#!/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
'''
UCCSD(T)
'''
[docs]
def kernel(mcc, eris, t1=None, t2=None):
if t1 is None or t2 is None:
t1, t2 = mcc.t1, mcc.t2
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))
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())
r = r6(w)
v = numpy.einsum('jbkc,ia->ijkabc', numpy.asarray(eris.ovov).conj(), t1a)
v+= numpy.einsum('jkbc,ai->ijkabc', t2aa, fvo) * .5
wvd = p6(w + v) / d3
et = numpy.einsum('ijkabc,ijkabc', wvd.conj(), r)
# 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())
r = r6(w)
v = numpy.einsum('jbkc,ia->ijkabc', numpy.asarray(eris.OVOV).conj(), t1b)
v+= numpy.einsum('jkbc,ai->ijkabc', t2bb, fVO) * .5
wvd = p6(w + v) / d3
et += numpy.einsum('ijkabc,ijkabc', wvd.conj(), r)
# baa
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())
r = w - w.transpose(0,2,1,3,4,5)
r = r + r.transpose(0,2,1,3,5,4)
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
w += v
d3 = lib.direct_sum('ia+jb+kc->ijkabc', eIA, eia, eia)
r /= d3
et += numpy.einsum('ijkabc,ijkabc', w.conj(), r)
# bba
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())
r = w - w.transpose(0,2,1,3,4,5)
r = r + r.transpose(0,2,1,3,5,4)
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
w += v
d3 = lib.direct_sum('ia+jb+kc->ijkabc', eia, eIA, eIA)
r /= d3
et += numpy.einsum('ijkabc,ijkabc', w.conj(), r)
et *= .25
return et
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. , -.757 , .587)],
[1 , (0. , .757 , .587)]]
mol.basis = '631g'
mol.build()
rhf = scf.RHF(mol)
rhf.conv_tol = 1e-14
rhf.scf()
mcc = cc.CCSD(rhf)
mcc.conv_tol = 1e-14
mcc.ccsd()
t1a = t1b = mcc.t1
t2ab = mcc.t2
t2aa = t2bb = t2ab - t2ab.transpose(1,0,2,3)
mcc = uccsd.UCCSD(scf.addons.convert_to_uhf(rhf))
e3a = kernel(mcc, mcc.ao2mo(), (t1a,t1b), (t2aa,t2ab,t2bb))
print(e3a - -0.00099642337843278096)
mol = gto.Mole()
mol.atom = [
[8 , (0. , 0. , 0.)],
[1 , (0. , -.757 , .587)],
[1 , (0. , .757 , .587)]]
mol.spin = 2
mol.basis = '3-21g'
mol.build()
mf = scf.UHF(mol).run(conv_tol=1e-14)
nao, nmo = mf.mo_coeff[0].shape
numpy.random.seed(10)
mf.mo_coeff = numpy.random.random((2,nao,nmo))
numpy.random.seed(12)
nocca, noccb = mol.nelec
nmo = mf.mo_occ[0].size
nvira = nmo - nocca
nvirb = nmo - noccb
t1a = .1 * numpy.random.random((nocca,nvira))
t1b = .1 * numpy.random.random((noccb,nvirb))
t2aa = .1 * numpy.random.random((nocca,nocca,nvira,nvira))
t2aa = t2aa - t2aa.transpose(0,1,3,2)
t2aa = t2aa - t2aa.transpose(1,0,2,3)
t2bb = .1 * numpy.random.random((noccb,noccb,nvirb,nvirb))
t2bb = t2bb - t2bb.transpose(0,1,3,2)
t2bb = t2bb - t2bb.transpose(1,0,2,3)
t2ab = .1 * numpy.random.random((nocca,noccb,nvira,nvirb))
t1 = t1a, t1b
t2 = t2aa, t2ab, t2bb
mcc = uccsd.UCCSD(scf.addons.convert_to_uhf(mf))
e3a = kernel(mcc, mcc.ao2mo(), [t1a,t1b], [t2aa, t2ab, t2bb])
print(e3a - 9877.2780859693339)
mycc = cc.GCCSD(scf.addons.convert_to_ghf(mf))
eris = mycc.ao2mo()
t1 = mycc.spatial2spin(t1, eris.orbspin)
t2 = mycc.spatial2spin(t2, eris.orbspin)
from pyscf.cc import gccsd_t
et = gccsd_t.kernel(mycc, eris, t1, t2)
print(et - 9877.2780859693339)
mol = gto.M()
numpy.random.seed(12)
nocca, noccb, nvira, nvirb = 3, 2, 4, 5
nmo = nocca + nvira
eris = cc.uccsd._ChemistsERIs()
eri1 = (numpy.random.random((3,nmo,nmo,nmo,nmo)) +
numpy.random.random((3,nmo,nmo,nmo,nmo)) * .8j - .5-.4j)
eri1 = eri1 + eri1.transpose(0,2,1,4,3).conj()
eri1[0] = eri1[0] + eri1[0].transpose(2,3,0,1)
eri1[2] = eri1[2] + eri1[2].transpose(2,3,0,1)
eri1 *= .1
eris.ovov = eri1[0,nocca:,:nocca,nocca:,:nocca].transpose(1,0,3,2).conj()
eris.ovvv = eri1[0,nocca:,:nocca,nocca:,nocca:].transpose(1,0,3,2).conj()
eris.ovoo = eri1[0,nocca:,:nocca,:nocca,:nocca].transpose(1,0,3,2).conj()
eris.OVOV = eri1[2,noccb:,:noccb,noccb:,:noccb].transpose(1,0,3,2).conj()
eris.OVVV = eri1[2,noccb:,:noccb,noccb:,noccb:].transpose(1,0,3,2).conj()
eris.OVOO = eri1[2,noccb:,:noccb,:noccb,:noccb].transpose(1,0,3,2).conj()
eris.ovOV = eri1[1,nocca:,:nocca,noccb:,:noccb].transpose(1,0,3,2).conj()
eris.ovVV = eri1[1,nocca:,:nocca,noccb:,noccb:].transpose(1,0,3,2).conj()
eris.ovOO = eri1[1,nocca:,:nocca,:noccb,:noccb].transpose(1,0,3,2).conj()
eris.OVov = eri1[1,nocca:,:nocca,noccb:,:noccb].transpose(3,2,1,0).conj()
eris.OVvv = eri1[1,nocca:,nocca:,noccb:,:noccb].transpose(3,2,1,0).conj()
eris.OVoo = eri1[1,:nocca,:nocca,noccb:,:noccb].transpose(3,2,1,0).conj()
t1a = .1 * numpy.random.random((nocca,nvira)) + numpy.random.random((nocca,nvira))*.1j
t1b = .1 * numpy.random.random((noccb,nvirb)) + numpy.random.random((noccb,nvirb))*.1j
t2aa = .1 * numpy.random.random((nocca,nocca,nvira,nvira)) + numpy.random.random((nocca,nocca,nvira,nvira))*.1j
t2aa = t2aa - t2aa.transpose(0,1,3,2)
t2aa = t2aa - t2aa.transpose(1,0,2,3)
t2bb = .1 * numpy.random.random((noccb,noccb,nvirb,nvirb)) + numpy.random.random((noccb,noccb,nvirb,nvirb))*.1j
t2bb = t2bb - t2bb.transpose(0,1,3,2)
t2bb = t2bb - t2bb.transpose(1,0,2,3)
t2ab = .1 * numpy.random.random((nocca,noccb,nvira,nvirb)) + numpy.random.random((nocca,noccb,nvira,nvirb))*.1j
f = (numpy.random.random((2,nmo,nmo)) * .4 +
numpy.random.random((2,nmo,nmo)) * .4j)
eris.focka = f[0]+f[0].T.conj() + numpy.diag(numpy.arange(nmo))
eris.fockb = f[1]+f[1].T.conj() + numpy.diag(numpy.arange(nmo))
t1 = t1a, t1b
t2 = t2aa, t2ab, t2bb
mcc = cc.UCCSD(scf.UHF(mol))
print(kernel(mcc, eris, t1, t2) - (-0.056092415718338388-0.011390417704868244j))
