def hyper_polarizability(polobj, with_cphf=True):
from pyscf.prop.nmr import uhf as uhf_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
occidxa = mo_occ[0] > 0
occidxb = mo_occ[1] > 0
mo0a, mo0b = mo_coeff
orboa = mo0a[:, occidxa]
orbva = mo0a[:, ~occidxa]
orbob = mo0b[:, occidxb]
orbvb = mo0b[:, ~occidxb]
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)
h1a = lib.einsum('xpq,pi,qj->xij', int_r, mo0a.conj(), orboa)
h1b = lib.einsum('xpq,pi,qj->xij', int_r, mo0b.conj(), orbob)
s1a = numpy.zeros_like(h1a)
s1b = numpy.zeros_like(h1b)
vind = polobj.gen_vind(mf, mo_coeff, mo_occ)
if with_cphf:
mo1, e1 = ucphf.solve(vind,
mo_energy,
mo_occ, (h1a, h1b), (s1a, s1b),
polobj.max_cycle_cphf,
polobj.conv_tol,
verbose=log)
else:
mo1, e1 = uhf_nmr._solve_mo1_uncoupled(mo_energy, mo_occ, (h1a, h1b),
(s1a, s1b))
mo1a = lib.einsum('xqi,pq->xpi', mo1[0], mo0a)
mo1b = lib.einsum('xqi,pq->xpi', mo1[1], mo0b)
dm1a = lib.einsum('xpi,qi->xpq', mo1a, orboa)
dm1b = lib.einsum('xpi,qi->xpq', mo1b, orbob)
dm1a = dm1a + dm1a.transpose(0, 2, 1)
dm1b = dm1b + dm1b.transpose(0, 2, 1)
vresp = _gen_uhf_response(mf, hermi=1)
h1ao = int_r + vresp(numpy.stack((dm1a, dm1b)))
s0 = mf.get_ovlp()
e3 = lib.einsum('xpq,ypi,zqi->xyz', h1ao[0], mo1a, mo1a)
e3 += lib.einsum('xpq,ypi,zqi->xyz', h1ao[1], mo1b, mo1b)
e3 -= lib.einsum('pq,xpi,yqj,zij->xyz', s0, mo1a, mo1a, e1[0])
e3 -= lib.einsum('pq,xpi,yqj,zij->xyz', s0, mo1b, mo1b, e1[1])
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 hyper_polarizability(polobj, with_cphf=True):
from pyscf.prop.nmr import uhf as uhf_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
occidxa = mo_occ[0] > 0
occidxb = mo_occ[1] > 0
mo0a, mo0b = mo_coeff
orboa = mo0a[:, occidxa]
orbva = mo0a[:,~occidxa]
orbob = mo0b[:, occidxb]
orbvb = mo0b[:,~occidxb]
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)
h1a = lib.einsum('xpq,pi,qj->xij', int_r, mo0a.conj(), orboa)
h1b = lib.einsum('xpq,pi,qj->xij', int_r, mo0b.conj(), orbob)
s1a = numpy.zeros_like(h1a)
s1b = numpy.zeros_like(h1b)
vind = polobj.gen_vind(mf, mo_coeff, mo_occ)
if with_cphf:
mo1, e1 = ucphf.solve(vind, mo_energy, mo_occ, (h1a,h1b), (s1a,s1b),
polobj.max_cycle_cphf, polobj.conv_tol, verbose=log)
else:
mo1, e1 = uhf_nmr._solve_mo1_uncoupled(mo_energy, mo_occ, (h1a,h1b),
(s1a,s1b))
mo1a = lib.einsum('xqi,pq->xpi', mo1[0], mo0a)
mo1b = lib.einsum('xqi,pq->xpi', mo1[1], mo0b)
dm1a = lib.einsum('xpi,qi->xpq', mo1a, orboa)
dm1b = lib.einsum('xpi,qi->xpq', mo1b, orbob)
dm1a = dm1a + dm1a.transpose(0,2,1)
dm1b = dm1b + dm1b.transpose(0,2,1)
vresp = _gen_uhf_response(mf, hermi=1)
h1ao = int_r + vresp(numpy.stack((dm1a, dm1b)))
s0 = mf.get_ovlp()
e3 = lib.einsum('xpq,ypi,zqi->xyz', h1ao[0], mo1a, mo1a)
e3 += lib.einsum('xpq,ypi,zqi->xyz', h1ao[1], mo1b, mo1b)
e3 -= lib.einsum('pq,xpi,yqj,zij->xyz', s0, mo1a, mo1a, e1[0])
e3 -= lib.einsum('pq,xpi,yqj,zij->xyz', s0, mo1b, mo1b, e1[1])
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 uhf as uhf_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
occidxa = mo_occ[0] > 0
occidxb = mo_occ[1] > 0
mo0a, mo0b = mo_coeff
orboa = mo0a[:, occidxa]
orbva = mo0a[:, ~occidxa]
orbob = mo0b[:, occidxb]
orbvb = mo0b[:, ~occidxb]
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)
h1a = lib.einsum('xpq,pi,qj->xij', int_r, mo0a.conj(), orboa)
h1b = lib.einsum('xpq,pi,qj->xij', int_r, mo0b.conj(), orbob)
s1a = numpy.zeros_like(h1a)
s1b = numpy.zeros_like(h1b)
vind = polobj.gen_vind(mf, mo_coeff, mo_occ)
if with_cphf:
mo1 = ucphf.solve(vind,
mo_energy,
mo_occ, (h1a, h1b), (s1a, s1b),
polobj.max_cycle_cphf,
polobj.conv_tol,
verbose=log)[0]
else:
mo1 = uhf_nmr._solve_mo1_uncoupled(mo_energy, mo_occ, (h1a, h1b),
(s1a, s1b))[0]
e2 = numpy.einsum('xpi,ypi->xy', h1a, mo1[0])
e2 += numpy.einsum('xpi,ypi->xy', h1b, mo1[1])
e2 = -(e2 + e2.T)
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 = rhf_g.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 = uhf_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
orboa = mo_coeff[0][:, mo_occ[0] > 0]
orbob = mo_coeff[1][:, mo_occ[1] > 0]
# for magnetic field
with mol.with_common_origin(mass_center):
h10 = .5 * mol.intor('int1e_cg_irxp', 3)
h10a = lib.einsum('xpq,pi,qj->xij', h10, mo_coeff[0].conj(), orboa)
h10b = lib.einsum('xpq,pi,qj->xij', h10, mo_coeff[1].conj(), orbob)
# for rotation part
with mol.with_common_origin(gauge_orig):
h01 = -mol.intor('int1e_cg_irxp', 3)
h01a = lib.einsum('xpq,pi,qj->xij', h01, mo_coeff[0].conj(), orboa)
h01b = lib.einsum('xpq,pi,qj->xij', h01, mo_coeff[1].conj(), orbob)
s10a = numpy.zeros_like(h10a)
s10b = numpy.zeros_like(h10b)
mo10 = uhf_nmr._solve_mo1_uncoupled(mo_energy, mo_occ, (h10a, h10b),
(s10a, s10b))[0]
mag_para = numpy.einsum('xji,yji->xy', mo10[0].conj(), h01a)
mag_para += numpy.einsum('xji,yji->xy', mo10[1].conj(), h01b)
mag_para = mag_para + mag_para.conj()
mag_para = rhf_g._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 = rhf_g.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 = uhf_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
orboa = mo_coeff[0][:,mo_occ[0]>0]
orbob = mo_coeff[1][:,mo_occ[1]>0]
# for magnetic field
with mol.with_common_origin(mass_center):
h10 = .5 * mol.intor('int1e_cg_irxp', 3)
h10a = lib.einsum('xpq,pi,qj->xij', h10, mo_coeff[0].conj(), orboa)
h10b = lib.einsum('xpq,pi,qj->xij', h10, mo_coeff[1].conj(), orbob)
# for rotation part
with mol.with_common_origin(gauge_orig):
h01 = -mol.intor('int1e_cg_irxp', 3)
h01a = lib.einsum('xpq,pi,qj->xij', h01, mo_coeff[0].conj(), orboa)
h01b = lib.einsum('xpq,pi,qj->xij', h01, mo_coeff[1].conj(), orbob)
s10a = numpy.zeros_like(h10a)
s10b = numpy.zeros_like(h10b)
mo10 = uhf_nmr._solve_mo1_uncoupled(mo_energy, mo_occ,
(h10a,h10b), (s10a,s10b))[0]
mag_para = numpy.einsum('xji,yji->xy', mo10[0].conj(), h01a)
mag_para+= numpy.einsum('xji,yji->xy', mo10[1].conj(), h01b)
mag_para = mag_para + mag_para.conj()
mag_para = rhf_g._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 polarizability(polobj, with_cphf=True):
from pyscf.prop.nmr import uhf as uhf_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
occidxa = mo_occ[0] > 0
occidxb = mo_occ[1] > 0
mo0a, mo0b = mo_coeff
orboa = mo0a[:, occidxa]
orbva = mo0a[:,~occidxa]
orbob = mo0b[:, occidxb]
orbvb = mo0b[:,~occidxb]
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)
h1a = lib.einsum('xpq,pi,qj->xij', int_r, mo0a.conj(), orboa)
h1b = lib.einsum('xpq,pi,qj->xij', int_r, mo0b.conj(), orbob)
s1a = numpy.zeros_like(h1a)
s1b = numpy.zeros_like(h1b)
vind = polobj.gen_vind(mf, mo_coeff, mo_occ)
if with_cphf:
mo1 = ucphf.solve(vind, mo_energy, mo_occ, (h1a,h1b), (s1a,s1b),
polobj.max_cycle_cphf, polobj.conv_tol,
verbose=log)[0]
else:
mo1 = uhf_nmr._solve_mo1_uncoupled(mo_energy, mo_occ, (h1a,h1b),
(s1a,s1b))[0]
e2 = numpy.einsum('xpi,ypi->xy', h1a, mo1[0])
e2+= numpy.einsum('xpi,ypi->xy', h1b, mo1[1])
e2 = -(e2 + e2.T)
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
