def kernel(method, efg_nuc=None):
log = lib.logger.Logger(method.stdout, method.verbose)
log.info(
'\n******** EFG for 4-component SCF methods (In testing) ********')
mol = method.mol
if efg_nuc is None:
efg_nuc = range(mol.natm)
c = lib.param.LIGHT_SPEED
dm = method.make_rdm1()
log.info('\nElectric Field Gradient Tensor Results')
n2c = mol.nao_2c()
coords = mol.atom_coords()
aoLa, aoLb = mol.eval_gto('GTOval_spinor', coords)
aoSa, aoSb = mol.eval_gto('GTOval_sp_spinor', coords)
efg = []
for i, atm_id in enumerate(efg_nuc):
# The electronic quadrupole operator (3 \vec{r} \vec{r} - r^2) / r^5
with mol.with_rinv_origin(coords[atm_id]):
ipipv = mol.intor('int1e_ipiprinv_spinor',
9).reshape(3, 3, n2c, n2c)
ipvip = mol.intor('int1e_iprinvip_spinor',
9).reshape(3, 3, n2c, n2c)
h1LL = ipipv + ipvip # (nabla i | r/r^3 | j)
h1LL = h1LL + h1LL.conj().transpose(0, 1, 3, 2)
trace = h1LL[0, 0] + h1LL[1, 1] + h1LL[2, 2]
h1LL[0, 0] -= trace
h1LL[1, 1] -= trace
h1LL[2, 2] -= trace
ipipv = mol.intor('int1e_ipipsprinvsp_spinor',
9).reshape(3, 3, n2c, n2c)
ipvip = mol.intor('int1e_ipsprinvspip_spinor',
9).reshape(3, 3, n2c, n2c)
h1SS = ipipv + ipvip # (nabla i | r/r^3 | j)
h1SS = h1SS + h1SS.conj().transpose(0, 1, 3, 2)
trace = h1SS[0, 0] + h1SS[1, 1] + h1SS[2, 2]
h1SS[0, 0] -= trace
h1SS[1, 1] -= trace
h1SS[2, 2] -= trace
fcLL = numpy.einsum('p,q->pq', aoLa[atm_id].conj(), aoLa[atm_id])
fcLL += numpy.einsum('p,q->pq', aoLb[atm_id].conj(), aoLb[atm_id])
fcSS = numpy.einsum('p,q->pq', aoSa[atm_id].conj(), aoSa[atm_id])
fcSS += numpy.einsum('p,q->pq', aoSb[atm_id].conj(), aoSb[atm_id])
fcsd = numpy.einsum('xyij,ji->xy', h1LL, dm[:n2c, :n2c])
fcsd += numpy.einsum('xyij,ji->xy', h1SS, dm[n2c:, n2c:]) * (.5 / c)**2
fc = numpy.einsum('ij,ji->', fcLL, dm[:n2c, :n2c])
fc += numpy.einsum('ij,ji->', fcSS, dm[n2c:, n2c:]) * (.5 / c)**2
efg_e = fcsd - 8 * numpy.pi / 3 * numpy.eye(3) * fc
efg_nuc = rhf_efg._get_quad_nuc(mol, atm_id)
v = efg_nuc - efg_e
efg.append(v)
rhf_efg._analyze(mol, atm_id, v.real, log)
return numpy.asarray(efg).real
def kernel(method, efg_nuc=None):
log = lib.logger.Logger(method.stdout, method.verbose)
log.info('\n******** EFG for 4-component SCF methods (In testing) ********')
mol = method.mol
if efg_nuc is None:
efg_nuc = range(mol.natm)
dm = method.make_rdm1()
log.info('\nElectric Field Gradient Tensor Results')
n2c = mol.nao_2c()
coords = mol.atom_coords()
aoLa, aoLb = mol.eval_gto('GTOval_spinor', coords)
aoSa, aoSb = mol.eval_gto('GTOval_sp_spinor', coords)
efg = []
for i, atm_id in enumerate(efg_nuc):
# The electronic quadrupole operator (3 \vec{r} \vec{r} - r^2) / r^5
with mol.with_rinv_origin(coords[atm_id]):
ipipv = mol.intor('int1e_ipiprinv_spinor', 9).reshape(3,3,n2c,n2c)
ipvip = mol.intor('int1e_iprinvip_spinor', 9).reshape(3,3,n2c,n2c)
h1LL = ipipv + ipvip # (nabla i | r/r^3 | j)
h1LL = h1LL + h1LL.conj().transpose(0,1,3,2)
trace = h1LL[0,0] + h1LL[1,1] + h1LL[2,2]
h1LL[0,0] -= trace
h1LL[1,1] -= trace
h1LL[2,2] -= trace
ipipv = mol.intor('int1e_ipipsprinvsp_spinor', 9).reshape(3,3,n2c,n2c)
ipvip = mol.intor('int1e_ipsprinvspip_spinor', 9).reshape(3,3,n2c,n2c)
h1SS = ipipv + ipvip # (nabla i | r/r^3 | j)
h1SS = h1SS + h1SS.conj().transpose(0,1,3,2)
trace = h1SS[0,0] + h1SS[1,1] + h1SS[2,2]
h1SS[0,0] -= trace
h1SS[1,1] -= trace
h1SS[2,2] -= trace
fcLL = numpy.einsum('p,q->pq', aoLa[atm_id].conj(), aoLa[atm_id])
fcLL+= numpy.einsum('p,q->pq', aoLb[atm_id].conj(), aoLb[atm_id])
fcSS = numpy.einsum('p,q->pq', aoSa[atm_id].conj(), aoSa[atm_id])
fcSS+= numpy.einsum('p,q->pq', aoSb[atm_id].conj(), aoSb[atm_id])
fcsd = numpy.einsum('xyij,ji->xy', h1LL, dm[:n2c,:n2c])
fcsd+= numpy.einsum('xyij,ji->xy', h1SS, dm[n2c:,n2c:])
fc = numpy.einsum('ij,ji->', fcLL, dm[:n2c,:n2c])
fc+= numpy.einsum('ij,ji->', fcSS, dm[n2c:,n2c:])
efg_e = fcsd - 8*numpy.pi/3 * numpy.eye(3) * fc
efg_nuc = rhf_efg._get_quad_nuc(mol, atm_id)
v = efg_nuc - efg_e
efg.append(v)
rhf_efg._analyze(mol, atm_id, v, log)
return numpy.asarray(efg)