def cart2spinor(l):
'''Cartesian to spinor for angular moment l'''
from pyscf import gto
return gto.cart2spinor_l(l)
def so_by_shell(mol, shls, ecpatm_id, ecpbas):
'''SO-ECP
i/2 <Pauli_matrix dot l U(r)>
'''
ish, jsh = shls
li = mol.bas_angular(ish)
npi = mol.bas_nprim(ish)
nci = mol.bas_nctr(ish)
ai = mol.bas_exp(ish)
ci = mol._libcint_ctr_coeff(ish)
icart = (li + 1) * (li + 2) // 2
lj = mol.bas_angular(jsh)
npj = mol.bas_nprim(jsh)
ncj = mol.bas_nctr(jsh)
aj = mol.bas_exp(jsh)
cj = mol._libcint_ctr_coeff(jsh)
jcart = (lj + 1) * (lj + 2) // 2
rc = mol.atom_coord(ecpatm_id)
rcb = rc - mol.bas_coord(jsh)
r_cb = numpy.linalg.norm(rcb)
rca = rc - mol.bas_coord(ish)
r_ca = numpy.linalg.norm(rca)
#rs, ws = radi.treutler(99)
rs, ws = radi.gauss_chebyshev(99)
i_fac_cache = cache_fac(li, rca)
j_fac_cache = cache_fac(lj, rcb)
g1 = numpy.zeros((nci, ncj, 3, icart, jcart), dtype=numpy.complex128)
for lc in range(5): # up to g function
ecpbasi = ecpbas[ecpbas[:, ANG_OF] == lc]
if len(ecpbasi) == 0:
continue
ur = rad_part(mol, ecpbasi, rs) * ws
idx = abs(ur) > 1e-80
rur = numpy.array(
[ur[idx] * rs[idx]**lab for lab in range(li + lj + 1)])
fi = facs_rad(mol, ish, lc, r_ca, rs)[:, :, idx].copy()
fj = facs_rad(mol, jsh, lc, r_cb, rs)[:, :, idx].copy()
angi = facs_ang(type2_ang_part(li, lc, -rca), li, lc, i_fac_cache)
angj = facs_ang(type2_ang_part(lj, lc, -rcb), lj, lc, j_fac_cache)
# Note the factor 2/(2l+1) in JCP 82 2664 is not multiplied here
# because the ECP parameter has been scaled by 2/(2l+1) in CRENBL
jmm = angular_moment_matrix(lc)
for ic in range(nci):
for jc in range(ncj):
rad_all = numpy.einsum('pr,ir,jr->pij', rur, fi[ic], fj[jc])
for i1 in range(li + 1):
for j1 in range(lj + 1):
g1[ic, jc] += numpy.einsum('pq,imp,jnq,lmn->lij',
rad_all[i1 + j1], angi[i1],
angj[j1], jmm)
g1 *= (numpy.pi * 4)**2
gspinor = numpy.empty((nci, ncj, li * 4 + 2, lj * 4 + 2),
dtype=numpy.complex128)
for ic in range(nci):
for jc in range(ncj):
ui = numpy.asarray(gto.cart2spinor_l(li))
uj = numpy.asarray(gto.cart2spinor_l(lj))
s = lib.PauliMatrices * .5j
gspinor[ic, jc] = numpy.einsum('sxy,spq,xpi,yqj->ij', s, g1[ic,
jc],
ui.conj(), uj)
return gspinor.transpose(0, 2, 1, 3).reshape(nci * (li * 4 + 2), -1)
