#!/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.
'''
MP2-F12 (In testing)
Refs:
* JCC 32, 2492 (2011); DOI:10.1002/jcc.21825
* JCP 139, 084112 (2013); DOI:10.1063/1.4818753
With strong orthogonalization ansatz 2
'''
import warnings
from functools import reduce
import numpy
import scipy.linalg
from pyscf import lib
from pyscf.lib import logger
from pyscf import gto
from pyscf import ao2mo
from pyscf.scf import jk
from pyscf.mp import mp2
warnings.warn('Module MP2-F12 is under testing')
# The cabs space, the complimentary space to the OBS.
[docs]
def find_cabs(mol, auxmol, lindep=1e-8):
cabs_mol = gto.conc_mol(mol, auxmol)
nao = mol.nao_nr()
s = cabs_mol.intor_symmetric('int1e_ovlp')
ls12 = scipy.linalg.solve(s[:nao,:nao], s[:nao,nao:], assume_a='pos')
s[nao:,nao:] -= s[nao:,:nao].dot(ls12)
w, v = scipy.linalg.eigh(s[nao:,nao:])
c2 = v[:,w>lindep]/numpy.sqrt(w[w>lindep])
c1 = ls12.dot(c2)
return cabs_mol, numpy.vstack((-c1,c2))
[docs]
def trans(eri, mos):
naoi, nmoi = mos[0].shape
naoj, nmoj = mos[1].shape
naok, nmok = mos[2].shape
naol, nmol = mos[3].shape
eri1 = numpy.dot(mos[0].T, eri.reshape(naoi,-1))
eri1 = eri1.reshape(nmoi,naoj,naok,naol)
eri1 = numpy.dot(mos[1].T, eri1.transpose(1,0,2,3).reshape(naoj,-1))
eri1 = eri1.reshape(nmoj,nmoi,naok,naol).transpose(1,0,2,3)
eri1 = numpy.dot(eri1.transpose(0,1,3,2).reshape(-1,naok), mos[2])
eri1 = eri1.reshape(nmoi,nmoj,naol,nmok).transpose(0,1,3,2)
eri1 = numpy.dot(eri1.reshape(-1,naol), mos[3])
eri1 = eri1.reshape(nmoi,nmoj,nmok,nmol)
return eri1
[docs]
def energy_f12(mf, auxmol, zeta):
logger.info(mf, '******** MP2-F12 (In testing) ********')
mol = mf.mol
mo_coeff = mf.mo_coeff
mo_energy = mf.mo_energy
nocc = numpy.count_nonzero(mf.mo_occ == 2)
cabs_mol, cabs_coeff = find_cabs(mol, auxmol)
nao, nmo = mo_coeff.shape
nca = cabs_coeff.shape[0]
mo_o = mo_coeff[:,:nocc]
Pcoeff = numpy.vstack((mo_coeff, numpy.zeros((nca-nao, nmo))))
Pcoeff = numpy.hstack((Pcoeff, cabs_coeff))
obs = (0, mol.nbas)
cbs = (0, cabs_mol.nbas)
mol.set_f12_zeta(zeta)
Y = mol.intor('int2e_yp')
Y = trans(Y, [mo_o]*4)
cabs_mol.set_f12_zeta(zeta)
R = cabs_mol.intor('int2e_stg', shls_slice=obs+cbs+obs+cbs)
RmPnQ = trans(R, [mo_o, Pcoeff, mo_o, Pcoeff])
Rmpnq = RmPnQ[:,:nmo,:,:nmo]
Rmlnc = RmPnQ[:nocc,:nocc,:nocc,nmo:]
Rmcnl = Rmlnc.transpose(2,3,0,1)
Rpiqj = Rmpnq.transpose(1,0,3,2)
Rlicj = Rmlnc.transpose(0,1,3,2)
Rcilj = Rlicj.transpose(2,3,0,1)
RRiQj = RmPnQ.transpose(1,0,3,2)
RmPnk = RmPnQ[:,:,:,:nocc]
RQikj = RmPnk.transpose(1,0,2,3)
Rmknc = Rmlnc
Rmpna = Rmpnq[:,:,:,nocc:nmo]
Rqiaj = Rpiqj[:,:,nocc:nmo,:]
RPicj = RRiQj[:,:,nmo:,:]
Rmcnb = RmPnQ[:,nmo:,:,nocc:nmo]
Rpibj = Rqiaj
cabs_mol.set_f12_zeta(zeta*2)
Rbar = cabs_mol.intor('int2e_stg', shls_slice=cbs+obs+obs+obs)
Rbar = Rbar.reshape(nca,nao,nao,nao)
Rbar_minj = trans(Rbar[:nao], [mo_o]*4)
Rbar_miPj = trans(Rbar, [Pcoeff, mo_o, mo_o, mo_o]).transpose(2,3,0,1)
tau = Rbar[:nao] * zeta**2
tau = trans(tau, [mo_o]*4)
v = cabs_mol.intor('int2e', shls_slice=cbs+obs+obs+obs)
v = v.reshape(nca,nao,nao,nao)
vpiqj = trans(v[:nao], [mo_coeff, mo_o, mo_coeff, mo_o])
vlicj = trans(v, [cabs_coeff, mo_o, mo_o, mo_o]).transpose(2,3,0,1)
vcilj = vlicj.transpose(2,3,0,1)
fPQ = mf.get_hcore(cabs_mol)
dm = numpy.dot(mo_o, mo_o.T) * 2
v = cabs_mol.intor('int2e', shls_slice=cbs+cbs+obs+obs)
v = v.reshape(nca,nca,nao,nao)
fPQ += numpy.einsum('pqij,ji->pq', v, dm)
fPQ = reduce(numpy.dot, (Pcoeff.T, fPQ, Pcoeff))
v = cabs_mol.intor('int2e', shls_slice=cbs+obs+obs+cbs)
v = v.reshape(nca,nao,nao,nca)
kPQ = numpy.einsum('pijq,ij->pq', v, dm)*.5
kPQ = reduce(numpy.dot, (Pcoeff.T, kPQ, Pcoeff))
tPQ = cabs_mol.intor_symmetric('int1e_kin')
tPQ = reduce(numpy.dot, (Pcoeff.T, tPQ, Pcoeff))
hPQ = fPQ - tPQ # hartree term
fPQ = hPQ - kPQ
tminj = numpy.zeros([nocc]*4)
for i in range(nocc):
for j in range(nocc):
tminj[i,i,j,j] = -3./(8*zeta)
tminj[i,j,j,i] = -1./(8*zeta)
tminj[i,i,i,i] = -.5/zeta
V = Y
V-= numpy.einsum('mpnq,piqj->minj', Rmpnq, vpiqj)
V-= numpy.einsum('mlnc,licj->minj', Rmlnc, vlicj)
V-= numpy.einsum('mcnl,cilj->minj', Rmcnl, vcilj)
emp2_f12 = numpy.einsum('minj,minj', V, tminj) * 4
emp2_f12-= numpy.einsum('minj,nimj', V, tminj) * 2
X = Rbar_minj
X-= numpy.einsum('mpnq,piqj->minj', Rmpnq, Rpiqj)
X-= numpy.einsum('mlnc,licj->minj', Rmlnc, Rlicj)
X-= numpy.einsum('mcnl,cilj->minj', Rmcnl, Rcilj)
tmp = numpy.einsum('miPj,nP->minj', Rbar_miPj, hPQ[:nocc])
B = (tmp + tmp.transpose(1,0,3,2)) * .5
tmp = numpy.einsum('mPnQ,PR->mRnQ', RmPnQ, kPQ)
B -= numpy.einsum('mRnQ,RiQj->minj', tmp, RRiQj)
tmp = numpy.einsum('mPnk,PQ->mQnk', RmPnk, fPQ)
B -= numpy.einsum('mQnk,Qikj->minj', tmp, RQikj)
tmp = numpy.einsum('mknc,kl->mlnc', Rmknc, fPQ[:nocc,:nocc])
B += numpy.einsum('mlnc,licj->minj', tmp, Rlicj)
tmp = numpy.einsum('mpna,pq->mqna', Rmpna, fPQ[:nmo,:nmo])
B -= numpy.einsum('mqna,qiaj->minj', tmp, Rqiaj)
tmp = numpy.einsum('mknc,kP->mPnc', Rmknc, fPQ[:nocc])
tmp1= numpy.einsum('mPnc,Picj->minj', tmp, RPicj)
tmp = numpy.einsum('mcnb,cp->mpnb', Rmcnb, fPQ[nmo:,:nmo])
tmp1+= numpy.einsum('mpnb,pibj->minj', tmp, Rpibj)
B -= tmp1 + tmp1.transpose(1,0,3,2)
B = B + B.transpose(2,3,0,1)
B += tau
e_mn = lib.direct_sum('i+j->ij', mo_energy[:nocc], mo_energy[:nocc])
tmp = numpy.einsum('mknl,kilj->minj', tminj, B)
emp2_f12+= numpy.einsum('minj,minj', tmp, tminj) * 2
emp2_f12-= numpy.einsum('minj,nimj', tmp, tminj)
tmp = numpy.einsum('mknl,kilj->minj', tminj, X)
emp2_f12-= numpy.einsum('mn,minj,minj', e_mn, tmp, tminj) * 2
emp2_f12+= numpy.einsum('mn,minj,nimj', e_mn, tmp, tminj)
return emp2_f12
if __name__ == '__main__':
from pyscf import scf
mol = gto.Mole()
#mol.atom = [
# [8 , (0. , 0. , 0.)],
# [1 , (0. , -0.757 , 0.587)],
# [1 , (0. , 0.757 , 0.587)]]
mol.atom = 'Ne 0 0 0'
mol.basis = 'cc-pvdz'
mol.build()
mf = scf.RHF(mol)
print(mf.scf())
e = mp2.MP2(mf).kernel()[0]
auxmol = mol.copy()
#auxmol.basis = 'cc-pVDZ-F12-OptRI'
auxmol.basis = ('ccpvdz-fit', 'cc-pVDZ-F12-OptRI')
#auxmol.basis = 'cc-pVTZ'
auxmol.build(False, False)
print('MP2', e)
e+= energy_f12(mf, auxmol, 1.)
print('MP2-F12', e)
print('e_tot', e+mf.e_tot)
