#!/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: Timothy Berkelbach <tim.berkelbach@gmail.com>
# Qiming Sun <osirpt.sun@gmail.com>
#
'''
UCCSD with spatial integrals
'''
from functools import reduce
import numpy as np
from pyscf import lib
from pyscf import ao2mo
from pyscf.lib import logger
from pyscf.cc import ccsd
from pyscf.ao2mo import _ao2mo
from pyscf.mp import ump2
from pyscf import scf
from pyscf import __config__
MEMORYMIN = getattr(__config__, 'cc_ccsd_memorymin', 2000)
# This is unrestricted (U)CCSD, in spatial-orbital form.
[docs]
def update_amps(cc, t1, t2, eris):
time0 = logger.process_clock(), logger.perf_counter()
log = logger.Logger(cc.stdout, cc.verbose)
t1a, t1b = t1
t2aa, t2ab, t2bb = t2
nocca, noccb, nvira, nvirb = t2ab.shape
mo_ea_o = eris.mo_energy[0][:nocca]
mo_ea_v = eris.mo_energy[0][nocca:] + cc.level_shift
mo_eb_o = eris.mo_energy[1][:noccb]
mo_eb_v = eris.mo_energy[1][noccb:] + cc.level_shift
fova = eris.focka[:nocca,nocca:]
fovb = eris.fockb[:noccb,noccb:]
u1a = np.zeros_like(t1a)
u1b = np.zeros_like(t1b)
#:eris_vvvv = ao2mo.restore(1, np.asarray(eris.vvvv), nvirb)
#:eris_VVVV = ao2mo.restore(1, np.asarray(eris.VVVV), nvirb)
#:eris_vvVV = _restore(np.asarray(eris.vvVV), nvira, nvirb)
#:u2aa += lib.einsum('ijef,aebf->ijab', tauaa, eris_vvvv) * .5
#:u2bb += lib.einsum('ijef,aebf->ijab', taubb, eris_VVVV) * .5
#:u2ab += lib.einsum('iJeF,aeBF->iJaB', tauab, eris_vvVV)
tauaa, tauab, taubb = make_tau(t2, t1, t1)
u2aa, u2ab, u2bb = cc._add_vvvv(None, (tauaa,tauab,taubb), eris)
u2aa *= .5
u2bb *= .5
Fooa = .5 * lib.einsum('me,ie->mi', fova, t1a)
Foob = .5 * lib.einsum('me,ie->mi', fovb, t1b)
Fvva = -.5 * lib.einsum('me,ma->ae', fova, t1a)
Fvvb = -.5 * lib.einsum('me,ma->ae', fovb, t1b)
Fooa += eris.focka[:nocca,:nocca] - np.diag(mo_ea_o)
Foob += eris.fockb[:noccb,:noccb] - np.diag(mo_eb_o)
Fvva += eris.focka[nocca:,nocca:] - np.diag(mo_ea_v)
Fvvb += eris.fockb[noccb:,noccb:] - np.diag(mo_eb_v)
dtype = u2aa.dtype
wovvo = np.zeros((nocca,nvira,nvira,nocca), dtype=dtype)
wOVVO = np.zeros((noccb,nvirb,nvirb,noccb), dtype=dtype)
woVvO = np.zeros((nocca,nvirb,nvira,noccb), dtype=dtype)
woVVo = np.zeros((nocca,nvirb,nvirb,nocca), dtype=dtype)
wOvVo = np.zeros((noccb,nvira,nvirb,nocca), dtype=dtype)
wOvvO = np.zeros((noccb,nvira,nvira,noccb), dtype=dtype)
mem_now = lib.current_memory()[0]
max_memory = max(0, cc.max_memory - mem_now - u2aa.size*8e-6)
if nvira > 0 and nocca > 0:
blksize = max(ccsd.BLKMIN, int(max_memory*1e6/8/(nvira**3*3+1)))
for p0,p1 in lib.prange(0, nocca, blksize):
ovvv = eris.get_ovvv(slice(p0,p1)) # ovvv = eris.ovvv[p0:p1]
ovvv = ovvv - ovvv.transpose(0,3,2,1)
Fvva += np.einsum('mf,mfae->ae', t1a[p0:p1], ovvv)
wovvo[p0:p1] += lib.einsum('jf,mebf->mbej', t1a, ovvv)
u1a += 0.5*lib.einsum('mief,meaf->ia', t2aa[p0:p1], ovvv)
u2aa[:,p0:p1] += lib.einsum('ie,mbea->imab', t1a, ovvv.conj())
tmp1aa = lib.einsum('ijef,mebf->ijmb', tauaa, ovvv)
u2aa -= lib.einsum('ijmb,ma->ijab', tmp1aa, t1a[p0:p1]*.5)
ovvv = tmp1aa = None
if nvirb > 0 and noccb > 0:
blksize = max(ccsd.BLKMIN, int(max_memory*1e6/8/(nvirb**3*3+1)))
for p0,p1 in lib.prange(0, noccb, blksize):
OVVV = eris.get_OVVV(slice(p0,p1)) # OVVV = eris.OVVV[p0:p1]
OVVV = OVVV - OVVV.transpose(0,3,2,1)
Fvvb += np.einsum('mf,mfae->ae', t1b[p0:p1], OVVV)
wOVVO[p0:p1] = lib.einsum('jf,mebf->mbej', t1b, OVVV)
u1b += 0.5*lib.einsum('MIEF,MEAF->IA', t2bb[p0:p1], OVVV)
u2bb[:,p0:p1] += lib.einsum('ie,mbea->imab', t1b, OVVV.conj())
tmp1bb = lib.einsum('ijef,mebf->ijmb', taubb, OVVV)
u2bb -= lib.einsum('ijmb,ma->ijab', tmp1bb, t1b[p0:p1]*.5)
OVVV = tmp1bb = None
if nvirb > 0 and nocca > 0:
blksize = max(ccsd.BLKMIN, int(max_memory*1e6/8/(nvira*nvirb**2*3+1)))
for p0,p1 in lib.prange(0, nocca, blksize):
ovVV = eris.get_ovVV(slice(p0,p1)) # ovVV = eris.ovVV[p0:p1]
Fvvb += np.einsum('mf,mfAE->AE', t1a[p0:p1], ovVV)
woVvO[p0:p1] = lib.einsum('JF,meBF->mBeJ', t1b, ovVV)
woVVo[p0:p1] = lib.einsum('jf,mfBE->mBEj',-t1a, ovVV)
u1b += lib.einsum('mIeF,meAF->IA', t2ab[p0:p1], ovVV)
u2ab[p0:p1] += lib.einsum('IE,maEB->mIaB', t1b, ovVV.conj())
tmp1ab = lib.einsum('iJeF,meBF->iJmB', tauab, ovVV)
u2ab -= lib.einsum('iJmB,ma->iJaB', tmp1ab, t1a[p0:p1])
ovVV = tmp1ab = None
if nvira > 0 and noccb > 0:
blksize = max(ccsd.BLKMIN, int(max_memory*1e6/8/(nvirb*nvira**2*3+1)))
for p0,p1 in lib.prange(0, noccb, blksize):
OVvv = eris.get_OVvv(slice(p0,p1)) # OVvv = eris.OVvv[p0:p1]
Fvva += np.einsum('MF,MFae->ae', t1b[p0:p1], OVvv)
wOvVo[p0:p1] = lib.einsum('jf,MEbf->MbEj', t1a, OVvv)
wOvvO[p0:p1] = lib.einsum('JF,MFbe->MbeJ',-t1b, OVvv)
u1a += lib.einsum('iMfE,MEaf->ia', t2ab[:,p0:p1], OVvv)
u2ab[:,p0:p1] += lib.einsum('ie,MBea->iMaB', t1a, OVvv.conj())
tmp1abba = lib.einsum('iJeF,MFbe->iJbM', tauab, OVvv)
u2ab -= lib.einsum('iJbM,MA->iJbA', tmp1abba, t1b[p0:p1])
OVvv = tmp1abba = None
eris_ovov = np.asarray(eris.ovov)
eris_ovoo = np.asarray(eris.ovoo)
Woooo = lib.einsum('je,nemi->mnij', t1a, eris_ovoo)
Woooo = Woooo - Woooo.transpose(0,1,3,2)
Woooo += np.asarray(eris.oooo).transpose(0,2,1,3)
Woooo += lib.einsum('ijef,menf->mnij', tauaa, eris_ovov) * .5
u2aa += lib.einsum('mnab,mnij->ijab', tauaa, Woooo*.5)
Woooo = tauaa = None
ovoo = eris_ovoo - eris_ovoo.transpose(2,1,0,3)
Fooa += np.einsum('ne,nemi->mi', t1a, ovoo)
u1a += 0.5*lib.einsum('mnae,meni->ia', t2aa, ovoo)
wovvo += lib.einsum('nb,nemj->mbej', t1a, ovoo)
ovoo = eris_ovoo = None
tilaa = make_tau_aa(t2[0], t1a, t1a, fac=0.5)
ovov = eris_ovov - eris_ovov.transpose(0,3,2,1)
Fvva -= .5 * lib.einsum('mnaf,menf->ae', tilaa, ovov)
Fooa += .5 * lib.einsum('inef,menf->mi', tilaa, ovov)
Fova = np.einsum('nf,menf->me',t1a, ovov)
u2aa += ovov.conj().transpose(0,2,1,3) * .5
wovvo -= 0.5*lib.einsum('jnfb,menf->mbej', t2aa, ovov)
woVvO += 0.5*lib.einsum('nJfB,menf->mBeJ', t2ab, ovov)
tmpaa = lib.einsum('jf,menf->mnej', t1a, ovov)
wovvo -= lib.einsum('nb,mnej->mbej', t1a, tmpaa)
eris_ovov = ovov = tmpaa = tilaa = None
eris_OVOV = np.asarray(eris.OVOV)
eris_OVOO = np.asarray(eris.OVOO)
WOOOO = lib.einsum('je,nemi->mnij', t1b, eris_OVOO)
WOOOO = WOOOO - WOOOO.transpose(0,1,3,2)
WOOOO += np.asarray(eris.OOOO).transpose(0,2,1,3)
WOOOO += lib.einsum('ijef,menf->mnij', taubb, eris_OVOV) * .5
u2bb += lib.einsum('mnab,mnij->ijab', taubb, WOOOO*.5)
WOOOO = taubb = None
OVOO = eris_OVOO - eris_OVOO.transpose(2,1,0,3)
Foob += np.einsum('ne,nemi->mi', t1b, OVOO)
u1b += 0.5*lib.einsum('mnae,meni->ia', t2bb, OVOO)
wOVVO += lib.einsum('nb,nemj->mbej', t1b, OVOO)
OVOO = eris_OVOO = None
tilbb = make_tau_aa(t2[2], t1b, t1b, fac=0.5)
OVOV = eris_OVOV - eris_OVOV.transpose(0,3,2,1)
Fvvb -= .5 * lib.einsum('MNAF,MENF->AE', tilbb, OVOV)
Foob += .5 * lib.einsum('inef,menf->mi', tilbb, OVOV)
Fovb = np.einsum('nf,menf->me',t1b, OVOV)
u2bb += OVOV.conj().transpose(0,2,1,3) * .5
wOVVO -= 0.5*lib.einsum('jnfb,menf->mbej', t2bb, OVOV)
wOvVo += 0.5*lib.einsum('jNbF,MENF->MbEj', t2ab, OVOV)
tmpbb = lib.einsum('jf,menf->mnej', t1b, OVOV)
wOVVO -= lib.einsum('nb,mnej->mbej', t1b, tmpbb)
eris_OVOV = OVOV = tmpbb = tilbb = None
eris_OVoo = np.asarray(eris.OVoo)
eris_ovOO = np.asarray(eris.ovOO)
Fooa += np.einsum('NE,NEmi->mi', t1b, eris_OVoo)
u1a -= lib.einsum('nMaE,MEni->ia', t2ab, eris_OVoo)
wOvVo -= lib.einsum('nb,MEnj->MbEj', t1a, eris_OVoo)
woVVo += lib.einsum('NB,NEmj->mBEj', t1b, eris_OVoo)
Foob += np.einsum('ne,neMI->MI', t1a, eris_ovOO)
u1b -= lib.einsum('mNeA,meNI->IA', t2ab, eris_ovOO)
woVvO -= lib.einsum('NB,meNJ->mBeJ', t1b, eris_ovOO)
wOvvO += lib.einsum('nb,neMJ->MbeJ', t1a, eris_ovOO)
WoOoO = lib.einsum('JE,NEmi->mNiJ', t1b, eris_OVoo)
WoOoO+= lib.einsum('je,neMI->nMjI', t1a, eris_ovOO)
WoOoO += np.asarray(eris.ooOO).transpose(0,2,1,3)
eris_OVoo = eris_ovOO = None
eris_ovOV = np.asarray(eris.ovOV)
WoOoO += lib.einsum('iJeF,meNF->mNiJ', tauab, eris_ovOV)
u2ab += lib.einsum('mNaB,mNiJ->iJaB', tauab, WoOoO)
WoOoO = None
tilab = make_tau_ab(t2[1], t1 , t1 , fac=0.5)
Fvva -= lib.einsum('mNaF,meNF->ae', tilab, eris_ovOV)
Fvvb -= lib.einsum('nMfA,nfME->AE', tilab, eris_ovOV)
Fooa += lib.einsum('iNeF,meNF->mi', tilab, eris_ovOV)
Foob += lib.einsum('nIfE,nfME->MI', tilab, eris_ovOV)
Fova += np.einsum('NF,meNF->me',t1b, eris_ovOV)
Fovb += np.einsum('nf,nfME->ME',t1a, eris_ovOV)
u2ab += eris_ovOV.conj().transpose(0,2,1,3)
wovvo += 0.5*lib.einsum('jNbF,meNF->mbej', t2ab, eris_ovOV)
wOVVO += 0.5*lib.einsum('nJfB,nfME->MBEJ', t2ab, eris_ovOV)
wOvVo -= 0.5*lib.einsum('jnfb,nfME->MbEj', t2aa, eris_ovOV)
woVvO -= 0.5*lib.einsum('JNFB,meNF->mBeJ', t2bb, eris_ovOV)
woVVo += 0.5*lib.einsum('jNfB,mfNE->mBEj', t2ab, eris_ovOV)
wOvvO += 0.5*lib.einsum('nJbF,neMF->MbeJ', t2ab, eris_ovOV)
tmpabab = lib.einsum('JF,meNF->mNeJ', t1b, eris_ovOV)
tmpbaba = lib.einsum('jf,nfME->MnEj', t1a, eris_ovOV)
woVvO -= lib.einsum('NB,mNeJ->mBeJ', t1b, tmpabab)
wOvVo -= lib.einsum('nb,MnEj->MbEj', t1a, tmpbaba)
woVVo += lib.einsum('NB,NmEj->mBEj', t1b, tmpbaba)
wOvvO += lib.einsum('nb,nMeJ->MbeJ', t1a, tmpabab)
tmpabab = tmpbaba = tilab = None
Fova += fova
Fovb += fovb
u1a += fova.conj()
u1a += np.einsum('ie,ae->ia', t1a, Fvva)
u1a -= np.einsum('ma,mi->ia', t1a, Fooa)
u1a -= np.einsum('imea,me->ia', t2aa, Fova)
u1a += np.einsum('iMaE,ME->ia', t2ab, Fovb)
u1b += fovb.conj()
u1b += np.einsum('ie,ae->ia',t1b,Fvvb)
u1b -= np.einsum('ma,mi->ia',t1b,Foob)
u1b -= np.einsum('imea,me->ia', t2bb, Fovb)
u1b += np.einsum('mIeA,me->IA', t2ab, Fova)
eris_oovv = np.asarray(eris.oovv)
eris_ovvo = np.asarray(eris.ovvo)
wovvo -= eris_oovv.transpose(0,2,3,1)
wovvo += eris_ovvo.transpose(0,2,1,3)
oovv = eris_oovv - eris_ovvo.transpose(0,3,2,1)
u1a-= np.einsum('nf,niaf->ia', t1a, oovv)
tmp1aa = lib.einsum('ie,mjbe->mbij', t1a, oovv)
u2aa += 2*lib.einsum('ma,mbij->ijab', t1a, tmp1aa)
eris_ovvo = eris_oovv = oovv = tmp1aa = None
eris_OOVV = np.asarray(eris.OOVV)
eris_OVVO = np.asarray(eris.OVVO)
wOVVO -= eris_OOVV.transpose(0,2,3,1)
wOVVO += eris_OVVO.transpose(0,2,1,3)
OOVV = eris_OOVV - eris_OVVO.transpose(0,3,2,1)
u1b-= np.einsum('nf,niaf->ia', t1b, OOVV)
tmp1bb = lib.einsum('ie,mjbe->mbij', t1b, OOVV)
u2bb += 2*lib.einsum('ma,mbij->ijab', t1b, tmp1bb)
eris_OVVO = eris_OOVV = OOVV = None
eris_ooVV = np.asarray(eris.ooVV)
eris_ovVO = np.asarray(eris.ovVO)
woVVo -= eris_ooVV.transpose(0,2,3,1)
woVvO += eris_ovVO.transpose(0,2,1,3)
u1b+= np.einsum('nf,nfAI->IA', t1a, eris_ovVO)
tmp1ab = lib.einsum('ie,meBJ->mBiJ', t1a, eris_ovVO)
tmp1ab+= lib.einsum('IE,mjBE->mBjI', t1b, eris_ooVV)
u2ab -= lib.einsum('ma,mBiJ->iJaB', t1a, tmp1ab)
eris_ooVV = eris_ovVO = tmp1ab = None
eris_OOvv = np.asarray(eris.OOvv)
eris_OVvo = np.asarray(eris.OVvo)
wOvvO -= eris_OOvv.transpose(0,2,3,1)
wOvVo += eris_OVvo.transpose(0,2,1,3)
u1a+= np.einsum('NF,NFai->ia', t1b, eris_OVvo)
tmp1ba = lib.einsum('IE,MEbj->MbIj', t1b, eris_OVvo)
tmp1ba+= lib.einsum('ie,MJbe->MbJi', t1a, eris_OOvv)
u2ab -= lib.einsum('MA,MbIj->jIbA', t1b, tmp1ba)
eris_OOvv = eris_OVvo = tmp1ba = None
u2aa += 2*lib.einsum('imae,mbej->ijab', t2aa, wovvo)
u2aa += 2*lib.einsum('iMaE,MbEj->ijab', t2ab, wOvVo)
u2bb += 2*lib.einsum('imae,mbej->ijab', t2bb, wOVVO)
u2bb += 2*lib.einsum('mIeA,mBeJ->IJAB', t2ab, woVvO)
u2ab += lib.einsum('imae,mBeJ->iJaB', t2aa, woVvO)
u2ab += lib.einsum('iMaE,MBEJ->iJaB', t2ab, wOVVO)
u2ab += lib.einsum('iMeA,MbeJ->iJbA', t2ab, wOvvO)
u2ab += lib.einsum('IMAE,MbEj->jIbA', t2bb, wOvVo)
u2ab += lib.einsum('mIeA,mbej->jIbA', t2ab, wovvo)
u2ab += lib.einsum('mIaE,mBEj->jIaB', t2ab, woVVo)
wovvo = wOVVO = woVvO = wOvVo = woVVo = wOvvO = None
Ftmpa = Fvva - .5*lib.einsum('mb,me->be', t1a, Fova)
Ftmpb = Fvvb - .5*lib.einsum('mb,me->be', t1b, Fovb)
u2aa += lib.einsum('ijae,be->ijab', t2aa, Ftmpa)
u2bb += lib.einsum('ijae,be->ijab', t2bb, Ftmpb)
u2ab += lib.einsum('iJaE,BE->iJaB', t2ab, Ftmpb)
u2ab += lib.einsum('iJeA,be->iJbA', t2ab, Ftmpa)
Ftmpa = Fooa + 0.5*lib.einsum('je,me->mj', t1a, Fova)
Ftmpb = Foob + 0.5*lib.einsum('je,me->mj', t1b, Fovb)
u2aa -= lib.einsum('imab,mj->ijab', t2aa, Ftmpa)
u2bb -= lib.einsum('imab,mj->ijab', t2bb, Ftmpb)
u2ab -= lib.einsum('iMaB,MJ->iJaB', t2ab, Ftmpb)
u2ab -= lib.einsum('mIaB,mj->jIaB', t2ab, Ftmpa)
eris_ovoo = np.asarray(eris.ovoo).conj()
eris_OVOO = np.asarray(eris.OVOO).conj()
eris_OVoo = np.asarray(eris.OVoo).conj()
eris_ovOO = np.asarray(eris.ovOO).conj()
ovoo = eris_ovoo - eris_ovoo.transpose(2,1,0,3)
OVOO = eris_OVOO - eris_OVOO.transpose(2,1,0,3)
u2aa -= lib.einsum('ma,jbim->ijab', t1a, ovoo)
u2bb -= lib.einsum('ma,jbim->ijab', t1b, OVOO)
u2ab -= lib.einsum('ma,JBim->iJaB', t1a, eris_OVoo)
u2ab -= lib.einsum('MA,ibJM->iJbA', t1b, eris_ovOO)
eris_ovoo = eris_OVoo = eris_OVOO = eris_ovOO = None
u2aa *= .5
u2bb *= .5
u2aa = u2aa - u2aa.transpose(0,1,3,2)
u2aa = u2aa - u2aa.transpose(1,0,2,3)
u2bb = u2bb - u2bb.transpose(0,1,3,2)
u2bb = u2bb - u2bb.transpose(1,0,2,3)
eia_a = lib.direct_sum('i-a->ia', mo_ea_o, mo_ea_v)
eia_b = lib.direct_sum('i-a->ia', mo_eb_o, mo_eb_v)
u1a /= eia_a
u1b /= eia_b
u2aa /= lib.direct_sum('ia+jb->ijab', eia_a, eia_a)
u2ab /= lib.direct_sum('ia+jb->ijab', eia_a, eia_b)
u2bb /= lib.direct_sum('ia+jb->ijab', eia_b, eia_b)
time0 = log.timer_debug1('update t1 t2', *time0)
t1new = u1a, u1b
t2new = u2aa, u2ab, u2bb
return t1new, t2new
[docs]
def energy(cc, t1=None, t2=None, eris=None):
'''UCCSD correlation energy'''
if t1 is None: t1 = cc.t1
if t2 is None: t2 = cc.t2
if eris is None: eris = cc.ao2mo()
t1a, t1b = t1
t2aa, t2ab, t2bb = t2
nocca, noccb, nvira, nvirb = t2ab.shape
eris_ovov = np.asarray(eris.ovov)
eris_OVOV = np.asarray(eris.OVOV)
eris_ovOV = np.asarray(eris.ovOV)
fova = eris.focka[:nocca,nocca:]
fovb = eris.fockb[:noccb,noccb:]
e = np.einsum('ia,ia', fova, t1a)
e += np.einsum('ia,ia', fovb, t1b)
e += 0.25*np.einsum('ijab,iajb',t2aa,eris_ovov)
e -= 0.25*np.einsum('ijab,ibja',t2aa,eris_ovov)
e += 0.25*np.einsum('ijab,iajb',t2bb,eris_OVOV)
e -= 0.25*np.einsum('ijab,ibja',t2bb,eris_OVOV)
e += np.einsum('iJaB,iaJB',t2ab,eris_ovOV)
e += 0.5*np.einsum('ia,jb,iajb',t1a,t1a,eris_ovov)
e -= 0.5*np.einsum('ia,jb,ibja',t1a,t1a,eris_ovov)
e += 0.5*np.einsum('ia,jb,iajb',t1b,t1b,eris_OVOV)
e -= 0.5*np.einsum('ia,jb,ibja',t1b,t1b,eris_OVOV)
e += np.einsum('ia,jb,iajb',t1a,t1b,eris_ovOV)
if abs(e.imag) > 1e-4:
logger.warn(cc, 'Non-zero imaginary part found in UCCSD energy %s', e)
return e.real
get_nocc = ump2.get_nocc
get_nmo = ump2.get_nmo
get_frozen_mask = ump2.get_frozen_mask
[docs]
def amplitudes_to_vector(t1, t2, out=None):
nocca, nvira = t1[0].shape
noccb, nvirb = t1[1].shape
sizea = nocca * nvira + nocca*(nocca-1)//2*nvira*(nvira-1)//2
sizeb = noccb * nvirb + noccb*(noccb-1)//2*nvirb*(nvirb-1)//2
sizeab = nocca * noccb * nvira * nvirb
vector = np.ndarray(sizea+sizeb+sizeab, t2[0].dtype, buffer=out)
ccsd.amplitudes_to_vector_s4(t1[0], t2[0], out=vector[:sizea])
ccsd.amplitudes_to_vector_s4(t1[1], t2[2], out=vector[sizea:])
vector[sizea+sizeb:] = t2[1].ravel()
return vector
[docs]
def vector_to_amplitudes(vector, nmo, nocc):
nocca, noccb = nocc
nmoa, nmob = nmo
nvira, nvirb = nmoa-nocca, nmob-noccb
nocc = nocca + noccb
nvir = nvira + nvirb
nov = nocc * nvir
size = nov + nocc*(nocc-1)//2*nvir*(nvir-1)//2
if vector.size == size:
#return ccsd.vector_to_amplitudes_s4(vector, nmo, nocc)
raise RuntimeError('Input vector is GCCSD vecotr')
else:
sizea = nocca * nvira + nocca*(nocca-1)//2*nvira*(nvira-1)//2
sizeb = noccb * nvirb + noccb*(noccb-1)//2*nvirb*(nvirb-1)//2
sections = np.cumsum([sizea, sizeb])
veca, vecb, t2ab = np.split(vector, sections)
t1a, t2aa = ccsd.vector_to_amplitudes_s4(veca, nmoa, nocca)
t1b, t2bb = ccsd.vector_to_amplitudes_s4(vecb, nmob, noccb)
t2ab = t2ab.copy().reshape(nocca,noccb,nvira,nvirb)
return (t1a,t1b), (t2aa,t2ab,t2bb)
[docs]
def amplitudes_from_rccsd(t1, t2):
t2aa = t2 - t2.transpose(0,1,3,2)
return (t1,t1), (t2aa,t2,t2aa)
def _add_vvVV(mycc, t1, t2ab, eris, out=None):
'''Ht2 = np.einsum('iJcD,acBD->iJaB', t2ab, vvVV)
without using symmetry in t2ab or Ht2
'''
time0 = logger.process_clock(), logger.perf_counter()
if t2ab.size == 0:
return np.zeros_like(t2ab)
if t1 is not None:
t2ab = make_tau_ab(t2ab, t1, t1)
log = logger.Logger(mycc.stdout, mycc.verbose)
nocca, noccb, nvira, nvirb = t2ab.shape
if mycc.direct: # AO direct CCSD
if getattr(eris, 'mo_coeff', None) is not None:
mo_a, mo_b = eris.mo_coeff
else:
moidxa, moidxb = mycc.get_frozen_mask()
mo_a = mycc.mo_coeff[0][:,moidxa]
mo_b = mycc.mo_coeff[1][:,moidxb]
# Note tensor t2ab may be t2bbab from eom_uccsd code. In that
# particular case, nocca, noccb do not equal to the actual number of
# alpha/beta occupied orbitals. orbva and orbvb cannot be indexed as
# mo_a[:,nocca:] and mo_b[:,noccb:]
orbva = mo_a[:,-nvira:]
orbvb = mo_b[:,-nvirb:]
tau = lib.einsum('ijab,pa->ijpb', t2ab, orbva)
tau = lib.einsum('ijab,pb->ijap', tau, orbvb)
time0 = logger.timer_debug1(mycc, 'vvvv-tau mo2ao', *time0)
buf = eris._contract_vvVV_t2(mycc, tau, mycc.direct, out, log)
mo = np.asarray(np.hstack((orbva, orbvb)), order='F')
Ht2 = _ao2mo.nr_e2(buf.reshape(nocca*noccb,-1), mo.conj(),
(0,nvira,nvira,nvira+nvirb), 's1', 's1')
return Ht2.reshape(t2ab.shape)
else:
return eris._contract_vvVV_t2(mycc, t2ab, mycc.direct, out, log)
def _add_vvvv(mycc, t1, t2, eris, out=None, with_ovvv=False, t2sym=None):
time0 = logger.process_clock(), logger.perf_counter()
log = logger.Logger(mycc.stdout, mycc.verbose)
if t1 is None:
t2aa, t2ab, t2bb = t2
else:
t2aa, t2ab, t2bb = make_tau(t2, t1, t1)
nocca, nvira = t2aa.shape[1:3]
noccb, nvirb = t2bb.shape[1:3]
if mycc.direct:
assert (t2sym is None)
if with_ovvv:
raise NotImplementedError
if getattr(eris, 'mo_coeff', None) is not None:
mo_a, mo_b = eris.mo_coeff
else:
moidxa, moidxb = mycc.get_frozen_mask()
mo_a = mycc.mo_coeff[0][:,moidxa]
mo_b = mycc.mo_coeff[1][:,moidxb]
nao = mo_a.shape[0]
otrila = np.tril_indices(nocca,-1)
otrilb = np.tril_indices(noccb,-1)
if nocca > 1:
tauaa = lib.einsum('xab,pa->xpb', t2aa[otrila], mo_a[:,nocca:])
tauaa = lib.einsum('xab,pb->xap', tauaa, mo_a[:,nocca:])
else:
tauaa = np.zeros((0,nao,nao))
if noccb > 1:
taubb = lib.einsum('xab,pa->xpb', t2bb[otrilb], mo_b[:,noccb:])
taubb = lib.einsum('xab,pb->xap', taubb, mo_b[:,noccb:])
else:
taubb = np.zeros((0,nao,nao))
tauab = lib.einsum('ijab,pa->ijpb', t2ab, mo_a[:,nocca:])
tauab = lib.einsum('ijab,pb->ijap', tauab, mo_b[:,noccb:])
tau = np.vstack((tauaa, taubb, tauab.reshape(nocca*noccb,nao,nao)))
tauaa = taubb = tauab = None
time0 = log.timer_debug1('vvvv-tau', *time0)
buf = ccsd._contract_vvvv_t2(mycc, mycc.mol, None, tau, out, log)
mo = np.asarray(np.hstack((mo_a[:,nocca:], mo_b[:,noccb:])), order='F')
u2aa = np.zeros_like(t2aa)
if nocca > 1:
u2tril = buf[:otrila[0].size]
u2tril = _ao2mo.nr_e2(u2tril.reshape(-1,nao**2), mo.conj(),
(0,nvira,0,nvira), 's1', 's1')
u2tril = u2tril.reshape(otrila[0].size,nvira,nvira)
u2aa[otrila[1],otrila[0]] = u2tril.transpose(0,2,1)
u2aa[otrila] = u2tril
u2bb = np.zeros_like(t2bb)
if noccb > 1:
u2tril = buf[otrila[0].size:otrila[0].size+otrilb[0].size]
u2tril = _ao2mo.nr_e2(u2tril.reshape(-1,nao**2), mo.conj(),
(nvira,nvira+nvirb,nvira,nvira+nvirb), 's1', 's1')
u2tril = u2tril.reshape(otrilb[0].size,nvirb,nvirb)
u2bb[otrilb[1],otrilb[0]] = u2tril.transpose(0,2,1)
u2bb[otrilb] = u2tril
if nocca*noccb > 0:
u2ab = _ao2mo.nr_e2(buf[-nocca*noccb:].reshape(nocca*noccb,nao**2), mo,
(0,nvira,nvira,nvira+nvirb), 's1', 's1')
u2ab = u2ab.reshape(t2ab.shape)
else:
u2ab = np.zeros_like(t2ab)
else:
assert (not with_ovvv)
if t2sym is None:
tmp = eris._contract_vvvv_t2(mycc, t2aa[np.tril_indices(nocca)],
mycc.direct, None)
u2aa = ccsd._unpack_t2_tril(tmp, nocca, nvira, None, 'jiba')
tmp = eris._contract_VVVV_t2(mycc, t2bb[np.tril_indices(noccb)],
mycc.direct, None)
u2bb = ccsd._unpack_t2_tril(tmp, noccb, nvirb, None, 'jiba')
u2ab = eris._contract_vvVV_t2(mycc, t2ab, mycc.direct, None)
else:
u2aa = eris._contract_vvvv_t2(mycc, t2aa, mycc.direct, None)
u2bb = eris._contract_VVVV_t2(mycc, t2bb, mycc.direct, None)
u2ab = eris._contract_vvVV_t2(mycc, t2ab, mycc.direct, None)
return u2aa,u2ab,u2bb
[docs]
class UCCSD(ccsd.CCSDBase):
conv_tol = getattr(__config__, 'cc_uccsd_UCCSD_conv_tol', 1e-7)
conv_tol_normt = getattr(__config__, 'cc_uccsd_UCCSD_conv_tol_normt', 1e-6)
# Attribute frozen can be
# * An integer : The same number of inner-most alpha and beta orbitals are frozen
# * One list : Same alpha and beta orbital indices to be frozen
# * A pair of list : First list is the orbital indices to be frozen for alpha
# orbitals, second list is for beta orbitals
def __init__(self, mf, frozen=None, mo_coeff=None, mo_occ=None):
assert isinstance(mf, scf.uhf.UHF)
ccsd.CCSDBase.__init__(self, mf, frozen, mo_coeff, mo_occ)
get_nocc = get_nocc
get_nmo = get_nmo
get_frozen_mask = get_frozen_mask
[docs]
def init_amps(self, eris=None):
time0 = logger.process_clock(), logger.perf_counter()
if eris is None:
eris = self.ao2mo(self.mo_coeff)
nocca, noccb = self.nocc
fova = eris.focka[:nocca,nocca:]
fovb = eris.fockb[:noccb,noccb:]
mo_ea_o = eris.mo_energy[0][:nocca]
mo_ea_v = eris.mo_energy[0][nocca:]
mo_eb_o = eris.mo_energy[1][:noccb]
mo_eb_v = eris.mo_energy[1][noccb:]
eia_a = lib.direct_sum('i-a->ia', mo_ea_o, mo_ea_v)
eia_b = lib.direct_sum('i-a->ia', mo_eb_o, mo_eb_v)
t1a = fova.conj() / eia_a
t1b = fovb.conj() / eia_b
eris_ovov = np.asarray(eris.ovov)
eris_OVOV = np.asarray(eris.OVOV)
eris_ovOV = np.asarray(eris.ovOV)
t2aa = eris_ovov.transpose(0,2,1,3) / lib.direct_sum('ia+jb->ijab', eia_a, eia_a)
t2ab = eris_ovOV.transpose(0,2,1,3) / lib.direct_sum('ia+jb->ijab', eia_a, eia_b)
t2bb = eris_OVOV.transpose(0,2,1,3) / lib.direct_sum('ia+jb->ijab', eia_b, eia_b)
t2aa = t2aa - t2aa.transpose(0,1,3,2)
t2bb = t2bb - t2bb.transpose(0,1,3,2)
e = np.einsum('iJaB,iaJB', t2ab, eris_ovOV)
e += 0.25*np.einsum('ijab,iajb', t2aa, eris_ovov)
e -= 0.25*np.einsum('ijab,ibja', t2aa, eris_ovov)
e += 0.25*np.einsum('ijab,iajb', t2bb, eris_OVOV)
e -= 0.25*np.einsum('ijab,ibja', t2bb, eris_OVOV)
self.emp2 = e.real
logger.info(self, 'Init t2, MP2 energy = %.15g', self.emp2)
logger.timer(self, 'init mp2', *time0)
return self.emp2, (t1a,t1b), (t2aa,t2ab,t2bb)
energy = energy
update_amps = update_amps
_add_vvvv = _add_vvvv
_add_vvVV = _add_vvVV
[docs]
def kernel(self, t1=None, t2=None, eris=None, mbpt2=False):
return self.ccsd(t1, t2, eris, mbpt2)
[docs]
def ccsd(self, t1=None, t2=None, eris=None, mbpt2=False):
'''Ground-state unrestricted (U)CCSD.
Kwargs:
mbpt2 : bool
Use one-shot MBPT2 approximation to CCSD.
'''
if mbpt2:
pt = ump2.UMP2(self._scf, self.frozen, self.mo_coeff, self.mo_occ)
self.e_corr, self.t2 = pt.kernel(eris=eris)
t2ab = self.t2[1]
nocca, noccb, nvira, nvirb = t2ab.shape
self.t1 = (np.zeros((nocca,nvira)), np.zeros((noccb,nvirb)))
return self.e_corr, self.t1, self.t2
return ccsd.CCSDBase.ccsd(self, t1, t2, eris)
[docs]
def solve_lambda(self, t1=None, t2=None, l1=None, l2=None,
eris=None):
from pyscf.cc import uccsd_lambda
if t1 is None: t1 = self.t1
if t2 is None: t2 = self.t2
if eris is None: eris = self.ao2mo(self.mo_coeff)
self.converged_lambda, self.l1, self.l2 = \
uccsd_lambda.kernel(self, eris, t1, t2, l1, l2,
max_cycle=self.max_cycle,
tol=self.conv_tol_normt,
verbose=self.verbose)
return self.l1, self.l2
[docs]
def ccsd_t(self, t1=None, t2=None, eris=None):
from pyscf.cc import uccsd_t
if t1 is None: t1 = self.t1
if t2 is None: t2 = self.t2
if eris is None: eris = self.ao2mo(self.mo_coeff)
return uccsd_t.kernel(self, eris, t1, t2, self.verbose)
uccsd_t = ccsd_t
[docs]
def make_rdm1(self, t1=None, t2=None, l1=None, l2=None, ao_repr=False,
with_frozen=True, with_mf=True):
'''Un-relaxed 1-particle density matrix in MO space
Returns:
dm1a, dm1b
'''
from pyscf.cc import uccsd_rdm
if t1 is None: t1 = self.t1
if t2 is None: t2 = self.t2
if l1 is None: l1 = self.l1
if l2 is None: l2 = self.l2
if l1 is None: l1, l2 = self.solve_lambda(t1, t2)
return uccsd_rdm.make_rdm1(self, t1, t2, l1, l2, ao_repr=ao_repr,
with_frozen=with_frozen, with_mf=with_mf)
[docs]
def make_rdm2(self, t1=None, t2=None, l1=None, l2=None, ao_repr=False,
with_frozen=True, with_dm1=True):
'''2-particle density matrix in spin-orbital basis.
'''
from pyscf.cc import uccsd_rdm
if t1 is None: t1 = self.t1
if t2 is None: t2 = self.t2
if l1 is None: l1 = self.l1
if l2 is None: l2 = self.l2
if l1 is None: l1, l2 = self.solve_lambda(t1, t2)
return uccsd_rdm.make_rdm2(self, t1, t2, l1, l2, ao_repr=ao_repr,
with_frozen=with_frozen, with_dm1=with_dm1)
[docs]
def spin_square(self, mo_coeff=None, s=None):
from pyscf.fci.spin_op import spin_square_general
if mo_coeff is None:
mo_coeff = self.mo_coeff
if s is None:
s = self._scf.get_ovlp()
dma,dmb = self.make_rdm1()
dmaa,dmab,dmbb = self.make_rdm2()
return spin_square_general(dma,dmb,dmaa,dmab,dmbb,mo_coeff,s)
[docs]
def ao2mo(self, mo_coeff=None):
nmoa, nmob = self.get_nmo()
nao = self.mo_coeff[0].shape[0]
nmo_pair = nmoa * (nmoa+1) // 2
nao_pair = nao * (nao+1) // 2
mem_incore = (max(nao_pair**2, nmoa**4) + nmo_pair**2) * 8/1e6
mem_now = lib.current_memory()[0]
if (self._scf._eri is not None and
(mem_incore+mem_now < self.max_memory or self.incore_complete)):
return _make_eris_incore(self, mo_coeff)
elif getattr(self._scf, 'with_df', None):
# TODO: Uncomment once there is an unrestricted DF-CCSD implementation
#logger.warn(self, 'UCCSD detected DF being used in the HF object. '
# 'MO integrals are computed based on the DF 3-index tensors.\n'
# 'It\'s recommended to use dfccsd.CCSD for the '
# 'DF-CCSD calculations')
return _make_df_eris_outcore(self, mo_coeff)
else:
return _make_eris_outcore(self, mo_coeff)
[docs]
def ipccsd(self, nroots=1, left=False, koopmans=False, guess=None,
partition=None, eris=None):
from pyscf.cc import eom_uccsd
return eom_uccsd.EOMIP(self).kernel(nroots, left, koopmans, guess,
partition, eris)
[docs]
def eaccsd(self, nroots=1, left=False, koopmans=False, guess=None,
partition=None, eris=None):
from pyscf.cc import eom_uccsd
return eom_uccsd.EOMEA(self).kernel(nroots, left, koopmans, guess,
partition, eris)
[docs]
def eeccsd(self, nroots=1, koopmans=False, guess=None, eris=None):
from pyscf.cc import eom_uccsd
return eom_uccsd.EOMEE(self).kernel(nroots, koopmans, guess, eris)
[docs]
def eomee_ccsd(self, nroots=1, koopmans=False, guess=None, eris=None):
from pyscf.cc import eom_uccsd
return eom_uccsd.EOMEESpinKeep(self).kernel(nroots, koopmans, guess, eris)
[docs]
def eomsf_ccsd(self, nroots=1, koopmans=False, guess=None, eris=None):
from pyscf.cc import eom_uccsd
return eom_uccsd.EOMEESpinFlip(self).kernel(nroots, koopmans, guess, eris)
[docs]
def eomip_method(self):
from pyscf.cc import eom_uccsd
return eom_uccsd.EOMIP(self)
[docs]
def eomea_method(self):
from pyscf.cc import eom_uccsd
return eom_uccsd.EOMEA(self)
[docs]
def eomee_method(self):
from pyscf.cc import eom_uccsd
return eom_uccsd.EOMEE(self)
[docs]
def nuc_grad_method(self):
from pyscf.grad import uccsd
return uccsd.Gradients(self)
[docs]
def amplitudes_to_vector(self, t1, t2, out=None):
return amplitudes_to_vector(t1, t2, out)
[docs]
def vector_to_amplitudes(self, vector, nmo=None, nocc=None):
if nocc is None: nocc = self.nocc
if nmo is None: nmo = self.nmo
return vector_to_amplitudes(vector, nmo, nocc)
[docs]
def vector_size(self, nmo=None, nocc=None):
if nocc is None: nocc = self.nocc
if nmo is None: nmo = self.nmo
nocca, noccb = nocc
nmoa, nmob = nmo
nvira, nvirb = nmoa-nocca, nmob-noccb
sizea = nocca * nvira + nocca*(nocca-1)//2*nvira*(nvira-1)//2
sizeb = noccb * nvirb + noccb*(noccb-1)//2*nvirb*(nvirb-1)//2
sizeab = nocca * noccb * nvira * nvirb
return sizea + sizeb + sizeab
[docs]
def amplitudes_from_rccsd(self, t1, t2):
return amplitudes_from_rccsd(t1, t2)
CCSD = UCCSD
class _ChemistsERIs(ccsd._ChemistsERIs):
def __init__(self, mol=None):
ccsd._ChemistsERIs.__init__(self, mol)
self.OOOO = None
self.OVOO = None
self.OVOV = None
self.OOVV = None
self.OVVO = None
self.OVVV = None
self.VVVV = None
self.ooOO = None
self.ovOO = None
self.ovOV = None
self.ooVV = None
self.ovVO = None
self.ovVV = None
self.vvVV = None
self.OVoo = None
self.OOvv = None
self.OVvo = None
def _common_init_(self, mycc, mo_coeff=None):
if mo_coeff is None:
mo_coeff = mycc.mo_coeff
mo_idx = mycc.get_frozen_mask()
self.mo_coeff = mo_coeff = \
(mo_coeff[0][:,mo_idx[0]], mo_coeff[1][:,mo_idx[1]])
# Note: Recomputed fock matrix since SCF may not be fully converged.
dm = mycc._scf.make_rdm1(mycc.mo_coeff, mycc.mo_occ)
vhf = mycc._scf.get_veff(mycc.mol, dm)
fockao = mycc._scf.get_fock(vhf=vhf, dm=dm)
self.focka = reduce(np.dot, (mo_coeff[0].conj().T, fockao[0], mo_coeff[0]))
self.fockb = reduce(np.dot, (mo_coeff[1].conj().T, fockao[1], mo_coeff[1]))
self.fock = (self.focka, self.fockb)
nocca, noccb = self.nocc = mycc.nocc
self.mol = mycc.mol
mo_ea = self.focka.diagonal().real
mo_eb = self.fockb.diagonal().real
self.mo_energy = (mo_ea, mo_eb)
gap_a = abs(mo_ea[:nocca,None] - mo_ea[None,nocca:])
gap_b = abs(mo_eb[:noccb,None] - mo_eb[None,noccb:])
if gap_a.size > 0:
gap_a = gap_a.min()
else:
gap_a = 1e9
if gap_b.size > 0:
gap_b = gap_b.min()
else:
gap_b = 1e9
if gap_a < 1e-5 or gap_b < 1e-5:
logger.warn(mycc, 'HOMO-LUMO gap (%s,%s) too small for UCCSD',
gap_a, gap_b)
return self
def get_ovvv(self, *slices):
return _get_ovvv_base(self.ovvv, *slices)
def get_ovVV(self, *slices):
return _get_ovvv_base(self.ovVV, *slices)
def get_OVvv(self, *slices):
return _get_ovvv_base(self.OVvv, *slices)
def get_OVVV(self, *slices):
return _get_ovvv_base(self.OVVV, *slices)
def _contract_VVVV_t2(self, mycc, t2, vvvv_or_direct=False, out=None, verbose=None):
if isinstance(vvvv_or_direct, np.ndarray):
vvvv = vvvv_or_direct
elif vvvv_or_direct:
vvvv = None
else:
vvvv = self.VVVV
return ccsd._contract_vvvv_t2(mycc, self.mol, vvvv, t2, out, verbose)
def _contract_vvVV_t2(self, mycc, t2, vvvv_or_direct=False, out=None, verbose=None):
if isinstance(vvvv_or_direct, np.ndarray):
vvvv = vvvv_or_direct
elif vvvv_or_direct:
vvvv = None
else:
vvvv = self.vvVV
return ccsd._contract_vvvv_t2(mycc, self.mol, vvvv, t2, out, verbose)
def _get_ovvv_base(ovvv, *slices):
if ovvv.ndim == 3:
ovw = np.asarray(ovvv[slices])
nocc, nvir, nvir_pair = ovw.shape
ovvv = lib.unpack_tril(ovw.reshape(nocc*nvir,nvir_pair))
nvir1 = ovvv.shape[2]
return ovvv.reshape(nocc,nvir,nvir1,nvir1)
elif slices:
return ovvv[slices]
else:
return ovvv
def _make_eris_incore(mycc, mo_coeff=None, ao2mofn=None):
eris = _ChemistsERIs()
eris._common_init_(mycc, mo_coeff)
nocca, noccb = mycc.nocc
nmoa, nmob = mycc.nmo
nvira, nvirb = nmoa-nocca, nmob-noccb
moa = eris.mo_coeff[0]
mob = eris.mo_coeff[1]
nmoa = moa.shape[1]
nmob = mob.shape[1]
if callable(ao2mofn):
eri_aa = ao2mofn(moa).reshape([nmoa]*4)
eri_bb = ao2mofn(mob).reshape([nmob]*4)
eri_ab = ao2mofn((moa,moa,mob,mob))
else:
eri_aa = ao2mo.restore(1, ao2mo.full(mycc._scf._eri, moa), nmoa)
eri_bb = ao2mo.restore(1, ao2mo.full(mycc._scf._eri, mob), nmob)
eri_ab = ao2mo.general(mycc._scf._eri, (moa,moa,mob,mob), compact=False)
eri_ba = eri_ab.reshape(nmoa,nmoa,nmob,nmob).transpose(2,3,0,1)
eri_aa = eri_aa.reshape(nmoa,nmoa,nmoa,nmoa)
eri_ab = eri_ab.reshape(nmoa,nmoa,nmob,nmob)
eri_ba = eri_ba.reshape(nmob,nmob,nmoa,nmoa)
eri_bb = eri_bb.reshape(nmob,nmob,nmob,nmob)
eris.oooo = eri_aa[:nocca,:nocca,:nocca,:nocca].copy()
eris.ovoo = eri_aa[:nocca,nocca:,:nocca,:nocca].copy()
eris.ovov = eri_aa[:nocca,nocca:,:nocca,nocca:].copy()
eris.oovv = eri_aa[:nocca,:nocca,nocca:,nocca:].copy()
eris.ovvo = eri_aa[:nocca,nocca:,nocca:,:nocca].copy()
eris.ovvv = eri_aa[:nocca,nocca:,nocca:,nocca:].copy()
eris.vvvv = eri_aa[nocca:,nocca:,nocca:,nocca:].copy()
eris.OOOO = eri_bb[:noccb,:noccb,:noccb,:noccb].copy()
eris.OVOO = eri_bb[:noccb,noccb:,:noccb,:noccb].copy()
eris.OVOV = eri_bb[:noccb,noccb:,:noccb,noccb:].copy()
eris.OOVV = eri_bb[:noccb,:noccb,noccb:,noccb:].copy()
eris.OVVO = eri_bb[:noccb,noccb:,noccb:,:noccb].copy()
eris.OVVV = eri_bb[:noccb,noccb:,noccb:,noccb:].copy()
eris.VVVV = eri_bb[noccb:,noccb:,noccb:,noccb:].copy()
eris.ooOO = eri_ab[:nocca,:nocca,:noccb,:noccb].copy()
eris.ovOO = eri_ab[:nocca,nocca:,:noccb,:noccb].copy()
eris.ovOV = eri_ab[:nocca,nocca:,:noccb,noccb:].copy()
eris.ooVV = eri_ab[:nocca,:nocca,noccb:,noccb:].copy()
eris.ovVO = eri_ab[:nocca,nocca:,noccb:,:noccb].copy()
eris.ovVV = eri_ab[:nocca,nocca:,noccb:,noccb:].copy()
eris.vvVV = eri_ab[nocca:,nocca:,noccb:,noccb:].copy()
#eris.OOoo = eri_ba[:noccb,:noccb,:nocca,:nocca].copy()
eris.OVoo = eri_ba[:noccb,noccb:,:nocca,:nocca].copy()
#eris.OVov = eri_ba[:noccb,noccb:,:nocca,nocca:].copy()
eris.OOvv = eri_ba[:noccb,:noccb,nocca:,nocca:].copy()
eris.OVvo = eri_ba[:noccb,noccb:,nocca:,:nocca].copy()
eris.OVvv = eri_ba[:noccb,noccb:,nocca:,nocca:].copy()
#eris.VVvv = eri_ba[noccb:,noccb:,nocca:,nocca:].copy()
if not callable(ao2mofn):
ovvv = eris.ovvv.reshape(nocca*nvira,nvira,nvira)
eris.ovvv = lib.pack_tril(ovvv).reshape(nocca,nvira,nvira*(nvira+1)//2)
eris.vvvv = ao2mo.restore(4, eris.vvvv, nvira)
OVVV = eris.OVVV.reshape(noccb*nvirb,nvirb,nvirb)
eris.OVVV = lib.pack_tril(OVVV).reshape(noccb,nvirb,nvirb*(nvirb+1)//2)
eris.VVVV = ao2mo.restore(4, eris.VVVV, nvirb)
ovVV = eris.ovVV.reshape(nocca*nvira,nvirb,nvirb)
eris.ovVV = lib.pack_tril(ovVV).reshape(nocca,nvira,nvirb*(nvirb+1)//2)
vvVV = eris.vvVV.reshape(nvira**2,nvirb**2)
idxa = np.tril_indices(nvira)
idxb = np.tril_indices(nvirb)
eris.vvVV = lib.take_2d(vvVV, idxa[0]*nvira+idxa[1], idxb[0]*nvirb+idxb[1])
OVvv = eris.OVvv.reshape(noccb*nvirb,nvira,nvira)
eris.OVvv = lib.pack_tril(OVvv).reshape(noccb,nvirb,nvira*(nvira+1)//2)
return eris
def _make_df_eris_outcore(mycc, mo_coeff=None):
cput0 = (logger.process_clock(), logger.perf_counter())
log = logger.Logger(mycc.stdout, mycc.verbose)
eris = _ChemistsERIs()
eris._common_init_(mycc, mo_coeff)
moa, mob = eris.mo_coeff
nocca, noccb = eris.nocc
nao = moa.shape[0]
nmoa = moa.shape[1]
nmob = mob.shape[1]
nvira = nmoa - nocca
nvirb = nmob - noccb
nvira_pair = nvira*(nvira+1)//2
nvirb_pair = nvirb*(nvirb+1)//2
naux = mycc._scf.with_df.get_naoaux()
# --- Three-center integrals
# (L|aa)
Loo = np.empty((naux,nocca,nocca))
Lov = np.empty((naux,nocca,nvira))
Lvo = np.empty((naux,nvira,nocca))
Lvv = np.empty((naux,nvira_pair))
# (L|bb)
LOO = np.empty((naux,noccb,noccb))
LOV = np.empty((naux,noccb,nvirb))
LVO = np.empty((naux,nvirb,noccb))
LVV = np.empty((naux,nvirb_pair))
p1 = 0
oa, va = np.s_[:nocca], np.s_[nocca:]
ob, vb = np.s_[:noccb], np.s_[noccb:]
# Transform three-center integrals to MO basis
einsum = lib.einsum
for eri1 in mycc._scf.with_df.loop():
eri1 = lib.unpack_tril(eri1).reshape(-1,nao,nao)
# (L|aa)
Lpq = einsum('Lab,ap,bq->Lpq', eri1, moa, moa)
p0, p1 = p1, p1 + Lpq.shape[0]
blk = np.s_[p0:p1]
Loo[blk] = Lpq[:,oa,oa]
Lov[blk] = Lpq[:,oa,va]
Lvo[blk] = Lpq[:,va,oa]
Lvv[blk] = lib.pack_tril(Lpq[:,va,va].reshape(-1,nvira,nvira))
# (L|bb)
Lpq = einsum('Lab,ap,bq->Lpq', eri1, mob, mob)
LOO[blk] = Lpq[:,ob,ob]
LOV[blk] = Lpq[:,ob,vb]
LVO[blk] = Lpq[:,vb,ob]
LVV[blk] = lib.pack_tril(Lpq[:,vb,vb].reshape(-1,nvirb,nvirb))
Loo = Loo.reshape(naux,nocca*nocca)
Lov = Lov.reshape(naux,nocca*nvira)
Lvo = Lvo.reshape(naux,nocca*nvira)
LOO = LOO.reshape(naux,noccb*noccb)
LOV = LOV.reshape(naux,noccb*nvirb)
LVO = LVO.reshape(naux,noccb*nvirb)
# --- Four-center integrals
dot = lib.ddot
eris.feri1 = lib.H5TmpFile()
# (aa|aa)
eris.oooo = eris.feri1.create_dataset('oooo', (nocca,nocca,nocca,nocca), 'f8')
eris.oovv = eris.feri1.create_dataset('oovv', (nocca,nocca,nvira,nvira), 'f8', chunks=(nocca,nocca,1,nvira))
eris.ovoo = eris.feri1.create_dataset('ovoo', (nocca,nvira,nocca,nocca), 'f8', chunks=(nocca,1,nocca,nocca))
eris.ovvo = eris.feri1.create_dataset('ovvo', (nocca,nvira,nvira,nocca), 'f8', chunks=(nocca,1,nvira,nocca))
eris.ovov = eris.feri1.create_dataset('ovov', (nocca,nvira,nocca,nvira), 'f8', chunks=(nocca,1,nocca,nvira))
eris.ovvv = eris.feri1.create_dataset('ovvv', (nocca,nvira,nvira_pair), 'f8')
eris.vvvv = eris.feri1.create_dataset('vvvv', (nvira_pair,nvira_pair), 'f8')
eris.oooo[:] = dot(Loo.T, Loo).reshape(nocca,nocca,nocca,nocca)
eris.ovoo[:] = dot(Lov.T, Loo).reshape(nocca,nvira,nocca,nocca)
eris.oovv[:] = lib.unpack_tril(dot(Loo.T, Lvv)).reshape(nocca,nocca,nvira,nvira)
eris.ovvo[:] = dot(Lov.T, Lvo).reshape(nocca,nvira,nvira,nocca)
eris.ovov[:] = dot(Lov.T, Lov).reshape(nocca,nvira,nocca,nvira)
eris.ovvv[:] = dot(Lov.T, Lvv).reshape(nocca,nvira,nvira_pair)
eris.vvvv[:] = dot(Lvv.T, Lvv)
# (bb|bb)
eris.OOOO = eris.feri1.create_dataset('OOOO', (noccb,noccb,noccb,noccb), 'f8')
eris.OOVV = eris.feri1.create_dataset('OOVV', (noccb,noccb,nvirb,nvirb), 'f8', chunks=(noccb,noccb,1,nvirb))
eris.OVOO = eris.feri1.create_dataset('OVOO', (noccb,nvirb,noccb,noccb), 'f8', chunks=(noccb,1,noccb,noccb))
eris.OVVO = eris.feri1.create_dataset('OVVO', (noccb,nvirb,nvirb,noccb), 'f8', chunks=(noccb,1,nvirb,noccb))
eris.OVOV = eris.feri1.create_dataset('OVOV', (noccb,nvirb,noccb,nvirb), 'f8', chunks=(noccb,1,noccb,nvirb))
eris.OVVV = eris.feri1.create_dataset('OVVV', (noccb,nvirb,nvirb_pair), 'f8')
eris.VVVV = eris.feri1.create_dataset('VVVV', (nvirb_pair,nvirb_pair), 'f8')
eris.OOOO[:] = dot(LOO.T, LOO).reshape(noccb,noccb,noccb,noccb)
eris.OVOO[:] = dot(LOV.T, LOO).reshape(noccb,nvirb,noccb,noccb)
eris.OOVV[:] = lib.unpack_tril(dot(LOO.T, LVV)).reshape(noccb,noccb,nvirb,nvirb)
eris.OVVO[:] = dot(LOV.T, LVO).reshape(noccb,nvirb,nvirb,noccb)
eris.OVOV[:] = dot(LOV.T, LOV).reshape(noccb,nvirb,noccb,nvirb)
eris.OVVV[:] = dot(LOV.T, LVV).reshape(noccb,nvirb,nvirb_pair)
eris.VVVV[:] = dot(LVV.T, LVV)
# (aa|bb)
eris.ooOO = eris.feri1.create_dataset('ooOO', (nocca,nocca,noccb,noccb), 'f8')
eris.ooVV = eris.feri1.create_dataset('ooVV', (nocca,nocca,nvirb,nvirb), 'f8', chunks=(nocca,nocca,1,nvirb))
eris.ovOO = eris.feri1.create_dataset('ovOO', (nocca,nvira,noccb,noccb), 'f8', chunks=(nocca,1,noccb,noccb))
eris.ovVO = eris.feri1.create_dataset('ovVO', (nocca,nvira,nvirb,noccb), 'f8', chunks=(nocca,1,nvirb,noccb))
eris.ovOV = eris.feri1.create_dataset('ovOV', (nocca,nvira,noccb,nvirb), 'f8', chunks=(nocca,1,noccb,nvirb))
eris.ovVV = eris.feri1.create_dataset('ovVV', (nocca,nvira,nvirb_pair), 'f8')
eris.vvVV = eris.feri1.create_dataset('vvVV', (nvira_pair,nvirb_pair), 'f8')
eris.ooOO[:] = dot(Loo.T, LOO).reshape(nocca,nocca,noccb,noccb)
eris.ovOO[:] = dot(Lov.T, LOO).reshape(nocca,nvira,noccb,noccb)
eris.ooVV[:] = lib.unpack_tril(dot(Loo.T, LVV)).reshape(nocca,nocca,nvirb,nvirb)
eris.ovVO[:] = dot(Lov.T, LVO).reshape(nocca,nvira,nvirb,noccb)
eris.ovOV[:] = dot(Lov.T, LOV).reshape(nocca,nvira,noccb,nvirb)
eris.ovVV[:] = dot(Lov.T, LVV).reshape(nocca,nvira,nvirb_pair)
eris.vvVV[:] = dot(Lvv.T, LVV)
# (bb|aa)
eris.OOvv = eris.feri1.create_dataset('OOvv', (noccb,noccb,nvira,nvira), 'f8', chunks=(noccb,noccb,1,nvira))
eris.OVoo = eris.feri1.create_dataset('OVoo', (noccb,nvirb,nocca,nocca), 'f8', chunks=(noccb,1,nocca,nocca))
eris.OVvo = eris.feri1.create_dataset('OVvo', (noccb,nvirb,nvira,nocca), 'f8', chunks=(noccb,1,nvira,nocca))
eris.OVvv = eris.feri1.create_dataset('OVvv', (noccb,nvirb,nvira_pair), 'f8')
eris.OVoo[:] = dot(LOV.T, Loo).reshape(noccb,nvirb,nocca,nocca)
eris.OOvv[:] = lib.unpack_tril(dot(LOO.T, Lvv)).reshape(noccb,noccb,nvira,nvira)
eris.OVvo[:] = dot(LOV.T, Lvo).reshape(noccb,nvirb,nvira,nocca)
eris.OVvv[:] = dot(LOV.T, Lvv).reshape(noccb,nvirb,nvira_pair)
log.timer('CCSD integral transformation', *cput0)
return eris
def _make_eris_outcore(mycc, mo_coeff=None):
eris = _ChemistsERIs()
eris._common_init_(mycc, mo_coeff)
nocca, noccb = mycc.nocc
nmoa, nmob = mycc.nmo
nvira, nvirb = nmoa-nocca, nmob-noccb
moa = eris.mo_coeff[0]
mob = eris.mo_coeff[1]
nmoa = moa.shape[1]
nmob = mob.shape[1]
orboa = moa[:,:nocca]
orbob = mob[:,:noccb]
orbva = moa[:,nocca:]
orbvb = mob[:,noccb:]
eris.feri = lib.H5TmpFile()
eris.oooo = eris.feri.create_dataset('oooo', (nocca,nocca,nocca,nocca), 'f8')
eris.ovoo = eris.feri.create_dataset('ovoo', (nocca,nvira,nocca,nocca), 'f8')
eris.ovov = eris.feri.create_dataset('ovov', (nocca,nvira,nocca,nvira), 'f8')
eris.oovv = eris.feri.create_dataset('oovv', (nocca,nocca,nvira,nvira), 'f8')
eris.ovvo = eris.feri.create_dataset('ovvo', (nocca,nvira,nvira,nocca), 'f8')
eris.ovvv = eris.feri.create_dataset('ovvv', (nocca,nvira,nvira*(nvira+1)//2), 'f8')
#eris.vvvv = eris.feri.create_dataset('vvvv', (nvira,nvira,nvira,nvira), 'f8')
eris.OOOO = eris.feri.create_dataset('OOOO', (noccb,noccb,noccb,noccb), 'f8')
eris.OVOO = eris.feri.create_dataset('OVOO', (noccb,nvirb,noccb,noccb), 'f8')
eris.OVOV = eris.feri.create_dataset('OVOV', (noccb,nvirb,noccb,nvirb), 'f8')
eris.OOVV = eris.feri.create_dataset('OOVV', (noccb,noccb,nvirb,nvirb), 'f8')
eris.OVVO = eris.feri.create_dataset('OVVO', (noccb,nvirb,nvirb,noccb), 'f8')
eris.OVVV = eris.feri.create_dataset('OVVV', (noccb,nvirb,nvirb*(nvirb+1)//2), 'f8')
#eris.VVVV = eris.feri.create_dataset('VVVV', (nvirb,nvirb,nvirb,nvirb), 'f8')
eris.ooOO = eris.feri.create_dataset('ooOO', (nocca,nocca,noccb,noccb), 'f8')
eris.ovOO = eris.feri.create_dataset('ovOO', (nocca,nvira,noccb,noccb), 'f8')
eris.ovOV = eris.feri.create_dataset('ovOV', (nocca,nvira,noccb,nvirb), 'f8')
eris.ooVV = eris.feri.create_dataset('ooVV', (nocca,nocca,nvirb,nvirb), 'f8')
eris.ovVO = eris.feri.create_dataset('ovVO', (nocca,nvira,nvirb,noccb), 'f8')
eris.ovVV = eris.feri.create_dataset('ovVV', (nocca,nvira,nvirb*(nvirb+1)//2), 'f8')
#eris.vvVV = eris.feri.create_dataset('vvVV', (nvira,nvira,nvirb,nvirb), 'f8')
eris.OVoo = eris.feri.create_dataset('OVoo', (noccb,nvirb,nocca,nocca), 'f8')
eris.OOvv = eris.feri.create_dataset('OOvv', (noccb,noccb,nvira,nvira), 'f8')
eris.OVvo = eris.feri.create_dataset('OVvo', (noccb,nvirb,nvira,nocca), 'f8')
eris.OVvv = eris.feri.create_dataset('OVvv', (noccb,nvirb,nvira*(nvira+1)//2), 'f8')
cput1 = logger.process_clock(), logger.perf_counter()
mol = mycc.mol
# <ij||pq> = <ij|pq> - <ij|qp> = (ip|jq) - (iq|jp)
tmpf = lib.H5TmpFile()
if nocca > 0:
ao2mo.general(mol, (orboa,moa,moa,moa), tmpf, 'aa')
buf = np.empty((nmoa,nmoa,nmoa))
for i in range(nocca):
lib.unpack_tril(tmpf['aa'][i*nmoa:(i+1)*nmoa], out=buf)
eris.oooo[i] = buf[:nocca,:nocca,:nocca]
eris.ovoo[i] = buf[nocca:,:nocca,:nocca]
eris.ovov[i] = buf[nocca:,:nocca,nocca:]
eris.oovv[i] = buf[:nocca,nocca:,nocca:]
eris.ovvo[i] = buf[nocca:,nocca:,:nocca]
eris.ovvv[i] = lib.pack_tril(buf[nocca:,nocca:,nocca:])
del (tmpf['aa'])
if noccb > 0:
buf = np.empty((nmob,nmob,nmob))
ao2mo.general(mol, (orbob,mob,mob,mob), tmpf, 'bb')
for i in range(noccb):
lib.unpack_tril(tmpf['bb'][i*nmob:(i+1)*nmob], out=buf)
eris.OOOO[i] = buf[:noccb,:noccb,:noccb]
eris.OVOO[i] = buf[noccb:,:noccb,:noccb]
eris.OVOV[i] = buf[noccb:,:noccb,noccb:]
eris.OOVV[i] = buf[:noccb,noccb:,noccb:]
eris.OVVO[i] = buf[noccb:,noccb:,:noccb]
eris.OVVV[i] = lib.pack_tril(buf[noccb:,noccb:,noccb:])
del (tmpf['bb'])
if nocca > 0:
buf = np.empty((nmoa,nmob,nmob))
ao2mo.general(mol, (orboa,moa,mob,mob), tmpf, 'ab')
for i in range(nocca):
lib.unpack_tril(tmpf['ab'][i*nmoa:(i+1)*nmoa], out=buf)
eris.ooOO[i] = buf[:nocca,:noccb,:noccb]
eris.ovOO[i] = buf[nocca:,:noccb,:noccb]
eris.ovOV[i] = buf[nocca:,:noccb,noccb:]
eris.ooVV[i] = buf[:nocca,noccb:,noccb:]
eris.ovVO[i] = buf[nocca:,noccb:,:noccb]
eris.ovVV[i] = lib.pack_tril(buf[nocca:,noccb:,noccb:])
del (tmpf['ab'])
if noccb > 0:
buf = np.empty((nmob,nmoa,nmoa))
ao2mo.general(mol, (orbob,mob,moa,moa), tmpf, 'ba')
for i in range(noccb):
lib.unpack_tril(tmpf['ba'][i*nmob:(i+1)*nmob], out=buf)
eris.OVoo[i] = buf[noccb:,:nocca,:nocca]
eris.OOvv[i] = buf[:noccb,nocca:,nocca:]
eris.OVvo[i] = buf[noccb:,nocca:,:nocca]
eris.OVvv[i] = lib.pack_tril(buf[noccb:,nocca:,nocca:])
del (tmpf['ba'])
buf = None
cput1 = logger.timer_debug1(mycc, 'transforming oopq, ovpq', *cput1)
if not mycc.direct:
ao2mo.full(mol, orbva, eris.feri, dataname='vvvv')
ao2mo.full(mol, orbvb, eris.feri, dataname='VVVV')
ao2mo.general(mol, (orbva,orbva,orbvb,orbvb), eris.feri, dataname='vvVV')
eris.vvvv = eris.feri['vvvv']
eris.VVVV = eris.feri['VVVV']
eris.vvVV = eris.feri['vvVV']
cput1 = logger.timer_debug1(mycc, 'transforming vvvv', *cput1)
return eris
[docs]
def make_tau(t2, t1, r1, fac=1, out=None):
t1a, t1b = t1
r1a, r1b = r1
tau1aa = make_tau_aa(t2[0], t1a, r1a, fac, out)
tau1bb = make_tau_aa(t2[2], t1b, r1b, fac, out)
tau1ab = make_tau_ab(t2[1], t1, r1, fac, out)
return tau1aa, tau1ab, tau1bb
[docs]
def make_tau_aa(t2aa, t1a, r1a, fac=1, out=None):
tau1aa = np.einsum('ia,jb->ijab', t1a, r1a)
tau1aa-= np.einsum('ia,jb->jiab', t1a, r1a)
tau1aa = tau1aa - tau1aa.transpose(0,1,3,2)
tau1aa *= fac * .5
tau1aa += t2aa
return tau1aa
[docs]
def make_tau_ab(t2ab, t1, r1, fac=1, out=None):
t1a, t1b = t1
r1a, r1b = r1
tau1ab = np.einsum('ia,jb->ijab', t1a, r1b)
tau1ab+= np.einsum('ia,jb->ijab', r1a, t1b)
tau1ab *= fac * .5
tau1ab += t2ab
return tau1ab
def _flops(nocc, nmo):
nocca, noccb = nocc
nmoa, nmob = nmo
nvira, nvirb = nmoa - nocca, nmob - noccb
# vvvv
fp = nocca**2 * nvira**4
fp += noccb**2 * nvirb**4
fp += nocca * nvira**2 * noccb * nvirb**2 * 2
# ovvv
fp += nocca**2 * nvira**3 * 2
fp += nocca**2 * nvira**3 * 2
fp += nocca**2 * nvira**3 * 2
fp += nocca**3 * nvira**3 * 2
fp += nocca**3 * nvira**2 * 2
# OVVV
fp += noccb**2 * nvirb**3 * 2
fp += noccb**2 * nvirb**3 * 2
fp += noccb**2 * nvirb**3 * 2
fp += noccb**3 * nvirb**3 * 2
fp += noccb**3 * nvirb**2 * 2
# ovVV
fp += nocca * nvira * noccb * nvirb**2 * 2
fp += nocca**2 * nvira * nvirb**2 * 2
fp += nocca * nvira * noccb * nvirb**2 * 2
fp += nocca * nvira * noccb * nvirb**2 * 2
fp += nocca**2 * nvira * noccb * nvirb**2 * 2
fp += nocca**2 * nvira * noccb * nvirb * 2
# OVvv
fp += nocca * nvira**2 * noccb * nvirb * 2
fp += nvira**2 * noccb**2 * nvirb * 2
fp += nocca * nvira**2 * noccb * nvirb * 2
fp += nocca * nvira**2 * noccb * nvirb * 2
fp += nocca * nvira**2 * noccb**2 * nvirb * 2
fp += nocca * nvira * noccb**2 * nvirb * 2
fp += nocca**4 * nvira * 2
fp += nocca**4 * nvira**2 * 2
fp += nocca**4 * nvira**2 * 2
fp += nocca**3 * nvira**2 * 2
fp += nocca**3 * nvira**2 * 2
fp += nocca**2 * nvira**3 * 2
fp += nocca**3 * nvira**2 * 2
fp += nocca**3 * nvira**3 * 2
fp += nocca**2 * nvira**2 * noccb * nvirb * 2
fp += nocca**3 * nvira**2 * 2
fp += nocca**3 * nvira**2 * 2
fp += noccb**4 * nvirb * 2
fp += noccb**4 * nvirb**2 * 2
fp += noccb**4 * nvirb**2 * 2
fp += noccb**3 * nvirb**2 * 2
fp += noccb**3 * nvirb**2 * 2
fp += noccb**2 * nvirb**3 * 2
fp += noccb**3 * nvirb**2 * 2
fp += noccb**3 * nvirb**3 * 2
fp += noccb**2 * nvirb**2 * nocca * nvira * 2
fp += noccb**3 * nvirb**2 * 2
fp += noccb**3 * nvirb**2 * 2
fp += nocca**2 * nvira * noccb * nvirb * 2
fp += nocca**2 * nvira * noccb * nvirb * 2
fp += nocca**2 * noccb * nvirb**2 * 2
fp += noccb**2 * nvirb * nocca * nvira * 2
fp += noccb**2 * nvirb * nocca * nvira * 2
fp += noccb**2 * nocca * nvira**2 * 2
fp += nocca**2 * noccb**2 * nvirb * 2
fp += nocca**2 * nvira * noccb**2 * 2
fp += nocca**2 * nvira * noccb**2 * nvirb * 2
fp += nocca**2 * nvira * noccb**2 * nvirb * 2
fp += nocca * nvira**2 * noccb * nvirb * 2
fp += nocca * nvira * noccb * nvirb**2 * 2
fp += nocca * nvira**2 * noccb * nvirb * 2
fp += nocca * nvira * noccb * nvirb**2 * 2
fp += nocca**2 * nvira**2 * noccb * nvirb * 2
fp += nocca * nvira * noccb**2 * nvirb**2 * 2
fp += nocca**2 * nvira**2 * noccb * nvirb * 2
fp += nocca * nvira * noccb**2 * nvirb**2 * 2
fp += nocca**2 * nvira * noccb * nvirb**2 * 2
fp += nocca * nvira**2 * noccb**2 * nvirb * 2
fp += nocca * nvira * noccb**2 * nvirb * 2
fp += nocca**2 * nvira * noccb * nvirb * 2
fp += nocca * nvira * noccb**2 * nvirb * 2
fp += nocca**2 * nvira * noccb * nvirb * 2
fp += nocca**2 * noccb * nvirb**2 * 2
fp += nocca * nvira**2 * noccb**2 * 2
fp += nocca**3 * nvira**2 * 2
fp += nocca**3 * nvira**2 * 2
fp += noccb**3 * nvirb**2 * 2
fp += noccb**3 * nvirb**2 * 2
fp += nocca**2 * nvira * noccb * nvirb * 2
fp += nocca**2 * noccb * nvirb**2 * 2
fp += nocca**2 * nvira * noccb * nvirb * 2
fp += noccb**2 * nvirb * nocca * nvira * 2
fp += noccb**2 * nocca * nvira**2 * 2
fp += noccb**2 * nvirb * nocca * nvira * 2
fp += nocca**3 * nvira**3 * 2
fp += nocca**2 * nvira**2 * noccb * nvirb * 2
fp += noccb**3 * nvirb**3 * 2
fp += noccb**2 * nvirb**2 * nocca * nvira * 2
fp += nocca**2 * nvira**2 * noccb * nvirb * 2
fp += nocca * nvira * noccb**2 * nvirb**2 * 2
fp += nocca * nvira**2 * noccb**2 * nvirb * 2
fp += nocca**2 * nvira**2 * noccb * nvirb * 2
fp += nocca**2 * nvira**2 * noccb * nvirb * 2
fp += nocca**2 * nvira * noccb * nvirb**2 * 2
fp += nocca**2 * nvira**3 * 2
fp += noccb**2 * nvirb**3 * 2
fp += nocca * nvira * noccb * nvirb**2 * 2
fp += nocca * nvira**2 * noccb * nvirb * 2
fp += nocca**3 * nvira**2 * 2
fp += noccb**3 * nvirb**2 * 2
fp += nocca * nvira * noccb**2 * nvirb * 2
fp += nocca**2 * nvira * noccb * nvirb * 2
fp += nocca**2 * nvira**3 * 2
fp += noccb**2 * nvirb**3 * 2
fp += nocca**2 * nvira * noccb * nvirb * 2
fp += nocca * nvira * noccb**2 * nvirb * 2
return fp
if __name__ == '__main__':
from pyscf import gto
mol = gto.Mole()
mol.atom = [['O', (0., 0., 0.)],
['O', (1.21, 0., 0.)]]
mol.basis = 'cc-pvdz'
mol.spin = 2
mol.build()
mf = scf.UHF(mol).run()
# Freeze 1s electrons
# also acceptable
#frozen = 4 or [2,2]
frozen = [[0,1], [0,1]]
ucc = UCCSD(mf, frozen=frozen)
eris = ucc.ao2mo()
ecc, t1, t2 = ucc.kernel(eris=eris)
print(ecc - -0.3486987472235819)
mol = gto.Mole()
mol.atom = [
[8 , (0. , 0. , 0.)],
[1 , (0. , -0.757 , 0.587)],
[1 , (0. , 0.757 , 0.587)]]
mol.basis = 'cc-pvdz'
mol.spin = 0
mol.build()
mf = scf.UHF(mol).run()
mycc = UCCSD(mf)
mycc.direct = True
ecc, t1, t2 = mycc.kernel()
print(ecc - -0.2133432712431435)
print(mycc.ccsd_t() - -0.003060021865720902)
e,v = mycc.ipccsd(nroots=8)
print(e[0] - 0.4335604332073799)
print(e[2] - 0.5187659896045407)
print(e[4] - 0.6782876002229172)
e,v = mycc.eaccsd(nroots=8)
print(e[0] - 0.16737886338859731)
print(e[2] - 0.24027613852009164)
print(e[4] - 0.51006797826488071)
e,v = mycc.eeccsd(nroots=4)
print(e[0] - 0.2757159395886167)
print(e[1] - 0.2757159395886167)
print(e[2] - 0.2757159395886167)
print(e[3] - 0.3005716731825082)