def solve_mo1(nmrobj, mo_energy=None, mo_coeff=None, mo_occ=None,
h1=None, s1=None, with_cphf=None):
if with_cphf is None:
with_cphf = nmrobj.cphf
libxc = nmrobj._scf._numint.libxc
with_cphf = with_cphf and libxc.is_hybrid_xc(nmrobj._scf.xc)
return uhf_nmr.solve_mo1(nmrobj, mo_energy, mo_coeff, mo_occ,
h1, s1, with_cphf)
def solve_mo1(nmrobj, mo_energy=None, mo_coeff=None, mo_occ=None,
h1=None, s1=None, with_cphf=None):
if with_cphf is None:
with_cphf = nmrobj.cphf
libxc = nmrobj._scf._numint.libxc
with_cphf = with_cphf and libxc.is_hybrid_xc(nmrobj._scf.xc)
return uhf_nmr.solve_mo1(nmrobj, mo_energy, mo_coeff, mo_occ,
h1, s1, with_cphf)
def para(magobj, gauge_orig=None, h1=None, s1=None, with_cphf=None):
'''Paramagnetic susceptibility tensor
Kwargs:
h1: A list of arrays. Shapes are [(3,nmo_a,nocc_a), (3,nmo_b,nocc_b)]
First order Fock matrices in MO basis.
s1: A list of arrays. Shapes are [(3,nmo_a,nocc_a), (3,nmo_b,nocc_b)]
First order overlap matrices in MO basis.
with_cphf : boolean or function(dm_mo) => v1_mo
If a boolean value is given, the value determines whether CPHF
equation will be solved or not. The induced potential will be
generated by the function gen_vind.
If a function is given, CPHF equation will be solved, and the
given function is used to compute induced potential
'''
log = logger.Logger(magobj.stdout, magobj.verbose)
cput1 = (time.clock(), time.time())
mol = magobj.mol
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]
if h1 is None:
# Imaginary part of F10
dm0 = (numpy.dot(orboa, orboa.T), numpy.dot(orbob, orbob.T))
h1 = magobj.get_fock(dm0, gauge_orig)
h1 = (lib.einsum('xpq,pi,qj->xij', h1[0], mo_coeff[0].conj(), orboa),
lib.einsum('xpq,pi,qj->xij', h1[1], mo_coeff[1].conj(), orbob))
cput1 = log.timer('first order Fock matrix', *cput1)
if s1 is None:
# Imaginary part of S10
s1 = magobj.get_ovlp(mol, gauge_orig)
s1 = (lib.einsum('xpq,pi,qj->xij', s1, mo_coeff[0].conj(), orboa),
lib.einsum('xpq,pi,qj->xij', s1, mo_coeff[1].conj(), orbob))
with_cphf = magobj.cphf
mo1, mo_e1 = uhf_nmr.solve_mo1(magobj, mo_energy, mo_coeff, mo_occ, h1, s1,
with_cphf)
cput1 = logger.timer(magobj, 'solving mo1 eqn', *cput1)
occidxa = mo_occ[0] > 0
occidxb = mo_occ[1] > 0
mag_para = numpy.einsum('yji,xji->xy', mo1[0], h1[0])
mag_para += numpy.einsum('yji,xji->xy', mo1[1], h1[1])
mag_para -= numpy.einsum('yji,xji,i->xy', mo1[0], s1[0],
mo_energy[0][occidxa])
mag_para -= numpy.einsum('yji,xji,i->xy', mo1[1], s1[1],
mo_energy[1][occidxb])
# + c.c.
mag_para = mag_para + mag_para.conj()
mag_para -= numpy.einsum('xij,yij->xy', s1[0][:, occidxa], mo_e1[0])
mag_para -= numpy.einsum('xij,yij->xy', s1[1][:, occidxb], mo_e1[1])
return -mag_para
def para(magobj, gauge_orig=None, h1=None, s1=None, with_cphf=None):
'''Paramagnetic susceptibility tensor
Kwargs:
h1: A list of arrays. Shapes are [(3,nmo_a,nocc_a), (3,nmo_b,nocc_b)]
First order Fock matrices in MO basis.
s1: A list of arrays. Shapes are [(3,nmo_a,nocc_a), (3,nmo_b,nocc_b)]
First order overlap matrices in MO basis.
with_cphf : boolean or function(dm_mo) => v1_mo
If a boolean value is given, the value determines whether CPHF
equation will be solved or not. The induced potential will be
generated by the function gen_vind.
If a function is given, CPHF equation will be solved, and the
given function is used to compute induced potential
'''
log = logger.Logger(magobj.stdout, magobj.verbose)
cput1 = (time.clock(), time.time())
mol = magobj.mol
mf = magobj._scf
mo_energy = magobj._scf.mo_energy
mo_coeff = magobj._scf.mo_coeff
mo_occ = magobj._scf.mo_occ
orboa = mo_coeff[0][:,mo_occ[0] > 0]
orbob = mo_coeff[1][:,mo_occ[1] > 0]
if h1 is None:
# Imaginary part of F10
dm0 = (numpy.dot(orboa, orboa.T), numpy.dot(orbob, orbob.T))
h1 = magobj.get_fock(dm0, gauge_orig)
h1 = (lib.einsum('xpq,pi,qj->xij', h1[0], mo_coeff[0].conj(), orboa),
lib.einsum('xpq,pi,qj->xij', h1[1], mo_coeff[1].conj(), orbob))
cput1 = log.timer('first order Fock matrix', *cput1)
if s1 is None:
# Imaginary part of S10
s1 = magobj.get_ovlp(mol, gauge_orig)
s1 = (lib.einsum('xpq,pi,qj->xij', s1, mo_coeff[0].conj(), orboa),
lib.einsum('xpq,pi,qj->xij', s1, mo_coeff[1].conj(), orbob))
with_cphf = magobj.cphf
mo1, mo_e1 = uhf_nmr.solve_mo1(magobj, mo_energy, mo_coeff, mo_occ,
h1, s1, with_cphf)
cput1 = logger.timer(magobj, 'solving mo1 eqn', *cput1)
occidxa = mo_occ[0] > 0
occidxb = mo_occ[1] > 0
mag_para = numpy.einsum('yji,xji->xy', mo1[0], h1[0])
mag_para+= numpy.einsum('yji,xji->xy', mo1[1], h1[1])
mag_para-= numpy.einsum('yji,xji,i->xy', mo1[0], s1[0], mo_energy[0][occidxa])
mag_para-= numpy.einsum('yji,xji,i->xy', mo1[1], s1[1], mo_energy[1][occidxb])
# + c.c.
mag_para = mag_para + mag_para.conj()
mag_para-= numpy.einsum('xij,yij->xy', s1[0][:,occidxa], mo_e1[0])
mag_para-= numpy.einsum('xij,yij->xy', s1[1][:,occidxb], mo_e1[1])
return -mag_para