def vind(mo1):
mo1aa, mo1ab, mo1ba, mo1bb = _split_mo1(mo1)
dm1aa = _dm1_mo2ao(mo1aa, orbva, orboa)
dm1ab = _dm1_mo2ao(mo1ab, orbva, orbob)
dm1ba = _dm1_mo2ao(mo1ba, orbvb, orboa)
dm1bb = _dm1_mo2ao(mo1bb, orbvb, orbob)
# imaginary Hermitian
dm1 = numpy.vstack([
dm1aa - dm1aa.transpose(0, 2, 1), dm1ab - dm1ba.transpose(0, 2, 1),
dm1ba - dm1ab.transpose(0, 2, 1), dm1bb - dm1bb.transpose(0, 2, 1)
])
v1 = vresp(dm1)
v1aa = _ao2mo.nr_e2(v1[:nset], mo_va_oa,
(0, nvira, nvira, nvira + nocca))
v1ab = _ao2mo.nr_e2(v1[nset * 1:nset * 2], mo_va_ob,
(0, nvira, nvira, nvira + noccb))
v1ba = _ao2mo.nr_e2(v1[nset * 2:nset * 3], mo_vb_oa,
(0, nvirb, nvirb, nvirb + nocca))
v1bb = _ao2mo.nr_e2(v1[nset * 3:], mo_vb_ob,
(0, nvirb, nvirb, nvirb + noccb))
v1aa = v1aa.reshape(nset, nvira, nocca)
v1ab = v1ab.reshape(nset, nvira, noccb)
v1ba = v1ba.reshape(nset, nvirb, nocca)
v1bb = v1bb.reshape(nset, nvirb, noccb)
v1aa *= eai_aa
v1ab *= eai_ab
v1ba *= eai_ba
v1bb *= eai_bb
v1mo = numpy.hstack((v1aa.reshape(nset, -1), v1ab.reshape(nset, -1),
v1ba.reshape(nset, -1), v1bb.reshape(nset, -1)))
return v1mo.ravel()
def vind(mo1):
mo1aa, mo1ab, mo1ba, mo1bb = _split_mo1(mo1)
dm1aa = _dm1_mo2ao(mo1aa, orbva, orboa)
dm1ab = _dm1_mo2ao(mo1ab, orbva, orbob)
dm1ba = _dm1_mo2ao(mo1ba, orbvb, orboa)
dm1bb = _dm1_mo2ao(mo1bb, orbvb, orbob)
dm1 = lib.asarray([
dm1aa + dm1aa.transpose(0, 2, 1),
dm1ab + dm1ba.transpose(0, 2, 1),
dm1ba + dm1ab.transpose(0, 2, 1),
dm1bb + dm1bb.transpose(0, 2, 1)
])
v1 = vresp(dm1)
v1aa = _ao2mo.nr_e2(v1[0], mo_va_oa,
(0, nvira, nvira, nvira + nocca))
v1ab = _ao2mo.nr_e2(v1[1], mo_va_ob,
(0, nvira, nvira, nvira + noccb))
v1ba = _ao2mo.nr_e2(v1[2], mo_vb_oa,
(0, nvirb, nvirb, nvirb + nocca))
v1bb = _ao2mo.nr_e2(v1[3], mo_vb_ob,
(0, nvirb, nvirb, nvirb + noccb))
v1aa = v1aa.reshape(nset, nvira, nocca)
v1ab = v1ab.reshape(nset, nvira, noccb)
v1ba = v1ba.reshape(nset, nvirb, nocca)
v1bb = v1bb.reshape(nset, nvirb, noccb)
v1aa *= eai_aa
v1ab *= eai_ab
v1ba *= eai_ba
v1bb *= eai_bb
v1mo = numpy.hstack(
(v1aa.reshape(nset, -1), v1ab.reshape(nset, -1),
v1ba.reshape(nset, -1), v1bb.reshape(nset, -1)))
return v1mo.ravel()
def vind(mo1):
mo1aa, mo1ab, mo1ba, mo1bb = _split_mo1(mo1)
dm1aa = _dm1_mo2ao(mo1aa, orbva, orboa)
dm1ab = _dm1_mo2ao(mo1ab, orbva, orbob)
dm1ba = _dm1_mo2ao(mo1ba, orbvb, orboa)
dm1bb = _dm1_mo2ao(mo1bb, orbvb, orbob)
dm1 = lib.asarray([dm1aa+dm1aa.transpose(0,2,1),
dm1ab+dm1ba.transpose(0,2,1),
dm1ba+dm1ab.transpose(0,2,1),
dm1bb+dm1bb.transpose(0,2,1)])
v1 = vresp(dm1)
v1aa = _ao2mo.nr_e2(v1[0], mo_va_oa, (0,nvira,nvira,nvira+nocca))
v1ab = _ao2mo.nr_e2(v1[1], mo_va_ob, (0,nvira,nvira,nvira+noccb))
v1ba = _ao2mo.nr_e2(v1[2], mo_vb_oa, (0,nvirb,nvirb,nvirb+nocca))
v1bb = _ao2mo.nr_e2(v1[3], mo_vb_ob, (0,nvirb,nvirb,nvirb+noccb))
v1aa = v1aa.reshape(nset,nvira,nocca)
v1ab = v1ab.reshape(nset,nvira,noccb)
v1ba = v1ba.reshape(nset,nvirb,nocca)
v1bb = v1bb.reshape(nset,nvirb,noccb)
v1aa *= eai_aa
v1ab *= eai_ab
v1ba *= eai_ba
v1bb *= eai_bb
v1mo = numpy.hstack((v1aa.reshape(nset,-1),
v1ab.reshape(nset,-1),
v1ba.reshape(nset,-1),
v1bb.reshape(nset,-1)))
return v1mo.ravel()
def vind(mo1):
mo1a = mo1.reshape(-1,nova+novb)[:,:nova].reshape(-1,nvira,nocca)
mo1b = mo1.reshape(-1,nova+novb)[:,nova:].reshape(-1,nvirb,noccb)
nset = mo1a.shape[0]
dm1a = _dm1_mo2ao(mo1a, orbva, orboa)
dm1b = _dm1_mo2ao(mo1b, orbvb, orbob)
dm1 = numpy.vstack([dm1a-dm1a.transpose(0,2,1),
dm1b-dm1b.transpose(0,2,1)])
v1 = vresp(dm1)
v1a = _ao2mo.nr_e2(v1[ :nset], mo_va_oa, (0,nvira,nvira,nvira+nocca))
v1b = _ao2mo.nr_e2(v1[nset: ], mo_vb_ob, (0,nvirb,nvirb,nvirb+noccb))
v1mo = numpy.hstack((v1a.reshape(nset,-1), v1b.reshape(nset,-1)))
return v1mo.ravel()
def vind(mo1):
mo1a = mo1.reshape(-1, nova + novb)[:, :nova].reshape(-1, nvira, nocca)
mo1b = mo1.reshape(-1, nova + novb)[:, nova:].reshape(-1, nvirb, noccb)
nset = mo1a.shape[0]
dm1a = _dm1_mo2ao(mo1a, orbva, orboa)
dm1b = _dm1_mo2ao(mo1b, orbvb, orbob)
dm1 = numpy.asarray(
[dm1a - dm1a.transpose(0, 2, 1), dm1b - dm1b.transpose(0, 2, 1)])
v1 = vresp(dm1)
v1a = _ao2mo.nr_e2(v1[0], mo_va_oa, (0, nvira, nvira, nvira + nocca))
v1b = _ao2mo.nr_e2(v1[1], mo_vb_ob, (0, nvirb, nvirb, nvirb + noccb))
v1mo = numpy.hstack((v1a.reshape(nset, -1), v1b.reshape(nset, -1)))
return v1mo.ravel()
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 * lib.param.G_ELECTRON
nuc_mag = .5 * (lib.param.E_MASS/lib.param.PROTON_MASS) # e*hbar/2m
au2MHz = lib.param.HARTREE2J / lib.param.PLANCK * 1e-6
fac = lib.param.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)
