#!/usr/bin/env python
# Copyright 2014-2021 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>
#
'''
GHF-CCSD(T) with spin-orbital integrals
'''
import numpy
from pyscf import lib
from pyscf.lib import logger
from pyscf.cc import gccsd
# spin-orbital formula
# JCP 98, 8718 (1993); DOI:10.1063/1.464480
[docs]
def kernel(cc, eris, t1=None, t2=None, max_memory=2000, verbose=logger.INFO):
assert (isinstance(eris, gccsd._PhysicistsERIs))
if t1 is None or t2 is None:
t1, t2 = cc.t1, cc.t2
nocc, nvir = t1.shape
bcei = numpy.asarray(eris.ovvv).conj().transpose(3,2,1,0)
majk = numpy.asarray(eris.ooov).conj().transpose(2,3,0,1)
bcjk = numpy.asarray(eris.oovv).conj().transpose(2,3,0,1)
mo_e = eris.mo_energy
eia = mo_e[:nocc,None] - mo_e[nocc:]
d3 = lib.direct_sum('ia+jb+kc->ijkabc', eia, eia, eia)
t3c =(numpy.einsum('jkae,bcei->ijkabc', t2, bcei) -
numpy.einsum('imbc,majk->ijkabc', t2, majk))
t3c = t3c - t3c.transpose(0,1,2,4,3,5) - t3c.transpose(0,1,2,5,4,3)
t3c = t3c - t3c.transpose(1,0,2,3,4,5) - t3c.transpose(2,1,0,3,4,5)
t3c /= d3
# e4 = numpy.einsum('ijkabc,ijkabc,ijkabc', t3c.conj(), d3, t3c) / 36
# sia = numpy.einsum('jkbc,ijkabc->ia', eris.oovv, t3c) * .25
# e5 = numpy.einsum('ia,ia', sia, t1.conj())
# et = e4 + e5
# return et
t3d = numpy.einsum('ia,bcjk->ijkabc', t1, bcjk)
t3d += numpy.einsum('ai,jkbc->ijkabc', eris.fock[nocc:,:nocc], t2)
t3d = t3d - t3d.transpose(0,1,2,4,3,5) - t3d.transpose(0,1,2,5,4,3)
t3d = t3d - t3d.transpose(1,0,2,3,4,5) - t3d.transpose(2,1,0,3,4,5)
t3d /= d3
et = numpy.einsum('ijkabc,ijkabc,ijkabc', (t3c+t3d).conj(), d3, t3c) / 36
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. , -.957 , .587)],
[1 , (0.2, .757 , .487)]]
mol.basis = '631g'
mol.build()
mf = scf.RHF(mol).run(conv_tol=1e-1)
mycc = cc.CCSD(mf).set(conv_tol=1e-11).run()
et = mycc.ccsd_t()
mycc = cc.GCCSD(scf.addons.convert_to_ghf(mf)).set(conv_tol=1e-11).run()
eris = mycc.ao2mo()
print(kernel(mycc, eris) - et)