def kernel(gobj, gauge_orig=None, mb='RKB', with_gaunt=False, verbose=None):
gobj.check_sanity()
gobj.dump_flags()
log = lib.logger.new_logger(gobj, verbose)
mf = gobj._scf
mol = mf.mol
# Add finite field to remove degeneracy
mag_field = numpy.ones(3) * 1e-6
h10 = dhf_nmr.make_h10rkb(mol, None, None, False, log)
sc = numpy.dot(mf.get_ovlp(), mf.mo_coeff)
h0 = reduce(numpy.dot, (sc * mf.mo_energy, sc.conj().T))
h10b = h0 + numpy.einsum('xij,x->ij', h10, mag_field)
h10b = reduce(numpy.dot, (mf.mo_coeff.conj().T, h10b, mf.mo_coeff))
mo_energy, v = numpy.linalg.eigh(h10b)
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())
dme = numpy.dot(orbo * mo_energy[occidx], orbo.conj().T)
h10 = dhf_nmr.make_h10(mol, dm0, gauge_orig, mb, with_gaunt, log)
s10 = dhf_nmr.make_s10(mol, gauge_orig, mb)
# Intrinsic muB = eh/2mc
# First order Dirac operator is 1/c * h10 => g ~ Tr(h10,DM)/c / mu_B = 2 Tr(h10,DM)
muB = .5 # Bohr magneton
g = (numpy.einsum('xij,ji->x', h10, dm0) -
numpy.einsum('xij,ji->x', s10, dme)) / muB
c = lib.param.LIGHT_SPEED
n4c = dm0.shape[0]
n2c = n4c // 2
Sigma = numpy.zeros_like(s10)
Sigma[:, :n2c, :n2c] = mol.intor('int1e_sigma_spinor', comp=3)
Sigma[:, n2c:,
n2c:] = .25 / c**2 * mol.intor('int1e_spsigmasp_spinor', comp=3)
effspin = numpy.einsum('xij,ji->x', Sigma, dm0) * .5
log.debug('Eff-spin %s', effspin.real)
g = (g / effspin).real
facppt = 1e3
gshift = (g - nist.G_ELECTRON) * facppt
log.note('G shift (ppt) %s', gshift)
return g
def kernel(gobj, gauge_orig=None, mb='RKB', with_gaunt=False, verbose=None):
gobj.check_sanity()
gobj.dump_flags()
log = lib.logger.new_logger(gobj, verbose)
mf = gobj._scf
mol = mf.mol
# Add finite field to remove degeneracy
mag_field = numpy.ones(3) * 1e-6
h10 = dhf_nmr.make_h10rkb(mol, None, None, False, log)
sc = numpy.dot(mf.get_ovlp(), mf.mo_coeff)
h0 = reduce(numpy.dot, (sc*mf.mo_energy, sc.conj().T))
h10b = h0 + numpy.einsum('xij,x->ij', h10, mag_field)
h10b = reduce(numpy.dot, (mf.mo_coeff.conj().T, h10b, mf.mo_coeff))
mo_energy, v = numpy.linalg.eigh(h10b)
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())
dme = numpy.dot(orbo * mo_energy[occidx], orbo.conj().T)
h10 = dhf_nmr.make_h10(mol, dm0, gauge_orig, mb, with_gaunt, log)
s10 = dhf_nmr.make_s10(mol, gauge_orig, mb)
# Intrinsic muB = eh/2mc
# First order Dirac operator is 1/c * h10 => g ~ Tr(h10,DM)/c / mu_B = 2 Tr(h10,DM)
muB = .5 # Bohr magneton
g = (numpy.einsum('xij,ji->x', h10, dm0) -
numpy.einsum('xij,ji->x', s10, dme)) / muB
c = lib.param.LIGHT_SPEED
n4c = dm0.shape[0]
n2c = n4c // 2
Sigma = numpy.zeros_like(s10)
Sigma[:,:n2c,:n2c] = mol.intor('int1e_sigma_spinor', comp=3)
Sigma[:,n2c:,n2c:] = .25/c**2 * mol.intor('int1e_spsigmasp_spinor', comp=3)
effspin = numpy.einsum('xij,ji->x', Sigma, dm0) * .5
log.debug('Eff-spin %s', effspin.real)
g = (g / effspin).real
facppt = 1e3
gshift = (g - nist.G_ELECTRON) * facppt
log.note('G shift (ppt) %s', gshift)
return g