#!/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>
#
'''
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, 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)
fvo = eris.fock[nocc:,:nocc]
mo_e = eris.mo_energy
eijk = lib.direct_sum('i+j+k->ijk', mo_e[:nocc], mo_e[:nocc], mo_e[:nocc])
eabc = lib.direct_sum('a+b+c->abc', mo_e[nocc:], mo_e[nocc:], mo_e[nocc:])
t2T = t2.transpose(2,3,0,1)
t1T = t1.T
def get_wv(a, b, c):
w = numpy.einsum('ejk,ei->ijk', t2T[a,:], bcei[b,c])
w -= numpy.einsum('im,mjk->ijk', t2T[b,c], majk[:,a])
v = numpy.einsum('i,jk->ijk', t1T[a], bcjk[b,c])
v += numpy.einsum('i,jk->ijk', fvo[a], t2T [b,c])
v += w
w = w + w.transpose(2,0,1) + w.transpose(1,2,0)
return w, v
et = 0
for a in range(nvir):
for b in range(a):
for c in range(b):
wabc, vabc = get_wv(a, b, c)
wcab, vcab = get_wv(c, a, b)
wbac, vbac = get_wv(b, a, c)
w = wabc + wcab - wbac
v = vabc + vcab - vbac
w /= eijk - eabc[a,b,c]
et += numpy.einsum('ijk,ijk', w, v.conj())
et /= 2
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(mf.to_ghf()).set(conv_tol=1e-11).run()
eris = mycc.ao2mo()
print(kernel(mycc, eris) - et)
numpy.random.seed(1)
mf.mo_coeff = numpy.random.random(mf.mo_coeff.shape) - .9
mycc = cc.GCCSD(mf.to_ghf())
eris = mycc.ao2mo()
nocc = 10
nvir = mol.nao_nr() * 2 - nocc
t1 = numpy.random.random((nocc,nvir))*.1 - .2
t2 = numpy.random.random((nocc,nocc,nvir,nvir))*.1 - .2
t2 = t2 - t2.transpose(1,0,2,3)
t2 = t2 - t2.transpose(0,1,3,2)
print(kernel(mycc, eris, t1, t2) - 263713.3945021223)