def get_transop(loc, pos):
# get dipole transition operator in local axis
dop = edrixs.get_trans_oper('t2gp32')
dop_g = np.zeros((2, 3, 6, 4), dtype=np.complex)
# transform to golobal axis
for i in range(2):
for j in range(3):
for k in range(3):
dop_g[i, j] += loc[i, j, k] * dop[k]
# RIXS settings
thin, thout, phi = 30 / 180.0 * np.pi, 60 / 180.0 * np.pi, 0.0
ein, eout = 11215.0, 11215.0 # eV
# Wavevector
kin, kout = edrixs.get_wavevector_rixs(thin, thout, phi, ein, eout)
# polarization pi-pi and pi-sigma
for key, alpha, beta in [('pp', 0, 0), ('ps', 0, np.pi / 2.0)]:
ei, ef = edrixs.dipole_polvec_rixs(thin, thout, phi, alpha, beta)
T_i = np.zeros((2, 6, 4), dtype=np.complex)
T_f = np.zeros((2, 4, 6), dtype=np.complex)
for i in range(2):
for j in range(3):
T_i[i] += dop_g[i, j] * ei[j]
T_f[i] += np.conj(np.transpose(dop_g[i, j] * ef[j]))
# multiply phase factor
T_i[i] = T_i[i] * np.exp(+1j * np.dot(pos[i], kin))
T_f[i] = T_f[i] * np.exp(-1j * np.dot(pos[i], kout))
transop_rixs_i = np.zeros((20, 20), dtype=np.complex)
transop_rixs_f = np.zeros((20, 20), dtype=np.complex)
for i in range(2):
off1, off2 = i * 6, 12 + i * 4
transop_rixs_i[off1:off1 + 6, off2:off2 + 4] = T_i[i]
transop_rixs_f[off2:off2 + 4, off1:off1 + 6] = T_f[i]
# write to file
edrixs.write_emat(transop_rixs_i, "rixs_" + key + "/transop_rixs_i.in")
edrixs.write_emat(transop_rixs_f, "rixs_" + key + "/transop_rixs_f.in")
# For XAS, use isotropic polarization
ei = np.array([1, 1, 1]) / np.sqrt(3.0)
T_i = np.zeros((2, 6, 4), dtype=np.complex)
for i in range(2):
for j in range(3):
T_i[i] += dop_g[i, j] * ei[j]
transop_xas = np.zeros((20, 20), dtype=np.complex128)
for i in range(2):
off1, off2 = i * 6, 12 + i * 4
transop_xas[off1:off1 + 6, off2:off2 + 4] = T_i[i]
edrixs.write_emat(transop_xas, "xas/transop_xas.in")
def get_transop(loc, pos):
dop = edrixs.get_trans_oper('t2gp')
dop_g = np.zeros((2, 3, 6, 6), dtype=np.complex)
for i in range(2):
dop_g[i, 0] = loc[i, 0, 0] * dop[0] + loc[i, 0, 1] * dop[1] + loc[
i, 0, 2] * dop[2]
dop_g[i, 1] = loc[i, 1, 0] * dop[0] + loc[i, 1, 1] * dop[1] + loc[
i, 1, 2] * dop[2]
dop_g[i, 2] = loc[i, 2, 0] * dop[0] + loc[i, 2, 1] * dop[1] + loc[
i, 2, 2] * dop[2]
# for RIXS
thin, thout, phi = 30 / 180.0 * np.pi, 60 / 180.0 * np.pi, 0.0
ein, eout = 11215.0, 11215.0 # eV
kin, kout = edrixs.get_wavevector_rixs(thin, thout, phi, ein, eout)
# polarization pi-pi and pi-sigma
for key, alpha, beta in [('pp', 0, 0), ('ps', 0, np.pi)]:
ei, ef = edrixs.dipole_polvec_rixs(thin, thout, phi, alpha, beta)
T_i = np.zeros((2, 6, 6), dtype=np.complex)
T_o = np.zeros((2, 6, 6), dtype=np.complex)
for i in range(2):
T_i[i] = (dop_g[i, 0] * ei[0] + dop_g[i, 1] * ei[1] +
dop_g[i, 2] * ei[2]) * np.exp(1j * np.dot(pos[i], kin))
T_o[i] = np.exp(-1j * np.dot(pos[i], kout)) * np.conj(
np.transpose(dop_g[i, 0] * ef[0] + dop_g[i, 1] * ef[1] +
dop_g[i, 2] * ef[2]))
transop_rixs_i = np.zeros((24, 24), dtype=np.complex)
transop_rixs_f = np.zeros((24, 24), dtype=np.complex)
for i in range(2):
off1, off2 = i * 6, 12 + i * 6
transop_rixs_i[off1:off1 + 6, off2:off2 + 6] = T_i[i]
transop_rixs_f[off2:off2 + 6, off1:off1 + 6] = T_o[i]
edrixs.write_emat(transop_rixs_i, "rixs_" + key + "/transop_rixs_i.in")
edrixs.write_emat(transop_rixs_f, "rixs_" + key + "/transop_rixs_f.in")
# For XAS
ei = np.array([1, 1, 1]) / np.sqrt(3.0)
T_i = np.zeros((2, 6, 6), dtype=np.complex)
for i in range(2):
T_i[i] = dop_g[i, 0] * ei[0] + dop_g[i, 1] * ei[1] + dop_g[i,
2] * ei[2]
transop_xas = np.zeros((24, 24), dtype=np.complex128)
for i in range(2):
off1, off2 = i * 6, 12 + i * 6
transop_xas[off1:off1 + 6, off2:off2 + 6] = T_i[i]
edrixs.write_emat(transop_xas, "xas/transop_xas.in")
def get_transop():
tmp = edrixs.get_trans_oper('t2gp')
dipole = np.zeros((3, 28, 28), dtype=np.complex)
for i in range(3):
tmp[i] = edrixs.cb_op2(tmp[i], edrixs.tmat_c2j(1), edrixs.tmat_c2j(1))
dipole[i, 0:6, 24:28] = tmp[i, 0:6, 2:6]
# for RIXS
thin, thout, phi = 45 / 180.0 * np.pi, 45 / 180.0 * np.pi, 0.0
# polarization pi-pi and pi-sigma
for key, alpha, beta in [('pp', 0, 0), ('ps', 0, np.pi)]:
ei, ef = edrixs.dipole_polvec_rixs(thin, thout, phi, alpha, beta)
transop_rixs_i = dipole[0] * ei[0] + dipole[1] * ei[1] + dipole[
2] * ei[2]
transop_rixs_f = np.conj(
np.transpose(dipole[0] * ef[0] + dipole[1] * ef[1] +
dipole[2] * ef[2]))
edrixs.write_emat(transop_rixs_i, "rixs_" + key + "/transop_rixs_i.in")
edrixs.write_emat(transop_rixs_f, "rixs_" + key + "/transop_rixs_f.in")
# For XAS
ei = np.array([1, 1, 1]) / np.sqrt(3.0)
transop_xas = dipole[0] * ei[0] + dipole[1] * ei[1] + dipole[2] * ei[2]
edrixs.write_emat(transop_xas, "xas/transop_xas.in")
def ed():
# 1-10: Ni-3d valence orbitals, 11-16: Ni-2p core orbitals
# Single particle basis: complex shperical Harmonics
ndorb, nporb, ntot = 10, 6, 16
emat_i = np.zeros((ntot, ntot), dtype=np.complex)
emat_n = np.zeros((ntot, ntot), dtype=np.complex)
# 4-index Coulomb interaction tensor, parameterized by
# Slater integrals, which are obtained from Cowan's code
F2_d, F4_d = 7.9521, 4.9387
# Averaged dd Coulomb interaction is set to be zero
F0_d = edrixs.get_F0('d', F2_d, F4_d)
G1_dp, G3_dp = 4.0509, 2.3037
# Averaged dp Coulomb interaction is set to be zero
F0_dp, F2_dp = edrixs.get_F0('dp', G1_dp, G3_dp), 7.33495
umat_i = edrixs.get_umat_slater(
'dp',
F0_d,
F2_d,
F4_d, # dd
0,
0,
0,
0, # dp
0,
0) # pp
umat_n = edrixs.get_umat_slater(
'dp',
F0_d,
F2_d,
F4_d, # dd
F0_dp,
F2_dp,
G1_dp,
G3_dp, # dp
0,
0) # pp
# Atomic spin-orbit coupling
zeta_d, zeta_p = 0.083, 11.24
emat_i[0:ndorb, 0:ndorb] += edrixs.atom_hsoc('d', zeta_d)
emat_n[0:ndorb, 0:ndorb] += edrixs.atom_hsoc('d', zeta_d)
emat_n[ndorb:ntot, ndorb:ntot] += edrixs.atom_hsoc('p', zeta_p)
# Tetragonal crystal field splitting terms,
# which are first defined in the real cubic Harmonics basis,
# and then transformed to complex shperical Harmonics basis.
dt, ds, dq = 0.011428, 0.035714, 0.13
tmp = np.zeros((5, 5), dtype=np.complex)
tmp[0, 0] = 6 * dq - 2 * ds - 6 * dt # d3z2-r2
tmp[1, 1] = -4 * dq - 1 * ds + 4 * dt # dzx
tmp[2, 2] = -4 * dq - 1 * ds + 4 * dt # dzy
tmp[3, 3] = 6 * dq + 2 * ds - 1 * dt # dx2-y2
tmp[4, 4] = -4 * dq + 2 * ds - 1 * dt # dxy
tmp[:, :] = edrixs.cb_op(tmp, edrixs.tmat_r2c('d'))
emat_i[0:ndorb:2, 0:ndorb:2] += tmp
emat_i[1:ndorb:2, 1:ndorb:2] += tmp
emat_n[0:ndorb:2, 0:ndorb:2] += tmp
emat_n[1:ndorb:2, 1:ndorb:2] += tmp
# Build Fock basis in its binary form
basis_i = edrixs.get_fock_bin_by_N(ndorb, 8, nporb, nporb)
basis_n = edrixs.get_fock_bin_by_N(ndorb, 9, nporb, nporb - 1)
ncfg_i, ncfg_n = len(basis_i), len(basis_n)
# Build many-body Hamiltonian in Fock basis
hmat_i = np.zeros((ncfg_i, ncfg_i), dtype=np.complex)
hmat_n = np.zeros((ncfg_n, ncfg_n), dtype=np.complex)
hmat_i[:, :] += edrixs.two_fermion(emat_i, basis_i, basis_i)
hmat_i[:, :] += edrixs.four_fermion(umat_i, basis_i)
hmat_n[:, :] += edrixs.two_fermion(emat_n, basis_n, basis_n)
hmat_n[:, :] += edrixs.four_fermion(umat_n, basis_n)
# Do exact-diagonalization to get eigenvalues and eigenvectors
eval_i, evec_i = np.linalg.eigh(hmat_i)
eval_n, evec_n = np.linalg.eigh(hmat_n)
# Build dipolar transition operators
dipole = np.zeros((3, ntot, ntot), dtype=np.complex)
T_abs = np.zeros((3, ncfg_n, ncfg_i), dtype=np.complex)
T_emi = np.zeros((3, ncfg_i, ncfg_n), dtype=np.complex)
tmp = edrixs.get_trans_oper('dp')
for i in range(3):
dipole[i, 0:ndorb, ndorb:ntot] = tmp[i]
# First, in the Fock basis
T_abs[i] = edrixs.two_fermion(dipole[i], basis_n, basis_i)
# Then, transfrom to the eigenvector basis
T_abs[i] = edrixs.cb_op2(T_abs[i], evec_n, evec_i)
T_emi[i] = np.conj(np.transpose(T_abs[i]))
return eval_i, eval_n, T_abs, T_emi
print("edrixs >>> Building Hamiltonian with a core-hole ...")
eval_n = np.zeros((2, ncfgs_n), dtype=np.float64)
evec_n = np.zeros((2, ncfgs_n, ncfgs_n), dtype=np.complex128)
for i in range(2):
hmat_n[i] += edrixs.two_fermion(emat_n[i], basis_n[i], basis_n[i])
hmat_n[i] += edrixs.four_fermion(umat_n[i], basis_n[i])
eval_n[i], evec_n[i] = scipy.linalg.eigh(hmat_n[i])
print("edrixs >>> Done!")
edrixs.write_tensor(eval_i, 'eval_i.dat')
edrixs.write_tensor(eval_n, 'eval_n.dat')
# Building transition operators
print("edrixs >>> building transition operators ...")
tran_ptod = edrixs.get_trans_oper('t2gp')
for i in range(3):
tran_ptod[i, :, :] = edrixs.cb_op2(tran_ptod[i],
edrixs.tmat_c2r('t2g', True),
edrixs.tmat_c2r('p', True))
dipole_n = np.zeros((2, 3, norbs, norbs), dtype=np.complex128)
dipole_n[0, :, 0:6, 12:18] = tran_ptod
dipole_n[1, :, 6:12, 18:24] = tran_ptod
trop_n = np.zeros((2, 3, ncfgs_n, ncfgs_i), dtype=np.complex128)
for i in range(2):
for j in range(3):
trop_n[i, j] = edrixs.two_fermion(dipole_n[i, j], basis_n[i],
basis_i)
trop_n[i, j] = edrixs.cb_op2(trop_n[i, j], evec_n[i], evec_i)
Ir_trop = np.zeros((2, 3, ncfgs_n, ncfgs_i), dtype=np.complex128)