def _atom_gyro_list(mol):
gyro = []
for ia in range(mol.natm):
symb = mol.atom_symbol(ia)
if symb in mol.nucprop:
prop = mol.nucprop[symb]
mass = prop.get('mass', None)
gyro.append(get_nuc_g_factor(symb, mass))
else:
# Get default isotope
gyro.append(get_nuc_g_factor(symb))
return numpy.array(gyro)
def _atom_gyro_list(mol):
gyro = []
for ia in range(mol.natm):
symb = mol.atom_symbol(ia)
if symb in mol.nucprop:
prop = mol.nucprop[symb]
mass = prop.get('mass', None)
gyro.append(get_nuc_g_factor(symb, mass))
else:
# Get default isotope
gyro.append(get_nuc_g_factor(symb))
return numpy.array(gyro)
def make_fcdip(hfcobj, dm0, hfc_nuc=None, verbose=None):
'''The contribution of Fermi-contact term and dipole-dipole interactions'''
log = logger.new_logger(hfcobj, verbose)
mol = hfcobj.mol
if hfc_nuc is None:
hfc_nuc = range(mol.natm)
if isinstance(dm0, numpy.ndarray) and dm0.ndim == 2: # RHF DM
return numpy.zeros((3,3))
dma, dmb = dm0
spindm = dma - dmb
effspin = mol.spin * .5
e_gyro = .5 * nist.G_ELECTRON
nuc_mag = .5 * (nist.E_MASS/nist.PROTON_MASS) # e*hbar/2m
au2MHz = nist.HARTREE2J / nist.PLANCK * 1e-6
fac = nist.ALPHA**2 / 2 / effspin * e_gyro * au2MHz
hfc = []
for i, atm_id in enumerate(hfc_nuc):
nuc_gyro = get_nuc_g_factor(mol.atom_symbol(atm_id)) * nuc_mag
h1 = _get_integrals_fcdip(mol, atm_id)
fcsd = numpy.einsum('xyij,ji->xy', h1, spindm)
h1fc = _get_integrals_fc(mol, atm_id)
fc = numpy.einsum('ij,ji', h1fc, spindm)
sd = fcsd + numpy.eye(3) * fc
log.info('FC of atom %d %s (in MHz)', atm_id, fac * nuc_gyro * fc)
if hfcobj.verbose >= logger.INFO:
_write(hfcobj, align(fac*nuc_gyro*sd)[0], 'SD of atom %d (in MHz)' % atm_id)
hfc.append(fac * nuc_gyro * fcsd)
return numpy.asarray(hfc)
def make_fcdip(hfcobj, dm0, hfc_nuc=None, verbose=None):
'''The contribution of Fermi-contact term and dipole-dipole interactions'''
log = logger.new_logger(hfcobj, verbose)
mol = hfcobj.mol
if hfc_nuc is None:
hfc_nuc = range(mol.natm)
if isinstance(dm0, numpy.ndarray) and dm0.ndim == 2: # RHF DM
return numpy.zeros((3,3))
dma, dmb = dm0
spindm = dma - dmb
effspin = mol.spin * .5
e_gyro = .5 * nist.G_ELECTRON
nuc_mag = .5 * (nist.E_MASS/nist.PROTON_MASS) # e*hbar/2m
au2MHz = nist.HARTREE2J / nist.PLANCK * 1e-6
fac = nist.ALPHA**2 / 2 / effspin * e_gyro * au2MHz
hfc = []
for i, atm_id in enumerate(hfc_nuc):
nuc_gyro = get_nuc_g_factor(mol.atom_symbol(atm_id)) * nuc_mag
h1 = _get_integrals_fcdip(mol, atm_id)
fcsd = numpy.einsum('xyij,ji->xy', h1, spindm)
h1fc = _get_integrals_fc(mol, atm_id)
fc = numpy.einsum('ij,ji', h1fc, spindm)
sd = fcsd + numpy.eye(3) * fc
log.info('FC of atom %d %s (in MHz)', atm_id, fac * nuc_gyro * fc)
if hfcobj.verbose >= logger.INFO:
_write(hfcobj, align(fac*nuc_gyro*sd)[0], 'SD of atom %d (in MHz)' % atm_id)
hfc.append(fac * nuc_gyro * fcsd)
return numpy.asarray(hfc)
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 = [
get_nuc_g_factor(mol.atom_symbol(ia)) for ia in range(natm)
]
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(hfcobj, with_gaunt=False, verbose=None):
log = lib.logger.new_logger(hfcobj, verbose)
mf = hfcobj._scf
mol = mf.mol
# Add finite field to remove degeneracy
nuc_spin = numpy.ones(3) * 1e-6
sc = numpy.dot(mf.get_ovlp(), mf.mo_coeff)
h0 = reduce(numpy.dot, (sc * mf.mo_energy, sc.conj().T))
c = lib.param.LIGHT_SPEED
n4c = h0.shape[0]
n2c = n4c // 2
Sigma = numpy.zeros((3, n4c, n4c), dtype=h0.dtype)
Sigma[:, :n2c, :n2c] = mol.intor('int1e_sigma_spinor', comp=3)
Sigma[:, n2c:,
n2c:] = .25 / c**2 * mol.intor('int1e_spsigmasp_spinor', comp=3)
hfc = []
for atm_id in range(mol.natm):
symb = mol.atom_symbol(atm_id)
nuc_mag = .5 * (nist.E_MASS / nist.PROTON_MASS) # e*hbar/2m
nuc_gyro = get_nuc_g_factor(symb) * nuc_mag
e_gyro = .5 * nist.G_ELECTRON
au2MHz = nist.HARTREE2J / nist.PLANCK * 1e-6
fac = nist.ALPHA**2 * nuc_gyro * e_gyro * au2MHz
#logger.debug('factor (MHz) %s', fac)
h01 = make_h01(mol, 0)
mo_occ = mf.mo_occ
mo_coeff = mf.mo_coeff
if 0:
h01b = h0 + numpy.einsum('xij,x->ij', h01, nuc_spin)
h01b = reduce(numpy.dot, (mf.mo_coeff.conj().T, h01b, mf.mo_coeff))
mo_energy, v = numpy.linalg.eigh(h01b)
mo_coeff = numpy.dot(mf.mo_coeff, v)
mo_occ = mf.get_occ(mo_energy, mo_coeff)
occidx = mo_occ > 0
orbo = mo_coeff[:, occidx]
dm0 = numpy.dot(orbo, orbo.T.conj())
e01 = numpy.einsum('xij,ji->x', h01, dm0) * fac
effspin = numpy.einsum('xij,ji->x', Sigma, dm0) * .5
log.debug('atom %d Eff-spin %s', atm_id, effspin.real)
e01 = (e01 / effspin).real
hfc.append(e01)
return numpy.asarray(hfc)
def kernel(hfcobj, with_gaunt=False, verbose=None):
log = lib.logger.new_logger(hfcobj, verbose)
mf = hfcobj._scf
mol = mf.mol
# Add finite field to remove degeneracy
nuc_spin = numpy.ones(3) * 1e-6
sc = numpy.dot(mf.get_ovlp(), mf.mo_coeff)
h0 = reduce(numpy.dot, (sc*mf.mo_energy, sc.conj().T))
c = lib.param.LIGHT_SPEED
n4c = h0.shape[0]
n2c = n4c // 2
Sigma = numpy.zeros((3,n4c,n4c), dtype=h0.dtype)
Sigma[:,:n2c,:n2c] = mol.intor('int1e_sigma_spinor', comp=3)
Sigma[:,n2c:,n2c:] = .25/c**2 * mol.intor('int1e_spsigmasp_spinor', comp=3)
hfc = []
for atm_id in range(mol.natm):
symb = mol.atom_symbol(atm_id)
nuc_mag = .5 * (nist.E_MASS/nist.PROTON_MASS) # e*hbar/2m
nuc_gyro = get_nuc_g_factor(symb) * nuc_mag
e_gyro = .5 * nist.G_ELECTRON
au2MHz = nist.HARTREE2J / nist.PLANCK * 1e-6
fac = nist.ALPHA**2 * nuc_gyro * e_gyro * au2MHz
#logger.debug('factor (MHz) %s', fac)
h01 = make_h01(mol, 0)
mo_occ = mf.mo_occ
mo_coeff = mf.mo_coeff
if 0:
h01b = h0 + numpy.einsum('xij,x->ij', h01, nuc_spin)
h01b = reduce(numpy.dot, (mf.mo_coeff.conj().T, h01b, mf.mo_coeff))
mo_energy, v = numpy.linalg.eigh(h01b)
mo_coeff = numpy.dot(mf.mo_coeff, v)
mo_occ = mf.get_occ(mo_energy, mo_coeff)
occidx = mo_occ > 0
orbo = mo_coeff[:,occidx]
dm0 = numpy.dot(orbo, orbo.T.conj())
e01 = numpy.einsum('xij,ji->x', h01, dm0) * fac
effspin = numpy.einsum('xij,ji->x', Sigma, dm0) * .5
log.debug('atom %d Eff-spin %s', atm_id, effspin.real)
e01 = (e01 / effspin).real
hfc.append(e01)
return numpy.asarray(hfc)
def make_pso_soc(hfcobj, hfc_nuc=None):
'''Spin-orbit coupling correction'''
mol = hfcobj.mol
if hfc_nuc is None:
hfc_nuc = range(mol.natm)
mf = hfcobj._scf
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
effspin = mol.spin * .5
e_gyro = .5 * nist.G_ELECTRON
nuc_mag = .5 * (nist.E_MASS/nist.PROTON_MASS) # e*hbar/2m
au2MHz = nist.HARTREE2J / nist.PLANCK * 1e-6
fac = nist.ALPHA**4 / 4 / effspin * e_gyro * au2MHz
occidxa = mo_occ[0] > 0
occidxb = mo_occ[1] > 0
orboa = mo_coeff[0][:, occidxa]
orbva = mo_coeff[0][:,~occidxa]
orbob = mo_coeff[1][:, occidxb]
orbvb = mo_coeff[1][:,~occidxb]
# Note sigma_z is considered in h1_soc integral.
# mo1b has the associated sign (-)
mo1a, mo1b = hfcobj.solve_mo1()[0]
dm1a = _dm1_mo2ao(mo1a, orbva, orboa)
dm1b = _dm1_mo2ao(mo1b, orbvb, orbob)
dm1 = dm1a + dm1b
dm1 = dm1 - dm1.transpose(0,2,1)
para = []
for n, atm_id in enumerate(hfc_nuc):
nuc_gyro = get_nuc_g_factor(mol.atom_symbol(atm_id)) * nuc_mag
# Imaginary part of H01 operator
# Im[A01 dot p] = Im[vec{r}/r^3 x vec{p}] = Im[-i p (1/r) x p] = -p (1/r) x p
mol.set_rinv_origin(mol.atom_coord(atm_id))
h1ao = -mol.intor_asymmetric('int1e_prinvxp', 3)
de = numpy.einsum('xij,yij->xy', h1ao, dm1)
de *= fac * nuc_gyro
if hfcobj.verbose >= logger.INFO:
_write(hfcobj, align(de)[0], 'PSO of atom %d (in MHz)' % atm_id)
para.append(de)
return numpy.asarray(para)
def make_pso_soc(hfcobj, hfc_nuc=None):
'''Spin-orbit coupling correction'''
mol = hfcobj.mol
if hfc_nuc is None:
hfc_nuc = range(mol.natm)
mf = hfcobj._scf
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
effspin = mol.spin * .5
e_gyro = .5 * nist.G_ELECTRON
nuc_mag = .5 * (nist.E_MASS / nist.PROTON_MASS) # e*hbar/2m
au2MHz = nist.HARTREE2J / nist.PLANCK * 1e-6
fac = nist.ALPHA**4 / 4 / effspin * e_gyro * au2MHz
occidxa = mo_occ[0] > 0
occidxb = mo_occ[1] > 0
orboa = mo_coeff[0][:, occidxa]
orbva = mo_coeff[0][:, ~occidxa]
orbob = mo_coeff[1][:, occidxb]
orbvb = mo_coeff[1][:, ~occidxb]
# Note sigma_z is considered in h1_soc integral.
# mo1b has the associated sign (-)
mo1a, mo1b = hfcobj.solve_mo1()[0]
dm1a = _dm1_mo2ao(mo1a, orbva, orboa)
dm1b = _dm1_mo2ao(mo1b, orbvb, orbob)
dm1 = dm1a + dm1b
dm1 = dm1 - dm1.transpose(0, 2, 1)
para = []
for n, atm_id in enumerate(hfc_nuc):
nuc_gyro = get_nuc_g_factor(mol.atom_symbol(atm_id)) * nuc_mag
# Imaginary part of H01 operator
# Im[A01 dot p] = Im[vec{r}/r^3 x vec{p}] = Im[-i p (1/r) x p] = -p (1/r) x p
mol.set_rinv_origin(mol.atom_coord(atm_id))
h1ao = -mol.intor_asymmetric('int1e_prinvxp', 3)
de = numpy.einsum('xij,yij->xy', h1ao, dm1)
de *= fac * nuc_gyro
if hfcobj.verbose >= logger.INFO:
_write(hfcobj, align(de)[0], 'PSO of atom %d (in MHz)' % atm_id)
para.append(de)
return numpy.asarray(para)
def make_pso_soc(hfcobj, hfc_nuc=None):
'''Spin-orbit coupling correction'''
mol = hfcobj.mol
if hfc_nuc is None:
hfc_nuc = range(mol.natm)
mf = hfcobj._scf
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
effspin = mol.spin * .5
e_gyro = .5 * nist.G_ELECTRON
nuc_mag = .5 * (nist.E_MASS/nist.PROTON_MASS) # e*hbar/2m
au2MHz = nist.HARTREE2J / nist.PLANCK * 1e-6
fac = nist.ALPHA**4 / 4 / effspin * e_gyro * au2MHz
occidxa = mo_occ[0] > 0
occidxb = mo_occ[1] > 0
orboa = mo_coeff[0][:, occidxa]
orbva = mo_coeff[0][:,~occidxa]
orbob = mo_coeff[1][:, occidxb]
orbvb = mo_coeff[1][:,~occidxb]
nocca = orboa.shape[1]
nvira = orbva.shape[1]
noccb = orbob.shape[1]
nvirb = orbvb.shape[1]
mo1a, mo1b = solve_mo1_pso(hfcobj, hfc_nuc)
mo1a = mo1a.reshape(len(hfc_nuc),3,nvira,nocca)
mo1b = mo1b.reshape(len(hfc_nuc),3,nvirb,noccb)
dm0 = hfcobj._scf.make_rdm1()
h1a, h1b = uhf_hfc.make_h1_soc(hfcobj, dm0)
h1a = numpy.asarray([reduce(numpy.dot, (orbva.T, x, orboa)) for x in h1a])
h1b = numpy.asarray([reduce(numpy.dot, (orbvb.T, x, orbob)) for x in h1b])
para = []
for n, atm_id in enumerate(hfc_nuc):
nuc_gyro = get_nuc_g_factor(mol.atom_symbol(atm_id)) * nuc_mag
e = numpy.einsum('xij,yij->xy', mo1a[n], h1a) * 2
e+= numpy.einsum('xij,yij->xy', mo1b[n], h1b) * 2
para.append(fac * nuc_gyro * e)
return numpy.asarray(para)
def make_pso_soc(hfcobj, hfc_nuc=None):
'''Spin-orbit coupling correction'''
mol = hfcobj.mol
if hfc_nuc is None:
hfc_nuc = range(mol.natm)
mf = hfcobj._scf
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
effspin = mol.spin * .5
e_gyro = .5 * nist.G_ELECTRON
nuc_mag = .5 * (nist.E_MASS / nist.PROTON_MASS) # e*hbar/2m
au2MHz = nist.HARTREE2J / nist.PLANCK * 1e-6
fac = nist.ALPHA**4 / 4 / effspin * e_gyro * au2MHz
occidxa = mo_occ[0] > 0
occidxb = mo_occ[1] > 0
orboa = mo_coeff[0][:, occidxa]
orbva = mo_coeff[0][:, ~occidxa]
orbob = mo_coeff[1][:, occidxb]
orbvb = mo_coeff[1][:, ~occidxb]
nocca = orboa.shape[1]
nvira = orbva.shape[1]
noccb = orbob.shape[1]
nvirb = orbvb.shape[1]
mo1a, mo1b = solve_mo1_pso(hfcobj, hfc_nuc)
mo1a = mo1a.reshape(len(hfc_nuc), 3, nvira, nocca)
mo1b = mo1b.reshape(len(hfc_nuc), 3, nvirb, noccb)
dm0 = hfcobj._scf.make_rdm1()
h1a, h1b = uhf_hfc.make_h1_soc(hfcobj, dm0)
h1a = numpy.asarray([reduce(numpy.dot, (orbva.T, x, orboa)) for x in h1a])
h1b = numpy.asarray([reduce(numpy.dot, (orbvb.T, x, orbob)) for x in h1b])
para = []
for n, atm_id in enumerate(hfc_nuc):
nuc_gyro = get_nuc_g_factor(mol.atom_symbol(atm_id)) * nuc_mag
e = numpy.einsum('xij,yij->xy', mo1a[n], h1a) * 2
e += numpy.einsum('xij,yij->xy', mo1b[n], h1b) * 2
para.append(fac * nuc_gyro * e)
return numpy.asarray(para)
def make_fcsd(hfcobj, dm0, hfc_nuc=None, verbose=None):
log = logger.new_logger(hfcobj, verbose)
mol = hfcobj.mol
if hfc_nuc is None:
hfc_nuc = range(mol.natm)
if isinstance(dm0, numpy.ndarray) and dm0.ndim == 2: # RHF DM
return numpy.zeros((3,3))
dma, dmb = dm0
spindm = dma - dmb
effspin = mol.spin * .5
e_gyro = .5 * nist.G_ELECTRON
nuc_mag = .5 * (nist.E_MASS/nist.PROTON_MASS) # e*hbar/2m
au2MHz = nist.HARTREE2J / nist.PLANCK * 1e-6
fac = nist.ALPHA**2 / 2 / effspin * e_gyro * au2MHz
coords = mol.atom_coords()
ao = numint.eval_ao(mol, coords)
nao = dma.shape[0]
hfc = []
for i, atm_id in enumerate(hfc_nuc):
nuc_gyro = get_nuc_g_factor(mol.atom_symbol(atm_id)) * nuc_mag
mol.set_rinv_origin(mol.atom_coord(atm_id))
# a01p[mu,sigma] the imaginary part of integral <vec{r}/r^3 cross p>
a01p = mol.intor('int1e_sa01sp', 12).reshape(3,4,nao,nao)
h1 = -(a01p[:,:3] + a01p[:,:3].transpose(0,1,3,2))
fcsd = numpy.einsum('xyij,ji->xy', h1, spindm)
fc = 8*numpy.pi/3 * numpy.einsum('i,j,ji', ao[atm_id], ao[atm_id], spindm)
sd = fcsd - numpy.eye(3) * fc
log.info('FC of atom %d %s (in MHz)', atm_id, fac * nuc_gyro * fc)
if hfcobj.verbose >= logger.INFO:
_write(hfcobj, align(fac*nuc_gyro*sd)[0], 'SD of atom %d (in MHz)' % atm_id)
hfc.append(fac * nuc_gyro * fcsd)
return numpy.asarray(hfc)
