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rcks.cc
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rcks.cc
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#include "rcks.h"
#include <libmints/view.h>
#include <libmints/mints.h>
#include <libfock/apps.h>
#include <libfock/v.h>
#include <libfock/jk.h>
#include <libdisp/dispersion.h>
#include <liboptions/liboptions.h>
#include <libciomr/libciomr.h>
#include <libqt/qt.h>
using namespace psi;
namespace psi{ namespace scf{
RCKS::RCKS(Options& options, boost::shared_ptr<PSIO> psio)
: RKS(options, psio), Vc(0.0), optimize_Vc(false), gradW_threshold_(1.0e-9),nW_opt(0), old_gradW(0.0), BFGS_hessW(0.0)
{
outfile->Printf("\n ==> Constrained DFT (RCKS) <==\n\n");
Vc = options.get_double("VC");
optimize_Vc = options.get_bool("OPTIMIZE_VC");
if(optimize_Vc){
outfile->Printf(" The constraint will be optimized.\n");
}else{
outfile->Printf(" The Lagrange multiplier for the constraint will be fixed: Vc = %f .\n",Vc);
}
gradW_threshold_ = options.get_double("W_CONVERGENCE");
outfile->Printf(" gradW threshold = :%9.2e\n",gradW_threshold_);
nfrag = basisset()->molecule()->nfragments();
outfile->Printf(" Number of fragments: %d\n",nfrag);
// Check the option CHARGE, if it is defined use it to define the constrained charges
int charge_size = options["CHARGE"].size();
if (charge_size > 0){
if (charge_size == nfrag){
for (int n = 0; n < charge_size; ++n){
constrained_charges.push_back(options["CHARGE"][n].to_double());
}
}else{
throw InputException("The number of charge constraints does not match the number of fragments", "CHARGE", __FILE__, __LINE__);
}
}
build_W_so();
Temp = SharedMatrix(factory_->create_matrix("Temp"));
Temp2 = SharedMatrix(factory_->create_matrix("Temp2"));
save_H_ = true;
for (int f = 0; f < nfrag; ++f){
outfile->Printf(" Fragment %d: constrained charge = %f .\n",f,constrained_charges[f]);
}
Nc = frag_nuclear_charge[0] - constrained_charges[0];
Nc -= frag_nuclear_charge[1] - constrained_charges[1];
outfile->Printf(" Constraining Tr[w rho] = Nc = %f .\n\n",Nc);
}
RCKS::~RCKS()
{
}
void RCKS::build_W_so()
{
// Allocate the total constraint matrix
W_tot = SharedMatrix(factory_->create_matrix("W_tot"));
// Compute the overlap matrix
boost::shared_ptr<BasisSet> basisset_ = basisset();
boost::shared_ptr<Molecule> mol = basisset_->molecule();
boost::shared_ptr<OneBodyAOInt> overlap(integral_->ao_overlap());
SharedMatrix S_ao(new Matrix("S_ao",basisset_->nbf(),basisset_->nbf()));
overlap->compute(S_ao);
// Form the S^(1/2) matrix
S_ao->power(1.0/2.0);
boost::shared_ptr<PetiteList> pet(new PetiteList(basisset_, integral_));
SharedMatrix AO2SO_ = pet->aotoso();
int min_a = 0;
int max_a = 0;
for (int f = 0; f < nfrag; ++f){
std::vector<int> flist;
std::vector<int> glist;
flist.push_back(f);
boost::shared_ptr<Molecule> frag = mol->extract_subsets(flist,glist);
// Compute the nuclear charge on each fragment
double frag_Z = 0.0;
for (int a = 0; a < frag->natom(); ++a){
frag_Z += frag->Z(a);
}
frag_nuclear_charge.push_back(frag_Z);
constrained_charges.push_back(double(frag->molecular_charge())); // TODO Remove the factor of 10.0!!!
// Form a copy of S_ao and zero the rows that are not on this fragment
max_a = min_a + frag->natom();
SharedMatrix S_f(S_ao->clone());
for (int rho = 0; rho < basisset_->nbf(); rho++) {
int shell = basisset_->function_to_shell(rho);
int A = basisset_->shell_to_center(shell);
if (A < min_a or max_a <= A){
S_f->scale_row(0,rho,0.0);
}
}
// If CHARGE is not defined, then read the charges from the fragment input
if(constrained_charges.size() != nfrag){
constrained_charges.push_back(double(frag->molecular_charge()));
}
// Form W_f = (S_f)^T * S_f and transform it to the SO basis
SharedMatrix W_f(new Matrix("W_f",basisset_->nbf(),basisset_->nbf()));
SharedMatrix W_f_so(factory_->create_matrix("W_f_so"));
W_f->gemm(true, false, 1.0, S_f, S_f, 0.0);
W_f_so->apply_symmetry(W_f,AO2SO_);
// Save W_f_so to the W_so vector
W_so.push_back(W_f_so);
min_a = max_a;
}
W_tot->zero();
W_tot->add(W_so[0]);
W_tot->subtract(W_so[1]);
}
void RCKS::form_F()
{
// On the first iteration save H_
if (save_H_){
H_copy = SharedMatrix(factory_->create_matrix("H_copy"));
H_copy->copy(H_);
save_H_ = false;
}
// Augement the one-electron potential (H_) with the CDFT terms
H_->copy(H_copy);
Temp->copy(W_tot);
Temp->scale(Vc);
H_->add(Temp); // Temp = Vc * W_tot
Fa_->copy(H_);
Fa_->add(G_);
gradient_of_W();
hessian_of_W();
outfile->Printf(" @CDFT Vc = %.7f gradW = %.7f hessW = %.7f\n",Vc,gradW,hessW);
if (debug_) {
Fa_->print();
J_->print();
K_->print();
G_->print();
}
}
double RCKS::compute_E()
{
// E_DFT = 2.0 D*H + 2.0 D*J - \alpha D*K + E_xc - Vc * Nc
double one_electron_E = 2.0*D_->vector_dot(H_) - Vc * Nc; // Added the CDFT contribution that is not included in H_
double coulomb_E = D_->vector_dot(J_);
std::map<std::string, double>& quad = potential_->quadrature_values();
double XC_E = quad["FUNCTIONAL"];
double exchange_E = 0.0;
double alpha = functional_->x_alpha();
double beta = 1.0 - alpha;
if (functional_->is_x_hybrid()) {
exchange_E -= alpha*Da_->vector_dot(K_);
}
if (functional_->is_x_lrc()) {
exchange_E -= beta*Da_->vector_dot(wK_);
}
double dashD_E = 0.0;
boost::shared_ptr<Dispersion> disp;
if (disp) {
dashD_E = disp->compute_energy(HF::molecule_);
}
double Etotal = 0.0;
Etotal += nuclearrep_;
Etotal += one_electron_E;
Etotal += coulomb_E;
Etotal += exchange_E;
Etotal += XC_E;
Etotal += dashD_E;
if (debug_) {
outfile->Printf( " => Energetics <=\n\n");
outfile->Printf( " Nuclear Repulsion Energy = %24.14f\n", nuclearrep_);
outfile->Printf( " One-Electron Energy = %24.14f\n", one_electron_E);
outfile->Printf( " Coulomb Energy = %24.14f\n", coulomb_E);
outfile->Printf( " Hybrid Exchange Energy = %24.14f\n", exchange_E);
outfile->Printf( " XC Functional Energy = %24.14f\n", XC_E);
outfile->Printf( " -D Energy = %24.14f\n\n", dashD_E);
}
return Etotal;
}
bool RCKS::test_convergency()
{
// energy difference
double ediff = E_ - Eold_;
// RMS of the density
Matrix D_rms;
D_rms.copy(D_);
D_rms.subtract(Dold_);
Drms_ = D_rms.rms();
if(optimize_Vc){
constraint_optimization();
return (fabs(ediff) < energy_threshold_ and Drms_ < density_threshold_ and std::fabs(gradW) < gradW_threshold_);
}
return (fabs(ediff) < energy_threshold_ and Drms_ < density_threshold_);
}
/// Gradient of W
///
/// Implements Eq. (6) of Phys. Rev. A 72, 024502 (2005).
void RCKS::gradient_of_W()
{
// gradW = 2.0 * D_->vector_dot(W_so[0]) - (frag_nuclear_charge[0] - constrained_charges[0]);
// gradW -= 2.0 * D_->vector_dot(W_so[1]) - (frag_nuclear_charge[1] - constrained_charges[1]);
gradW = 2.0 * D_->vector_dot(W_tot) - Nc;
outfile->Printf(" gradW(1) = %.9f\n",gradW);
// Transform W_tot to the MO basis
Temp->transform(W_tot,Ca_);
// Transform Fa_ to the MO basis
Temp2->transform(Fa_,Ca_);
gradW_mo_resp = 0.0;
for (int h = 0; h < nirrep_; h++) {
int nmo = nmopi_[h];
int nvir = nmopi_[h]-doccpi_[h];
int nocc = doccpi_[h];
if (nvir == 0 or nocc == 0) continue;
double** Temp_h = Temp->pointer(h);
double** Temp2_h = Temp2->pointer(h);
double* eps = epsilon_a_->pointer(h);
for (int i = 0; i < nocc; ++i){
for (int a = nocc; a < nmo; ++a){
gradW_mo_resp += 4.0 * Temp_h[a][i] * Temp2_h[a][i] / (Temp2_h[i][i] - Temp2_h[a][a]);// ;(eps[i] - eps[a]);
}
}
}
}
// SharedMatrix eigvec= factory_->create_shared_matrix("L");
// SharedVector eigval(factory_->create_vector());
// // Transform W_tot to the MO basis
// Temp->transform(W_tot,Ca_);
// // Diagonalize W
// Temp->diagonalize(eigvec,eigval);
// eigvec->print();
// eigval->print();
/// Hessian of W
///
/// Implements Eq. (7) of Phys. Rev. A 72, 024502 (2005).
void RCKS::hessian_of_W()
{
hessW = 0.0;
// Transform W_tot to the MO basis
Temp->transform(W_tot,Ca_);
for (int h = 0; h < nirrep_; h++) {
int nmo = nmopi_[h];
int nvir = nmopi_[h]-doccpi_[h];
int nocc = doccpi_[h];
if (nvir == 0 or nocc == 0) continue;
double** Temp_h = Temp->pointer(h);
double* eps = epsilon_a_->pointer(h);
for (int i = 0; i < nocc; ++i){
for (int a = nocc; a < nmo; ++a){
//outfile->Printf(" -> (%d,%d): (%f)^2 / (%f - %f) = %f\n",i,a,Temp_h[a][i],eps[i],eps[a],std::pow(Temp_h[a][i],2.0) / (eps[i] - eps[a]));
hessW += Temp_h[a][i] * Temp_h[a][i] / (eps[i] - eps[a]);
}
}
}
hessW *= 4.0; // 2 for the complex conjugate and 2 for the spin cases
}
/// Optimize the Lagrange multiplier
void RCKS::constraint_optimization()
{
outfile->Printf( " ==> Constraint optimization <==\n");
if(psi::scf::KS::options_.get_str("W_ALGORITHM") == "NEWTON"){
// Optimize Vc once you have a good gradient and the gradient is not converged
if (std::fabs(gradW_mo_resp / gradW) < 0.1 and std::fabs(gradW) > gradW_threshold_){
// First step, do a Newton with the hessW information
if(nW_opt == 0){
old_Vc = Vc;
old_gradW = gradW;
// Use the crappy Hessian to do a Newton step with trust radius
double new_Vc = Vc - gradW / hessW;
double threshold = 0.5;
if(std::fabs(new_Vc - Vc) > threshold){
new_Vc = Vc + (new_Vc > Vc ? threshold : -threshold);
}
outfile->Printf( " hessW = %f\n",hessW);
Vc = new_Vc;
}else{
if(std::fabs(Vc - old_Vc) > 1.0e-3){
// We landed somewhere else, update the Hessian
BFGS_hessW = (gradW - old_gradW) / (Vc - old_Vc);
outfile->Printf( " BFGS_hessW = %f\n",BFGS_hessW);
old_Vc = Vc;
old_gradW = gradW;
}
double new_Vc = Vc - gradW / BFGS_hessW;
Vc = new_Vc;
}
// Reset the DIIS subspace
diis_manager_->reset_subspace();
}
}else if (psi::scf::KS::options_.get_str("W_ALGORITHM") == "QUADRATIC"){
if (std::fabs(gradW_mo_resp / gradW) < 0.25 and std::fabs(gradW) > gradW_threshold_){
// Transform W_tot to the MO basis
Temp->transform(W_tot,Ca_);
double numerator = 0.0;
for (int h = 0; h < nirrep_; h++) {
int nocc = doccpi_[h];
double** Temp_h = Temp->pointer(h);
for (int i = 0; i < nocc; ++i){
numerator += 2.0 * Temp_h[i][i];
}
}
numerator -= Nc;
Temp->power(2.0);
double denominator = 0.0;
for (int h = 0; h < nirrep_; h++) {
int nocc = doccpi_[h];
double** Temp_h = Temp->pointer(h);
for (int i = 0; i < nocc; ++i){
denominator += 2.0 * Temp_h[i][i];
}
}
Vc += 0.5 * numerator / denominator;
}
}
nW_opt += 1;
}
void RCKS::Lowdin2()
{
outfile->Printf( " ==> Lowdin Charges <==\n\n");
for (int f = 0; f < nfrag; ++f){
double Q_f = -2.0 * D_->vector_dot(W_so[f]);
Q_f += frag_nuclear_charge[f];
outfile->Printf( " Fragment %d: charge = %.6f\n",f,Q_f);
}
}
void RCKS::Lowdin()
{
// Compute the overlap matrix
boost::shared_ptr<BasisSet> basisset_ = basisset();
boost::shared_ptr<OneBodyAOInt> overlap(integral_->ao_overlap());
SharedMatrix S_ao(new Matrix("S_ao",basisset_->nbf(),basisset_->nbf()));
SharedMatrix D_ao(new Matrix("D_ao",basisset_->nbf(),basisset_->nbf()));
SharedMatrix L_ao(new Matrix("L_ao",basisset_->nbf(),basisset_->nbf()));
overlap->compute(S_ao);
// Form the S^(1/2) matrix
S_ao->power(1.0/2.0);
boost::shared_ptr<PetiteList> pet(new PetiteList(basisset_, integral_));
SharedMatrix SO2AO_ = pet->sotoao();
D_ao->remove_symmetry(D_,SO2AO_);
L_ao->transform(D_ao,S_ao);
L_ao->print();
boost::shared_ptr<Molecule> mol = basisset_->molecule();
SharedVector Qa(new Vector(mol->natom()));
double* Qa_pointer = Qa->pointer();
for (int a = 0; a < mol->natom(); ++a){
Qa->set(a,mol->Z(a));
}
for (int mu = 0; mu < basisset_->nbf(); mu++) {
double charge = L_ao->get(0,mu,mu);
int shell = basisset_->function_to_shell(mu);
int A = basisset_->shell_to_center(shell);
Qa_pointer[A] -= 2.0 * charge;
}
Qa->print();
int nfrag = mol->nfragments();
outfile->Printf( "\n There are %d fragments in this molecule\n", nfrag);
int a = 0;
for (int f = 0; f < nfrag; ++f){
std::vector<int> flist;
std::vector<int> glist;
flist.push_back(f);
boost::shared_ptr<Molecule> frag = mol->extract_subsets(flist,glist);
double fcharge = 0.0;
for (int n = 0; n < frag->natom(); ++n){
fcharge += Qa_pointer[a];
++a;
}
outfile->Printf(" Fragment %d, charge = %.8f, constrained charge = %.8f:\n",f,fcharge,double(frag->molecular_charge()));
}
}
}} // Namespaces