def make_fc(sscobj, nuc_pair=None):
'''Only Fermi-contact'''
if nuc_pair is None: nuc_pair = sscobj.nuc_pair
mol = sscobj.mol
mo_coeff = sscobj._scf.mo_coeff
mo_occ = sscobj._scf.mo_occ
atm1dic, atm2dic = _uniq_atoms(nuc_pair)
h1 = make_h1_fc(mol, mo_coeff, mo_occ, sorted(atm2dic.keys()))
mo1aa, mo1ab, mo1ba, mo1bb = solve_mo1_fc(sscobj, h1)
h1 = None
h1aa, h1ab, h1ba, h1bb = make_h1_fc(mol, mo_coeff, mo_occ, sorted(atm1dic.keys()))
para = []
for i,j in nuc_pair:
at1 = atm1dic[i]
at2 = atm2dic[j]
# If GHF orbitals are considered, spin matrices of FC+SD part can be
# explicitly considered as below. However, it is inconsistent to RHF
# results for closed shell systems. To make UHF and RHF code
# consistent, only z-component is considered.
# [See Eq. (19) of JCP 113, 3530 (2000); DOI:10.1063/1.1286806]
if ZZ_ONLY:
ez = numpy.einsum('ij,ij', h1aa[at1], mo1aa[at2]) * 2 # *2 for +c.c.
ez += numpy.einsum('ij,ij', h1bb[at1], mo1bb[at2]) * 2
para.append(ez * numpy.eye(3))
else:
ez = numpy.einsum('ij,ij', h1aa[at1], mo1aa[at2]) * 2 # *2 for +c.c.
ez += numpy.einsum('ij,ij', h1bb[at1], mo1bb[at2]) * 2
ex = numpy.einsum('ij,ij', h1ab[at1], mo1ab[at2]) * 2
ex += numpy.einsum('ij,ij', h1ba[at1], mo1ba[at2]) * 2
ey = ex
para.append((ex + ey + ez) / 3 * numpy.eye(3))
return numpy.asarray(para) * nist.ALPHA**4
def make_fc(sscobj, nuc_pair=None):
'''Only Fermi-contact'''
if nuc_pair is None: nuc_pair = sscobj.nuc_pair
mol = sscobj.mol
mo_coeff = sscobj._scf.mo_coeff
mo_occ = sscobj._scf.mo_occ
atm1dic, atm2dic = _uniq_atoms(nuc_pair)
h1 = make_h1_fc(mol, mo_coeff, mo_occ, sorted(atm2dic.keys()))
mo1aa, mo1ab, mo1ba, mo1bb = solve_mo1_fc(sscobj, h1)
h1 = None
h1aa, h1ab, h1ba, h1bb = make_h1_fc(mol, mo_coeff, mo_occ, sorted(atm1dic.keys()))
para = []
for i,j in nuc_pair:
at1 = atm1dic[i]
at2 = atm2dic[j]
# If GHF orbitals are considered, spin matrices of FC+SD part can be
# explicitly considered as below. However, it is inconsistent to RHF
# results for closed shell systems. To make UHF and RHF code
# consistent, only z-component is considered.
# (See Eq. (19) of JCP, 113, 3530)
if ZZ_ONLY:
ez = numpy.einsum('ij,ij', h1aa[at1], mo1aa[at2]) * 2 # *2 for +c.c.
ez += numpy.einsum('ij,ij', h1bb[at1], mo1bb[at2]) * 2
para.append(ez * numpy.eye(3))
else:
ez = numpy.einsum('ij,ij', h1aa[at1], mo1aa[at2]) * 2 # *2 for +c.c.
ez += numpy.einsum('ij,ij', h1bb[at1], mo1bb[at2]) * 2
ex = numpy.einsum('ij,ij', h1ab[at1], mo1ab[at2]) * 2
ex += numpy.einsum('ij,ij', h1ba[at1], mo1ba[at2]) * 2
ey = ex
para.append((ex + ey + ez) / 3 * numpy.eye(3))
return numpy.asarray(para) * nist.ALPHA**4
def make_pso(sscobj, mol, mo1, mo_coeff, mo_occ, nuc_pair=None):
if nuc_pair is None: nuc_pair = sscobj.nuc_pair
atm1dic, atm2dic = _uniq_atoms(nuc_pair)
h1a, h1b = make_h1_pso(mol, mo_coeff, mo_occ, sorted(atm1dic.keys()))
mo1a, mo1b = mo1
nvira, nocca = h1a[0].shape
nvirb, noccb = h1b[0].shape
mo1a = mo1a.reshape(len(atm2dic), 3, nvira, nocca)
mo1b = mo1b.reshape(len(atm2dic), 3, nvirb, noccb)
h1a = numpy.asarray(h1a).reshape(len(atm1dic), 3, nvira, nocca)
h1b = numpy.asarray(h1b).reshape(len(atm1dic), 3, nvirb, noccb)
para = []
for i, j in nuc_pair:
# PSO = -Tr(Im[h1_ov], Im[mo1_vo]) + cc = 2 * Tr(Im[h1_vo], Im[mo1_vo])
e = numpy.einsum('xij,yij->xy', h1a[atm1dic[i]], mo1a[atm2dic[j]]) * 2
e += numpy.einsum('xij,yij->xy', h1b[atm1dic[i]], mo1b[atm2dic[j]]) * 2
para.append(e)
return numpy.asarray(para) * nist.ALPHA**4
def make_pso(sscobj, mol, mo1, mo_coeff, mo_occ, nuc_pair=None):
if nuc_pair is None: nuc_pair = sscobj.nuc_pair
atm1dic, atm2dic = _uniq_atoms(nuc_pair)
h1a, h1b = make_h1_pso(mol, mo_coeff, mo_occ, sorted(atm1dic.keys()))
mo1a, mo1b = mo1
nvira, nocca = h1a[0].shape
nvirb, noccb = h1b[0].shape
mo1a = mo1a.reshape(len(atm2dic),3,nvira,nocca)
mo1b = mo1b.reshape(len(atm2dic),3,nvirb,noccb)
h1a = numpy.asarray(h1a).reshape(len(atm1dic),3,nvira,nocca)
h1b = numpy.asarray(h1b).reshape(len(atm1dic),3,nvirb,noccb)
para = []
for i,j in nuc_pair:
# PSO = -Tr(Im[h1_ov], Im[mo1_vo]) + cc = 2 * Tr(Im[h1_vo], Im[mo1_vo])
e = numpy.einsum('xij,yij->xy', h1a[atm1dic[i]], mo1a[atm2dic[j]]) * 2
e+= numpy.einsum('xij,yij->xy', h1b[atm1dic[i]], mo1b[atm2dic[j]]) * 2
para.append(e)
return numpy.asarray(para) * nist.ALPHA**4
def make_fcsd(sscobj, nuc_pair=None):
'''FC + SD contributions to 2nd order energy'''
if nuc_pair is None: nuc_pair = sscobj.nuc_pair
mol = sscobj.mol
mo_coeff = sscobj._scf.mo_coeff
mo_occ = sscobj._scf.mo_occ
atm1dic, atm2dic = _uniq_atoms(nuc_pair)
h1 = make_h1_fcsd(mol, mo_coeff, mo_occ, sorted(atm2dic.keys()))
mo1aa, mo1ab, mo1ba, mo1bb = solve_mo1_fc(sscobj, h1)
h1 = None
h1aa, h1ab, h1ba, h1bb = make_h1_fcsd(mol, mo_coeff, mo_occ,
sorted(atm1dic.keys()))
mo1aa = mo1aa.reshape(h1aa.shape)
mo1ab = mo1ab.reshape(h1ab.shape)
mo1ba = mo1ba.reshape(h1ba.shape)
mo1bb = mo1bb.reshape(h1bb.shape)
para = []
for i, j in nuc_pair:
at1 = atm1dic[i]
at2 = atm2dic[j]
# If GHF orbitals are considered, spin matrices of FC+SD part can be
# explicitly considered as below. However, it is inconsistent to RHF
# results for closed shell systems. To make UHF and RHF code
# consistent, only z-component is considered.
if ZZ_ONLY:
e = numpy.einsum('xwij,ywij->xy', h1aa[at1], mo1aa[at2])
e += numpy.einsum('xwij,ywij->xy', h1bb[at1], mo1bb[at2])
else:
# x contributions
e = numpy.einsum('xij,yij->xy', h1ab[at1, 0], mo1ab[at2, 0])
e += numpy.einsum('xij,yij->xy', h1ba[at1, 0], mo1ba[at2, 0])
# y contributions
e += numpy.einsum('xij,yij->xy', h1ab[at1, 1], mo1ab[at2, 1])
e += numpy.einsum('xij,yij->xy', h1ba[at1, 1], mo1ba[at2, 1])
# z contribution
e += numpy.einsum('xij,yij->xy', h1aa[at1, 2], mo1aa[at2, 2])
e += numpy.einsum('xij,yij->xy', h1bb[at1, 2], mo1bb[at2, 2])
para.append(e * 2) # *2 for +c.c.
return numpy.asarray(para) * nist.ALPHA**4
def make_fcsd(sscobj, nuc_pair=None):
'''FC + SD contributions to 2nd order energy'''
if nuc_pair is None: nuc_pair = sscobj.nuc_pair
mol = sscobj.mol
mo_coeff = sscobj._scf.mo_coeff
mo_occ = sscobj._scf.mo_occ
atm1dic, atm2dic = _uniq_atoms(nuc_pair)
h1 = make_h1_fcsd(mol, mo_coeff, mo_occ, sorted(atm2dic.keys()))
mo1aa, mo1ab, mo1ba, mo1bb = solve_mo1_fc(sscobj, h1)
h1 = None
h1aa, h1ab, h1ba, h1bb = make_h1_fcsd(mol, mo_coeff, mo_occ,
sorted(atm1dic.keys()))
nocca = numpy.count_nonzero(mo_occ[0] > 0)
nvira = numpy.count_nonzero(mo_occ[0] == 0)
noccb = numpy.count_nonzero(mo_occ[1] > 0)
nvirb = numpy.count_nonzero(mo_occ[1] == 0)
mo1aa = numpy.asarray(mo1aa).reshape(-1, 3, 3, nvira, nocca)
mo1ab = numpy.asarray(mo1ab).reshape(-1, 3, 3, nvira, noccb)
mo1ba = numpy.asarray(mo1ba).reshape(-1, 3, 3, nvirb, nocca)
mo1bb = numpy.asarray(mo1bb).reshape(-1, 3, 3, nvirb, noccb)
h1aa = numpy.asarray(h1aa).reshape(-1, 3, 3, nvira, nocca)
h1ab = numpy.asarray(h1ab).reshape(-1, 3, 3, nvira, noccb)
h1ba = numpy.asarray(h1ba).reshape(-1, 3, 3, nvirb, nocca)
h1bb = numpy.asarray(h1bb).reshape(-1, 3, 3, nvirb, noccb)
para = []
for i, j in nuc_pair:
at1 = atm1dic[i]
at2 = atm2dic[j]
# x contributions
e = numpy.einsum('xij,yij->xy', h1ab[at1, 0], mo1ab[at2, 0])
e += numpy.einsum('xij,yij->xy', h1ba[at1, 0], mo1ba[at2, 0])
# y contributions
e += numpy.einsum('xij,yij->xy', h1ab[at1, 1], mo1ab[at2, 1])
e += numpy.einsum('xij,yij->xy', h1ba[at1, 1], mo1ba[at2, 1])
# z contribution
e += numpy.einsum('xij,yij->xy', h1aa[at1, 2], mo1aa[at2, 2])
e += numpy.einsum('xij,yij->xy', h1bb[at1, 2], mo1bb[at2, 2])
para.append(e * 2) # *2 for +c.c.
return numpy.asarray(para) * nist.ALPHA**4
def make_fcsd(sscobj, nuc_pair=None):
'''FC + SD contributions to 2nd order energy'''
if nuc_pair is None: nuc_pair = sscobj.nuc_pair
mol = sscobj.mol
mo_coeff = sscobj._scf.mo_coeff
mo_occ = sscobj._scf.mo_occ
atm1dic, atm2dic = _uniq_atoms(nuc_pair)
h1 = make_h1_fcsd(mol, mo_coeff, mo_occ, sorted(atm2dic.keys()))
mo1aa, mo1ab, mo1ba, mo1bb = solve_mo1_fc(sscobj, h1)
h1 = None
h1aa, h1ab, h1ba, h1bb = make_h1_fcsd(mol, mo_coeff, mo_occ, sorted(atm1dic.keys()))
mo1aa = mo1aa.reshape(h1aa.shape)
mo1ab = mo1ab.reshape(h1ab.shape)
mo1ba = mo1ba.reshape(h1ba.shape)
mo1bb = mo1bb.reshape(h1bb.shape)
para = []
for i,j in nuc_pair:
at1 = atm1dic[i]
at2 = atm2dic[j]
# If GHF orbitals are considered, spin matrices of FC+SD part can be
# explicitly considered as below. However, it is inconsistent to RHF
# results for closed shell systems. To make UHF and RHF code
# consistent, only z-component is considered.
if ZZ_ONLY:
e = numpy.einsum('xwij,ywij->xy', h1aa[at1], mo1aa[at2])
e+= numpy.einsum('xwij,ywij->xy', h1bb[at1], mo1bb[at2])
else:
# x contributions
e = numpy.einsum('xij,yij->xy', h1ab[at1,0], mo1ab[at2,0])
e+= numpy.einsum('xij,yij->xy', h1ba[at1,0], mo1ba[at2,0])
# y contributions
e+= numpy.einsum('xij,yij->xy', h1ab[at1,1], mo1ab[at2,1])
e+= numpy.einsum('xij,yij->xy', h1ba[at1,1], mo1ba[at2,1])
# z contribution
e+= numpy.einsum('xij,yij->xy', h1aa[at1,2], mo1aa[at2,2])
e+= numpy.einsum('xij,yij->xy', h1bb[at1,2], mo1bb[at2,2])
para.append(e*2) # *2 for +c.c.
return numpy.asarray(para) * nist.ALPHA**4
def make_fc(sscobj, nuc_pair=None):
'''Only Fermi-contact'''
if nuc_pair is None: nuc_pair = sscobj.nuc_pair
mol = sscobj.mol
mo_coeff = sscobj._scf.mo_coeff
mo_occ = sscobj._scf.mo_occ
atm1dic, atm2dic = _uniq_atoms(nuc_pair)
h1 = make_h1_fc(mol, mo_coeff, mo_occ, sorted(atm2dic.keys()))
mo1aa, mo1ab, mo1ba, mo1bb = solve_mo1_fc(sscobj, h1)
h1 = None
h1aa, h1ab, h1ba, h1bb = make_h1_fc(mol, mo_coeff, mo_occ, sorted(atm1dic.keys()))
para = []
for i,j in nuc_pair:
at1 = atm1dic[i]
at2 = atm2dic[j]
ez = numpy.einsum('ij,ij', h1aa[at1], mo1aa[at2]) * 2 # *2 for +c.c.
ez += numpy.einsum('ij,ij', h1bb[at1], mo1bb[at2]) * 2
ex = numpy.einsum('ij,ij', h1ab[at1], mo1ab[at2]) * 2
ex += numpy.einsum('ij,ij', h1ba[at1], mo1ba[at2]) * 2
ey = ex
para.append(numpy.diag([ex,ey,ez]))
return numpy.asarray(para) * lib.param.ALPHA**4
