def kernel(self, mo1=None):
if len(self.nuc_pair) == 0:
return
cput0 = (logger.process_clock(), logger.perf_counter())
self.check_sanity()
self.dump_flags()
mol = self.mol
dm0 = self._scf.make_rdm1()
mo_coeff = self._scf.mo_coeff
mo_occ = self._scf.mo_occ
ssc_dia = self.make_dso(mol, dm0)
if mo1 is None:
mo1 = self.mo10 = self.solve_mo1()[0]
ssc_pso = self.make_pso(mol, mo1, mo_coeff, mo_occ)
e11 = ssc_dia + ssc_pso
if self.with_fcsd:
ssc_fcsd = self.make_fcsd(self.nuc_pair)
e11 += ssc_fcsd
elif self.with_fc:
ssc_fc = self.make_fc(self.nuc_pair)
e11 += ssc_fc
logger.timer(self, 'spin-spin coupling', *cput0)
if self.verbose > logger.QUIET:
nuc_mag = .5 * (nist.E_MASS / nist.PROTON_MASS) # e*hbar/2m
au2Hz = nist.HARTREE2J / nist.PLANCK
#logger.debug('Unit AU -> Hz %s', au2Hz*nuc_mag**2)
iso_ssc = au2Hz * nuc_mag**2 * numpy.einsum('kii->k', e11) / 3
natm = mol.natm
ktensor = numpy.zeros((natm, natm))
for k, (i, j) in enumerate(self.nuc_pair):
ktensor[i, j] = ktensor[j, i] = iso_ssc[k]
if self.verbose >= logger.DEBUG:
_write(
self.stdout, e11[k],
'\nSSC E11 between %d %s and %d %s' %
(i, self.mol.atom_symbol(i), j,
self.mol.atom_symbol(j)))
# _write(self.stdout, ssc_dia [k], 'dia-magnetism')
# _write(self.stdout, ssc_para[k], 'para-magnetism')
gyro = rhf_ssc._atom_gyro_list(mol)
jtensor = numpy.einsum('ij,i,j->ij', ktensor, gyro, gyro)
label = [
'%2d %-2s' % (ia, mol.atom_symbol(ia)) for ia in range(natm)
]
logger.note(self, 'Reduced spin-spin coupling constant K (Hz)')
tools.dump_mat.dump_tri(self.stdout, ktensor, label)
logger.info(self, '\nNuclear g factor %s', gyro)
logger.note(self, 'Spin-spin coupling constant J (Hz)')
tools.dump_mat.dump_tri(self.stdout, jtensor, label)
return e11
def kernel(self, mo1=None):
if len(self.nuc_pair) == 0:
return
cput0 = (time.clock(), time.time())
self.check_sanity()
self.dump_flags()
mol = self.mol
dm0 = self._scf.make_rdm1()
mo_coeff = self._scf.mo_coeff
mo_occ = self._scf.mo_occ
ssc_dia = self.make_dso(mol, dm0)
if mo1 is None:
mo1 = self.mo10 = self.solve_mo1()[0]
ssc_pso = self.make_pso(mol, mo1, mo_coeff, mo_occ)
e11 = ssc_dia + ssc_pso
if self.with_fcsd:
ssc_fcsd = self.make_fcsd(self.nuc_pair)
e11 += ssc_fcsd
elif self.with_fc:
ssc_fc = self.make_fc(self.nuc_pair)
e11 += ssc_fc
logger.timer(self, 'spin-spin coupling', *cput0)
if self.verbose > logger.QUIET:
nuc_mag = .5 * (nist.E_MASS/nist.PROTON_MASS) # e*hbar/2m
au2Hz = nist.HARTREE2J / nist.PLANCK
#logger.debug('Unit AU -> Hz %s', au2Hz*nuc_mag**2)
iso_ssc = au2Hz * nuc_mag ** 2 * numpy.einsum('kii->k', e11) / 3
natm = mol.natm
ktensor = numpy.zeros((natm,natm))
for k, (i, j) in enumerate(self.nuc_pair):
ktensor[i,j] = ktensor[j,i] = iso_ssc[k]
if self.verbose >= logger.DEBUG:
_write(self.stdout, ssc_dia[k]+ssc_para[k],
'\nSSC E11 between %d %s and %d %s' \
% (i, self.mol.atom_symbol(i),
j, self.mol.atom_symbol(j)))
# _write(self.stdout, ssc_dia [k], 'dia-magnetism')
# _write(self.stdout, ssc_para[k], 'para-magnetism')
gyro = rhf_ssc._atom_gyro_list(mol)
jtensor = numpy.einsum('ij,i,j->ij', ktensor, gyro, gyro)
label = ['%2d %-2s'%(ia, mol.atom_symbol(ia)) for ia in range(natm)]
logger.note(self, 'Reduced spin-spin coupling constant K (Hz)')
tools.dump_mat.dump_tri(self.stdout, ktensor, label)
logger.info(self, '\nNuclear g factor %s', gyro)
logger.note(self, 'Spin-spin coupling constant J (Hz)')
tools.dump_mat.dump_tri(self.stdout, jtensor, label)
return e11
def para(nsrobj, mo10=None, mo_coeff=None, mo_occ=None, shielding_nuc=None):
'''Paramagnetic part of NSR shielding tensors.
'''
if shielding_nuc is None: shielding_nuc = nsrobj.shielding_nuc
# The first order Hamiltonian for rotation part is the same to the
# first order Hamiltonian for magnetic field except a factor of 2.
nsr_para = rhf_nmr.para(nsrobj, mo10, mo_coeff, mo_occ,
shielding_nuc)[0] * 2
mol = nsrobj.mol
im, mass_center = inertia_tensor(mol)
nsr_para = _safe_solve(im, nsr_para)
unit = _atom_gyro_list(mol)[shielding_nuc] * nist.ALPHA**2
return numpy.einsum('ixy,i->ixy', nsr_para, unit)
def nuc(mol, shielding_nuc):
'''Nuclear contributions'''
im, mass_center = inertia_tensor(mol)
charges = mol.atom_charges()
coords = mol.atom_coords()
nsr_nuc = []
for n, atm_id in enumerate(shielding_nuc):
rkl = coords - coords[atm_id]
d = numpy.linalg.norm(rkl, axis=1)
d[atm_id] = 1e100
e11 = numpy.einsum('z,zx,zy->xy', charges / d**3, rkl, rkl)
e11 = numpy.eye(3) * e11.trace() - e11
nsr_nuc.append(e11)
nsr_nuc = _safe_solve(im, numpy.asarray(nsr_nuc))
unit = _atom_gyro_list(mol)[shielding_nuc] * nist.ALPHA**2
return numpy.einsum('ixy,i->ixy', nsr_nuc, unit)
def dia(nsrobj, gauge_orig=None, shielding_nuc=None, dm0=None):
'''Diamagnetic part of NSR tensors.
'''
if shielding_nuc is None: shielding_nuc = nsrobj.shielding_nuc
if dm0 is None: dm0 = nsrobj._scf.make_rdm1()
mol = nsrobj.mol
im, mass_center = inertia_tensor(mol)
if gauge_orig is None:
ao_coords = rhf_mag._get_ao_coords(mol)
# Eq. (34) of JCP, 105, 2804
nsr_dia = rhf_nmr.dia(nsrobj, gauge_orig, shielding_nuc, dm0)
for n, atm_id in enumerate(shielding_nuc):
coord = mol.atom_coord(atm_id)
with mol.with_common_origin(coord):
with mol.with_rinv_origin(coord):
# a11part = (B dot) -1/2 frac{\vec{r}_N}{r_N^3} r_N (dot mu)
h11 = mol.intor('int1e_cg_a11part', comp=9)
e11 = numpy.einsum('xpq,qp->x', h11, dm0).reshape(3, 3)
nsr_dia[n] -= e11 - numpy.eye(3) * e11.trace()
nsr_dia[n] *= 2
else:
nsr_dia = []
for n, atm_id in enumerate(shielding_nuc):
coord = mol.atom_coord(atm_id)
with mol.with_rinv_origin(coord):
with mol.with_common_origin(gauge_orig):
# a11part = (B dot) -1/2 frac{\vec{r}_N}{r_N^3} (r-R_c) (dot mu)
h11 = mol.intor('int1e_cg_a11part', comp=9)
e11 = numpy.einsum('xpq,qp->x', h11, dm0).reshape(3, 3)
with mol.with_common_origin(coord):
# a11part = (B dot) -1/2 frac{\vec{r}_N}{r_N^3} r_N (dot mu)
h11 = mol.intor('int1e_cg_a11part', comp=9)
# e11 ~ (B dot) -1/2 frac{\vec{r}_N}{r_N^3} (R_N-R_c) (dot mu)
e11 -= numpy.einsum('xpq,qp->x', h11, dm0).reshape(3, 3)
e11 = e11 - numpy.eye(3) * e11.trace()
nsr_dia.append(e11)
nsr_dia = _safe_solve(im, numpy.asarray(nsr_dia))
unit = _atom_gyro_list(mol)[shielding_nuc] * nist.ALPHA**2
return numpy.einsum('ixy,i->ixy', nsr_dia, unit)