Source code for pyscf.mp.mp2f12_slow

#!/usr/bin/env python
# Copyright 2014-2020 The PySCF Developers. All Rights Reserved.
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# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
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#     http://www.apache.org/licenses/LICENSE-2.0
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'''
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)