Source code for pyscf.cc.uccsd_t_lambda
#!/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>
#
'''
Spin-free lambda equation of UHF-CCSD(T)
'''
import numpy
from pyscf import lib
from pyscf.lib import logger
from pyscf.cc import ccsd_lambda
from pyscf.cc import uccsd_lambda
[docs]
def kernel(mycc, eris=None, t1=None, t2=None, l1=None, l2=None,
max_cycle=50, tol=1e-8, verbose=logger.INFO):
return ccsd_lambda.kernel(mycc, eris, t1, t2, l1, l2, max_cycle, tol,
verbose, make_intermediates, update_lambda)
[docs]
def make_intermediates(mycc, t1, t2, eris):
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))
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))
imds = uccsd_lambda.make_intermediates(mycc, t1, t2, eris)
t1a, t1b = t1
t2aa, t2ab, t2bb = t2
nocca, noccb = t2ab.shape[:2]
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
imds.l1a_t = numpy.einsum('ijkabc,jbkc->ia', rw.conj(),
numpy.asarray(eris.ovov)) / eia * .25
wvd = r6(p6(w * 2 + v)) / d3
l2_t = numpy.einsum('ijkabc,kceb->ijae', wvd, numpy.asarray(eris.get_ovvv()).conj())
l2_t -= numpy.einsum('ijkabc,iajm->mkbc', wvd, numpy.asarray(eris.ovoo).conj())
l2_t = l2_t + l2_t.transpose(1,0,3,2)
l2_t += numpy.einsum('ijkabc,ai->jkbc', rw, fvo)
imds.l2aa_t = l2_t.conj() / lib.direct_sum('ia+jb->ijab', eia, eia) * .5
# 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
imds.l1b_t = numpy.einsum('ijkabc,jbkc->ia', rw.conj(),
numpy.asarray(eris.OVOV)) / eIA * .25
wvd = r6(p6(w * 2 + v)) / d3
l2_t = numpy.einsum('ijkabc,kceb->ijae', wvd, numpy.asarray(eris.get_OVVV()).conj())
l2_t -= numpy.einsum('ijkabc,iajm->mkbc', wvd, numpy.asarray(eris.OVOO).conj())
l2_t = l2_t + l2_t.transpose(1,0,3,2)
l2_t += numpy.einsum('ijkabc,ai->jkbc', rw, fVO)
imds.l2bb_t = l2_t.conj() / lib.direct_sum('ia+jb->ijab', eIA, eIA) * .5
# baa
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
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
imds.l1a_t += numpy.einsum('ijkabc,kcia->jb', rw.conj(),
numpy.asarray(eris.ovOV)) / eia * .5
imds.l1b_t += numpy.einsum('ijkabc,jbkc->ia', rw.conj(),
numpy.asarray(eris.ovov)) / eIA * .25
wvd = r4(w * 2 + v) / d3
l2_t = numpy.einsum('ijkabc,iaec->jkbe', wvd, numpy.asarray(eris.get_OVvv()).conj())
l2_t -= numpy.einsum('ijkabc,iakm->jmbc', wvd, numpy.asarray(eris.OVoo).conj())
l2_t = l2_t + l2_t.transpose(1,0,3,2)
l2_t += numpy.einsum('ijkabc,ai->jkbc', rw, fVO)
imds.l2aa_t += l2_t.conj() / lib.direct_sum('ia+jb->ijab', eia, eia) * .5
l2_t = numpy.einsum('ijkabc,kceb->jiea', wvd, numpy.asarray(eris.get_ovvv()).conj())
l2_t += numpy.einsum('ijkabc,kcea->jibe', wvd, numpy.asarray(eris.get_ovVV()).conj())
l2_t -= numpy.einsum('ijkabc,kcjm->miba', wvd, numpy.asarray(eris.ovoo).conj())
l2_t -= numpy.einsum('ijkabc,kcim->jmba', wvd, numpy.asarray(eris.ovOO).conj())
l2_t += numpy.einsum('ijkabc,bj->kica', rw, fvo)
imds.l2ab_t = l2_t.conj() / lib.direct_sum('ia+jb->ijab', eia, eIA) * .5
# 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
imds.l1a_t += numpy.einsum('ijkabc,jbkc->ia', rw.conj(),
numpy.asarray(eris.OVOV)) / eia * .25
imds.l1b_t += numpy.einsum('ijkabc,iakc->jb', rw.conj(),
numpy.asarray(eris.ovOV)) / eIA * .5
wvd = r4(w * 2 + v) / d3
l2_t = numpy.einsum('ijkabc,iaec->jkbe', wvd, numpy.asarray(eris.get_ovVV()).conj())
l2_t -= numpy.einsum('ijkabc,iakm->jmbc', wvd, numpy.asarray(eris.ovOO).conj())
l2_t = l2_t + l2_t.transpose(1,0,3,2)
l2_t += numpy.einsum('ijkabc,ai->jkbc', rw, fvo)
imds.l2bb_t += l2_t.conj() / lib.direct_sum('ia+jb->ijab', eIA, eIA) * .5
l2_t = numpy.einsum('ijkabc,kceb->ijae', wvd, numpy.asarray(eris.get_OVVV()).conj())
l2_t += numpy.einsum('ijkabc,kcea->ijeb', wvd, numpy.asarray(eris.get_OVvv()).conj())
l2_t -= numpy.einsum('ijkabc,kcjm->imab', wvd, numpy.asarray(eris.OVOO).conj())
l2_t -= numpy.einsum('ijkabc,kcim->mjab', wvd, numpy.asarray(eris.OVoo).conj())
l2_t += numpy.einsum('ijkabc,bj->ikac', rw, fVO)
imds.l2ab_t += l2_t.conj() / lib.direct_sum('ia+jb->ijab', eia, eIA) * .5
return imds
[docs]
def update_lambda(mycc, t1, t2, l1, l2, eris=None, imds=None):
if eris is None: eris = mycc.ao2mo()
if imds is None: imds = make_intermediates(mycc, t1, t2, eris)
l1, l2 = uccsd_lambda.update_lambda(mycc, t1, t2, l1, l2, eris, imds)
l1a, l1b = l1
l2aa, l2ab, l2bb = l2
l1a += imds.l1a_t
l1b += imds.l1b_t
l2aa += imds.l2aa_t
l2ab += imds.l2ab_t
l2bb += imds.l2bb_t
return (l1a, l1b), (l2aa, l2ab, l2bb)
if __name__ == '__main__':
from pyscf import gto
from pyscf import scf
from pyscf import cc
mol = gto.Mole()
mol.atom = [
[8 , (0. , 0. , 0.)],
[1 , (0. , -0.757 , 0.587)],
[1 , (0. , 0.757 , 0.587)]]
mol.basis = '631g'
mol.spin = 0
mol.build()
mf0 = mf = scf.RHF(mol).run(conv_tol=1)
mf = scf.addons.convert_to_uhf(mf)
mycc = cc.UCCSD(mf)
eris = mycc.ao2mo()
from pyscf.cc import ccsd_t_lambda_slow as ccsd_t_lambda
mycc0 = cc.CCSD(mf0)
eris0 = mycc0.ao2mo()
mycc0.kernel(eris=eris0)
t1 = mycc0.t1
t2 = mycc0.t2
imds = ccsd_t_lambda.make_intermediates(mycc0, t1, t2, eris0)
l1, l2 = ccsd_t_lambda.update_lambda(mycc0, t1, t2, t1, t2, eris0, imds)
l1ref, l2ref = ccsd_t_lambda.update_lambda(mycc0, t1, t2, l1, l2, eris0, imds)
t1 = (t1, t1)
t2aa = t2 - t2.transpose(1,0,2,3)
t2 = (t2aa, t2, t2aa)
l1 = (l1, l1)
l2aa = l2 - l2.transpose(1,0,2,3)
l2 = (l2aa, l2, l2aa)
imds = make_intermediates(mycc, t1, t2, eris)
l1, l2 = update_lambda(mycc, t1, t2, l1, l2, eris, imds)
print(abs(l2[1]-l2[1].transpose(1,0,2,3)-l2[0]).max())
print(abs(l2[1]-l2[1].transpose(0,1,3,2)-l2[2]).max())
print(abs(l1[0]-l1ref).max())
print(abs(l2[1]-l2ref).max())