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/*
CheMPS2: a spin-adapted implementation of DMRG for ab initio quantum chemistry
Copyright (C) 2013-2018 Sebastian Wouters
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License along
with this program; if not, write to the Free Software Foundation, Inc.,
51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
*/
#include <stdlib.h>
#include <sys/time.h>
#include <unistd.h>
#include <iostream>
#include "Cumulant.h"
/*void CheMPS2::Cumulant::gamma4_fock_contract_ham_slow(const Problem * prob, const ThreeDM * the3DM, const TwoDM * the2DM, double * fock, double * result){
struct timeval start, end;
gettimeofday(&start, NULL);
const int L = prob->gL();
for ( int cnt = 0; cnt < L*L*L*L*L*L; cnt++ ){ result[ cnt ] = 0.0; }
int * irreps = new int[ L ];
for ( int orb = 0; orb < L; orb++ ){ irreps[ orb ] = prob->gIrrep(( prob->gReorder() ) ? prob->gf1( orb ) : orb ); }
#pragma omp parallel for schedule(dynamic)
for ( int i = 0; i < L; i++ ){
for ( int j = i; j < L; j++ ){
for ( int k = i; k < L; k++ ){
const int irrep_ijk = Irreps::directProd( Irreps::directProd( irreps[ i ], irreps[ j ] ), irreps[ k ] );
for ( int p = i; p < L; p++ ){
for ( int q = i; q < L; q++ ){
for ( int r = q; r < L; r++ ){
const int irrep_pqr = Irreps::directProd( Irreps::directProd( irreps[ p ], irreps[ q ] ), irreps[ r ] );
if ( irrep_ijk == irrep_pqr ){
double value = 0.0;
for ( int l = 0; l < L; l++ ){
for ( int s = 0; s < L; s++ ){
if ( irreps[ l ] == irreps[ s ] ){
value += fock[ l + L * s ] * gamma4_ham(prob, the3DM, the2DM, i, j, k, l, p, q, r, s);
}
}
}
result[ i + L * ( j + L * ( k + L * ( p + L * ( q + L * r )))) ] = value;
result[ i + L * ( k + L * ( j + L * ( p + L * ( r + L * q )))) ] = value;
result[ j + L * ( i + L * ( k + L * ( q + L * ( p + L * r )))) ] = value;
result[ k + L * ( i + L * ( j + L * ( r + L * ( p + L * q )))) ] = value;
result[ j + L * ( k + L * ( i + L * ( q + L * ( r + L * p )))) ] = value;
result[ k + L * ( j + L * ( i + L * ( r + L * ( q + L * p )))) ] = value;
result[ p + L * ( q + L * ( r + L * ( i + L * ( j + L * k )))) ] = value;
result[ p + L * ( r + L * ( q + L * ( i + L * ( k + L * j )))) ] = value;
result[ q + L * ( p + L * ( r + L * ( j + L * ( i + L * k )))) ] = value;
result[ r + L * ( p + L * ( q + L * ( k + L * ( i + L * j )))) ] = value;
result[ q + L * ( r + L * ( p + L * ( j + L * ( k + L * i )))) ] = value;
result[ r + L * ( q + L * ( p + L * ( k + L * ( j + L * i )))) ] = value;
}
}
}
}
}
}
}
delete [] irreps;
gettimeofday(&end, NULL);
const double elapsed = (end.tv_sec - start.tv_sec) + 1e-6 * (end.tv_usec - start.tv_usec);
std::cout << "Cumulant :: Contraction of cu(4)-4RDM with CASPT2 Fock operator took " << elapsed << " seconds." << std::endl;
}*/
void CheMPS2::Cumulant::gamma4_fock_contract_ham(const Problem * prob, const ThreeDM * the3DM, const TwoDM * the2DM, double * fock, double * result){
struct timeval start, end;
gettimeofday(&start, NULL);
const int L = prob->gL();
/* Clear result */
for ( int cnt = 0; cnt < L*L*L*L*L*L; cnt++ ){ result[ cnt ] = 0.0; }
/* Construct an array with the orbital irreps in Hamiltonian indices */
int * irreps = new int[ L ];
for ( int orb = 0; orb < L; orb++ ){ irreps[ orb ] = prob->gIrrep(( prob->gReorder() ) ? prob->gf1( orb ) : orb ); }
/* Helper arrays with partial (mult) or full (dot) contractions of objects with the CASPT2 Fock operator */
double * G3dotF = new double[ L*L*L*L ];
double * lambda2 = new double[ L*L*L*L ];
double * G2multF = new double[ L*L*L*L ];
double * L2multF = new double[ L*L*L*L ];
double * gamma1 = new double[ L*L ];
double * G1multF = new double[ L*L ];
double * G2dotF = new double[ L*L ];
double * L2dotF = new double[ L*L ];
for ( int cnt = 0; cnt < L*L*L*L; cnt++ ){ G3dotF[ cnt ] = 0.0; }
for ( int cnt = 0; cnt < L*L*L*L; cnt++ ){ lambda2[ cnt ] = 0.0; }
for ( int cnt = 0; cnt < L*L*L*L; cnt++ ){ G2multF[ cnt ] = 0.0; }
for ( int cnt = 0; cnt < L*L*L*L; cnt++ ){ L2multF[ cnt ] = 0.0; }
for ( int cnt = 0; cnt < L*L; cnt++ ){ gamma1[ cnt ] = 0.0; }
for ( int cnt = 0; cnt < L*L; cnt++ ){ G1multF[ cnt ] = 0.0; }
for ( int cnt = 0; cnt < L*L; cnt++ ){ G2dotF[ cnt ] = 0.0; }
for ( int cnt = 0; cnt < L*L; cnt++ ){ L2dotF[ cnt ] = 0.0; }
double G1dotF = 0.0;
/* Fill gamma1 */
for ( int i = 0; i < L; i++ ){
for ( int j = i; j < L; j++ ){
const double value = the2DM->get1RDM_HAM( i, j );
gamma1[ i + L * j ] = value;
gamma1[ j + L * i ] = value;
}
}
/* Build G3dotF[i,j,p,q] = sum_[l,s] Gamma3[i,j,l,p,q,s] F[l,s]
Build lambda2[i,j,p,q] = Lambda2[i,j,p,q] */
for ( int i = 0; i < L; i++ ){
for ( int j = i; j < L; j++ ){
const int irrep_ij = Irreps::directProd( irreps[ i ], irreps[ j ] );
for ( int p = i; p < L; p++ ){
for ( int q = i; q < L; q++ ){
const int irrep_pq = Irreps::directProd( irreps[ p ], irreps[ q ] );
if ( irrep_ij == irrep_pq ){
{ // sum_[l,s] Gamma3[i,j,l,p,q,s] F[l,s]
double value = 0.0;
for ( int l = 0; l < L; l++ ){
for ( int s = 0; s < L; s++ ){
if ( irreps[ l ] == irreps[ s ] ){
value += the3DM->get_ham_index(i,j,l,p,q,s) * fock[ l + L * s ];
}
}
}
G3dotF[ i + L * ( j + L * ( p + L * q )) ] = value;
G3dotF[ j + L * ( i + L * ( q + L * p )) ] = value;
G3dotF[ p + L * ( q + L * ( i + L * j )) ] = value;
G3dotF[ q + L * ( p + L * ( j + L * i )) ] = value;
}
{ // Lambda2[i,j,p,q]
const double val_lambda = the2DM->getTwoDMA_HAM( i, j, p, q )
- gamma1[ i + L * p ] * gamma1[ j + L * q ]
+ gamma1[ i + L * q ] * gamma1[ j + L * p ] * 0.5;
lambda2[ i + L * ( j + L * ( p + L * q )) ] = val_lambda;
lambda2[ j + L * ( i + L * ( q + L * p )) ] = val_lambda;
lambda2[ p + L * ( q + L * ( i + L * j )) ] = val_lambda;
lambda2[ q + L * ( p + L * ( j + L * i )) ] = val_lambda;
}
}
}
}
}
}
/* Build G1multF[i,j] = sum_[p] Gamma1[i,p] F[p,j]
Build G1dotF = sum_[i,j] Gamma1[i,j] F[j,i] */
for ( int i = 0; i < L; i++ ){
for ( int j = 0; j < L; j++ ){
if ( irreps[ i ] == irreps[ j ] ){
double value = 0.0;
for ( int p = 0; p < L; p++ ){
if ( irreps[ j ] == irreps[ p ] ){
value += gamma1[ i + L * p ] * fock[ p + L * j ];
}
}
G1multF[ i + L * j ] = value;
}
}
G1dotF += G1multF[ i * ( L + 1 ) ];
}
/* Build G2dotF[i,j] = sum_[p,q] Gamma2[i,p,j,q] F[p,q]
Build L2dotF[i,j] = sum_[p,q] Lambda2[i,p,j,q] F[p,q] */
for ( int i = 0; i < L; i++ ){
for ( int j = i; j < L; j++ ){
if ( irreps[ i ] == irreps[ j ] ){
double val_gamma = 0.0;
double val_lambda = 0.0;
for ( int p = 0; p < L; p++ ){
for ( int q = 0; q < L; q++ ){
if ( irreps[ p ] == irreps[ q ] ){
val_gamma += fock[ p + L * q ] * the2DM->getTwoDMA_HAM( i, p, j, q );
val_lambda += fock[ p + L * q ] * lambda2[ i + L * ( p + L * ( j + L * q )) ];
}
}
}
G2dotF[ i + L * j ] = val_gamma;
G2dotF[ j + L * i ] = val_gamma;
L2dotF[ i + L * j ] = val_lambda;
L2dotF[ j + L * i ] = val_lambda;
}
}
}
/* Build G2multF[i,s,j,k] = sum_[l] Gamma2[i,l,j,k] F[l,s]
Build L2multF[i,s,j,k] = sum_[l] Lambda2[i,l,j,k] F[l,s] */
for ( int i = 0; i < L; i++ ){
for ( int j = 0; j < L; j++ ){
const int irrep_ij = Irreps::directProd( irreps[ i ], irreps[ j ] );
for ( int k = 0; k < L; k++ ){
for ( int s = 0; s < L; s++ ){
const int irrep_ks = Irreps::directProd( irreps[ k ], irreps[ s ] );
if ( irrep_ij == irrep_ks ){
double val_gamma = 0.0;
double val_lambda = 0.0;
for ( int l = 0; l < L; l++ ){
if ( irreps[ l ] == irreps[ s ] ){
val_gamma += fock[ l + L * s ] * the2DM->getTwoDMA_HAM( i, l, j, k );
val_lambda += fock[ l + L * s ] * lambda2[ i + L * ( l + L * ( j + L * k ) ) ];
}
}
G2multF[ i + L * ( s + L * ( j + L * k ) ) ] = val_gamma;
L2multF[ i + L * ( s + L * ( j + L * k ) ) ] = val_lambda;
}
}
}
}
}
/* Fill result */
#pragma omp parallel for schedule(dynamic)
for ( int i = 0; i < L; i++ ){
for ( int j = i; j < L; j++ ){
for ( int k = i; k < L; k++ ){
const int irrep_ijk = Irreps::directProd( Irreps::directProd( irreps[ i ], irreps[ j ] ), irreps[ k ] );
for ( int p = i; p < L; p++ ){
for ( int q = i; q < L; q++ ){
for ( int r = q; r < L; r++ ){
const int irrep_pqr = Irreps::directProd( Irreps::directProd( irreps[ p ], irreps[ q ] ), irreps[ r ] );
if ( irrep_ijk == irrep_pqr ){
double dm3_contribution = 0.0;
double gamma2_part1 = 0.0;
double gamma2_part2 = 0.0;
double lambda2_part1 = 0.0;
double lambda2_part2 = 0.0;
for ( int ls = 0; ls < L; ls++ ){
dm3_contribution += ( the3DM->get_ham_index( ls, j, k, p, q, r ) * G1multF[ i + L * ls ]
+ the3DM->get_ham_index( i, ls, k, p, q, r ) * G1multF[ j + L * ls ]
+ the3DM->get_ham_index( i, j, ls, p, q, r ) * G1multF[ k + L * ls ]
+ the3DM->get_ham_index( i, j, k, ls, q, r ) * G1multF[ p + L * ls ]
+ the3DM->get_ham_index( i, j, k, p, ls, r ) * G1multF[ q + L * ls ]
+ the3DM->get_ham_index( i, j, k, p, q, ls ) * G1multF[ r + L * ls ] );
gamma2_part1 += ( the2DM->getTwoDMA_HAM( i, j, p, ls ) * G2multF[ k + L * ( ls + L * ( r + L * q )) ]
+ the2DM->getTwoDMA_HAM( i, j, ls, q ) * G2multF[ k + L * ( ls + L * ( r + L * p )) ]
+ the2DM->getTwoDMA_HAM( i, k, p, ls ) * G2multF[ j + L * ( ls + L * ( q + L * r )) ]
+ the2DM->getTwoDMA_HAM( i, k, ls, r ) * G2multF[ j + L * ( ls + L * ( q + L * p )) ]
+ the2DM->getTwoDMA_HAM( k, j, ls, q ) * G2multF[ i + L * ( ls + L * ( p + L * r )) ]
+ the2DM->getTwoDMA_HAM( k, j, r, ls ) * G2multF[ i + L * ( ls + L * ( p + L * q )) ] );
gamma2_part2 += ( the2DM->getTwoDMA_HAM( i, j, r, ls ) * ( G2multF[ k + L * ( ls + L * ( p + L * q )) ]
+ 0.5 * G2multF[ k + L * ( ls + L * ( q + L * p )) ] )
+ the2DM->getTwoDMA_HAM( i, j, ls, r ) * ( G2multF[ k + L * ( ls + L * ( q + L * p )) ]
+ 0.5 * G2multF[ k + L * ( ls + L * ( p + L * q )) ] )
+ the2DM->getTwoDMA_HAM( i, k, q, ls ) * ( G2multF[ j + L * ( ls + L * ( p + L * r )) ]
+ 0.5 * G2multF[ j + L * ( ls + L * ( r + L * p )) ] )
+ the2DM->getTwoDMA_HAM( i, k, ls, q ) * ( G2multF[ j + L * ( ls + L * ( r + L * p )) ]
+ 0.5 * G2multF[ j + L * ( ls + L * ( p + L * r )) ] )
+ the2DM->getTwoDMA_HAM( k, j, p, ls ) * ( G2multF[ i + L * ( ls + L * ( r + L * q )) ]
+ 0.5 * G2multF[ i + L * ( ls + L * ( q + L * r )) ] )
+ the2DM->getTwoDMA_HAM( k, j, ls, p ) * ( G2multF[ i + L * ( ls + L * ( q + L * r )) ]
+ 0.5 * G2multF[ i + L * ( ls + L * ( r + L * q )) ] ) );
lambda2_part1 += ( lambda2[ i + L * ( j + L * ( p + L * ls )) ] * L2multF[ k + L * ( ls + L * ( r + L * q )) ]
+ lambda2[ i + L * ( j + L * ( ls + L * q )) ] * L2multF[ k + L * ( ls + L * ( r + L * p )) ]
+ lambda2[ i + L * ( k + L * ( p + L * ls )) ] * L2multF[ j + L * ( ls + L * ( q + L * r )) ]
+ lambda2[ i + L * ( k + L * ( ls + L * r )) ] * L2multF[ j + L * ( ls + L * ( q + L * p )) ]
+ lambda2[ k + L * ( j + L * ( ls + L * q )) ] * L2multF[ i + L * ( ls + L * ( p + L * r )) ]
+ lambda2[ k + L * ( j + L * ( r + L * ls )) ] * L2multF[ i + L * ( ls + L * ( p + L * q )) ] );
lambda2_part2 += ( lambda2[ i + L * ( j + L * ( r + L * ls )) ] * ( L2multF[ k + L * ( ls + L * ( p + L * q )) ]
+ 0.5 * L2multF[ k + L * ( ls + L * ( q + L * p )) ] )
+ lambda2[ i + L * ( j + L * ( ls + L * r )) ] * ( L2multF[ k + L * ( ls + L * ( q + L * p )) ]
+ 0.5 * L2multF[ k + L * ( ls + L * ( p + L * q )) ] )
+ lambda2[ i + L * ( k + L * ( q + L * ls )) ] * ( L2multF[ j + L * ( ls + L * ( p + L * r )) ]
+ 0.5 * L2multF[ j + L * ( ls + L * ( r + L * p )) ] )
+ lambda2[ i + L * ( k + L * ( ls + L * q )) ] * ( L2multF[ j + L * ( ls + L * ( r + L * p )) ]
+ 0.5 * L2multF[ j + L * ( ls + L * ( p + L * r )) ] )
+ lambda2[ k + L * ( j + L * ( p + L * ls )) ] * ( L2multF[ i + L * ( ls + L * ( r + L * q )) ]
+ 0.5 * L2multF[ i + L * ( ls + L * ( q + L * r )) ] )
+ lambda2[ k + L * ( j + L * ( ls + L * p )) ] * ( L2multF[ i + L * ( ls + L * ( q + L * r )) ]
+ 0.5 * L2multF[ i + L * ( ls + L * ( r + L * q )) ] ) );
}
const double contracted_value = ( the3DM->get_ham_index( i, j, k, p, q, r ) * G1dotF
+ G3dotF[ i + L * ( j + L * ( p + L * q )) ] * gamma1[ k + L * r ]
- 0.5 * G3dotF[ i + L * ( j + L * ( r + L * q )) ] * gamma1[ k + L * p ]
- 0.5 * G3dotF[ i + L * ( j + L * ( p + L * r )) ] * gamma1[ k + L * q ]
+ G3dotF[ i + L * ( k + L * ( p + L * r )) ] * gamma1[ j + L * q ]
- 0.5 * G3dotF[ i + L * ( k + L * ( q + L * r )) ] * gamma1[ j + L * p ]
- 0.5 * G3dotF[ i + L * ( k + L * ( p + L * q )) ] * gamma1[ j + L * r ]
+ G3dotF[ j + L * ( k + L * ( q + L * r )) ] * gamma1[ i + L * p ]
- 0.5 * G3dotF[ j + L * ( k + L * ( p + L * r )) ] * gamma1[ i + L * q ]
- 0.5 * G3dotF[ j + L * ( k + L * ( q + L * p )) ] * gamma1[ i + L * r ]
- 0.5 * dm3_contribution
- the2DM->getTwoDMA_HAM( i, j, p, q ) * G2dotF[ k + L * r ]
+ 0.5 * the2DM->getTwoDMA_HAM( i, j, p, r ) * G2dotF[ k + L * q ]
+ 0.5 * the2DM->getTwoDMA_HAM( i, j, r, q ) * G2dotF[ k + L * p ]
- the2DM->getTwoDMA_HAM( i, k, p, r ) * G2dotF[ j + L * q ]
+ 0.5 * the2DM->getTwoDMA_HAM( i, k, p, q ) * G2dotF[ j + L * r ]
+ 0.5 * the2DM->getTwoDMA_HAM( i, k, q, r ) * G2dotF[ j + L * p ]
- the2DM->getTwoDMA_HAM( k, j, r, q ) * G2dotF[ i + L * p ]
+ 0.5 * the2DM->getTwoDMA_HAM( k, j, p, q ) * G2dotF[ i + L * r ]
+ 0.5 * the2DM->getTwoDMA_HAM( k, j, r, p ) * G2dotF[ i + L * q ]
+ 0.5 * gamma2_part1
- gamma2_part2 / 3.0
+ 2 * lambda2[ i + L * ( j + L * ( p + L * q )) ] * L2dotF[ k + L * r ]
- lambda2[ i + L * ( j + L * ( p + L * r )) ] * L2dotF[ k + L * q ]
- lambda2[ i + L * ( j + L * ( r + L * q )) ] * L2dotF[ k + L * p ]
+ 2 * lambda2[ i + L * ( k + L * ( p + L * r )) ] * L2dotF[ j + L * q ]
- lambda2[ i + L * ( k + L * ( p + L * q )) ] * L2dotF[ j + L * r ]
- lambda2[ i + L * ( k + L * ( q + L * r )) ] * L2dotF[ j + L * p ]
+ 2 * lambda2[ k + L * ( j + L * ( r + L * q )) ] * L2dotF[ i + L * p ]
- lambda2[ k + L * ( j + L * ( p + L * q )) ] * L2dotF[ i + L * r ]
- lambda2[ k + L * ( j + L * ( r + L * p )) ] * L2dotF[ i + L * q ]
- lambda2_part1
+ lambda2_part2 / 1.5 );
result[ i + L * ( j + L * ( k + L * ( p + L * ( q + L * r )))) ] = contracted_value;
result[ i + L * ( k + L * ( j + L * ( p + L * ( r + L * q )))) ] = contracted_value;
result[ j + L * ( i + L * ( k + L * ( q + L * ( p + L * r )))) ] = contracted_value;
result[ k + L * ( i + L * ( j + L * ( r + L * ( p + L * q )))) ] = contracted_value;
result[ j + L * ( k + L * ( i + L * ( q + L * ( r + L * p )))) ] = contracted_value;
result[ k + L * ( j + L * ( i + L * ( r + L * ( q + L * p )))) ] = contracted_value;
result[ p + L * ( q + L * ( r + L * ( i + L * ( j + L * k )))) ] = contracted_value;
result[ p + L * ( r + L * ( q + L * ( i + L * ( k + L * j )))) ] = contracted_value;
result[ q + L * ( p + L * ( r + L * ( j + L * ( i + L * k )))) ] = contracted_value;
result[ r + L * ( p + L * ( q + L * ( k + L * ( i + L * j )))) ] = contracted_value;
result[ q + L * ( r + L * ( p + L * ( j + L * ( k + L * i )))) ] = contracted_value;
result[ r + L * ( q + L * ( p + L * ( k + L * ( j + L * i )))) ] = contracted_value;
}
}
}
}
}
}
}
delete [] G3dotF;
delete [] lambda2;
delete [] G2multF;
delete [] L2multF;
delete [] gamma1;
delete [] G1multF;
delete [] G2dotF;
delete [] L2dotF;
delete [] irreps;
gettimeofday(&end, NULL);
const double elapsed = (end.tv_sec - start.tv_sec) + 1e-6 * (end.tv_usec - start.tv_usec);
std::cout << "Cumulant :: Contraction of cu(4)-4RDM with CASPT2 Fock operator took " << elapsed << " seconds." << std::endl;
}
double CheMPS2::Cumulant::lambda2_ham(const TwoDM * the2DM, const int i, const int j, const int p, const int q){
const double value = the2DM->getTwoDMA_HAM( i, j, p, q )
- the2DM->get1RDM_HAM( i, p ) * the2DM->get1RDM_HAM( j, q )
+ the2DM->get1RDM_HAM( i, q ) * the2DM->get1RDM_HAM( j, p ) * 0.5;
return value;
}
double CheMPS2::Cumulant::gamma4_ham(const Problem * prob, const ThreeDM * the3DM, const TwoDM * the2DM, const int i, const int j, const int k, const int l,
const int p, const int q, const int r, const int s){
//Prob assumes you use DMRG orbs... f1 converts HAM orbs to DMRG orbs
const int irrep_i = prob->gIrrep(( prob->gReorder() ) ? prob->gf1( i ) : i );
const int irrep_j = prob->gIrrep(( prob->gReorder() ) ? prob->gf1( j ) : j );
const int irrep_k = prob->gIrrep(( prob->gReorder() ) ? prob->gf1( k ) : k );
const int irrep_l = prob->gIrrep(( prob->gReorder() ) ? prob->gf1( l ) : l );
const int irrep_p = prob->gIrrep(( prob->gReorder() ) ? prob->gf1( p ) : p );
const int irrep_q = prob->gIrrep(( prob->gReorder() ) ? prob->gf1( q ) : q );
const int irrep_r = prob->gIrrep(( prob->gReorder() ) ? prob->gf1( r ) : r );
const int irrep_s = prob->gIrrep(( prob->gReorder() ) ? prob->gf1( s ) : s );
const int irrep_ij = Irreps::directProd( irrep_i, irrep_j );
const int irrep_kl = Irreps::directProd( irrep_k, irrep_l );
const int irrep_pq = Irreps::directProd( irrep_p, irrep_q );
const int irrep_rs = Irreps::directProd( irrep_r, irrep_s );
if ( Irreps::directProd( irrep_ij, irrep_kl ) != Irreps::directProd( irrep_pq, irrep_rs ) ){ return 0.0; }
const double part1 = ( the3DM->get_ham_index(i,j,k,p,q,r) * the2DM->get1RDM_HAM(l,s)
- 0.5 * the3DM->get_ham_index(i,j,k,s,q,r) * the2DM->get1RDM_HAM(l,p)
- 0.5 * the3DM->get_ham_index(i,j,k,p,s,r) * the2DM->get1RDM_HAM(l,q)
- 0.5 * the3DM->get_ham_index(i,j,k,p,q,s) * the2DM->get1RDM_HAM(l,r)
+ the3DM->get_ham_index(i,j,l,p,q,s) * the2DM->get1RDM_HAM(k,r)
- 0.5 * the3DM->get_ham_index(i,j,l,r,q,s) * the2DM->get1RDM_HAM(k,p)
- 0.5 * the3DM->get_ham_index(i,j,l,p,r,s) * the2DM->get1RDM_HAM(k,q)
- 0.5 * the3DM->get_ham_index(i,j,l,p,q,r) * the2DM->get1RDM_HAM(k,s)
+ the3DM->get_ham_index(i,k,l,p,r,s) * the2DM->get1RDM_HAM(j,q)
- 0.5 * the3DM->get_ham_index(i,k,l,q,r,s) * the2DM->get1RDM_HAM(j,p)
- 0.5 * the3DM->get_ham_index(i,k,l,p,q,s) * the2DM->get1RDM_HAM(j,r)
- 0.5 * the3DM->get_ham_index(i,k,l,p,r,q) * the2DM->get1RDM_HAM(j,s)
+ the3DM->get_ham_index(j,k,l,q,r,s) * the2DM->get1RDM_HAM(i,p)
- 0.5 * the3DM->get_ham_index(j,k,l,p,r,s) * the2DM->get1RDM_HAM(i,q)
- 0.5 * the3DM->get_ham_index(j,k,l,q,p,s) * the2DM->get1RDM_HAM(i,r)
- 0.5 * the3DM->get_ham_index(j,k,l,q,r,p) * the2DM->get1RDM_HAM(i,s) );
const double part2 = ( the2DM->getTwoDMA_HAM(i,j,p,q) * the2DM->getTwoDMA_HAM(k,l,r,s)
- the2DM->getTwoDMA_HAM(i,j,p,r) * the2DM->getTwoDMA_HAM(k,l,q,s) * 0.5
- the2DM->getTwoDMA_HAM(i,j,p,s) * the2DM->getTwoDMA_HAM(k,l,r,q) * 0.5
- the2DM->getTwoDMA_HAM(i,j,r,q) * the2DM->getTwoDMA_HAM(k,l,p,s) * 0.5
- the2DM->getTwoDMA_HAM(i,j,s,q) * the2DM->getTwoDMA_HAM(k,l,r,p) * 0.5
+ the2DM->getTwoDMA_HAM(i,j,r,s) * the2DM->getTwoDMA_HAM(k,l,p,q) / 3.0
+ the2DM->getTwoDMA_HAM(i,j,r,s) * the2DM->getTwoDMA_HAM(k,l,q,p) / 6.0
+ the2DM->getTwoDMA_HAM(i,j,s,r) * the2DM->getTwoDMA_HAM(k,l,p,q) / 6.0
+ the2DM->getTwoDMA_HAM(i,j,s,r) * the2DM->getTwoDMA_HAM(k,l,q,p) / 3.0
+ the2DM->getTwoDMA_HAM(i,k,p,r) * the2DM->getTwoDMA_HAM(j,l,q,s)
- the2DM->getTwoDMA_HAM(i,k,p,q) * the2DM->getTwoDMA_HAM(j,l,r,s) * 0.5
- the2DM->getTwoDMA_HAM(i,k,p,s) * the2DM->getTwoDMA_HAM(j,l,q,r) * 0.5
- the2DM->getTwoDMA_HAM(i,k,q,r) * the2DM->getTwoDMA_HAM(j,l,p,s) * 0.5
- the2DM->getTwoDMA_HAM(i,k,s,r) * the2DM->getTwoDMA_HAM(j,l,q,p) * 0.5
+ the2DM->getTwoDMA_HAM(i,k,q,s) * the2DM->getTwoDMA_HAM(j,l,p,r) / 3.0
+ the2DM->getTwoDMA_HAM(i,k,s,q) * the2DM->getTwoDMA_HAM(j,l,p,r) / 6.0
+ the2DM->getTwoDMA_HAM(i,k,q,s) * the2DM->getTwoDMA_HAM(j,l,r,p) / 6.0
+ the2DM->getTwoDMA_HAM(i,k,s,q) * the2DM->getTwoDMA_HAM(j,l,r,p) / 3.0
+ the2DM->getTwoDMA_HAM(i,l,p,s) * the2DM->getTwoDMA_HAM(k,j,r,q)
- the2DM->getTwoDMA_HAM(i,l,p,r) * the2DM->getTwoDMA_HAM(k,j,s,q) * 0.5
- the2DM->getTwoDMA_HAM(i,l,p,q) * the2DM->getTwoDMA_HAM(k,j,r,s) * 0.5
- the2DM->getTwoDMA_HAM(i,l,r,s) * the2DM->getTwoDMA_HAM(k,j,p,q) * 0.5
- the2DM->getTwoDMA_HAM(i,l,q,s) * the2DM->getTwoDMA_HAM(k,j,r,p) * 0.5
+ the2DM->getTwoDMA_HAM(i,l,r,q) * the2DM->getTwoDMA_HAM(k,j,p,s) / 3.0
+ the2DM->getTwoDMA_HAM(i,l,q,r) * the2DM->getTwoDMA_HAM(k,j,p,s) / 6.0
+ the2DM->getTwoDMA_HAM(i,l,r,q) * the2DM->getTwoDMA_HAM(k,j,s,p) / 6.0
+ the2DM->getTwoDMA_HAM(i,l,q,r) * the2DM->getTwoDMA_HAM(k,j,s,p) / 3.0 );
const double part3 = ( lambda2_ham(the2DM,i,j,p,q) * lambda2_ham(the2DM,k,l,r,s)
- lambda2_ham(the2DM,i,j,p,r) * lambda2_ham(the2DM,k,l,q,s) * 0.5
- lambda2_ham(the2DM,i,j,p,s) * lambda2_ham(the2DM,k,l,r,q) * 0.5
- lambda2_ham(the2DM,i,j,r,q) * lambda2_ham(the2DM,k,l,p,s) * 0.5
- lambda2_ham(the2DM,i,j,s,q) * lambda2_ham(the2DM,k,l,r,p) * 0.5
+ lambda2_ham(the2DM,i,j,r,s) * lambda2_ham(the2DM,k,l,p,q) / 3.0
+ lambda2_ham(the2DM,i,j,r,s) * lambda2_ham(the2DM,k,l,q,p) / 6.0
+ lambda2_ham(the2DM,i,j,s,r) * lambda2_ham(the2DM,k,l,p,q) / 6.0
+ lambda2_ham(the2DM,i,j,s,r) * lambda2_ham(the2DM,k,l,q,p) / 3.0
+ lambda2_ham(the2DM,i,k,p,r) * lambda2_ham(the2DM,j,l,q,s)
- lambda2_ham(the2DM,i,k,p,q) * lambda2_ham(the2DM,j,l,r,s) * 0.5
- lambda2_ham(the2DM,i,k,p,s) * lambda2_ham(the2DM,j,l,q,r) * 0.5
- lambda2_ham(the2DM,i,k,q,r) * lambda2_ham(the2DM,j,l,p,s) * 0.5
- lambda2_ham(the2DM,i,k,s,r) * lambda2_ham(the2DM,j,l,q,p) * 0.5
+ lambda2_ham(the2DM,i,k,q,s) * lambda2_ham(the2DM,j,l,p,r) / 3.0
+ lambda2_ham(the2DM,i,k,s,q) * lambda2_ham(the2DM,j,l,p,r) / 6.0
+ lambda2_ham(the2DM,i,k,q,s) * lambda2_ham(the2DM,j,l,r,p) / 6.0
+ lambda2_ham(the2DM,i,k,s,q) * lambda2_ham(the2DM,j,l,r,p) / 3.0
+ lambda2_ham(the2DM,i,l,p,s) * lambda2_ham(the2DM,k,j,r,q)
- lambda2_ham(the2DM,i,l,p,r) * lambda2_ham(the2DM,k,j,s,q) * 0.5
- lambda2_ham(the2DM,i,l,p,q) * lambda2_ham(the2DM,k,j,r,s) * 0.5
- lambda2_ham(the2DM,i,l,r,s) * lambda2_ham(the2DM,k,j,p,q) * 0.5
- lambda2_ham(the2DM,i,l,q,s) * lambda2_ham(the2DM,k,j,r,p) * 0.5
+ lambda2_ham(the2DM,i,l,r,q) * lambda2_ham(the2DM,k,j,p,s) / 3.0
+ lambda2_ham(the2DM,i,l,q,r) * lambda2_ham(the2DM,k,j,p,s) / 6.0
+ lambda2_ham(the2DM,i,l,r,q) * lambda2_ham(the2DM,k,j,s,p) / 6.0
+ lambda2_ham(the2DM,i,l,q,r) * lambda2_ham(the2DM,k,j,s,p) / 3.0 );
return ( part1 - part2 + 2 * part3 );
}
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