def gen_vind(mf, mo_coeff, mo_occ):
nao, nmoa = mo_coeff[0].shape
nmob = mo_coeff[1].shape[1]
mocca = mo_coeff[0][:,mo_occ[0]>0]
moccb = mo_coeff[1][:,mo_occ[1]>0]
nocca = mocca.shape[1]
noccb = moccb.shape[1]
vresp = _gen_uhf_response(mf, mo_coeff, mo_occ, hermi=1)
def fx(mo1):
mo1 = mo1.reshape(-1,nmoa*nocca+nmob*noccb)
nset = len(mo1)
dm1 = numpy.empty((2,nset,nao,nao))
for i, x in enumerate(mo1):
xa = x[:nmoa*nocca].reshape(nmoa,nocca)
xb = x[nmoa*nocca:].reshape(nmob,noccb)
dma = reduce(numpy.dot, (mo_coeff[0], xa, mocca.T))
dmb = reduce(numpy.dot, (mo_coeff[1], xb, moccb.T))
dm1[0,i] = dma + dma.T
dm1[1,i] = dmb + dmb.T
v1 = vresp(dm1)
v1vo = numpy.empty_like(mo1)
for i in range(nset):
v1vo[i,:nmoa*nocca] = reduce(numpy.dot, (mo_coeff[0].T, v1[0,i], mocca)).ravel()
v1vo[i,nmoa*nocca:] = reduce(numpy.dot, (mo_coeff[1].T, v1[1,i], moccb)).ravel()
return v1vo
return fx
def gen_vind(mf, mo_coeff, mo_occ):
'''Induced potential'''
vresp = _gen_uhf_response(mf, with_j=False, hermi=0)
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]
nocca = orboa.shape[1]
noccb = orbob.shape[1]
nvira = orbva.shape[1]
nvirb = orbvb.shape[1]
nova = nocca * nvira
novb = noccb * nvirb
mo_va_oa = numpy.asarray(numpy.hstack((orbva,orboa)), order='F')
mo_vb_ob = numpy.asarray(numpy.hstack((orbvb,orbob)), order='F')
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()
return vind
def gen_vind(self, mf, mo_coeff, mo_occ):
'''Induced potential'''
vresp = _gen_uhf_response(mf, hermi=1)
occidxa = mo_occ[0] > 0
occidxb = mo_occ[1] > 0
mo0a, mo0b = mo_coeff
orboa = mo0a[:, occidxa]
orbob = mo0b[:, occidxb]
nocca = orboa.shape[1]
noccb = orbob.shape[1]
nmoa = mo0a.shape[1]
nmob = mo0b.shape[1]
def vind(mo1):
mo1 = mo1.reshape(-1,nmoa*nocca+nmob*noccb)
mo1a = mo1[:,:nmoa*nocca].reshape(-1,nmoa,nocca)
mo1b = mo1[:,nmoa*nocca:].reshape(-1,nmob,noccb)
dm1a = lib.einsum('xai,pa,qi->xpq', mo1a, mo0a, orboa.conj())
dm1b = lib.einsum('xai,pa,qi->xpq', mo1b, mo0b, orbob.conj())
dm1a = dm1a + dm1a.transpose(0,2,1).conj()
dm1b = dm1b + dm1b.transpose(0,2,1).conj()
v1ao = vresp(numpy.stack((dm1a,dm1b)))
v1a = lib.einsum('xpq,pi,qj->xij', v1ao[0], mo0a.conj(), orboa)
v1b = lib.einsum('xpq,pi,qj->xij', v1ao[1], mo0b.conj(), orbob)
v1mo = numpy.hstack((v1a.reshape(-1,nmoa*nocca),
v1b.reshape(-1,nmob*noccb)))
return v1mo.ravel()
return vind
def gen_vind(self, mf, mo_coeff, mo_occ):
'''Induced potential'''
vresp = _gen_uhf_response(mf, hermi=1)
occidxa = mo_occ[0] > 0
occidxb = mo_occ[1] > 0
mo0a, mo0b = mo_coeff
orboa = mo0a[:, occidxa]
orbob = mo0b[:, occidxb]
nocca = orboa.shape[1]
noccb = orbob.shape[1]
nmoa = mo0a.shape[1]
nmob = mo0b.shape[1]
def vind(mo1):
mo1 = mo1.reshape(-1, nmoa * nocca + nmob * noccb)
mo1a = mo1[:, :nmoa * nocca].reshape(-1, nmoa, nocca)
mo1b = mo1[:, nmoa * nocca:].reshape(-1, nmob, noccb)
dm1a = lib.einsum('xai,pa,qi->xpq', mo1a, mo0a, orboa.conj())
dm1b = lib.einsum('xai,pa,qi->xpq', mo1b, mo0b, orbob.conj())
dm1a = dm1a + dm1a.transpose(0, 2, 1).conj()
dm1b = dm1b + dm1b.transpose(0, 2, 1).conj()
v1ao = vresp(numpy.stack((dm1a, dm1b)))
v1a = lib.einsum('xpq,pi,qj->xij', v1ao[0], mo0a.conj(), orboa)
v1b = lib.einsum('xpq,pi,qj->xij', v1ao[1], mo0b.conj(), orbob)
v1mo = numpy.hstack(
(v1a.reshape(-1, nmoa * nocca), v1b.reshape(-1, nmob * noccb)))
return v1mo.ravel()
return vind
def gen_vind(mf, mo_coeff, mo_occ):
'''Induced potential associated with h1_PSO'''
vresp = _gen_uhf_response(mf, with_j=False, hermi=0)
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]
nocca = orboa.shape[1]
noccb = orbob.shape[1]
nvira = orbva.shape[1]
nvirb = orbvb.shape[1]
nova = nocca * nvira
novb = noccb * nvirb
mo_va_oa = numpy.asarray(numpy.hstack((orbva, orboa)), order='F')
mo_vb_ob = numpy.asarray(numpy.hstack((orbvb, orbob)), order='F')
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()
return vind
def gen_vind(self, mf, mo_coeff, mo_occ):
'''Induced potential'''
vresp = _gen_uhf_response(self._scf, hermi=2)
occidxa = mo_occ[0] > 0
occidxb = mo_occ[1] > 0
orboa = mo_coeff[0][:,occidxa]
orbob = mo_coeff[1][:,occidxb]
nocca = orboa.shape[1]
noccb = orbob.shape[1]
nao, nmo = mo_coeff[0].shape
nvira = nmo - nocca
def vind(mo1):
mo1a = mo1.reshape(3,-1)[:,:nocca*nmo].reshape(3,nmo,nocca)
mo1b = mo1.reshape(3,-1)[:,nocca*nmo:].reshape(3,nmo,noccb)
dm1a = [reduce(numpy.dot, (mo_coeff[0], x, orboa.T.conj())) for x in mo1a]
dm1b = [reduce(numpy.dot, (mo_coeff[1], x, orbob.T.conj())) for x in mo1b]
dm1 = numpy.asarray(([d1-d1.conj().T for d1 in dm1a],
[d1-d1.conj().T for d1 in dm1b]))
v1ao = vresp(dm1)
v1a = [reduce(numpy.dot, (mo_coeff[0].T.conj(), x, orboa)) for x in v1ao[0]]
v1b = [reduce(numpy.dot, (mo_coeff[1].T.conj(), x, orbob)) for x in v1ao[1]]
v1mo = numpy.hstack((numpy.asarray(v1a).reshape(3,-1),
numpy.asarray(v1b).reshape(3,-1)))
return v1mo.ravel()
return vind
def gen_vind(mf, mo_coeff, mo_occ):
nao, nmoa = mo_coeff[0].shape
nmob = mo_coeff[1].shape[1]
mocca = mo_coeff[0][:, mo_occ[0] > 0]
moccb = mo_coeff[1][:, mo_occ[1] > 0]
nocca = mocca.shape[1]
noccb = moccb.shape[1]
vresp = _gen_uhf_response(mf, mo_coeff, mo_occ, hermi=1)
def fx(mo1):
mo1 = mo1.reshape(-1, nmoa * nocca + nmob * noccb)
nset = len(mo1)
dm1 = numpy.empty((2, nset, nao, nao))
for i, x in enumerate(mo1):
xa = x[:nmoa * nocca].reshape(nmoa, nocca)
xb = x[nmoa * nocca:].reshape(nmob, noccb)
dma = reduce(numpy.dot, (mo_coeff[0], xa, mocca.T))
dmb = reduce(numpy.dot, (mo_coeff[1], xb, moccb.T))
dm1[0, i] = dma + dma.T
dm1[1, i] = dmb + dmb.T
v1 = vresp(dm1)
v1vo = numpy.empty_like(mo1)
for i in range(nset):
v1vo[i, :nmoa * nocca] = reduce(
numpy.dot, (mo_coeff[0].T, v1[0, i], mocca)).ravel()
v1vo[i, nmoa * nocca:] = reduce(
numpy.dot, (mo_coeff[1].T, v1[1, i], moccb)).ravel()
return v1vo
return fx
def gen_vind(mf, mo_coeff, mo_occ):
'''Induced potential'''
vresp = _gen_uhf_response(mf, hermi=2)
occidxa = mo_occ[0] > 0
occidxb = mo_occ[1] > 0
orboa = mo_coeff[0][:,occidxa]
orbob = mo_coeff[1][:,occidxb]
nocca = orboa.shape[1]
noccb = orbob.shape[1]
nao, nmo = mo_coeff[0].shape
nvira = nmo - nocca
def vind(mo1):
mo1a = mo1.reshape(3,-1)[:,:nocca*nmo].reshape(3,nmo,nocca)
mo1b = mo1.reshape(3,-1)[:,nocca*nmo:].reshape(3,nmo,noccb)
dm1a = [reduce(numpy.dot, (mo_coeff[0], x, orboa.T.conj())) for x in mo1a]
dm1b = [reduce(numpy.dot, (mo_coeff[1], x, orbob.T.conj())) for x in mo1b]
dm1 = numpy.asarray(([d1-d1.conj().T for d1 in dm1a],
[d1-d1.conj().T for d1 in dm1b]))
v1ao = vresp(dm1)
v1a = [reduce(numpy.dot, (mo_coeff[0].T.conj(), x, orboa)) for x in v1ao[0]]
v1b = [reduce(numpy.dot, (mo_coeff[1].T.conj(), x, orbob)) for x in v1ao[1]]
v1mo = numpy.hstack((numpy.asarray(v1a).reshape(3,-1),
numpy.asarray(v1b).reshape(3,-1)))
return v1mo.ravel()
return vind
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 ucphf_with_freq(mf,
mo_energy,
mo_occ,
h1,
freq=0,
max_cycle=20,
tol=1e-9,
hermi=False,
verbose=logger.WARN):
log = logger.new_logger(verbose=verbose)
t0 = (time.clock(), time.time())
occidxa = mo_occ[0] > 0
occidxb = mo_occ[1] > 0
viridxa = ~occidxa
viridxb = ~occidxb
mo_ea, mo_eb = mo_energy
# e_ai - freq may produce very small elements which can cause numerical
# issue in krylov solver
LEVEL_SHIF = 0.1
e_ai_a = lib.direct_sum('a-i->ai', mo_ea[viridxa], mo_ea[occidxa]).ravel()
e_ai_b = lib.direct_sum('a-i->ai', mo_eb[viridxb], mo_eb[occidxb]).ravel()
diag = (e_ai_a - freq, e_ai_b - freq, e_ai_a + freq, e_ai_b + freq)
diag[0][diag[0] < LEVEL_SHIF] += LEVEL_SHIF
diag[1][diag[1] < LEVEL_SHIF] += LEVEL_SHIF
diag[2][diag[2] < LEVEL_SHIF] += LEVEL_SHIF
diag[3][diag[3] < LEVEL_SHIF] += LEVEL_SHIF
mo0a, mo0b = mf.mo_coeff
nao, nmoa = mo0a.shape
nmob = mo0b.shape
orbva = mo0a[:, viridxa]
orbvb = mo0b[:, viridxb]
orboa = mo0a[:, occidxa]
orbob = mo0b[:, occidxb]
nvira = orbva.shape[1]
nvirb = orbvb.shape[1]
nocca = orboa.shape[1]
noccb = orbob.shape[1]
h1a = h1[0].reshape(-1, nvira * nocca)
h1b = h1[1].reshape(-1, nvirb * noccb)
ncomp = h1a.shape[0]
mo1base = numpy.hstack(
(-h1a / diag[0], -h1b / diag[1], -h1a / diag[2], -h1b / diag[3]))
offsets = numpy.cumsum((nocca * nvira, noccb * nvirb, nocca * nvira))
vresp = _gen_uhf_response(mf, hermi=0)
def vind(xys):
nz = len(xys)
dm1a = numpy.empty((nz, nao, nao))
dm1b = numpy.empty((nz, nao, nao))
for i in range(nz):
xa, xb, ya, yb = numpy.split(xys[i], offsets)
dmx = reduce(numpy.dot, (orbva, xa.reshape(nvira, nocca), orboa.T))
dmy = reduce(numpy.dot,
(orboa, ya.reshape(nvira, nocca).T, orbva.T))
dm1a[i] = dmx + dmy # AX + BY
dmx = reduce(numpy.dot, (orbvb, xb.reshape(nvirb, noccb), orbob.T))
dmy = reduce(numpy.dot,
(orbob, yb.reshape(nvirb, noccb).T, orbvb.T))
dm1b[i] = dmx + dmy # AX + BY
v1ao = vresp(numpy.stack((dm1a, dm1b)))
v1voa = lib.einsum('xpq,pi,qj->xij', v1ao[0], orbva,
orboa).reshape(nz, -1)
v1vob = lib.einsum('xpq,pi,qj->xij', v1ao[1], orbvb,
orbob).reshape(nz, -1)
v1ova = lib.einsum('xpq,pi,qj->xji', v1ao[0], orboa,
orbva).reshape(nz, -1)
v1ovb = lib.einsum('xpq,pi,qj->xji', v1ao[1], orbob,
orbvb).reshape(nz, -1)
for i in range(nz):
xa, xb, ya, yb = numpy.split(xys[i], offsets)
v1voa[i] += (e_ai_a - freq - diag[0]) * xa
v1voa[i] /= diag[0]
v1vob[i] += (e_ai_b - freq - diag[1]) * xb
v1vob[i] /= diag[1]
v1ova[i] += (e_ai_a + freq - diag[2]) * ya
v1ova[i] /= diag[2]
v1ovb[i] += (e_ai_b + freq - diag[3]) * yb
v1ovb[i] /= diag[3]
v = numpy.hstack((v1voa, v1vob, v1ova, v1ovb))
return v
# FIXME: krylov solver is not accurate enough for many freqs. Using tight
# tol and lindep could offer small help. A better linear equation solver
# is needed.
mo1 = lib.krylov(vind,
mo1base,
tol=tol,
max_cycle=max_cycle,
hermi=hermi,
lindep=1e-18,
verbose=log)
log.timer('krylov solver in CPHF', *t0)
dm1a = numpy.empty((ncomp, nao, nao))
dm1b = numpy.empty((ncomp, nao, nao))
for i in range(ncomp):
xa, xb, ya, yb = numpy.split(mo1[i], offsets)
dmx = reduce(numpy.dot, (orbva, xa.reshape(nvira, nocca) * 2, orboa.T))
dmy = reduce(numpy.dot,
(orboa, ya.reshape(nvira, nocca).T * 2, orbva.T))
dm1a[i] = dmx + dmy
dmx = reduce(numpy.dot, (orbvb, xb.reshape(nvirb, noccb) * 2, orbob.T))
dmy = reduce(numpy.dot,
(orbob, yb.reshape(nvirb, noccb).T * 2, orbvb.T))
dm1b[i] = dmx + dmy
v1ao = vresp(numpy.stack((dm1a, dm1b)))
mo_e1_a = lib.einsum('xpq,pi,qj->xij', v1ao[0], orboa, orboa)
mo_e1_b = lib.einsum('xpq,pi,qj->xij', v1ao[1], orbob, orbob)
mo_e1 = (mo_e1_a, mo_e1_b)
xa, xb, ya, yb = numpy.split(mo1, offsets, axis=1)
mo1 = (xa.reshape(ncomp, nvira, nocca), xb.reshape(ncomp, nvirb, noccb),
ya.reshape(ncomp, nvira, nocca), yb.reshape(ncomp, nvirb, noccb))
return mo1, mo_e1
def solve_mo1(sscobj, h1):
cput1 = (time.clock(), time.time())
log = logger.Logger(sscobj.stdout, sscobj.verbose)
mol = sscobj.mol
mo_energy = sscobj._scf.mo_energy
mo_coeff = sscobj._scf.mo_coeff
mo_occ = sscobj._scf.mo_occ
h1aa, h1ab, h1ba, h1bb = h1
nset = len(h1aa)
eai_aa = 1. / lib.direct_sum('a-i->ai', mo_energy[0][mo_occ[0] == 0],
mo_energy[0][mo_occ[0] > 0])
eai_ab = 1. / lib.direct_sum('a-i->ai', mo_energy[0][mo_occ[0] == 0],
mo_energy[1][mo_occ[1] > 0])
eai_ba = 1. / lib.direct_sum('a-i->ai', mo_energy[1][mo_occ[1] == 0],
mo_energy[0][mo_occ[0] > 0])
eai_bb = 1. / lib.direct_sum('a-i->ai', mo_energy[1][mo_occ[1] == 0],
mo_energy[1][mo_occ[1] > 0])
mo1 = (numpy.asarray(h1aa) * -eai_aa, numpy.asarray(h1ab) * -eai_ab,
numpy.asarray(h1ba) * -eai_ba, numpy.asarray(h1bb) * -eai_bb)
h1aa = h1ab = h1ba = h1bb = None
if not sscobj.cphf:
return mo1
orboa = mo_coeff[0][:, mo_occ[0] > 0]
orbva = mo_coeff[0][:, mo_occ[0] == 0]
orbob = mo_coeff[1][:, mo_occ[1] > 0]
orbvb = mo_coeff[1][:, mo_occ[1] == 0]
nocca = orboa.shape[1]
nvira = orbva.shape[1]
noccb = orbob.shape[1]
nvirb = orbvb.shape[1]
p1 = nvira * nocca
p2 = p1 + nvira * noccb
p3 = p2 + nvirb * nocca
def _split_mo1(mo1):
mo1 = mo1.reshape(nset, -1)
mo1aa = mo1[:, :p1].reshape(nset, nvira, nocca)
mo1ab = mo1[:, p1:p2].reshape(nset, nvira, noccb)
mo1ba = mo1[:, p2:p3].reshape(nset, nvirb, nocca)
mo1bb = mo1[:, p3:].reshape(nset, nvirb, noccb)
return mo1aa, mo1ab, mo1ba, mo1bb
mo1 = numpy.hstack((mo1[0].reshape(nset, -1), mo1[1].reshape(nset, -1),
mo1[2].reshape(nset, -1), mo1[3].reshape(nset, -1)))
vresp = _gen_uhf_response(mf, with_j=False, hermi=0)
mo_va_oa = numpy.asarray(numpy.hstack((orbva, orboa)), order='F')
mo_va_ob = numpy.asarray(numpy.hstack((orbva, orbob)), order='F')
mo_vb_oa = numpy.asarray(numpy.hstack((orbvb, orboa)), order='F')
mo_vb_ob = numpy.asarray(numpy.hstack((orbvb, orbob)), order='F')
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()
mo1 = lib.krylov(vind, mo1.ravel(), tol=1e-9, max_cycle=20, verbose=log)
log.timer('solving FC CPHF eqn', *cput1)
mo1 = _split_mo1(mo1)
return mo1
def gen_tdhf_operation(mf, fock_ao=None, singlet=True, wfnsym=None):
'''Generate function to compute
[ A B][X]
[-B -A][Y]
'''
mol = mf.mol
mo_coeff = mf.mo_coeff
assert (mo_coeff[0].dtype == numpy.double)
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
nao, nmo = mo_coeff[0].shape
occidxa = numpy.where(mo_occ[0] > 0)[0]
occidxb = numpy.where(mo_occ[1] > 0)[0]
viridxa = numpy.where(mo_occ[0] == 0)[0]
viridxb = numpy.where(mo_occ[1] == 0)[0]
nocca = len(occidxa)
noccb = len(occidxb)
nvira = len(viridxa)
nvirb = len(viridxb)
orboa = mo_coeff[0][:, occidxa]
orbob = mo_coeff[1][:, occidxb]
orbva = mo_coeff[0][:, viridxa]
orbvb = mo_coeff[1][:, viridxb]
if wfnsym is not None and mol.symmetry:
if isinstance(wfnsym, str):
wfnsym = symm.irrep_name2id(mol.groupname, wfnsym)
orbsyma, orbsymb = uhf_symm.get_orbsym(mol, mo_coeff)
wfnsym = wfnsym % 10 # convert to D2h subgroup
orbsyma = orbsyma % 10
orbsymb = orbsymb % 10
sym_forbida = (orbsyma[occidxa, None] ^ orbsyma[viridxa]) != wfnsym
sym_forbidb = (orbsymb[occidxb, None] ^ orbsymb[viridxb]) != wfnsym
sym_forbid = numpy.hstack((sym_forbida.ravel(), sym_forbidb.ravel()))
e_ia_a = (mo_energy[0][viridxa, None] - mo_energy[0][occidxa]).T
e_ia_b = (mo_energy[1][viridxb, None] - mo_energy[1][occidxb]).T
e_ia = hdiag = numpy.hstack((e_ia_a.reshape(-1), e_ia_b.reshape(-1)))
if wfnsym is not None and mol.symmetry:
hdiag[sym_forbid] = 0
hdiag = numpy.hstack((hdiag.ravel(), hdiag.ravel()))
mo_a = numpy.asarray(numpy.hstack((orboa, orbva)), order='F')
mo_b = numpy.asarray(numpy.hstack((orbob, orbvb)), order='F')
mem_now = lib.current_memory()[0]
max_memory = max(2000, mf.max_memory * .8 - mem_now)
vresp = _gen_uhf_response(mf, hermi=0, max_memory=max_memory)
def vind(xys):
nz = len(xys)
if wfnsym is not None and mol.symmetry:
# shape(nz,2,-1): 2 ~ X,Y
xys = numpy.copy(xys).reshape(nz, 2, -1)
xys[:, :, sym_forbid] = 0
dms = numpy.empty((2, nz, nao, nao)) # 2 ~ alpha,beta
for i in range(nz):
x, y = xys[i].reshape(2, -1)
xa = x[:nocca * nvira].reshape(nocca, nvira)
xb = x[nocca * nvira:].reshape(noccb, nvirb)
ya = y[:nocca * nvira].reshape(nocca, nvira)
yb = y[nocca * nvira:].reshape(noccb, nvirb)
dmx = reduce(numpy.dot, (orboa, xa, orbva.T))
dmy = reduce(numpy.dot, (orbva, ya.T, orboa.T))
dms[0, i] = dmx + dmy # AX + BY
dmx = reduce(numpy.dot, (orbob, xb, orbvb.T))
dmy = reduce(numpy.dot, (orbvb, yb.T, orbob.T))
dms[1, i] = dmx + dmy # AX + BY
v1ao = vresp(dms)
v1avo = _ao2mo.nr_e2(v1ao[0], mo_a, (nocca, nmo, 0, nocca))
v1bvo = _ao2mo.nr_e2(v1ao[1], mo_b, (noccb, nmo, 0, noccb))
v1aov = _ao2mo.nr_e2(v1ao[0], mo_a, (0, nocca, nocca, nmo))
v1bov = _ao2mo.nr_e2(v1ao[1], mo_b, (0, noccb, noccb, nmo))
hx = numpy.empty((nz, 2, nvira * nocca + nvirb * noccb),
dtype=v1avo.dtype)
for i in range(nz):
x, y = xys[i].reshape(2, -1)
hx[i, 0, :nvira * nocca] = v1aov[i].ravel()
hx[i, 0, nvira * nocca:] = v1bov[i].ravel()
hx[i, 0] += e_ia * x # AX
hx[i,
1, :nvira * nocca] = -v1avo[i].reshape(nvira, nocca).T.ravel()
hx[i, 1,
nvira * nocca:] = -v1bvo[i].reshape(nvirb, noccb).T.ravel()
hx[i, 1] -= e_ia * y #-AY
if wfnsym is not None and mol.symmetry:
hx[:, :, sym_forbid] = 0
return hx.reshape(nz, -1)
return vind, hdiag
def gen_tda_operation(mf, fock_ao=None, wfnsym=None):
'''(A+B)x
Kwargs:
wfnsym : int or str
Point group symmetry irrep symbol or ID for excited CIS wavefunction.
'''
mol = mf.mol
mo_coeff = mf.mo_coeff
assert (mo_coeff[0].dtype == numpy.double)
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
nao, nmo = mo_coeff[0].shape
occidxa = numpy.where(mo_occ[0] > 0)[0]
occidxb = numpy.where(mo_occ[1] > 0)[0]
viridxa = numpy.where(mo_occ[0] == 0)[0]
viridxb = numpy.where(mo_occ[1] == 0)[0]
nocca = len(occidxa)
noccb = len(occidxb)
nvira = len(viridxa)
nvirb = len(viridxb)
orboa = mo_coeff[0][:, occidxa]
orbob = mo_coeff[1][:, occidxb]
orbva = mo_coeff[0][:, viridxa]
orbvb = mo_coeff[1][:, viridxb]
if wfnsym is not None and mol.symmetry:
if isinstance(wfnsym, str):
wfnsym = symm.irrep_name2id(mol.groupname, wfnsym)
orbsyma, orbsymb = uhf_symm.get_orbsym(mol, mo_coeff)
wfnsym = wfnsym % 10 # convert to D2h subgroup
orbsyma = orbsyma % 10
orbsymb = orbsymb % 10
sym_forbida = (orbsyma[occidxa, None] ^ orbsyma[viridxa]) != wfnsym
sym_forbidb = (orbsymb[occidxb, None] ^ orbsymb[viridxb]) != wfnsym
sym_forbid = numpy.hstack((sym_forbida.ravel(), sym_forbidb.ravel()))
e_ia_a = (mo_energy[0][viridxa, None] - mo_energy[0][occidxa]).T
e_ia_b = (mo_energy[1][viridxb, None] - mo_energy[1][occidxb]).T
e_ia = hdiag = numpy.hstack((e_ia_a.reshape(-1), e_ia_b.reshape(-1)))
if wfnsym is not None and mol.symmetry:
hdiag[sym_forbid] = 0
mo_a = numpy.asarray(numpy.hstack((orboa, orbva)), order='F')
mo_b = numpy.asarray(numpy.hstack((orbob, orbvb)), order='F')
mem_now = lib.current_memory()[0]
max_memory = max(2000, mf.max_memory * .8 - mem_now)
vresp = _gen_uhf_response(mf, hermi=0, max_memory=max_memory)
def vind(zs):
nz = len(zs)
if wfnsym is not None and mol.symmetry:
zs = numpy.copy(zs)
zs[:, sym_forbid] = 0
dmov = numpy.empty((2, nz, nao, nao))
for i, z in enumerate(zs):
za = z[:nocca * nvira].reshape(nocca, nvira)
zb = z[nocca * nvira:].reshape(noccb, nvirb)
dmov[0, i] = reduce(numpy.dot, (orboa, za, orbva.conj().T))
dmov[1, i] = reduce(numpy.dot, (orbob, zb, orbvb.conj().T))
v1ao = vresp(dmov)
v1a = _ao2mo.nr_e2(v1ao[0], mo_a,
(0, nocca, nocca, nmo)).reshape(-1, nocca, nvira)
v1b = _ao2mo.nr_e2(v1ao[1], mo_b,
(0, noccb, noccb, nmo)).reshape(-1, noccb, nvirb)
for i, z in enumerate(zs):
za = z[:nocca * nvira].reshape(nocca, nvira)
zb = z[nocca * nvira:].reshape(noccb, nvirb)
v1a[i] += numpy.einsum('ia,ia->ia', e_ia_a, za)
v1b[i] += numpy.einsum('ia,ia->ia', e_ia_b, zb)
hx = numpy.hstack((v1a.reshape(nz, -1), v1b.reshape(nz, -1)))
if wfnsym is not None and mol.symmetry:
hx[:, sym_forbid] = 0
return hx
return vind, hdiag
def solve_mo1_fc(sscobj, h1):
cput1 = (time.clock(), time.time())
log = logger.Logger(sscobj.stdout, sscobj.verbose)
mol = sscobj.mol
mf = sscobj._scf
mo_energy = mf.mo_energy
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
h1aa, h1ab, h1ba, h1bb = h1
eai_aa = 1. / lib.direct_sum('a-i->ai', mo_energy[0][mo_occ[0] == 0],
mo_energy[0][mo_occ[0] > 0])
eai_ab = 1. / lib.direct_sum('a-i->ai', mo_energy[0][mo_occ[0] == 0],
mo_energy[1][mo_occ[1] > 0])
eai_ba = 1. / lib.direct_sum('a-i->ai', mo_energy[1][mo_occ[1] == 0],
mo_energy[0][mo_occ[0] > 0])
eai_bb = 1. / lib.direct_sum('a-i->ai', mo_energy[1][mo_occ[1] == 0],
mo_energy[1][mo_occ[1] > 0])
mo1aa = numpy.asarray(h1aa) * -eai_aa
mo1ab = numpy.asarray(h1ab) * -eai_ab
mo1ba = numpy.asarray(h1ba) * -eai_ba
mo1bb = numpy.asarray(h1bb) * -eai_bb
mo1_fc = (mo1aa, mo1ab, mo1ba, mo1bb)
if not sscobj.cphf:
return mo1_fc
orboa = mo_coeff[0][:, mo_occ[0] > 0]
orbva = mo_coeff[0][:, mo_occ[0] == 0]
orbob = mo_coeff[1][:, mo_occ[1] > 0]
orbvb = mo_coeff[1][:, mo_occ[1] == 0]
nocca = orboa.shape[1]
nvira = orbva.shape[1]
noccb = orbob.shape[1]
nvirb = orbvb.shape[1]
nao = mol.nao
vresp = _gen_uhf_response(mf, with_j=False, hermi=1)
if ZZ_ONLY:
# To make UHF/UKS and RHF/RKS code consistent, only z-component is
# considered.
nvars = nvira * nocca + nvirb * noccb
nset = h1aa.size // eai_aa.size
def _split_mo1(mo1):
mo1 = mo1.reshape(nset, nvars)
mo1aa = mo1[:, :nvira * nocca].reshape(nset, nvira, nocca)
mo1bb = mo1[:, nvira * nocca:].reshape(nset, nvirb, noccb)
return mo1aa, mo1ab, mo1ba, mo1bb
mo1_fc = numpy.hstack(
(mo1_fc[0].reshape(nset, -1), mo1_fc[3].reshape(nset, -1)))
mo_va_oa = numpy.asarray(numpy.hstack((orbva, orboa)), order='F')
mo_vb_ob = numpy.asarray(numpy.hstack((orbvb, orbob)), order='F')
def vind(mo1):
mo1aa, mo1ab, mo1ba, mo1bb = _split_mo1(mo1)
dm1aa = _dm1_mo2ao(mo1aa, orbva, orboa)
dm1bb = _dm1_mo2ao(mo1bb, orbvb, orbob)
dm1 = lib.asarray([
dm1aa + dm1aa.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))
v1bb = _ao2mo.nr_e2(v1[1], mo_vb_ob,
(0, nvirb, nvirb, nvirb + noccb))
v1aa = v1aa.reshape(nset, nvira, nocca)
v1bb = v1bb.reshape(nset, nvirb, noccb)
v1aa *= eai_aa
v1bb *= eai_bb
v1mo = numpy.hstack((v1aa.reshape(nset,
-1), v1bb.reshape(nset, -1)))
return v1mo.ravel()
else:
segs = (nvira * nocca, nvira * noccb, nvirb * nocca, nvirb * noccb)
sections = numpy.cumsum(segs[:3])
nvars = numpy.sum(segs)
nset = h1aa.size // eai_aa.size
def _split_mo1(mo1):
mo1 = numpy.split(mo1.reshape(nset, nvars), sections, axis=1)
mo1aa = mo1[0].reshape(nset, nvira, nocca)
mo1ab = mo1[1].reshape(nset, nvira, noccb)
mo1ba = mo1[2].reshape(nset, nvirb, nocca)
mo1bb = mo1[3].reshape(nset, nvirb, noccb)
return mo1aa, mo1ab, mo1ba, mo1bb
mo1_fc = numpy.hstack(
(mo1_fc[0].reshape(nset, -1), mo1_fc[1].reshape(nset, -1),
mo1_fc[2].reshape(nset, -1), mo1_fc[3].reshape(nset, -1)))
mo_va_oa = numpy.asarray(numpy.hstack((orbva, orboa)), order='F')
mo_va_ob = numpy.asarray(numpy.hstack((orbva, orbob)), order='F')
mo_vb_oa = numpy.asarray(numpy.hstack((orbvb, orboa)), order='F')
mo_vb_ob = numpy.asarray(numpy.hstack((orbvb, orbob)), order='F')
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()
mo1 = lib.krylov(vind,
mo1_fc.ravel(),
tol=sscobj.conv_tol,
max_cycle=sscobj.max_cycle_cphf,
verbose=log)
log.timer('solving FC CPHF eqn', *cput1)
mo1_fc = _split_mo1(mo1)
return mo1_fc
def _gen_hop_uhf_external(mf, with_symmetry=True, verbose=None):
mol = mf.mol
mo_coeff = mf.mo_coeff
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
occidxa = numpy.where(mo_occ[0]>0)[0]
occidxb = numpy.where(mo_occ[1]>0)[0]
viridxa = numpy.where(mo_occ[0]==0)[0]
viridxb = numpy.where(mo_occ[1]==0)[0]
nocca = len(occidxa)
noccb = len(occidxb)
nvira = len(viridxa)
nvirb = len(viridxb)
orboa = mo_coeff[0][:,occidxa]
orbob = mo_coeff[1][:,occidxb]
orbva = mo_coeff[0][:,viridxa]
orbvb = mo_coeff[1][:,viridxb]
if with_symmetry and mol.symmetry:
orbsyma, orbsymb = uhf_symm.get_orbsym(mol, mo_coeff)
sym_forbida = orbsyma[viridxa].reshape(-1,1) != orbsyma[occidxa]
sym_forbidb = orbsymb[viridxb].reshape(-1,1) != orbsymb[occidxb]
sym_forbid1 = numpy.hstack((sym_forbida.ravel(), sym_forbidb.ravel()))
h1e = mf.get_hcore()
dm0 = mf.make_rdm1(mo_coeff, mo_occ)
fock_ao = h1e + mf.get_veff(mol, dm0)
focka = reduce(numpy.dot, (mo_coeff[0].conj().T, fock_ao[0], mo_coeff[0]))
fockb = reduce(numpy.dot, (mo_coeff[1].conj().T, fock_ao[1], mo_coeff[1]))
fooa = focka[occidxa[:,None],occidxa]
fvva = focka[viridxa[:,None],viridxa]
foob = fockb[occidxb[:,None],occidxb]
fvvb = fockb[viridxb[:,None],viridxb]
h_diaga =(focka[viridxa,viridxa].reshape(-1,1) - focka[occidxa,occidxa])
h_diagb =(fockb[viridxb,viridxb].reshape(-1,1) - fockb[occidxb,occidxb])
hdiag1 = numpy.hstack((h_diaga.reshape(-1), h_diagb.reshape(-1)))
if with_symmetry and mol.symmetry:
hdiag1[sym_forbid1] = 0
mem_now = lib.current_memory()[0]
max_memory = max(2000, mf.max_memory*.8-mem_now)
vrespz = _gen_uhf_response(mf, with_j=False, hermi=2)
def hop_real2complex(x1):
if with_symmetry and mol.symmetry:
x1 = x1.copy()
x1[sym_forbid1] = 0
x1a = x1[:nvira*nocca].reshape(nvira,nocca)
x1b = x1[nvira*nocca:].reshape(nvirb,noccb)
x2a = numpy.einsum('pr,rq->pq', fvva, x1a)
x2a-= numpy.einsum('sq,ps->pq', fooa, x1a)
x2b = numpy.einsum('pr,rq->pq', fvvb, x1b)
x2b-= numpy.einsum('qs,ps->pq', foob, x1b)
d1a = reduce(numpy.dot, (orbva, x1a, orboa.conj().T))
d1b = reduce(numpy.dot, (orbvb, x1b, orbob.conj().T))
dm1 = numpy.array((d1a-d1a.conj().T, d1b-d1b.conj().T))
v1 = vrespz(dm1)
x2a += reduce(numpy.dot, (orbva.conj().T, v1[0], orboa))
x2b += reduce(numpy.dot, (orbvb.conj().T, v1[1], orbob))
x2 = numpy.hstack((x2a.ravel(), x2b.ravel()))
if with_symmetry and mol.symmetry:
x2[sym_forbid1] = 0
return x2
if with_symmetry and mol.symmetry:
orbsyma, orbsymb = uhf_symm.get_orbsym(mol, mo_coeff)
sym_forbidab = orbsyma[viridxa].reshape(-1,1) != orbsymb[occidxb]
sym_forbidba = orbsymb[viridxb].reshape(-1,1) != orbsyma[occidxa]
sym_forbid2 = numpy.hstack((sym_forbidab.ravel(), sym_forbidba.ravel()))
hdiagab = fvva.diagonal().reshape(-1,1) - foob.diagonal()
hdiagba = fvvb.diagonal().reshape(-1,1) - fooa.diagonal()
hdiag2 = numpy.hstack((hdiagab.ravel(), hdiagba.ravel()))
if with_symmetry and mol.symmetry:
hdiag2[sym_forbid2] = 0
vresp1 = _gen_uhf_response(mf, with_j=False, hermi=0)
# Spin flip GHF solution is not considered
def hop_uhf2ghf(x1):
if with_symmetry and mol.symmetry:
x1 = x1.copy()
x1[sym_forbid2] = 0
x1ab = x1[:nvira*noccb].reshape(nvira,noccb)
x1ba = x1[nvira*noccb:].reshape(nvirb,nocca)
x2ab = numpy.einsum('pr,rq->pq', fvva, x1ab)
x2ab-= numpy.einsum('sq,ps->pq', foob, x1ab)
x2ba = numpy.einsum('pr,rq->pq', fvvb, x1ba)
x2ba-= numpy.einsum('qs,ps->pq', fooa, x1ba)
d1ab = reduce(numpy.dot, (orbva, x1ab, orbob.conj().T))
d1ba = reduce(numpy.dot, (orbvb, x1ba, orboa.conj().T))
dm1 = numpy.array((d1ab+d1ba.conj().T, d1ba+d1ab.conj().T))
v1 = vresp1(dm1)
x2ab += reduce(numpy.dot, (orbva.conj().T, v1[0], orbob))
x2ba += reduce(numpy.dot, (orbvb.conj().T, v1[1], orboa))
x2 = numpy.hstack((x2ab.real.ravel(), x2ba.real.ravel()))
if with_symmetry and mol.symmetry:
x2[sym_forbid2] = 0
return x2
return hop_real2complex, hdiag1, hop_uhf2ghf, hdiag2
def solve_mo1_fc(sscobj, h1):
cput1 = (time.clock(), time.time())
log = logger.Logger(sscobj.stdout, sscobj.verbose)
mol = sscobj.mol
mf = sscobj._scf
mo_energy = mf.mo_energy
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
h1aa, h1ab, h1ba, h1bb = h1
eai_aa = 1. / lib.direct_sum('a-i->ai', mo_energy[0][mo_occ[0]==0], mo_energy[0][mo_occ[0]>0])
eai_ab = 1. / lib.direct_sum('a-i->ai', mo_energy[0][mo_occ[0]==0], mo_energy[1][mo_occ[1]>0])
eai_ba = 1. / lib.direct_sum('a-i->ai', mo_energy[1][mo_occ[1]==0], mo_energy[0][mo_occ[0]>0])
eai_bb = 1. / lib.direct_sum('a-i->ai', mo_energy[1][mo_occ[1]==0], mo_energy[1][mo_occ[1]>0])
mo1aa = numpy.asarray(h1aa) * -eai_aa
mo1ab = numpy.asarray(h1ab) * -eai_ab
mo1ba = numpy.asarray(h1ba) * -eai_ba
mo1bb = numpy.asarray(h1bb) * -eai_bb
mo1_fc = (mo1aa, mo1ab, mo1ba, mo1bb)
if not sscobj.cphf:
return mo1_fc
orboa = mo_coeff[0][:,mo_occ[0]> 0]
orbva = mo_coeff[0][:,mo_occ[0]==0]
orbob = mo_coeff[1][:,mo_occ[1]> 0]
orbvb = mo_coeff[1][:,mo_occ[1]==0]
nocca = orboa.shape[1]
nvira = orbva.shape[1]
noccb = orbob.shape[1]
nvirb = orbvb.shape[1]
nao = mol.nao
vresp = _gen_uhf_response(mf, with_j=False, hermi=1)
if ZZ_ONLY:
# To make UHF/UKS and RHF/RKS code consistent, only z-component is
# considered.
nvars = nvira*nocca + nvirb*noccb
nset = h1aa.size // eai_aa.size
def _split_mo1(mo1):
mo1 = mo1.reshape(nset,nvars)
mo1aa = mo1[:,:nvira*nocca].reshape(nset,nvira,nocca)
mo1bb = mo1[:,nvira*nocca:].reshape(nset,nvirb,noccb)
return mo1aa, mo1ab, mo1ba, mo1bb
mo1_fc = numpy.hstack((mo1_fc[0].reshape(nset,-1),
mo1_fc[3].reshape(nset,-1)))
mo_va_oa = numpy.asarray(numpy.hstack((orbva,orboa)), order='F')
mo_vb_ob = numpy.asarray(numpy.hstack((orbvb,orbob)), order='F')
def vind(mo1):
mo1aa, mo1ab, mo1ba, mo1bb = _split_mo1(mo1)
dm1aa = _dm1_mo2ao(mo1aa, orbva, orboa)
dm1bb = _dm1_mo2ao(mo1bb, orbvb, orbob)
dm1 = lib.asarray([dm1aa+dm1aa.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))
v1bb = _ao2mo.nr_e2(v1[1], mo_vb_ob, (0,nvirb,nvirb,nvirb+noccb))
v1aa = v1aa.reshape(nset,nvira,nocca)
v1bb = v1bb.reshape(nset,nvirb,noccb)
v1aa *= eai_aa
v1bb *= eai_bb
v1mo = numpy.hstack((v1aa.reshape(nset,-1),
v1bb.reshape(nset,-1)))
return v1mo.ravel()
else:
segs = (nvira*nocca, nvira*noccb, nvirb*nocca, nvirb*noccb)
sections = numpy.cumsum(segs[:3])
nvars = numpy.sum(segs)
nset = h1aa.size // eai_aa.size
def _split_mo1(mo1):
mo1 = numpy.split(mo1.reshape(nset,nvars), sections, axis=1)
mo1aa = mo1[0].reshape(nset,nvira,nocca)
mo1ab = mo1[1].reshape(nset,nvira,noccb)
mo1ba = mo1[2].reshape(nset,nvirb,nocca)
mo1bb = mo1[3].reshape(nset,nvirb,noccb)
return mo1aa, mo1ab, mo1ba, mo1bb
mo1_fc = numpy.hstack((mo1_fc[0].reshape(nset,-1),
mo1_fc[1].reshape(nset,-1),
mo1_fc[2].reshape(nset,-1),
mo1_fc[3].reshape(nset,-1)))
mo_va_oa = numpy.asarray(numpy.hstack((orbva,orboa)), order='F')
mo_va_ob = numpy.asarray(numpy.hstack((orbva,orbob)), order='F')
mo_vb_oa = numpy.asarray(numpy.hstack((orbvb,orboa)), order='F')
mo_vb_ob = numpy.asarray(numpy.hstack((orbvb,orbob)), order='F')
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()
mo1 = lib.krylov(vind, mo1_fc.ravel(), tol=sscobj.conv_tol,
max_cycle=sscobj.max_cycle_cphf, verbose=log)
log.timer('solving FC CPHF eqn', *cput1)
mo1_fc = _split_mo1(mo1)
return mo1_fc
def _gen_hop_uhf_external(mf, with_symmetry=True, verbose=None):
mol = mf.mol
mo_coeff = mf.mo_coeff
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
occidxa = numpy.where(mo_occ[0] > 0)[0]
occidxb = numpy.where(mo_occ[1] > 0)[0]
viridxa = numpy.where(mo_occ[0] == 0)[0]
viridxb = numpy.where(mo_occ[1] == 0)[0]
nocca = len(occidxa)
noccb = len(occidxb)
nvira = len(viridxa)
nvirb = len(viridxb)
orboa = mo_coeff[0][:, occidxa]
orbob = mo_coeff[1][:, occidxb]
orbva = mo_coeff[0][:, viridxa]
orbvb = mo_coeff[1][:, viridxb]
if with_symmetry and mol.symmetry:
orbsyma, orbsymb = uhf_symm.get_orbsym(mol, mo_coeff)
sym_forbida = orbsyma[viridxa].reshape(-1, 1) != orbsyma[occidxa]
sym_forbidb = orbsymb[viridxb].reshape(-1, 1) != orbsymb[occidxb]
sym_forbid1 = numpy.hstack((sym_forbida.ravel(), sym_forbidb.ravel()))
h1e = mf.get_hcore()
dm0 = mf.make_rdm1(mo_coeff, mo_occ)
fock_ao = h1e + mf.get_veff(mol, dm0)
focka = reduce(numpy.dot, (mo_coeff[0].T, fock_ao[0], mo_coeff[0]))
fockb = reduce(numpy.dot, (mo_coeff[1].T, fock_ao[1], mo_coeff[1]))
fooa = focka[occidxa[:, None], occidxa]
fvva = focka[viridxa[:, None], viridxa]
foob = fockb[occidxb[:, None], occidxb]
fvvb = fockb[viridxb[:, None], viridxb]
h_diaga = (focka[viridxa, viridxa].reshape(-1, 1) -
focka[occidxa, occidxa])
h_diagb = (fockb[viridxb, viridxb].reshape(-1, 1) -
fockb[occidxb, occidxb])
hdiag1 = numpy.hstack((h_diaga.reshape(-1), h_diagb.reshape(-1)))
if with_symmetry and mol.symmetry:
hdiag1[sym_forbid1] = 0
mem_now = lib.current_memory()[0]
max_memory = max(2000, mf.max_memory * .8 - mem_now)
vrespz = _gen_uhf_response(mf, with_j=False, hermi=2)
def hop_real2complex(x1):
if with_symmetry and mol.symmetry:
x1 = x1.copy()
x1[sym_forbid1] = 0
x1a = x1[:nvira * nocca].reshape(nvira, nocca)
x1b = x1[nvira * nocca:].reshape(nvirb, noccb)
x2a = numpy.einsum('pr,rq->pq', fvva, x1a)
x2a -= numpy.einsum('sq,ps->pq', fooa, x1a)
x2b = numpy.einsum('pr,rq->pq', fvvb, x1b)
x2b -= numpy.einsum('qs,ps->pq', foob, x1b)
d1a = reduce(numpy.dot, (orbva, x1a, orboa.T.conj()))
d1b = reduce(numpy.dot, (orbvb, x1b, orbob.T.conj()))
dm1 = numpy.array((d1a - d1a.T.conj(), d1b - d1b.T.conj()))
v1 = vrespz(dm1)
x2a += reduce(numpy.dot, (orbva.T.conj(), v1[0], orboa))
x2b += reduce(numpy.dot, (orbvb.T.conj(), v1[1], orbob))
x2 = numpy.hstack((x2a.ravel(), x2b.ravel()))
if with_symmetry and mol.symmetry:
x2[sym_forbid1] = 0
return x2
if with_symmetry and mol.symmetry:
orbsyma, orbsymb = uhf_symm.get_orbsym(mol, mo_coeff)
sym_forbidab = orbsyma[viridxa].reshape(-1, 1) != orbsymb[occidxb]
sym_forbidba = orbsymb[viridxb].reshape(-1, 1) != orbsyma[occidxa]
sym_forbid2 = numpy.hstack(
(sym_forbidab.ravel(), sym_forbidba.ravel()))
hdiagab = fvva.diagonal().reshape(-1, 1) - foob.diagonal()
hdiagba = fvvb.diagonal().reshape(-1, 1) - fooa.diagonal()
hdiag2 = numpy.hstack((hdiagab.ravel(), hdiagba.ravel()))
if with_symmetry and mol.symmetry:
hdiag2[sym_forbid2] = 0
vresp1 = _gen_uhf_response(mf, with_j=False, hermi=0)
# Spin flip GHF solution is not considered
def hop_uhf2ghf(x1):
if with_symmetry and mol.symmetry:
x1 = x1.copy()
x1[sym_forbid2] = 0
x1ab = x1[:nvira * noccb].reshape(nvira, noccb)
x1ba = x1[nvira * noccb:].reshape(nvirb, nocca)
x2ab = numpy.einsum('pr,rq->pq', fvva, x1ab)
x2ab -= numpy.einsum('sq,ps->pq', foob, x1ab)
x2ba = numpy.einsum('pr,rq->pq', fvvb, x1ba)
x2ba -= numpy.einsum('qs,ps->pq', fooa, x1ba)
d1ab = reduce(numpy.dot, (orbva, x1ab, orbob.T.conj()))
d1ba = reduce(numpy.dot, (orbvb, x1ba, orboa.T.conj()))
dm1 = numpy.array((d1ab + d1ba.T.conj(), d1ba + d1ab.T.conj()))
v1 = vresp1(dm1)
x2ab += reduce(numpy.dot, (orbva.T.conj(), v1[0], orbob))
x2ba += reduce(numpy.dot, (orbvb.T.conj(), v1[1], orboa))
x2 = numpy.hstack((x2ab.ravel(), x2ba.ravel()))
if with_symmetry and mol.symmetry:
x2[sym_forbid2] = 0
return x2
return hop_real2complex, hdiag1, hop_uhf2ghf, hdiag2
def get_vind(self, mf):
wfnsym = self.wfnsym
singlet = self.singlet
mol = mf.mol
mo_coeff = mf.mo_coeff
assert(mo_coeff[0].dtype == numpy.double)
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
nao, nmo = mo_coeff[0].shape
occidxa = numpy.where(mo_occ[0]>0)[0]
occidxb = numpy.where(mo_occ[1]>0)[0]
viridxa = numpy.where(mo_occ[0]==0)[0]
viridxb = numpy.where(mo_occ[1]==0)[0]
nocca = len(occidxa)
noccb = len(occidxb)
nvira = len(viridxa)
nvirb = len(viridxb)
orboa = mo_coeff[0][:,occidxa]
orbob = mo_coeff[1][:,occidxb]
orbva = mo_coeff[0][:,viridxa]
orbvb = mo_coeff[1][:,viridxb]
if wfnsym is not None and mol.symmetry:
if isinstance(wfnsym, str):
wfnsym = symm.irrep_name2id(mol.groupname, wfnsym)
orbsyma, orbsymb = uhf_symm.get_orbsym(mol, mo_coeff)
wfnsym = wfnsym % 10 # convert to D2h subgroup
orbsyma = orbsyma % 10
orbsymb = orbsymb % 10
sym_forbida = (orbsyma[occidxa,None] ^ orbsyma[viridxa]) != wfnsym
sym_forbidb = (orbsymb[occidxb,None] ^ orbsymb[viridxb]) != wfnsym
sym_forbid = numpy.hstack((sym_forbida.ravel(), sym_forbidb.ravel()))
e_ia_a = (mo_energy[0][viridxa,None] - mo_energy[0][occidxa]).T
e_ia_b = (mo_energy[1][viridxb,None] - mo_energy[1][occidxb]).T
e_ia = numpy.hstack((e_ia_a.reshape(-1), e_ia_b.reshape(-1)))
if wfnsym is not None and mol.symmetry:
e_ia[sym_forbid] = 0
d_ia = numpy.sqrt(e_ia).ravel()
ed_ia = e_ia.ravel() * d_ia
hdiag = e_ia.ravel() ** 2
vresp = _gen_uhf_response(mf, mo_coeff, mo_occ, hermi=1)
def vind(zs):
nz = len(zs)
if wfnsym is not None and mol.symmetry:
zs = numpy.copy(zs)
zs[:,sym_forbid] = 0
dmov = numpy.empty((2,nz,nao,nao))
for i in range(nz):
z = d_ia * zs[i]
za = z[:nocca*nvira].reshape(nocca,nvira)
zb = z[nocca*nvira:].reshape(noccb,nvirb)
dm = reduce(numpy.dot, (orboa, za, orbva.T))
dmov[0,i] = dm + dm.T
dm = reduce(numpy.dot, (orbob, zb, orbvb.T))
dmov[1,i] = dm + dm.T
v1ao = vresp(dmov)
v1a = _ao2mo.nr_e2(v1ao[0], mo_coeff[0], (0,nocca,nocca,nmo))
v1b = _ao2mo.nr_e2(v1ao[1], mo_coeff[1], (0,noccb,noccb,nmo))
hx = numpy.hstack((v1a.reshape(nz,-1), v1b.reshape(nz,-1)))
for i, z in enumerate(zs):
hx[i] += ed_ia * z
hx[i] *= d_ia
return hx
return vind, hdiag
def ucphf_with_freq(mf, mo_energy, mo_occ, h1, freq=0,
max_cycle=20, tol=1e-9, hermi=False, verbose=logger.WARN):
log = logger.new_logger(verbose=verbose)
t0 = (time.clock(), time.time())
occidxa = mo_occ[0] > 0
occidxb = mo_occ[1] > 0
viridxa = ~occidxa
viridxb = ~occidxb
mo_ea, mo_eb = mo_energy
# e_ai - freq may produce very small elements which can cause numerical
# issue in krylov solver
LEVEL_SHIF = 0.1
e_ai_a = lib.direct_sum('a-i->ai', mo_ea[viridxa], mo_ea[occidxa]).ravel()
e_ai_b = lib.direct_sum('a-i->ai', mo_eb[viridxb], mo_eb[occidxb]).ravel()
diag = (e_ai_a - freq,
e_ai_b - freq,
e_ai_a + freq,
e_ai_b + freq)
diag[0][diag[0] < LEVEL_SHIF] += LEVEL_SHIF
diag[1][diag[1] < LEVEL_SHIF] += LEVEL_SHIF
diag[2][diag[2] < LEVEL_SHIF] += LEVEL_SHIF
diag[3][diag[3] < LEVEL_SHIF] += LEVEL_SHIF
mo0a, mo0b = mf.mo_coeff
nao, nmoa = mo0a.shape
nmob = mo0b.shape
orbva = mo0a[:,viridxa]
orbvb = mo0b[:,viridxb]
orboa = mo0a[:,occidxa]
orbob = mo0b[:,occidxb]
nvira = orbva.shape[1]
nvirb = orbvb.shape[1]
nocca = orboa.shape[1]
noccb = orbob.shape[1]
h1a = h1[0].reshape(-1,nvira*nocca)
h1b = h1[1].reshape(-1,nvirb*noccb)
ncomp = h1a.shape[0]
mo1base = numpy.hstack((-h1a/diag[0],
-h1b/diag[1],
-h1a/diag[2],
-h1b/diag[3]))
offsets = numpy.cumsum((nocca*nvira, noccb*nvirb, nocca*nvira))
vresp = _gen_uhf_response(mf, hermi=0)
def vind(xys):
nz = len(xys)
dm1a = numpy.empty((nz,nao,nao))
dm1b = numpy.empty((nz,nao,nao))
for i in range(nz):
xa, xb, ya, yb = numpy.split(xys[i], offsets)
dmx = reduce(numpy.dot, (orbva, xa.reshape(nvira,nocca) , orboa.T))
dmy = reduce(numpy.dot, (orboa, ya.reshape(nvira,nocca).T, orbva.T))
dm1a[i] = dmx + dmy # AX + BY
dmx = reduce(numpy.dot, (orbvb, xb.reshape(nvirb,noccb) , orbob.T))
dmy = reduce(numpy.dot, (orbob, yb.reshape(nvirb,noccb).T, orbvb.T))
dm1b[i] = dmx + dmy # AX + BY
v1ao = vresp(numpy.stack((dm1a,dm1b)))
v1voa = lib.einsum('xpq,pi,qj->xij', v1ao[0], orbva, orboa).reshape(nz,-1)
v1vob = lib.einsum('xpq,pi,qj->xij', v1ao[1], orbvb, orbob).reshape(nz,-1)
v1ova = lib.einsum('xpq,pi,qj->xji', v1ao[0], orboa, orbva).reshape(nz,-1)
v1ovb = lib.einsum('xpq,pi,qj->xji', v1ao[1], orbob, orbvb).reshape(nz,-1)
for i in range(nz):
xa, xb, ya, yb = numpy.split(xys[i], offsets)
v1voa[i] += (e_ai_a - freq - diag[0]) * xa
v1voa[i] /= diag[0]
v1vob[i] += (e_ai_b - freq - diag[1]) * xb
v1vob[i] /= diag[1]
v1ova[i] += (e_ai_a + freq - diag[2]) * ya
v1ova[i] /= diag[2]
v1ovb[i] += (e_ai_b + freq - diag[3]) * yb
v1ovb[i] /= diag[3]
v = numpy.hstack((v1voa, v1vob, v1ova, v1ovb))
return v
# FIXME: krylov solver is not accurate enough for many freqs. Using tight
# tol and lindep could offer small help. A better linear equation solver
# is needed.
mo1 = lib.krylov(vind, mo1base, tol=tol, max_cycle=max_cycle,
hermi=hermi, lindep=1e-18, verbose=log)
log.timer('krylov solver in CPHF', *t0)
dm1a = numpy.empty((ncomp,nao,nao))
dm1b = numpy.empty((ncomp,nao,nao))
for i in range(ncomp):
xa, xb, ya, yb = numpy.split(mo1[i], offsets)
dmx = reduce(numpy.dot, (orbva, xa.reshape(nvira,nocca) *2, orboa.T))
dmy = reduce(numpy.dot, (orboa, ya.reshape(nvira,nocca).T*2, orbva.T))
dm1a[i] = dmx + dmy
dmx = reduce(numpy.dot, (orbvb, xb.reshape(nvirb,noccb) *2, orbob.T))
dmy = reduce(numpy.dot, (orbob, yb.reshape(nvirb,noccb).T*2, orbvb.T))
dm1b[i] = dmx + dmy
v1ao = vresp(numpy.stack((dm1a,dm1b)))
mo_e1_a = lib.einsum('xpq,pi,qj->xij', v1ao[0], orboa, orboa)
mo_e1_b = lib.einsum('xpq,pi,qj->xij', v1ao[1], orbob, orbob)
mo_e1 = (mo_e1_a, mo_e1_b)
xa, xb, ya, yb = numpy.split(mo1, offsets, axis=1)
mo1 = (xa.reshape(ncomp,nvira,nocca),
xb.reshape(ncomp,nvirb,noccb),
ya.reshape(ncomp,nvira,nocca),
yb.reshape(ncomp,nvirb,noccb))
return mo1, mo_e1
def get_vind(self, mf):
wfnsym = self.wfnsym
singlet = self.singlet
mol = mf.mol
mo_coeff = mf.mo_coeff
assert (mo_coeff[0].dtype == numpy.double)
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
nao, nmo = mo_coeff[0].shape
occidxa = numpy.where(mo_occ[0] > 0)[0]
occidxb = numpy.where(mo_occ[1] > 0)[0]
viridxa = numpy.where(mo_occ[0] == 0)[0]
viridxb = numpy.where(mo_occ[1] == 0)[0]
nocca = len(occidxa)
noccb = len(occidxb)
nvira = len(viridxa)
nvirb = len(viridxb)
orboa = mo_coeff[0][:, occidxa]
orbob = mo_coeff[1][:, occidxb]
orbva = mo_coeff[0][:, viridxa]
orbvb = mo_coeff[1][:, viridxb]
if wfnsym is not None and mol.symmetry:
if isinstance(wfnsym, str):
wfnsym = symm.irrep_name2id(mol.groupname, wfnsym)
orbsyma, orbsymb = uhf_symm.get_orbsym(mol, mo_coeff)
wfnsym = wfnsym % 10 # convert to D2h subgroup
orbsyma = orbsyma % 10
orbsymb = orbsymb % 10
sym_forbida = (orbsyma[occidxa, None] ^ orbsyma[viridxa]) != wfnsym
sym_forbidb = (orbsymb[occidxb, None] ^ orbsymb[viridxb]) != wfnsym
sym_forbid = numpy.hstack(
(sym_forbida.ravel(), sym_forbidb.ravel()))
e_ia_a = (mo_energy[0][viridxa, None] - mo_energy[0][occidxa]).T
e_ia_b = (mo_energy[1][viridxb, None] - mo_energy[1][occidxb]).T
e_ia = numpy.hstack((e_ia_a.reshape(-1), e_ia_b.reshape(-1)))
if wfnsym is not None and mol.symmetry:
e_ia[sym_forbid] = 0
d_ia = numpy.sqrt(e_ia).ravel()
ed_ia = e_ia.ravel() * d_ia
hdiag = e_ia.ravel()**2
vresp = _gen_uhf_response(mf, mo_coeff, mo_occ, hermi=1)
def vind(zs):
nz = len(zs)
if wfnsym is not None and mol.symmetry:
zs = numpy.copy(zs)
zs[:, sym_forbid] = 0
dmov = numpy.empty((2, nz, nao, nao))
for i in range(nz):
z = d_ia * zs[i]
za = z[:nocca * nvira].reshape(nocca, nvira)
zb = z[nocca * nvira:].reshape(noccb, nvirb)
dm = reduce(numpy.dot, (orboa, za, orbva.T))
dmov[0, i] = dm + dm.T
dm = reduce(numpy.dot, (orbob, zb, orbvb.T))
dmov[1, i] = dm + dm.T
v1ao = vresp(dmov)
v1a = _ao2mo.nr_e2(v1ao[0], mo_coeff[0], (0, nocca, nocca, nmo))
v1b = _ao2mo.nr_e2(v1ao[1], mo_coeff[1], (0, noccb, noccb, nmo))
hx = numpy.hstack((v1a.reshape(nz, -1), v1b.reshape(nz, -1)))
for i, z in enumerate(zs):
hx[i] += ed_ia * z
hx[i] *= d_ia
return hx
return vind, hdiag