for i in range(6, 12):
emat_n[1, i, i] -= core_v
basis_i = edrixs.get_fock_bin_by_N(12, 9, 12, 12)
basis_n = []
tmp = edrixs.get_fock_bin_by_N(12, 10, 6, 5, 6, 6)
basis_n.append(tmp)
tmp = edrixs.get_fock_bin_by_N(12, 10, 6, 6, 6, 5)
basis_n.append(tmp)
ncfgs_i, ncfgs_n = len(basis_i), len(basis_n[0])
hmat_i = np.zeros((ncfgs_i, ncfgs_i), dtype=np.complex128)
hmat_n = np.zeros((2, ncfgs_n, ncfgs_n), dtype=np.complex128)
print("edrixs >>> building Hamiltonian without core-hole ...")
hmat_i[:, :] += edrixs.two_fermion(emat_i, basis_i, basis_i)
hmat_i[:, :] += edrixs.four_fermion(umat_i, basis_i)
eval_i, evec_i = scipy.linalg.eigh(hmat_i)
print("edrixs >>> Done!")
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')
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
def get_s_l_ls_values_n(l,basis,evec,ref,ndorb,ntot):
"""
For the 2p to 3d transitions
Calaculate the S_x-, S_y-, S_z-, and S^2-Values after diagonalization
Calaculate the L_x-, L_y-, L_z-, and L^2-Values after diagonalization
Calaculate the LS-Values after diagonalization
Parameters
----------
ndorb: int
Total number of 3d-electrons
ntot:
Total number of electrons
l: int
The overall-angular moment l
evac: 2d complex array
The impurity vector after demoralization.
basis: list of array
Left fock basis :math:`<F_{l}|`.
AND:
Right fock basis :math:`|F_{r}>`.
rb = lb
Returns
-------
spin_prop: list of numpy-arrays
Expectation-Value of S_x, S_y, S_z, and S^2
lang_prop: list of numpy-arrays
Expectation-Value of L_x, L_y, L_z, and L^2
ls: float-numpy-array
Expectation-Value of LS
"""
# Creating the intial Spin-Hamiltonian, which has to be a 16*16 for 2p3d
hh_sx = np.zeros_like(ref)
hh_sy = np.zeros_like(ref)
hh_sz = np.zeros_like(ref)
hh_sx[0:ndorb,0:ndorb] += edrixs.get_sx(l=l)
hh_sy[0:ndorb,0:ndorb] += edrixs.get_sy(l=l)
hh_sz[0:ndorb,0:ndorb] += edrixs.get_sz(l=l)
hh_sx[ndorb:ntot,ndorb:ntot] += edrixs.get_sx(l=l-1)
hh_sy[ndorb:ntot,ndorb:ntot] += edrixs.get_sy(l=l-1)
hh_sz[ndorb:ntot,ndorb:ntot] += edrixs.get_sz(l=l-1)
# Setting up the Spin-Hamiltonian
h_sx = edrixs.two_fermion(hh_sx, basis, basis)
h_sy = edrixs.two_fermion(hh_sy, basis, basis)
h_sz = edrixs.two_fermion(hh_sz, basis, basis)
# Calculating the S-Expectation-Value depending on the Wavefunction-Coefficient
sx = edrixs.cb_op2(h_sx, evec, evec)
sy = edrixs.cb_op2(h_sy, evec, evec)
sz = edrixs.cb_op2(h_sz, evec, evec)
# S2-Value has to be calculated as the mutated-product of the single xyz-Hamiltonian consistent with theory
s2 = edrixs.cb_op2(np.matmul(h_sx,h_sx)+np.matmul(h_sy,h_sy)+np.matmul(h_sz,h_sz), evec, evec)
# Probably are more elegant way is possible as s2 = sx**2 + sy**2 + sz**2, however generates more numerical noise
# ls = np.matmul(sx,sx)+np.matmul(sy,sy)+np.matmul(sz,sz)
# Summarize everything as a list
spin_prop = [sx.diagonal().real,sy.diagonal().real,sz.diagonal().real,s2.diagonal().real]
print("Done with Sx-,Sy-,Sz-, and S2-values!")
# Creating the intial Angular-Hamiltonian, which has to be a 16*16 for 2p3d
hh_lx = np.zeros_like(ref)
hh_ly = np.zeros_like(ref)
hh_lz = np.zeros_like(ref)
hh_lx[0:ndorb,0:ndorb] += edrixs.get_lx(l=l,ispin=True)
hh_ly[0:ndorb,0:ndorb] += edrixs.get_ly(l=l,ispin=True)
hh_lz[0:ndorb,0:ndorb] += edrixs.get_lz(l=l,ispin=True)
hh_lx[ndorb:ntot,ndorb:ntot] += edrixs.get_lx(l=l-1,ispin=True)
hh_ly[ndorb:ntot,ndorb:ntot] += edrixs.get_ly(l=l-1,ispin=True)
hh_lz[ndorb:ntot,ndorb:ntot] += edrixs.get_lz(l=l-1,ispin=True)
# Setting up the Angular-Hamiltonian
h_lx = edrixs.two_fermion(hh_lx, basis, basis)
h_ly = edrixs.two_fermion(hh_ly, basis, basis)
h_lz = edrixs.two_fermion(hh_lz, basis, basis)
# Calculating the L-Expectation-Value depending on the Wavefunction-Coefficient
lx = edrixs.cb_op2(h_lx, evec, evec)
ly = edrixs.cb_op2(h_ly, evec, evec)
lz = edrixs.cb_op2(h_lz, evec, evec)
# L2-Value has to be calculated as the mutated-product of the single xyz-Hamiltonian consistent with theory
l2 = edrixs.cb_op2(np.matmul(h_lx,h_lx)+np.matmul(h_ly,h_ly)+np.matmul(h_lz,h_lz), evec, evec)
# Probably are more elegant way is possible as l2 = lx**2 + ly**2 + lz**2, however generates more numerical noise
# l2 = np.matmul(lx,lx)+np.matmul(ly,ly)+np.matmul(lz,lz)
lang_prop = [lx.diagonal().real,ly.diagonal().real,lz.diagonal().real,l2.diagonal().real]
print("Done with Lx-,Ly-,Lz-, and L2-values!")
# L2-Value has to be calculated as the mutated-product of the single xyz-Hamiltonian consistent with theory
ls = edrixs.cb_op2(np.matmul(h_lx,h_sx)+np.matmul(h_ly,h_sy)+np.matmul(h_lz,h_sz), evec, evec)
# Probably are more elegant way is possible as l2 = lx**2 + ly**2 + lz**2, however generates more numerical noise
# ls = np.matmul(lx,sx)+np.matmul(ly,sy)+np.matmul(sz,sz)
print("Done with LS-values!")
return spin_prop, lang_prop, ls.diagonal().real