#!/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.
import tempfile
import h5py
import numpy as np
from pyscf import lib
#einsum = np.einsum
einsum = lib.einsum
# Ref: Gauss and Stanton, J. Chem. Phys. 103, 3561 (1995) Table III
# Section (a)
[docs]
def make_tau(t2, t1a, t1b, fac=1, out=None):
tmp = einsum('ia,jb->ijab',t1a,t1b)
t1t1 = tmp - tmp.transpose(1,0,2,3) - tmp.transpose(0,1,3,2) + tmp.transpose(1,0,3,2)
tau1 = t2 + fac*0.50*t1t1
return tau1
[docs]
def cc_Fvv(t1,t2,eris):
nocc, nvir = t1.shape
fov = eris.fock[:nocc,nocc:]
fvv = eris.fock[nocc:,nocc:]
eris_vovv = np.array(eris.ovvv).transpose(1,0,3,2)
tau_tilde = make_tau(t2,t1,t1,fac=0.5)
Fae = ( fvv - 0.5*einsum('me,ma->ae',fov,t1)
+ einsum('mf,amef->ae',t1,eris_vovv)
- 0.5*einsum('mnaf,mnef->ae',tau_tilde,eris.oovv) )
return Fae
[docs]
def cc_Foo(t1,t2,eris):
nocc, nvir = t1.shape
fov = eris.fock[:nocc,nocc:]
foo = eris.fock[:nocc,:nocc]
tau_tilde = make_tau(t2,t1,t1,fac=0.5)
Fmi = (foo + 0.5*einsum('me,ie->mi',fov,t1)
+ einsum('ne,mnie->mi',t1,eris.ooov)
+ 0.5*einsum('inef,mnef->mi',tau_tilde,eris.oovv) )
return Fmi
[docs]
def cc_Fov(t1,t2,eris):
nocc, nvir = t1.shape
fov = eris.fock[:nocc,nocc:]
Fme = fov + einsum('nf,mnef->me',t1,eris.oovv)
return Fme
[docs]
def cc_Woooo(t1,t2,eris):
tau = make_tau(t2,t1,t1)
tmp = einsum('je,mnie->mnij',t1,eris.ooov)
Wmnij = eris.oooo + tmp - tmp.transpose(0,1,3,2)
Wmnij += 0.25*einsum('ijef,mnef->mnij',tau,eris.oovv)
return Wmnij
[docs]
def cc_Wvvvv(t1,t2,eris):
tau = make_tau(t2,t1,t1)
#eris_vovv = np.array(eris.ovvv).transpose(1,0,3,2)
#tmp = einsum('mb,amef->abef',t1,eris_vovv)
#Wabef = eris.vvvv - tmp + tmp.transpose(1,0,2,3)
#Wabef += 0.25*einsum('mnab,mnef->abef',tau,eris.oovv)
if t1.dtype == np.complex128: ds_type = 'c16'
else: ds_type = 'f8'
_tmpfile1 = tempfile.NamedTemporaryFile(dir=lib.param.TMPDIR)
fimd = h5py.File(_tmpfile1.name)
nocc, nvir = t1.shape
Wabef = fimd.create_dataset('vvvv', (nvir,nvir,nvir,nvir), ds_type)
for a in range(nvir):
Wabef[a] = eris.vvvv[a]
Wabef[a] -= einsum('mb,mfe->bef',t1,eris.ovvv[:,a,:,:])
Wabef[a] += einsum('m,mbfe->bef',t1[:,a],eris.ovvv)
Wabef[a] += 0.25*einsum('mnb,mnef->bef',tau[:,:,a,:],eris.oovv)
return Wabef
[docs]
def cc_Wovvo(t1,t2,eris):
eris_ovvo = -np.array(eris.ovov).transpose(0,1,3,2)
eris_oovo = -np.array(eris.ooov).transpose(0,1,3,2)
Wmbej = eris_ovvo.copy()
Wmbej += einsum('jf,mbef->mbej',t1,eris.ovvv)
Wmbej += -einsum('nb,mnej->mbej',t1,eris_oovo)
Wmbej += -0.5*einsum('jnfb,mnef->mbej',t2,eris.oovv)
Wmbej += -einsum('jf,nb,mnef->mbej',t1,t1,eris.oovv)
return Wmbej
### Section (b)
[docs]
def Fvv(t1,t2,eris):
ccFov = cc_Fov(t1,t2,eris)
Fae = cc_Fvv(t1,t2,eris) - 0.5*einsum('ma,me->ae',t1,ccFov)
return Fae
[docs]
def Foo(t1,t2,eris):
ccFov = cc_Fov(t1,t2,eris)
Fmi = cc_Foo(t1,t2,eris) + 0.5*einsum('ie,me->mi',t1,ccFov)
return Fmi
[docs]
def Fov(t1,t2,eris):
Fme = cc_Fov(t1,t2,eris)
return Fme
[docs]
def Woooo(t1,t2,eris):
tau = make_tau(t2,t1,t1)
Wmnij = cc_Woooo(t1,t2,eris) + 0.25*einsum('ijef,mnef->mnij',tau,eris.oovv)
return Wmnij
[docs]
def Wvvvv(t1,t2,eris):
tau = make_tau(t2,t1,t1)
#Wabef = cc_Wvvvv(t1,t2,eris) + 0.25*einsum('mnab,mnef->abef',tau,eris.oovv)
if t1.dtype == np.complex128: ds_type = 'c16'
else: ds_type = 'f8'
_tmpfile1 = tempfile.NamedTemporaryFile(dir=lib.param.TMPDIR)
fimd = h5py.File(_tmpfile1.name)
nocc, nvir = t1.shape
Wabef = fimd.create_dataset('vvvv', (nvir,nvir,nvir,nvir), ds_type)
#_cc_Wvvvv = cc_Wvvvv(t1,t2,eris)
for a in range(nvir):
#Wabef[a] = _cc_Wvvvv[a]
Wabef[a] = eris.vvvv[a]
Wabef[a] -= einsum('mb,mfe->bef',t1,eris.ovvv[:,a,:,:])
Wabef[a] += einsum('m,mbfe->bef',t1[:,a],eris.ovvv)
#Wabef[a] += 0.25*einsum('mnb,mnef->bef',tau[:,:,a,:],eris.oovv)
#Wabef[a] += 0.25*einsum('mnb,mnef->bef',tau[:,:,a,:],eris.oovv)
Wabef[a] += 0.5*einsum('mnb,mnef->bef',tau[:,:,a,:],eris.oovv)
return Wabef
[docs]
def Wovvo(t1,t2,eris):
Wmbej = cc_Wovvo(t1,t2,eris) - 0.5*einsum('jnfb,mnef->mbej',t2,eris.oovv)
return Wmbej
[docs]
def Wooov(t1,t2,eris):
Wmnie = eris.ooov + einsum('if,mnfe->mnie',t1,eris.oovv)
return Wmnie
[docs]
def Wvovv(t1,t2,eris):
eris_vovv = -np.array(eris.ovvv).transpose(1,0,2,3)
Wamef = eris_vovv - einsum('na,nmef->amef',t1,eris.oovv)
return Wamef
[docs]
def Wovoo(t1,t2,eris):
eris_ovvo = -np.array(eris.ovov).transpose(0,1,3,2)
tmp1 = einsum('mnie,jnbe->mbij',eris.ooov,t2)
tmp2 = (einsum('ie,mbej->mbij',t1,eris_ovvo)
- einsum('ie,njbf,mnef->mbij',t1,t2,eris.oovv))
FFov = Fov(t1,t2,eris)
WWoooo = Woooo(t1,t2,eris)
tau = make_tau(t2,t1,t1)
Wmbij = (eris.ovoo - einsum('me,ijbe->mbij',FFov,t2)
- einsum('nb,mnij->mbij',t1,WWoooo)
+ 0.5 * einsum('mbef,ijef->mbij',eris.ovvv,tau)
+ tmp1 - tmp1.transpose(0,1,3,2)
+ tmp2 - tmp2.transpose(0,1,3,2) )
return Wmbij
[docs]
def Wvvvo(t1,t2,eris,_Wvvvv=None):
eris_ovvo = -np.array(eris.ovov).transpose(0,1,3,2)
eris_vvvo = -np.array(eris.ovvv).transpose(2,3,1,0).conj()
eris_oovo = -np.array(eris.ooov).transpose(0,1,3,2)
tmp1 = einsum('mbef,miaf->abei',eris.ovvv,t2)
tmp2 = (einsum('ma,mbei->abei',t1,eris_ovvo)
- einsum('ma,nibf,mnef->abei',t1,t2,eris.oovv))
FFov = Fov(t1,t2,eris)
tau = make_tau(t2,t1,t1)
Wabei = eris_vvvo
Wabei += -einsum('me,miab->abei',FFov,t2)
Wabei += 0.5 * einsum('mnei,mnab->abei',eris_oovo,tau)
Wabei += -tmp1 + tmp1.transpose(1,0,2,3)
Wabei += -tmp2 + tmp2.transpose(1,0,2,3)
nocc,nvir = t1.shape
if _Wvvvv is None:
_Wvvvv = Wvvvv(t1,t2,eris)
for a in range(nvir):
Wabei[a] += einsum('if,bef->bei',t1,_Wvvvv[a])
return Wabei
[docs]
def Wvvvo_incore(t1,t2,eris):
eris_ovvo = -np.array(eris.ovov).transpose(0,1,3,2)
eris_vvvo = -np.array(eris.ovvv).transpose(2,3,1,0).conj()
eris_oovo = -np.array(eris.ooov).transpose(0,1,3,2)
tmp1 = einsum('mbef,miaf->abei',eris.ovvv,t2)
tmp2 = (einsum('ma,mbei->abei',t1,eris_ovvo)
- einsum('ma,nibf,mnef->abei',t1,t2,eris.oovv))
FFov = Fov(t1,t2,eris)
WWvvvv = Wvvvv(t1,t2,eris)
tau = make_tau(t2,t1,t1)
Wabei = (eris_vvvo - einsum('me,miab->abei',FFov,t2)
+ einsum('if,abef->abei',t1,WWvvvv)
+ 0.5 * einsum('mnei,mnab->abei',eris_oovo,tau)
- tmp1 + tmp1.transpose(1,0,2,3)
- tmp2 + tmp2.transpose(1,0,2,3) )
return Wabei
