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caspt2grad.cc
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//
// BAGEL - Brilliantly Advanced General Electronic Structure Library
// Filename: caspt2grad.cc
// Copyright (C) 2013 Quantum Simulation Technologies, Inc.
//
// Author: Toru Shiozaki <shiozaki@qsimulate.com>
// Maintainer: QSimulate
//
// This file is part of the BAGEL package.
//
// 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 3 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, see <http://www.gnu.org/licenses/>.
//
#include <bagel_config.h>
#include <src/scf/hf/fock.h>
#include <src/grad/cpcasscf.h>
#include <src/grad/gradeval.h>
#include <src/multi/casscf/cassecond.h>
#include <src/multi/casscf/casnoopt.h>
#include <src/multi/casscf/qvec.h>
#include <src/smith/smith.h>
#include <src/smith/caspt2grad.h>
#include <src/prop/multipole.h>
#include <src/prop/hyperfine.h>
#include <src/prop/moprint.h>
using namespace std;
using namespace bagel;
CASPT2Grad::CASPT2Grad(shared_ptr<const PTree> inp, shared_ptr<const Geometry> geom, shared_ptr<const Reference> ref)
: Method(inp, geom, ref) {
#ifdef COMPILE_SMITH
Timer timer;
// compute CASSCF first
if (inp->get<string>("algorithm", "") != "noopt") {
auto cas = make_shared<CASSecond>(inp, geom, ref);
cas->compute();
ref_ = cas->conv_to_ref();
fci_ = cas->fci();
thresh_ = cas->thresh();
} else {
auto cas = make_shared<CASNoopt>(inp, geom, ref);
cas->compute();
ref_ = cas->conv_to_ref();
if (ref_->nact())
fci_ = cas->fci();
thresh_ = cas->thresh();
}
// gradient/property calculation
do_hyperfine_ = inp->get<bool>("hyperfine", false);
timer.tick_print("Reference calculation");
cout << endl << " === DF-CASPT2Grad calculation ===" << endl << endl;
#else
throw logic_error("CASPT2 gradients require SMITH-generated code. Please compile BAGEL with --enable-smith");
#endif
}
// compute smith and set rdms and ci deriv to a member
void CASPT2Grad::compute() {
#ifdef COMPILE_SMITH
// construct SMITH here
shared_ptr<PTree> smithinput = idata_->get_child("smith");
smithinput->put("_grad", true);
smithinput->put("_hyperfine", do_hyperfine_);
smith_ = make_shared<Smith>(smithinput, ref_->geom(), ref_);
smith_->compute();
#endif
}
template<>
void GradEval<CASPT2Grad>::compute_dipole() const {
#ifdef COMPILE_SMITH
const int nmobasis = ref_->coeff()->mdim();
const int nclosed = ref_->nclosed();
const int nact = ref_->nact();
const int nstate = ref_->nstate();
vector<vector<double>> state_dipole;
vector<vector<double>> transition_dipole;
for (int istate = 0; istate != nstate; ++istate) {
task_->compute_gradient(istate, istate, make_shared<NacmType>("interstate"), /*nocider=*/true);
{
auto d0ms = make_shared<Matrix>(nmobasis, nmobasis);
if (nact)
d0ms->add_block(1.0, nclosed, nclosed, nact, nact, task_->d10ms());
for (int i = 0; i != nclosed; ++i)
d0ms->element(i,i) = 2.0;
{
const string dmlabel = "CASPT2 unrelaxed dipole moment: " + to_string(istate);
auto dtotao = make_shared<Matrix>(*(task_->smith()->algo()->coeff()) * (*d0ms + *(task_->d11()) + *(task_->d1())) ^ *(task_->smith()->algo()->coeff()));
Dipole dipole(geom_, dtotao, dmlabel);
auto moment = dipole.compute();
state_dipole.push_back(moment);
}
}
}
for (int istate = 1; istate != nstate; ++istate) {
for (int jstate = 0; jstate != istate; ++jstate) {
task_->compute_gradient(istate, jstate, make_shared<NacmType>("interstate"), /*nocider=*/true);
{
auto d0ms = make_shared<Matrix>(nmobasis, nmobasis);
if (nact)
d0ms->add_block(1.0, nclosed, nclosed, nact, nact, task_->d10ms());
{
const string dmlabel = "CASPT2 unrelaxed dipole moment: " + to_string(istate) + " - " + to_string(jstate);
auto dtotao = make_shared<Matrix>(*(task_->smith()->algo()->coeff()) * (*d0ms + *(task_->d11()) + *(task_->d1())) ^ *(task_->smith()->algo()->coeff()));
Dipole dipole(geom_, dtotao, dmlabel);
auto moment = dipole.compute();
transition_dipole.push_back(moment);
}
}
}
}
cout << " * CASPT2 dipole moments" << endl << endl;
for (int istate = 0; istate != nstate; ++istate) {
cout << " * State " << setw(11) << istate << " : ";
cout << " (" << setw(12) << setprecision(6) << state_dipole[istate][0] << ", " << setw(12) << state_dipole[istate][1]
<< ", " << setw(12) << state_dipole[istate][2] << ") a.u." << endl << endl;
}
for (int istate = 1, counter = 0; istate != nstate; ++istate) {
for (int jstate = 0; jstate != istate; ++jstate, ++counter) {
cout << " * Transition " << setw(2) << istate << " -" << setw(2) << jstate << " : ";
cout << " (" << setw(12) << setprecision(6) << transition_dipole[counter][0] << ", " << setw(12) << transition_dipole[counter][1]
<< ", " << setw(12) << transition_dipole[counter][2] << ") a.u." << endl;
const double egap = energyvec()[istate] - energyvec()[jstate];
auto moment = transition_dipole[counter];
const double r2 = moment[0] * moment[0] + moment[1] * moment[1] + moment[2] * moment[2];
const double fnm = (2.0 / 3.0) * egap * r2;
cout << " * Oscillator strength : " << setprecision(6) << setw(10) << fnm << " a.u." << endl << endl;
}
}
#endif
}
void CASPT2Grad::compute_gradient(const int istate, const int jstate, shared_ptr<const NacmType> nacmtype, const bool nocider) {
#ifdef COMPILE_SMITH
const int nclosed = ref_->nclosed();
const int nact = ref_->nact();
const int nocc = ref_->nocc();
target_ = istate;
smith_->compute_gradient(istate, jstate, nacmtype, nocider);
coeff_ = smith_->coeff();
if (nact && !nocider)
cideriv_ = smith_->cideriv()->copy();
ncore_ = smith_->algo()->info()->ncore();
wf1norm_ = smith_->wf1norm();
msrot_ = smith_->msrot();
nstates_ = wf1norm_.size();
assert(msrot_->ndim() == nstates_ && msrot_->mdim() == nstates_);
assert(nstates_ == smith_->algo()->info()->ciwfn()->nstates());
Timer timer;
// save correlated density matrices d(1), d(2), and ci derivatives
auto d1tmp = make_shared<Matrix>(*smith_->dm1());
auto d11tmp = make_shared<Matrix>(*smith_->dm11());
d1tmp->symmetrize();
d11tmp->symmetrize();
// a factor of 2 from the Hylleraas functional (which is not included in the generated code)
d11tmp->scale(2.0);
auto d1set = [this](shared_ptr<const Matrix> d1t) {
if (!ncore_) {
return d1t->copy();
} else {
auto out = make_shared<Matrix>(coeff_->mdim(), coeff_->mdim());
out->copy_block(ncore_, ncore_, coeff_->mdim()-ncore_, coeff_->mdim()-ncore_, d1t);
return out;
}
};
d1_ = d1set(d1tmp);
d11_ = d1set(d11tmp);
// XMS density matrix
if (smith_->dcheck()) {
shared_ptr<const Matrix> dc = smith_->dcheck();
assert(dc->ndim() == nact && dc->mdim() == nact);
auto tmp = make_shared<Matrix>(nocc, nocc);
tmp->add_block(1.0, nclosed, nclosed, nact, nact, dc);
dcheck_ = tmp;
}
// spin density matrices
if (do_hyperfine_) {
auto sd11tmp = make_shared<Matrix>(*smith_->sdm11());
sd11tmp->symmetrize();
sd11tmp->scale(2.0);
sd1_ = d1set(smith_->sdm1());
sd11_ = d1set(sd11tmp);
}
if (nact) {
d10ms_ = make_shared<RDM<1>>(nact);
d20ms_ = make_shared<RDM<2>>(nact);
for (int ist = 0; ist != nstates_; ++ist) {
const double ims = msrot(ist, jstate);
for (int jst = 0; jst != nstates_; ++jst) {
const double jms = msrot(jst, istate);
shared_ptr<const RDM<1>> rdm1t;
shared_ptr<const RDM<2>> rdm2t;
tie(rdm1t, rdm2t) = ref_->rdm12(jst, ist, /*recompute*/true);
d10ms_->ax_plus_y(ims*jms, *rdm1t);
d20ms_->ax_plus_y(ims*jms, *rdm2t);
}
}
}
d2_ = smith_->dm2();
if (istate != jstate) {
auto vd1tmp = make_shared<Matrix>(*smith_->vd1());
vd1_ = d1set(vd1tmp);
auto d10IJ = make_shared<Matrix>(*(ref_->rdm1_mat_tr(d10ms_)->resize(coeff_->mdim(),coeff_->mdim())));
*vd1_ += *d10IJ;
cout << " * NACME Target states: " << istate << " - " << jstate << endl;
const double energy1 = smith_->algo()->energy(istate);
const double energy2 = smith_->algo()->energy(jstate);
cout << " * Energy gap is: " << setprecision(10) << (energy1 - energy2) * au2eV__ << " eV" << endl << endl;
} else {
energy_ = smith_->algo()->energy(istate);
cout << " * CASPT2 energy: " << setprecision(12) << setw(15) << energy_ << endl;
}
#endif
}
template<>
vector<double> GradEval<CASPT2Grad>::energyvec() const {
#ifdef COMPILE_SMITH
return task_->smith()->algo()->energyvec();
#else
return vector<double>();
#endif
}
template<>
shared_ptr<GradFile> GradEval<CASPT2Grad>::compute(const string jobtitle, shared_ptr<const GradInfo> gradinfo) {
#ifdef COMPILE_SMITH
const int istate = gradinfo->target_state();
const int jstate = (jobtitle == "nacme") ? gradinfo->target_state2() : istate;
task_->compute_gradient(istate, jstate, gradinfo->nacmtype(), !gradinfo->cider_eval());
Timer timer;
shared_ptr<const Reference> ref = task_->ref();
auto fci = task_->fci();
const double egap = task_->smith()->algo()->energy(jstate) - task_->smith()->algo()->energy(istate);
const int nclosed = ref->nclosed();
const int nact = ref->nact();
// second order density matrix
shared_ptr<const Matrix> d1 = task_->d1();
// first order density matrices
shared_ptr<const Matrix> d11 = task_->d11();
shared_ptr<const Dvec> cider = nact ? task_->cideriv() : nullptr;
shared_ptr<const Matrix> coeff = task_->coeff();
const int ncore = task_->ncore();
const int nocc = ref->nocc();
const int nmobasis = coeff->mdim();
// d0 including core
auto d0ms = make_shared<Matrix>(nmobasis, nmobasis);
if (nact)
d0ms->add_block(1.0, nclosed, nclosed, nact, nact, task_->d10ms());
if (jobtitle == "nacme") {
d0ms->symmetrize();
} else {
for (int i = 0; i != nclosed; ++i)
d0ms->element(i,i) = 2.0;
}
const MatView ocoeff = coeff->slice(0, nocc);
if (jobtitle == "nacme") {
const string tdmlabel = "Transition dipole moment between " + to_string(istate) + " - " + to_string(jstate);
auto dtotao = make_shared<Matrix>(*coeff * (*d0ms + *d11 + *d1) ^ *coeff);
Dipole dipole(geom_, dtotao, tdmlabel);
auto moment = dipole.compute();
const double r2 = moment[0] * moment[0] + moment[1] * moment[1] + moment[2] * moment[2];
const double fnm = (2.0 / 3.0) * egap * r2;
cout << " * Oscillator strength for transition between " << istate << " - "
<< jstate << setprecision(6) << setw(10) << fnm << " a.u." << endl << endl;
} else {
auto dtotao = make_shared<Matrix>(*coeff * (*d0ms + *d11 + *d1) ^ *coeff);
Dipole dipole(geom_, dtotao, "CASPT2 unrelaxed");
dipole.compute();
}
if (!gradinfo->cider_eval()) {
return make_shared<GradFile>(geom_->natom());
}
// compute Yrs
shared_ptr<const DFHalfDist> half = ref->geom()->df()->compute_half_transform(ocoeff);
shared_ptr<const DFHalfDist> halfj = half->apply_J();
shared_ptr<const DFHalfDist> halfjj = halfj->apply_J();
shared_ptr<Matrix> yrs;
shared_ptr<const DFFullDist> fulld1; // (gamma| ir) D(ir,js)
tie(yrs, fulld1) = task_->compute_Y(half, halfj, halfjj, /*nacme=*/(jobtitle=="nacme"));
timer.tick_print("Yrs evaluation");
// solve CPCASSCF
shared_ptr<Matrix> g0 = yrs;
shared_ptr<Dvec> g1 = nact ? cider->copy() : make_shared<Dvec>(make_shared<Determinants>(), 1);
if (jobtitle == "nacme" && (gradinfo->nacmtype()->is_full() || gradinfo->nacmtype()->is_etf()))
task_->augment_Y(d0ms, g0, g1, halfj, istate, jstate, egap);
timer.tick_print("Yrs non-Lagrangian terms");
auto grad = make_shared<PairFile<Matrix, Dvec>>(g0, g1);
shared_ptr<const Dvec> civector;
if (nact) {
civector = ref->ciwfn()->civectors();
} else {
auto civec = make_shared<Dvec>(make_shared<Determinants>(), 1);
civec->data(0)->element(0,0) = 1.0;
civector = civec;
}
auto cp = make_shared<CPCASSCF>(grad, civector, halfj, ref, fci, ncore, task_->smith()->algo()->info()->shift_imag(), coeff);
shared_ptr<const Matrix> zmat, xmat, smallz;
shared_ptr<const Dvec> zvec;
tie(zmat, zvec, xmat, smallz) = cp->solve(task_->thresh(), gradinfo->maxziter(), task_->dcheck(), /*xms*/!!task_->dcheck());
timer.tick_print("Z-CASSCF solution");
// form relaxed 1RDM
// form Zd + dZ^+
shared_ptr<const Matrix> d0sa = nact ? ref->rdm1_mat()->resize(nmobasis, nmobasis) : d0ms;
auto dm = make_shared<Matrix>(*zmat * *d0sa + (*d0sa ^ *zmat));
auto dtot = make_shared<Matrix>(*d0ms + *d11 + *d1 + *dm);
if (smallz)
*dtot += *smallz;
// form zdensity
shared_ptr<const RDM<1>> zrdm1;
shared_ptr<const RDM<2>> zrdm2;
if (nact) {
auto detex = make_shared<Determinants>(nact, fci->nelea(), fci->neleb(), false, /*mute=*/true);
tie(zrdm1, zrdm2) = fci->compute_rdm12_av_from_dvec(ref->ciwfn()->civectors(), zvec, detex);
shared_ptr<Matrix> zrdm1_mat = zrdm1->rdm1_mat(nclosed, false)->resize(nmobasis, nmobasis);
zrdm1_mat->symmetrize();
dtot->ax_plus_y(1.0, zrdm1_mat);
}
// compute relaxed dipole to check
auto dtotao = make_shared<Matrix>(*coeff * *dtot ^ *coeff);
{
Dipole dipole(geom_, dtotao, "CASPT2 relaxed");
dipole_ = dipole.compute();
}
// print relaxed density if requested
if (gradinfo->density_print()) {
auto density_print = make_shared<MOPrint>(gradinfo->moprint_info(), geom_, ref_, /*is_density=*/true, make_shared<const ZMatrix>(*dtotao, 1.0));
density_print->compute();
}
// xmat in the AO basis
auto xmatao = make_shared<Matrix>(*coeff * *xmat ^ *coeff);
shared_ptr<Matrix> qxmatao;
if (jobtitle == "nacme") {
auto qxmat = task_->vd1()->resize(nmobasis, nmobasis);
if (gradinfo->nacmtype()->is_full())
qxmat->scale(egap);
else
qxmat->zero();
qxmatao = make_shared<Matrix>(*coeff * *qxmat ^ *coeff);
}
// two-body part
// first make occ-occ part (copy-and-paste from src/casscf/supercigrad.cc)
shared_ptr<const DFFullDist> qij = halfjj->compute_second_transform(ocoeff);
shared_ptr<DFHalfDist> qri;
{
shared_ptr<const Matrix> ztrans = make_shared<Matrix>(*coeff * zmat->slice(0,nocc));
if (nact) {
RDM<2> D(*task_->d20ms()+*zrdm2);
RDM<1> dd(*task_->d10ms()+*zrdm1);
// symetrize dd (zrdm1 needs symmetrization)
for (int i = 0; i != nact; ++i)
for (int j = 0; j != nact; ++j)
dd(j,i) = dd(i,j) = 0.5*(dd(j,i)+dd(i,j));
shared_ptr<DFFullDist> qijd;
if (jobtitle == "nacme")
qijd = qij->apply_2rdm_tran(D, dd, nclosed, nact);
else
qijd = qij->apply_2rdm(D, dd, nclosed, nact);
qijd->ax_plus_y(2.0, halfjj->compute_second_transform(ztrans)->apply_2rdm(*ref->rdm2_av(), *ref->rdm1_av(), nclosed, nact));
qri = qijd->back_transform(ocoeff);
shared_ptr<const DFFullDist> qijd2 = qij->apply_2rdm(*ref->rdm2_av(), *ref->rdm1_av(), nclosed, nact);
qri->ax_plus_y(2.0, qijd2->back_transform(ztrans));
} else {
shared_ptr<DFFullDist> qijd = qij->apply_closed_2RDM();
qijd->ax_plus_y(2.0, halfjj->compute_second_transform(ztrans)->apply_closed_2RDM());
qri = qijd->back_transform(ocoeff);
shared_ptr<const DFFullDist> qijd2 = qij->apply_closed_2RDM();
qri->ax_plus_y(2.0, qijd2->back_transform(ztrans));
}
}
// computing hyperfine coupling
if (task_->do_hyperfine()) {
shared_ptr<Matrix> dhfcc = task_->spin_density_unrelaxed();
{ // for the time being, print unrelaxed HFCC
HyperFine hfcc(geom_, dhfcc, fci->det()->nspin(), "CASPT2 unrelaxed");
hfcc.compute();
}
dhfcc->ax_plus_y(1.0, task_->spin_density_relax(zrdm1, zrdm2, zmat));
HyperFine hfcc(geom_, dhfcc, fci->det()->nspin(), "CASPT2 relaxed");
hfcc.compute();
}
// D1 part. 2.0 seems to come from the difference between smith and bagel (?)
qri->ax_plus_y(2.0, fulld1->apply_J()->back_transform(coeff));
// contributions from non-separable part
shared_ptr<Matrix> qq = qri->form_aux_2index(halfjj, 1.0);
// separable part: see Gyorffy appendix
vector<shared_ptr<const Matrix>> da;
vector<shared_ptr<const VectorB>> ca;
auto separable_pair = [&,this](shared_ptr<const Matrix> d0occ, shared_ptr<const Matrix> d1bas) {
shared_ptr<const Matrix> d0mo = make_shared<Matrix>(*d0occ ^ ocoeff);
shared_ptr<const Matrix> d0ao = make_shared<Matrix>(ocoeff * *d0mo);
shared_ptr<const Matrix> d1ao = make_shared<Matrix>(*coeff * *d1bas ^ *coeff);
shared_ptr<const VectorB> cd0 = geom_->df()->compute_cd(d0ao);
shared_ptr<const VectorB> cd1 = geom_->df()->compute_cd(d1ao);
ca.push_back(cd0);
da.push_back(d1ao);
shared_ptr<DFHalfDist> sepd = halfjj->apply_density(d1ao);
sepd = sepd->transform_occ(d0occ);
qri->ax_plus_y(-1.0, sepd);
qri->add_direct_product(cd1, d0mo, 1.0);
*qq += (*cd0 ^ *cd1) * 2.0;
*qq += *halfjj->form_aux_2index(sepd, -1.0);
return make_tuple(cd0, d1ao);
};
separable_pair(d0sa->get_submatrix(0,0,nocc,nocc), d1);
if (smallz)
separable_pair(d0sa->get_submatrix(0,0,nocc,nocc), smallz);
// back transform the rest
shared_ptr<DFDist> qrs = qri->back_transform(ocoeff);
qrs->add_direct_product(ca, da, 1.0);
timer.tick_print("Effective densities");
// compute gradients
shared_ptr<GradFile> gradient = contract_gradient(dtotao, xmatao, qrs, qq, qxmatao);
if ((jobtitle == "nacme") && !(gradinfo->nacmtype()->is_noweight()))
gradient->scale(1.0/egap);
gradient->print();
timer.tick_print("Gradient integral contraction");
if (jobtitle == "force")
energy_ = task_->energy();
else
energy_ = 0.0;
return gradient;
#else
throw logic_error("CASPT2 gradients require SMITH-generated code. Please compile BAGEL with --enable-smith");
return nullptr;
#endif
}