): dThetadRv_MM = dThetadR_qvMM[kpt.q, v] 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 momd_skvnm[kpt.s, kpt.k] = np.einsum("k,nm->knm", wfs.kd.ibzk_kc[kpt.k], 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