int main(void){
#ifdef CHEMPS2_MPI_COMPILATION
CheMPS2::MPIchemps2::mpi_init();
#endif
CheMPS2::Initialize::Init();
//Square 2D Hubbard model with PBC
const int L_linear = 3; // Linear size
const int L_square = L_linear * L_linear; // Number of orbitals
const int group = 0; // C1 symmetry
const double U = 5.0; // On-site repulsion
const double T = -1.0; // Hopping term
const int N = 9; // Number of electrons
const int TwoS = 1; // Two times the spin
const int Irrep = 0; // Irrep = A (C1 symmetry)
//Create the Hamiltonian (eightfold permutation symmetry is OK for site basis)
int * irreps = new int[L_square];
for (int cnt=0; cnt<L_square; cnt++){ irreps[cnt] = 0; }
//The Hamiltonian initializes all its matrix elements to 0.0
CheMPS2::Hamiltonian * Ham = new CheMPS2::Hamiltonian(L_square, group, irreps);
delete [] irreps;
//Fill with the site-basis matrix elements
for (int cnt=0; cnt<L_square; cnt++){ Ham->setVmat(cnt,cnt,cnt,cnt,U); }
for (int ix=0; ix<L_linear; ix++){
for (int iy=0; iy<L_linear; iy++){
const int idx1 = ix + L_linear * iy; // This site
const int idx2 = (( ix + 1 ) % L_linear) + L_linear * iy; // Right neighbour (PBC)
const int idx3 = ix + L_linear * ((( iy + 1 ) % L_linear)); //Upper neighbour (PBC)
Ham->setTmat(idx1,idx2,T);
Ham->setTmat(idx1,idx3,T);
}
}
//The problem object
CheMPS2::Problem * Prob = new CheMPS2::Problem(Ham, TwoS, N, Irrep);
//The convergence scheme
CheMPS2::ConvergenceScheme * OptScheme = new CheMPS2::ConvergenceScheme(2);
//OptScheme->setInstruction(instruction, DSU(2), Econvergence, maxSweeps, noisePrefactor);
OptScheme->setInstruction(0, 500, 1e-10, 3, 0.05);
OptScheme->setInstruction(1, 1000, 1e-10, 10, 0.0 );
//Run ground state calculation
CheMPS2::DMRG * theDMRG = new CheMPS2::DMRG(Prob, OptScheme);
const double EnergySite = theDMRG->Solve();
theDMRG->calc2DMandCorrelations();
//Clean up DMRG
if (CheMPS2::DMRG_storeMpsOnDisk){ theDMRG->deleteStoredMPS(); }
if (CheMPS2::DMRG_storeRenormOptrOnDisk){ theDMRG->deleteStoredOperators(); }
delete theDMRG;
//Hack: overwrite the matrix elements in momentum space (4-fold symmetry!!!) directly in the Problem object
theDMRG = new CheMPS2::DMRG(Prob, OptScheme); // Prob->construct_mxelem() is called now
for (int orb1=0; orb1<L_square; orb1++){
const int k1x = orb1 % L_linear;
const int k1y = orb1 / L_linear;
const double Telem1 = 2*T*( cos((2*M_PI*k1x)/L_linear)
+ cos((2*M_PI*k1y)/L_linear) );
for (int orb2=0; orb2<L_square; orb2++){
const int k2x = orb2 % L_linear;
const int k2y = orb2 / L_linear;
const double Telem2 = 2*T*( cos((2*M_PI*k2x)/L_linear)
+ cos((2*M_PI*k2y)/L_linear) );
for (int orb3=0; orb3<L_square; orb3++){
const int k3x = orb3 % L_linear;
const int k3y = orb3 / L_linear;
for (int orb4=0; orb4<L_square; orb4++){
const int k4x = orb4 % L_linear;
const int k4y = orb4 / L_linear;
const bool kx_conservation = (((k1x+k2x) % L_linear) == ((k3x+k4x) % L_linear))?true:false;
const bool ky_conservation = (((k1y+k2y) % L_linear) == ((k3y+k4y) % L_linear))?true:false;
double temp = 0.0;
if ( kx_conservation && ky_conservation ){ temp += U/L_square; }
if (( orb1 == orb3 ) && ( orb2 == orb4 )){ temp += (Telem1+Telem2)/(N-1); }
Prob->setMxElement(orb1,orb2,orb3,orb4,temp);
}
}
}
}
theDMRG->PreSolve(); // New matrix elements require reconstruction of complementary renormalized operators
const double EnergyMomentum = theDMRG->Solve();
theDMRG->calc2DMandCorrelations();
//Clean up
if (CheMPS2::DMRG_storeMpsOnDisk){ theDMRG->deleteStoredMPS(); }
if (CheMPS2::DMRG_storeRenormOptrOnDisk){ theDMRG->deleteStoredOperators(); }
delete theDMRG;
delete OptScheme;
delete Prob;
delete Ham;
//Check succes
const bool success = ( fabs( EnergySite - EnergyMomentum ) < 1e-8 ) ? true : false;
#ifdef CHEMPS2_MPI_COMPILATION
CheMPS2::MPIchemps2::mpi_finalize();
#endif
cout << "================> Did test 10 succeed : ";
if (success){
cout << "yes" << endl;
return 0; //Success
}
cout << "no" << endl;
return 7; //Fail
}
double CheMPS2::CASSCF::caspt2( const int Nelectrons, const int TwoS, const int Irrep, ConvergenceScheme * OptScheme, const int rootNum, DMRGSCFoptions * scf_options, const double IPEA, const double IMAG, const bool PSEUDOCANONICAL, const bool CHECKPOINT, const bool CUMULANT ){
#ifdef CHEMPS2_MPI_COMPILATION
const bool am_i_master = ( MPIchemps2::mpi_rank() == MPI_CHEMPS2_MASTER );
#else
const bool am_i_master = true;
#endif
const int num_elec = Nelectrons - 2 * iHandler->getNOCCsum();
assert( num_elec >= 0 );
if ( CASPT2::vector_length( iHandler ) == 0 ){
if ( am_i_master ){
cout << "CheMPS2::CASSCF::caspt2 : There are no CASPT2 excitations between the CORE, ACTIVE, and VIRTUAL orbital spaces." << endl;
}
return 0.0;
}
//Determine the maximum NORB(irrep) and the max_block_size for the ERI orbital rotation
const int maxlinsize = iHandler->getNORBmax();
const long long fullsize = ((long long) maxlinsize ) * ((long long) maxlinsize ) * ((long long) maxlinsize ) * ((long long) maxlinsize );
const string tmp_filename = tmp_folder + "/" + CheMPS2::DMRGSCF_eri_storage_name;
const int dmrgsize_power4 = nOrbDMRG * nOrbDMRG * nOrbDMRG * nOrbDMRG;
//For (ERI rotation, update unitary, block diagonalize, orbital localization)
DMRGSCFintegrals * theRotatedTEI = new DMRGSCFintegrals( iHandler );
const int temp_work_size = (( fullsize > CheMPS2::DMRGSCF_max_mem_eri_tfo ) ? CheMPS2::DMRGSCF_max_mem_eri_tfo : fullsize );
const int work_mem_size = max( max( temp_work_size , maxlinsize * maxlinsize * 4 ) , dmrgsize_power4 );
const int tot_dmrg_power6 = dmrgsize_power4 * nOrbDMRG * nOrbDMRG;
double * mem1 = new double[ work_mem_size ];
double * mem2 = new double[ ( PSEUDOCANONICAL ) ? work_mem_size : max( work_mem_size, tot_dmrg_power6 ) ];
// Rotate to pseudocanonical orbitals
if ( PSEUDOCANONICAL ){
assert( successful_solve ); // DMRG1RDM needs to be set by CASSCF::solve for buildQmatACT()
buildTmatrix();
buildQmatOCC();
buildQmatACT();
construct_fock( theFmatrix, theTmatrix, theQmatOCC, theQmatACT, iHandler );
block_diagonalize( 'O', theFmatrix, unitary, mem1, mem2, iHandler, false, NULL, NULL, NULL );
block_diagonalize( 'A', theFmatrix, unitary, mem1, mem2, iHandler, false, NULL, NULL, NULL );
block_diagonalize( 'V', theFmatrix, unitary, mem1, mem2, iHandler, false, NULL, NULL, NULL );
} else {
if ( successful_solve == false ){
assert( scf_options->getStoreUnitary() );
if ( am_i_master ){
struct stat file_info;
const int file_stat = stat( (scf_options->getUnitaryStorageName()).c_str(), &file_info );
assert( file_stat == 0 );
unitary->loadU( scf_options->getUnitaryStorageName() );
}
#ifdef CHEMPS2_MPI_COMPILATION
unitary->broadcast( MPI_CHEMPS2_MASTER );
#endif
}
}
// Fill active space Hamiltonian
Hamiltonian * HamAS = new Hamiltonian( nOrbDMRG, SymmInfo.getGroupNumber(), iHandler->getIrrepOfEachDMRGorbital() );
Problem * Prob = new Problem( HamAS, TwoS, num_elec, Irrep );
Prob->SetupReorderD2h(); // Doesn't matter if the group isn't D2h, Prob checks it.
buildTmatrix();
buildQmatOCC();
fillConstAndTmatDMRG( HamAS );
if ( am_i_master ){
DMRGSCFrotations::rotate( VMAT_ORIG, HamAS->getVmat(), NULL, 'A', 'A', 'A', 'A', iHandler, unitary, mem1, mem2, work_mem_size, tmp_filename );
}
#ifdef CHEMPS2_MPI_COMPILATION
HamAS->getVmat()->broadcast( MPI_CHEMPS2_MASTER );
#endif
double E_CASSCF = 0.0;
double * three_dm = new double[ tot_dmrg_power6 ];
double * contract = new double[ tot_dmrg_power6 ];
for ( int cnt = 0; cnt < tot_dmrg_power6; cnt++ ){ contract[ cnt ] = 0.0; }
int next_hamorb1 = 0;
int next_hamorb2 = 0;
const bool make_checkpt = (( CUMULANT == false ) && ( CHECKPOINT ));
bool checkpt_loaded = false;
if ( make_checkpt ){
assert(( OptScheme != NULL ) || ( rootNum > 1 ));
checkpt_loaded = read_f4rdm_checkpoint( CheMPS2::DMRGSCF_f4rdm_name, &next_hamorb1, &next_hamorb2, tot_dmrg_power6, contract );
}
// Solve the active space problem
if (( OptScheme == NULL ) && ( rootNum == 1 )){ // Do FCI
if ( am_i_master ){
const int nalpha = ( num_elec + TwoS ) / 2;
const int nbeta = ( num_elec - TwoS ) / 2;
const double workmem = 1000.0; // 1GB
const int verbose = 2;
CheMPS2::FCI * theFCI = new CheMPS2::FCI( HamAS, nalpha, nbeta, Irrep, workmem, verbose );
double * inoutput = new double[ theFCI->getVecLength(0) ];
theFCI->ClearVector( theFCI->getVecLength(0), inoutput );
inoutput[ theFCI->LowestEnergyDeterminant() ] = 1.0;
E_CASSCF = theFCI->GSDavidson( inoutput );
theFCI->Fill2RDM( inoutput, DMRG2DM ); // 2-RDM
theFCI->Fill3RDM( inoutput, three_dm ); // 3-RDM
setDMRG1DM( num_elec, nOrbDMRG, DMRG1DM, DMRG2DM ); // 1-RDM
buildQmatACT();
construct_fock( theFmatrix, theTmatrix, theQmatOCC, theQmatACT, iHandler );
copy_active( theFmatrix, mem2, iHandler ); // Fock
theFCI->Fock4RDM( inoutput, three_dm, mem2, contract ); // trace( Fock * 4-RDM )
delete theFCI;
delete [] inoutput;
}
#ifdef CHEMPS2_MPI_COMPILATION
MPIchemps2::broadcast_array_double( &E_CASSCF, 1, MPI_CHEMPS2_MASTER );
MPIchemps2::broadcast_array_double( DMRG2DM, dmrgsize_power4, MPI_CHEMPS2_MASTER );
MPIchemps2::broadcast_array_double( three_dm, tot_dmrg_power6, MPI_CHEMPS2_MASTER );
MPIchemps2::broadcast_array_double( contract, tot_dmrg_power6, MPI_CHEMPS2_MASTER );
setDMRG1DM( num_elec, nOrbDMRG, DMRG1DM, DMRG2DM );
#endif
} else { // Do the DMRG sweeps
assert( OptScheme != NULL );
for ( int cnt = 0; cnt < dmrgsize_power4; cnt++ ){ DMRG2DM[ cnt ] = 0.0; } // Clear the 2-RDM
CheMPS2::DMRG * theDMRG = new DMRG( Prob, OptScheme, make_checkpt, tmp_folder );
for ( int state = 0; state < rootNum; state++ ){
if ( state > 0 ){ theDMRG->newExcitation( fabs( E_CASSCF ) ); }
if ( checkpt_loaded == false ){ E_CASSCF = theDMRG->Solve(); }
if (( state == 0 ) && ( rootNum > 1 )){ theDMRG->activateExcitations( rootNum - 1 ); }
}
theDMRG->calc_rdms_and_correlations( true );
copy2DMover( theDMRG->get2DM(), nOrbDMRG, DMRG2DM ); // 2-RDM
setDMRG1DM( num_elec, nOrbDMRG, DMRG1DM, DMRG2DM ); // 1-RDM
buildQmatACT();
construct_fock( theFmatrix, theTmatrix, theQmatOCC, theQmatACT, iHandler );
copy_active( theFmatrix, mem2, iHandler ); // Fock
if ( CUMULANT ){
CheMPS2::Cumulant::gamma4_fock_contract_ham( Prob, theDMRG->get3DM(), theDMRG->get2DM(), mem2, contract );
} else {
for ( int ham_orbz = 0; ham_orbz < nOrbDMRG; ham_orbz++ ){
if (( next_hamorb1 == ham_orbz ) && ( next_hamorb2 == ham_orbz )){
theDMRG->Symm4RDM( three_dm, ham_orbz, ham_orbz, false );
int size = tot_dmrg_power6;
double f_zz = 0.5 * mem2[ ham_orbz + nOrbDMRG * ham_orbz ];
int inc1 = 1;
daxpy_( &size, &f_zz, three_dm, &inc1, contract, &inc1 ); // trace( Fock * 4-RDM )
if ( ham_orbz == nOrbDMRG - 1 ){
next_hamorb1 = 0;
next_hamorb2 = 1;
} else {
next_hamorb1 = ham_orbz + 1;
next_hamorb2 = ham_orbz + 1;
}
if ( make_checkpt ){ write_f4rdm_checkpoint( CheMPS2::DMRGSCF_f4rdm_name, &next_hamorb1, &next_hamorb2, tot_dmrg_power6, contract ); }
}
}
if ( PSEUDOCANONICAL == false ){
for ( int ham_orb1 = 0; ham_orb1 < nOrbDMRG; ham_orb1++ ){
for ( int ham_orb2 = ham_orb1 + 1; ham_orb2 < nOrbDMRG; ham_orb2++ ){
if (( next_hamorb1 == ham_orb1 ) && ( next_hamorb2 == ham_orb2 )){
if ( HamAS->getOrbitalIrrep( ham_orb1 ) == HamAS->getOrbitalIrrep( ham_orb2 ) ){
theDMRG->Symm4RDM( three_dm, ham_orb1, ham_orb2, false );
int size = tot_dmrg_power6;
double f_12 = 0.5 * ( mem2[ ham_orb1 + nOrbDMRG * ham_orb2 ] + mem2[ ham_orb2 + nOrbDMRG * ham_orb1 ] );
int inc1 = 1;
daxpy_( &size, &f_12, three_dm, &inc1, contract, &inc1 ); // trace( Fock * 4-RDM )
}
if ( ham_orb2 == nOrbDMRG - 1 ){
next_hamorb1 = next_hamorb1 + 1;
next_hamorb2 = next_hamorb1 + 1;
} else {
next_hamorb2 = next_hamorb2 + 1;
}
if (( HamAS->getOrbitalIrrep( ham_orb1 ) == HamAS->getOrbitalIrrep( ham_orb2 ) ) && ( make_checkpt )){
write_f4rdm_checkpoint( CheMPS2::DMRGSCF_f4rdm_name, &next_hamorb1, &next_hamorb2, tot_dmrg_power6, contract );
}
}
}
}
}
}
theDMRG->get3DM()->fill_ham_index( 1.0, false, three_dm, 0, nOrbDMRG );
if (( CheMPS2::DMRG_storeMpsOnDisk ) && ( make_checkpt == false )){ theDMRG->deleteStoredMPS(); }
if ( CheMPS2::DMRG_storeRenormOptrOnDisk ){ theDMRG->deleteStoredOperators(); }
delete theDMRG;
}
delete Prob;
delete HamAS;
if ( PSEUDOCANONICAL == false ){
if ( am_i_master ){ cout << "CASPT2 : Deviation from pseudocanonical = " << deviation_from_blockdiag( theFmatrix, iHandler ) << endl; }
block_diagonalize( 'O', theFmatrix, unitary, mem1, mem2, iHandler, false, NULL, NULL, NULL );
block_diagonalize( 'A', theFmatrix, unitary, mem1, mem2, iHandler, false, DMRG2DM, three_dm, contract ); // 2-RDM, 3-RDM, and trace( Fock * cu(4)-4-RDM )
block_diagonalize( 'V', theFmatrix, unitary, mem1, mem2, iHandler, false, NULL, NULL, NULL );
setDMRG1DM( num_elec, nOrbDMRG, DMRG1DM, DMRG2DM ); // 1-RDM
buildTmatrix();
buildQmatOCC();
buildQmatACT();
construct_fock( theFmatrix, theTmatrix, theQmatOCC, theQmatACT, iHandler ); // Fock
}
// Calculate the matrix elements needed to calculate the CASPT2 V-vector
if ( am_i_master ){
DMRGSCFrotations::rotate( VMAT_ORIG, NULL, theRotatedTEI, 'C', 'C', 'F', 'F', iHandler, unitary, mem1, mem2, work_mem_size, tmp_filename );
DMRGSCFrotations::rotate( VMAT_ORIG, NULL, theRotatedTEI, 'C', 'V', 'C', 'V', iHandler, unitary, mem1, mem2, work_mem_size, tmp_filename );
delete_file( tmp_filename );
}
delete [] mem1;
delete [] mem2;
double E_CASPT2 = 0.0;
if ( am_i_master ){
cout << "CASPT2 : Deviation from pseudocanonical = " << deviation_from_blockdiag( theFmatrix, iHandler ) << endl;
CheMPS2::CASPT2 * myCASPT2 = new CheMPS2::CASPT2( iHandler, theRotatedTEI, theTmatrix, theFmatrix, DMRG1DM, DMRG2DM, three_dm, contract, IPEA );
delete theRotatedTEI;
delete [] three_dm;
delete [] contract;
E_CASPT2 = myCASPT2->solve( IMAG );
delete myCASPT2;
} else {
delete theRotatedTEI;
delete [] three_dm;
delete [] contract;
}
#ifdef CHEMPS2_MPI_COMPILATION
MPIchemps2::broadcast_array_double( &E_CASPT2, 1, MPI_CHEMPS2_MASTER );
#endif
return E_CASPT2;
}
int main(void){
#ifdef CHEMPS2_MPI_COMPILATION
CheMPS2::MPIchemps2::mpi_init();
#endif
CheMPS2::Initialize::Init();
//The Hamiltonian: 1D Hubbard model
const int L = 10;
const int Group = 0;
const double U = 2.0;
const double T = -1.0;
int * irreps = new int[L];
for (int cnt=0; cnt<L; cnt++){ irreps[cnt] = 0; }
//The Hamiltonian initializes all its matrix elements to 0.0
CheMPS2::Hamiltonian * Ham = new CheMPS2::Hamiltonian(L, Group, irreps);
delete [] irreps;
for (int cnt=0; cnt<L; cnt++){ Ham->setVmat(cnt,cnt,cnt,cnt,U); }
for (int cnt=0; cnt<L-1; cnt++){ Ham->setTmat(cnt,cnt+1,T); }
//The targeted state
const int TwoS = 5;
const int N = 9;
const int Irrep = 0;
CheMPS2::Problem * Prob = new CheMPS2::Problem(Ham, TwoS, N, Irrep);
//The convergence scheme
CheMPS2::ConvergenceScheme * OptScheme = new CheMPS2::ConvergenceScheme(2);
//OptScheme->setInstruction(instruction, DSU(2), Econvergence, maxSweeps, noisePrefactor);
OptScheme->setInstruction(0, 30, 1e-10, 3, 0.1);
OptScheme->setInstruction(1, 1000, 1e-10, 10, 0.0);
//Run ground state calculation
CheMPS2::DMRG * theDMRG = new CheMPS2::DMRG(Prob, OptScheme);
const double EnergyDMRG = theDMRG->Solve();
theDMRG->calc2DMandCorrelations();
#ifdef CHEMPS2_MPI_COMPILATION
if ( CheMPS2::MPIchemps2::mpi_rank() == MPI_CHEMPS2_MASTER )
#endif
{
theDMRG->getCorrelations()->Print();
}
//Clean up DMRG
if (CheMPS2::DMRG_storeMpsOnDisk){ theDMRG->deleteStoredMPS(); }
if (CheMPS2::DMRG_storeRenormOptrOnDisk){ theDMRG->deleteStoredOperators(); }
delete theDMRG;
delete OptScheme;
delete Prob;
//Calculate FCI reference energy
double EnergyFCI = 0.0;
#ifdef CHEMPS2_MPI_COMPILATION
if ( CheMPS2::MPIchemps2::mpi_rank() == MPI_CHEMPS2_MASTER )
#endif
{
const int Nel_up = ( N + TwoS ) / 2;
const int Nel_down = ( N - TwoS ) / 2;
const double maxMemWorkMB = 10.0;
const int FCIverbose = 1;
CheMPS2::FCI * theFCI = new CheMPS2::FCI(Ham, Nel_up, Nel_down, Irrep, maxMemWorkMB, FCIverbose);
EnergyFCI = theFCI->GSDavidson(NULL);
delete theFCI;
}
#ifdef CHEMPS2_MPI_COMPILATION
CheMPS2::MPIchemps2::broadcast_array_double( &EnergyFCI, 1, MPI_CHEMPS2_MASTER );
#endif
//Clean up the Hamiltonian
delete Ham;
//Check succes
const bool success = ( fabs( EnergyDMRG - EnergyFCI ) < 1e-8 ) ? true : false;
#ifdef CHEMPS2_MPI_COMPILATION
CheMPS2::MPIchemps2::mpi_finalize();
#endif
cout << "================> Did test 4 succeed : ";
if (success){
cout << "yes" << endl;
return 0; //Success
}
cout << "no" << endl;
return 7; //Fail
}