def hyper_polarizability(polobj, with_cphf=True):
from pyscf.prop.nmr import rhf as rhf_nmr
log = logger.new_logger(polobj)
mf = polobj._scf
mol = mf.mol
mo_energy = mf.mo_energy
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
occidx = mo_occ > 0
orbo = mo_coeff[:, occidx]
orbv = mo_coeff[:, ~occidx]
charges = mol.atom_charges()
coords = mol.atom_coords()
charge_center = numpy.einsum('i,ix->x', charges, coords) / charges.sum()
with mol.with_common_orig(charge_center):
int_r = mol.intor_symmetric('int1e_r', comp=3)
h1 = lib.einsum('xpq,pi,qj->xij', int_r, mo_coeff.conj(), orbo)
s1 = numpy.zeros_like(h1)
vind = polobj.gen_vind(mf, mo_coeff, mo_occ)
if with_cphf:
mo1, e1 = cphf.solve(vind,
mo_energy,
mo_occ,
h1,
s1,
polobj.max_cycle_cphf,
polobj.conv_tol,
verbose=log)
else:
mo1, e1 = rhf_nmr._solve_mo1_uncoupled(mo_energy, mo_occ, h1, s1)
mo1 = lib.einsum('xqi,pq->xpi', mo1, mo_coeff)
dm1 = lib.einsum('xpi,qi->xpq', mo1, orbo) * 2
dm1 = dm1 + dm1.transpose(0, 2, 1)
vresp = mf.gen_response(hermi=1)
h1ao = int_r + vresp(dm1)
# *2 for double occupancy
e3 = lib.einsum('xpq,ypi,zqi->xyz', h1ao, mo1, mo1) * 2
e3 -= lib.einsum('pq,xpi,yqj,zij->xyz', mf.get_ovlp(), mo1, mo1, e1) * 2
e3 = (e3 + e3.transpose(1, 2, 0) + e3.transpose(2, 0, 1) +
e3.transpose(0, 2, 1) + e3.transpose(1, 0, 2) +
e3.transpose(2, 1, 0))
e3 = -e3
log.debug('Static hyper polarizability tensor\n%s', e3)
return e3
def polarizability(polobj, with_cphf=True):
from pyscf.prop.nmr import rhf as rhf_nmr
log = logger.new_logger(polobj)
mf = polobj._scf
mol = mf.mol
mo_energy = mf.mo_energy
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
occidx = mo_occ > 0
orbo = mo_coeff[:, occidx]
orbv = mo_coeff[:, ~occidx]
charges = mol.atom_charges()
coords = mol.atom_coords()
charge_center = numpy.einsum('i,ix->x', charges, coords) / charges.sum()
with mol.with_common_orig(charge_center):
int_r = mol.intor_symmetric('int1e_r', comp=3)
h1 = lib.einsum('xpq,pi,qj->xij', int_r, mo_coeff.conj(), orbo)
s1 = numpy.zeros_like(h1)
vind = polobj.gen_vind(mf, mo_coeff, mo_occ)
if with_cphf:
mo1 = cphf.solve(vind,
mo_energy,
mo_occ,
h1,
s1,
polobj.max_cycle_cphf,
polobj.conv_tol,
verbose=log)[0]
else:
mo1 = rhf_nmr._solve_mo1_uncoupled(mo_energy, mo_occ, h1, s1)[0]
e2 = numpy.einsum('xpi,ypi->xy', h1, mo1)
# *-1 from the definition of dipole moment. *2 for double occupancy
e2 = (e2 + e2.T) * -2
if mf.verbose >= logger.INFO:
xx, yy, zz = e2.diagonal()
log.note('Isotropic polarizability %.12g', (xx + yy + zz) / 3)
log.note('Polarizability anisotropy %.12g',
(.5 * ((xx - yy)**2 + (yy - zz)**2 + (zz - xx)**2))**.5)
log.debug('Static polarizability tensor\n%s', e2)
return e2
def para(magobj, gauge_orig=None, h1=None, s1=None, with_cphf=None):
'''Part of rotational g-tensors from the first order wavefunctions. Unit
hbar/mu_N is not included. This part may be different to the conventional
para-magnetic contributions of rotational g-tensors.
'''
mol = magobj.mol
im, mass_center = inertia_tensor(mol)
if gauge_orig is None:
# The first order Hamiltonian for rotation part is the same to the
# first order Hamiltonian for magnetic field except a factor of 2. It can
# be computed using the magnetizability code.
mag_para = rhf_mag.para(magobj, gauge_orig, h1, s1, with_cphf) * 2
else:
mf = magobj._scf
mo_energy = mf.mo_energy
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
orbo = mo_coeff[:,mo_occ>0]
# for magnetic field
with mol.with_common_origin(mass_center):
h10 = .5 * mol.intor('int1e_cg_irxp', 3)
h10 = lib.einsum('xpq,pi,qj->xij', h10, mo_coeff.conj(), orbo)
# for rotation part
with mol.with_common_origin(gauge_orig):
h01 = -mol.intor('int1e_cg_irxp', 3)
h01 = lib.einsum('xpq,pi,qj->xij', h01, mo_coeff.conj(), orbo)
s10 = numpy.zeros_like(h10)
mo10 = rhf_nmr._solve_mo1_uncoupled(mo_energy, mo_occ, h10, s10)[0]
mag_para = numpy.einsum('xji,yji->xy', mo10.conj(), h01)
mag_para = (mag_para + mag_para.conj()) * 2 # *2 for double occupancy
mag_para = _safe_solve(im, mag_para)
# unit = hbar/mu_N, mu_N is nuclear magneton
unit = -2 * nist.PROTON_MASS_AU
return mag_para * unit
def para(magobj, gauge_orig=None, h1=None, s1=None, with_cphf=None):
'''Part of rotational g-tensors from the first order wavefunctions. Unit
hbar/mu_N is not included. This part may be different to the conventional
para-magnetic contributions of rotational g-tensors.
'''
mol = magobj.mol
im, mass_center = inertia_tensor(mol)
if gauge_orig is None:
# The first order Hamiltonian for rotation part is the same to the
# first order Hamiltonian for magnetic field except a factor of 2. It can
# be computed using the magnetizability code.
mag_para = rhf_mag.para(magobj, gauge_orig, h1, s1, with_cphf) * 2
else:
mf = magobj._scf
mo_energy = mf.mo_energy
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
orbo = mo_coeff[:,mo_occ>0]
# for magnetic field
with mol.with_common_origin(mass_center):
h10 = .5 * mol.intor('int1e_cg_irxp', 3)
h10 = lib.einsum('xpq,pi,qj->xij', h10, mo_coeff.conj(), orbo)
# for rotation part
with mol.with_common_origin(gauge_orig):
h01 = -mol.intor('int1e_cg_irxp', 3)
h01 = lib.einsum('xpq,pi,qj->xij', h01, mo_coeff.conj(), orbo)
s10 = numpy.zeros_like(h10)
mo10 = rhf_nmr._solve_mo1_uncoupled(mo_energy, mo_occ, h10, s10)[0]
mag_para = numpy.einsum('xji,yji->xy', mo10.conj(), h01)
mag_para = (mag_para + mag_para.conj()) * 2 # *2 for double occupancy
mag_para = _safe_solve(im, mag_para)
# unit = hbar/mu_N, mu_N is nuclear magneton
unit = -2 * nist.PROTON_MASS_AU
return mag_para * unit
def hyper_polarizability(polobj, with_cphf=True):
from pyscf.prop.nmr import rhf as rhf_nmr
log = logger.new_logger(polobj)
mf = polobj._scf
mol = mf.mol
mo_energy = mf.mo_energy
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
occidx = mo_occ > 0
orbo = mo_coeff[:, occidx]
orbv = mo_coeff[:,~occidx]
charges = mol.atom_charges()
coords = mol.atom_coords()
charge_center = numpy.einsum('i,ix->x', charges, coords) / charges.sum()
with mol.with_common_orig(charge_center):
int_r = mol.intor_symmetric('int1e_r', comp=3)
h1 = lib.einsum('xpq,pi,qj->xij', int_r, mo_coeff.conj(), orbo)
s1 = numpy.zeros_like(h1)
vind = polobj.gen_vind(mf, mo_coeff, mo_occ)
if with_cphf:
mo1, e1 = cphf.solve(vind, mo_energy, mo_occ, h1, s1,
polobj.max_cycle_cphf, polobj.conv_tol, verbose=log)
else:
mo1, e1 = rhf_nmr._solve_mo1_uncoupled(mo_energy, mo_occ, h1, s1)
mo1 = lib.einsum('xqi,pq->xpi', mo1, mo_coeff)
dm1 = lib.einsum('xpi,qi->xpq', mo1, orbo) * 2
dm1 = dm1 + dm1.transpose(0,2,1)
vresp = _gen_rhf_response(mf, hermi=1)
h1ao = int_r + vresp(dm1)
# *2 for double occupancy
e3 = lib.einsum('xpq,ypi,zqi->xyz', h1ao, mo1, mo1) * 2
e3 -= lib.einsum('pq,xpi,yqj,zij->xyz', mf.get_ovlp(), mo1, mo1, e1) * 2
e3 = (e3 + e3.transpose(1,2,0) + e3.transpose(2,0,1) +
e3.transpose(0,2,1) + e3.transpose(1,0,2) + e3.transpose(2,1,0))
e3 = -e3
log.debug('Static hyper polarizability tensor\n%s', e3)
return e3
def polarizability(polobj, with_cphf=True):
from pyscf.prop.nmr import rhf as rhf_nmr
log = logger.new_logger(polobj)
mf = polobj._scf
mol = mf.mol
mo_energy = mf.mo_energy
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
occidx = mo_occ > 0
orbo = mo_coeff[:, occidx]
orbv = mo_coeff[:,~occidx]
charges = mol.atom_charges()
coords = mol.atom_coords()
charge_center = numpy.einsum('i,ix->x', charges, coords) / charges.sum()
with mol.with_common_orig(charge_center):
int_r = mol.intor_symmetric('int1e_r', comp=3)
h1 = lib.einsum('xpq,pi,qj->xij', int_r, mo_coeff.conj(), orbo)
s1 = numpy.zeros_like(h1)
vind = polobj.gen_vind(mf, mo_coeff, mo_occ)
if with_cphf:
mo1 = cphf.solve(vind, mo_energy, mo_occ, h1, s1,
polobj.max_cycle_cphf, polobj.conv_tol,
verbose=log)[0]
else:
mo1 = rhf_nmr._solve_mo1_uncoupled(mo_energy, mo_occ, h1, s1)[0]
e2 = numpy.einsum('xpi,ypi->xy', h1, mo1)
# *-1 from the definition of dipole moment. *2 for double occupancy
e2 = (e2 + e2.T) * -2
if mf.verbose >= logger.INFO:
xx, yy, zz = e2.diagonal()
log.note('Isotropic polarizability %.12g', (xx+yy+zz)/3)
log.note('Polarizability anisotropy %.12g',
(.5 * ((xx-yy)**2 + (yy-zz)**2 + (zz-xx)**2))**.5)
log.debug('Static polarizability tensor\n%s', e2)
return e2