#!/usr/bin/env python
# Copyright 2014-2020 The PySCF Developers. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#
# Author: Qiming Sun <osirpt.sun@gmail.com>
#
import numpy
from pyscf import lib
from pyscf.cc import uccsd_rdm
def _gamma1_intermediates(mycc, t1, t2, l1, l2, eris=None, for_grad=False):
d1 = uccsd_rdm._gamma1_intermediates(mycc, t1, t2, l1, l2)
if eris is None: eris = mycc.ao2mo()
t1a, t1b = t1
t2aa, t2ab, t2bb = t2
nocca, noccb, nvira, nvirb = t2ab.shape
mo_ea, mo_eb = eris.mo_energy
eia = mo_ea[:nocca,None] - mo_ea[nocca:]
eIA = mo_eb[:noccb,None] - mo_eb[noccb:]
fvo = eris.focka[nocca:,:nocca]
fVO = eris.fockb[noccb:,:noccb]
# aaa
d3 = lib.direct_sum('ia+jb+kc->ijkabc', eia, eia, eia)
w = numpy.einsum('ijae,kceb->ijkabc', t2aa, numpy.asarray(eris.get_ovvv()).conj())
w-= numpy.einsum('mkbc,iajm->ijkabc', t2aa, numpy.asarray(eris.ovoo).conj())
v = numpy.einsum('jbkc,ia->ijkabc', numpy.asarray(eris.ovov).conj(), t1a)
v+= numpy.einsum('jkbc,ai->ijkabc', t2aa, fvo) * .5
rw = p6(r6(w)) / d3
wvd = p6(w + v) / d3
goo = numpy.einsum('iklabc,jklabc->ij', wvd.conj(), rw) * .125
gvv = numpy.einsum('ijkacd,ijkbcd->ab', wvd, rw.conj()) * .125
gvo = numpy.einsum('jkbc,ijkabc->ai', t2aa.conj(), rw) * .125
# bbb
d3 = lib.direct_sum('ia+jb+kc->ijkabc', eIA, eIA, eIA)
w = numpy.einsum('ijae,kceb->ijkabc', t2bb, numpy.asarray(eris.get_OVVV()).conj())
w-= numpy.einsum('imab,kcjm->ijkabc', t2bb, numpy.asarray(eris.OVOO).conj())
v = numpy.einsum('jbkc,ia->ijkabc', numpy.asarray(eris.OVOV).conj(), t1b)
v+= numpy.einsum('jkbc,ai->ijkabc', t2bb, fVO) * .5
rw = p6(r6(w)) / d3
wvd = p6(w + v) / d3
gOO = numpy.einsum('iklabc,jklabc->ij', wvd.conj(), rw) * .125
gVV = numpy.einsum('ijkacd,ijkbcd->ab', wvd, rw.conj()) * .125
gVO = numpy.einsum('jkbc,ijkabc->ai', t2bb.conj(), rw) * .125
# baa
d3 = lib.direct_sum('ia+jb+kc->ijkabc', eIA, eia, eia)
w = numpy.einsum('jIeA,kceb->IjkAbc', t2ab, numpy.asarray(eris.get_ovvv()).conj()) * 2
w += numpy.einsum('jIbE,kcEA->IjkAbc', t2ab, numpy.asarray(eris.get_ovVV()).conj()) * 2
w += numpy.einsum('jkbe,IAec->IjkAbc', t2aa, numpy.asarray(eris.get_OVvv()).conj())
w -= numpy.einsum('mIbA,kcjm->IjkAbc', t2ab, numpy.asarray(eris.ovoo).conj()) * 2
w -= numpy.einsum('jMbA,kcIM->IjkAbc', t2ab, numpy.asarray(eris.ovOO).conj()) * 2
w -= numpy.einsum('jmbc,IAkm->IjkAbc', t2aa, numpy.asarray(eris.OVoo).conj())
v = numpy.einsum('jbkc,IA->IjkAbc', numpy.asarray(eris.ovov).conj(), t1b)
v += numpy.einsum('kcIA,jb->IjkAbc', numpy.asarray(eris.ovOV).conj(), t1a)
v += numpy.einsum('kcIA,jb->IjkAbc', numpy.asarray(eris.ovOV).conj(), t1a)
v += numpy.einsum('jkbc,AI->IjkAbc', t2aa, fVO) * .5
v += numpy.einsum('kIcA,bj->IjkAbc', t2ab, fvo) * 2
rw = r4(w) / d3
wvd = (w + v) / d3
goo += numpy.einsum('kilabc,kjlabc->ij', wvd.conj(), rw) * .25
goo += numpy.einsum('kliabc,kljabc->ij', wvd.conj(), rw) * .25
gOO += numpy.einsum('iklabc,jklabc->ij', wvd.conj(), rw) * .25
gvv += numpy.einsum('ijkcad,ijkcbd->ab', wvd, rw.conj()) * .25
gvv += numpy.einsum('ijkcda,ijkcdb->ab', wvd, rw.conj()) * .25
gVV += numpy.einsum('ijkacd,ijkbcd->ab', wvd, rw.conj()) * .25
gvo += numpy.einsum('kica,ijkabc->bj', t2ab.conj(), rw) * .5
gVO += numpy.einsum('jkbc,ijkabc->ai', t2aa.conj(), rw) * .125
# bba
d3 = lib.direct_sum('ia+jb+kc->ijkabc', eia, eIA, eIA)
w = numpy.einsum('ijae,kceb->ijkabc', t2ab, numpy.asarray(eris.get_OVVV()).conj()) * 2
w += numpy.einsum('ijeb,kcea->ijkabc', t2ab, numpy.asarray(eris.get_OVvv()).conj()) * 2
w += numpy.einsum('jkbe,iaec->ijkabc', t2bb, numpy.asarray(eris.get_ovVV()).conj())
w -= numpy.einsum('imab,kcjm->ijkabc', t2ab, numpy.asarray(eris.OVOO).conj()) * 2
w -= numpy.einsum('mjab,kcim->ijkabc', t2ab, numpy.asarray(eris.OVoo).conj()) * 2
w -= numpy.einsum('jmbc,iakm->ijkabc', t2bb, numpy.asarray(eris.ovOO).conj())
v = numpy.einsum('jbkc,ia->ijkabc', numpy.asarray(eris.OVOV).conj(), t1a)
v += numpy.einsum('iakc,jb->ijkabc', numpy.asarray(eris.ovOV).conj(), t1b)
v += numpy.einsum('iakc,jb->ijkabc', numpy.asarray(eris.ovOV).conj(), t1b)
v += numpy.einsum('JKBC,ai->iJKaBC', t2bb, fvo) * .5
v += numpy.einsum('iKaC,BJ->iJKaBC', t2ab, fVO) * 2
rw = r4(w) / d3
wvd = (w + v) / d3
goo += numpy.einsum('iklabc,jklabc->ij', wvd.conj(), rw) * .25
gOO += numpy.einsum('kilabc,kjlabc->ij', wvd.conj(), rw) * .25
gOO += numpy.einsum('kliabc,kljabc->ij', wvd.conj(), rw) * .25
gvv += numpy.einsum('ijkacd,ijkbcd->ab', wvd, rw.conj()) * .25
gVV += numpy.einsum('ijkcad,ijkcbd->ab', wvd, rw.conj()) * .25
gVV += numpy.einsum('ijkcda,ijkcdb->ab', wvd, rw.conj()) * .25
gVO += numpy.einsum('ikac,ijkabc->bj', t2ab.conj(), rw) * .5
gvo += numpy.einsum('jkbc,ijkabc->ai', t2bb.conj(), rw) * .125
doo, dOO = d1[0]
dov, dOV = d1[1]
dvo, dVO = d1[2]
dvv, dVV = d1[3]
if for_grad:
doo -= goo
dOO -= gOO
dvv += gvv
dVV += gVV
else:
doo[numpy.diag_indices(nocca)] -= goo.diagonal()
dOO[numpy.diag_indices(noccb)] -= gOO.diagonal()
dvv[numpy.diag_indices(nvira)] += gvv.diagonal()
dVV[numpy.diag_indices(nvirb)] += gVV.diagonal()
dvo += gvo
dVO += gVO
return d1
# gamma2 intermediates in Chemist's notation
def _gamma2_intermediates(mycc, t1, t2, l1, l2, eris=None,
compress_vvvv=False):
d2 = uccsd_rdm._gamma2_intermediates(mycc, t1, t2, l1, l2)
if eris is None: eris = mycc.ao2mo()
dovov, dovOV, dOVov, dOVOV = d2[0]
dvvvv, dvvVV, dVVvv, dVVVV = d2[1]
doooo, dooOO, dOOoo, dOOOO = d2[2]
doovv, dooVV, dOOvv, dOOVV = d2[3]
dovvo, dovVO, dOVvo, dOVVO = d2[4]
dvvov, dvvOV, dVVov, dVVOV = d2[5]
dovvv, dovVV, dOVvv, dOVVV = d2[6]
dooov, dooOV, dOOov, dOOOV = d2[7]
t1a, t1b = t1
t2aa, t2ab, t2bb = t2
nocca, noccb, nvira, nvirb = t2ab.shape
nmoa = eris.focka.shape[0]
nmob = eris.fockb.shape[0]
mo_ea, mo_eb = eris.mo_energy
eia = mo_ea[:nocca,None] - mo_ea[nocca:]
eIA = mo_eb[:noccb,None] - mo_eb[noccb:]
fvo = eris.focka[nocca:,:nocca]
fVO = eris.fockb[noccb:,:noccb]
# aaa
d3 = lib.direct_sum('ia+jb+kc->ijkabc', eia, eia, eia)
w = numpy.einsum('ijae,kceb->ijkabc', t2aa, numpy.asarray(eris.get_ovvv()).conj())
w-= numpy.einsum('mkbc,iajm->ijkabc', t2aa, numpy.asarray(eris.ovoo).conj())
v = numpy.einsum('jbkc,ia->ijkabc', numpy.asarray(eris.ovov).conj(), t1a)
v+= numpy.einsum('jkbc,ai->ijkabc', t2aa, fvo) * .5
rw = r6(p6(w)) / d3
wvd = r6(p6(w * 2 + v)) / d3
dovov += numpy.einsum('ia,ijkabc->jbkc', t1a, rw.conj()) * 0.25
# *(1/8) instead of (1/4) because ooov appears 4 times in the 2pdm tensor due
# to symmetrization, and its contribution is scaled by 1/2 in Tr(H,2pdm)
dooov -= numpy.einsum('mkbc,ijkabc->jmia', t2aa, wvd.conj()) * .125
dovvv += numpy.einsum('kjcf,ijkabc->iafb', t2aa, wvd.conj()) * .125
# bbb
d3 = lib.direct_sum('ia+jb+kc->ijkabc', eIA, eIA, eIA)
w = numpy.einsum('ijae,kceb->ijkabc', t2bb, numpy.asarray(eris.get_OVVV()).conj())
w-= numpy.einsum('imab,kcjm->ijkabc', t2bb, numpy.asarray(eris.OVOO).conj())
v = numpy.einsum('jbkc,ia->ijkabc', numpy.asarray(eris.OVOV).conj(), t1b)
v+= numpy.einsum('jkbc,ai->ijkabc', t2bb, fVO) * .5
rw = r6(p6(w)) / d3
wvd = r6(p6(w * 2 + v)) / d3
dOVOV += numpy.einsum('ia,ijkabc->jbkc', t1b, rw.conj()) * .25
dOOOV -= numpy.einsum('mkbc,ijkabc->jmia', t2bb, wvd.conj()) * .125
dOVVV += numpy.einsum('kjcf,ijkabc->iafb', t2bb, wvd.conj()) * .125
# baa
d3 = lib.direct_sum('ia+jb+kc->ijkabc', eIA, eia, eia)
w = numpy.einsum('jIeA,kceb->IjkAbc', t2ab, numpy.asarray(eris.get_ovvv()).conj()) * 2
w += numpy.einsum('jIbE,kcEA->IjkAbc', t2ab, numpy.asarray(eris.get_ovVV()).conj()) * 2
w += numpy.einsum('jkbe,IAec->IjkAbc', t2aa, numpy.asarray(eris.get_OVvv()).conj())
w -= numpy.einsum('mIbA,kcjm->IjkAbc', t2ab, numpy.asarray(eris.ovoo).conj()) * 2
w -= numpy.einsum('jMbA,kcIM->IjkAbc', t2ab, numpy.asarray(eris.ovOO).conj()) * 2
w -= numpy.einsum('jmbc,IAkm->IjkAbc', t2aa, numpy.asarray(eris.OVoo).conj())
v = numpy.einsum('jbkc,IA->IjkAbc', numpy.asarray(eris.ovov).conj(), t1b)
v += numpy.einsum('kcIA,jb->IjkAbc', numpy.asarray(eris.ovOV).conj(), t1a)
v += numpy.einsum('kcIA,jb->IjkAbc', numpy.asarray(eris.ovOV).conj(), t1a)
v += numpy.einsum('jkbc,AI->IjkAbc', t2aa, fVO) * .5
v += numpy.einsum('kIcA,bj->IjkAbc', t2ab, fvo) * 2
rw = r4(w) / d3
wvd = r4(w * 2 + v) / d3
dovvv += numpy.einsum('jiea,ijkabc->kceb', t2ab, wvd.conj()) * .25
dovVV += numpy.einsum('jibe,ijkabc->kcea', t2ab, wvd.conj()) * .25
dOVvv += numpy.einsum('jkbe,ijkabc->iaec', t2aa, wvd.conj()) * .125
dooov -= numpy.einsum('miba,ijkabc->jmkc', t2ab, wvd.conj()) * .25
dOOov -= numpy.einsum('jmba,ijkabc->imkc', t2ab, wvd.conj()) * .25
dooOV -= numpy.einsum('jmbc,ijkabc->kmia', t2aa, wvd.conj()) * .125
dovov += numpy.einsum('ia,ijkabc->jbkc', t1b, rw.conj()) * .25
#dOVov += numpy.einsum('jb,ijkabc->iakc', t1a, rw.conj()) * .25
dovOV += numpy.einsum('jb,ijkabc->kcia', t1a, rw.conj()) * .25
# bba
d3 = lib.direct_sum('ia+jb+kc->ijkabc', eia, eIA, eIA)
w = numpy.einsum('ijae,kceb->ijkabc', t2ab, numpy.asarray(eris.get_OVVV()).conj()) * 2
w += numpy.einsum('ijeb,kcea->ijkabc', t2ab, numpy.asarray(eris.get_OVvv()).conj()) * 2
w += numpy.einsum('jkbe,iaec->ijkabc', t2bb, numpy.asarray(eris.get_ovVV()).conj())
w -= numpy.einsum('imab,kcjm->ijkabc', t2ab, numpy.asarray(eris.OVOO).conj()) * 2
w -= numpy.einsum('mjab,kcim->ijkabc', t2ab, numpy.asarray(eris.OVoo).conj()) * 2
w -= numpy.einsum('jmbc,iakm->ijkabc', t2bb, numpy.asarray(eris.ovOO).conj())
v = numpy.einsum('jbkc,ia->ijkabc', numpy.asarray(eris.OVOV).conj(), t1a)
v += numpy.einsum('iakc,jb->ijkabc', numpy.asarray(eris.ovOV).conj(), t1b)
v += numpy.einsum('iakc,jb->ijkabc', numpy.asarray(eris.ovOV).conj(), t1b)
v += numpy.einsum('JKBC,ai->iJKaBC', t2bb, fvo) * .5
v += numpy.einsum('iKaC,BJ->iJKaBC', t2ab, fVO) * 2
rw = r4(w) / d3
wvd = r4(w * 2 + v) / d3
dOVVV += numpy.einsum('ijae,ijkabc->kceb', t2ab, wvd.conj()) * .25
dOVvv += numpy.einsum('ijeb,ijkabc->kcea', t2ab, wvd.conj()) * .25
dovVV += numpy.einsum('jkbe,ijkabc->iaec', t2bb, wvd.conj()) * .125
dOOOV -= numpy.einsum('imab,ijkabc->jmkc', t2ab, wvd.conj()) * .25
dooOV -= numpy.einsum('mjab,ijkabc->imkc', t2ab, wvd.conj()) * .25
dOOov -= numpy.einsum('jmbc,ijkabc->kmia', t2bb, wvd.conj()) * .125
dOVOV += numpy.einsum('ia,ijkabc->jbkc', t1a, rw.conj()) * .25
dovOV += numpy.einsum('jb,ijkabc->iakc', t1b, rw.conj()) * .25
#dOVov += numpy.einsum('jb,ijkabc->kcia', t1b, rw.conj()) * .25
if compress_vvvv:
nmoa, nmob = mycc.nmo
nocca, noccb, nvira, nvirb = t2ab.shape
idxa = numpy.tril_indices(nvira)
idxa = idxa[0] * nvira + idxa[1]
idxb = numpy.tril_indices(nvirb)
idxb = idxb[0] * nvirb + idxb[1]
dvvvv = dvvvv + dvvvv.transpose(1,0,2,3)
dvvvv = lib.take_2d(dvvvv.reshape(nvira**2,nvira**2), idxa, idxa)
dvvvv *= .5
dvvVV = dvvVV + dvvVV.transpose(1,0,2,3)
dvvVV = lib.take_2d(dvvVV.reshape(nvira**2,nvirb**2), idxa, idxb)
dVVVV = dVVVV + dVVVV.transpose(1,0,2,3)
dVVVV = lib.take_2d(dVVVV.reshape(nvirb**2,nvirb**2), idxb, idxb)
dVVVV *= .5
d2 = ((dovov, dovOV, dOVov, dOVOV),
(dvvvv, dvvVV, dVVvv, dVVVV),
(doooo, dooOO, dOOoo, dOOOO),
(doovv, dooVV, dOOvv, dOOVV),
(dovvo, dovVO, dOVvo, dOVVO),
(dvvov, dvvOV, dVVov, dVVOV),
(dovvv, dovVV, dOVvv, dOVVV),
(dooov, dooOV, dOOov, dOOOV))
return d2
def _gamma2_outcore(mycc, t1, t2, l1, l2, eris, h5fobj, compress_vvvv=False):
return _gamma2_intermediates(mycc, t1, t2, l1, l2, eris, compress_vvvv)
[docs]
def make_rdm1(mycc, t1, t2, l1, l2, eris=None, ao_repr=False):
d1 = _gamma1_intermediates(mycc, t1, t2, l1, l2, eris)
return uccsd_rdm._make_rdm1(mycc, d1, True, ao_repr=ao_repr)
# rdm2 in Chemist's notation
[docs]
def make_rdm2(mycc, t1, t2, l1, l2, eris=None):
d1 = _gamma1_intermediates(mycc, t1, t2, l1, l2, eris)
d2 = _gamma2_intermediates(mycc, t1, t2, l1, l2, eris)
return uccsd_rdm._make_rdm2(mycc, d1, d2, True, True)
[docs]
def p6(t):
return (t + t.transpose(1,2,0,4,5,3) +
t.transpose(2,0,1,5,3,4) + t.transpose(0,2,1,3,5,4) +
t.transpose(2,1,0,5,4,3) + t.transpose(1,0,2,4,3,5))
[docs]
def r6(w):
return (w + w.transpose(2,0,1,3,4,5) + w.transpose(1,2,0,3,4,5)
- w.transpose(2,1,0,3,4,5) - w.transpose(0,2,1,3,4,5)
- w.transpose(1,0,2,3,4,5))
[docs]
def r4(w):
w = w - w.transpose(0,2,1,3,4,5)
w = w + w.transpose(0,2,1,3,5,4)
return w