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rs_functionals.cc
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/*
* @BEGIN LICENSE
*
* mydft by Psi4 Developer, a plugin to:
*
* Psi4: an open-source quantum chemistry software package
*
* Copyright (c) 2007-2016 The Psi4 Developers.
*
* The copyrights for code used from other parties are included in
* the corresponding files.
*
* 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.
*
* @END LICENSE
*/
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <algorithm>
#include <vector>
#include <utility>
#include <tuple>
#include "psi4/libpsi4util/libpsi4util.h"
// for dft
#include "psi4/libfock/v.h"
#include "psi4/libfunctional/superfunctional.h"
// for grid
#include "psi4/libfock/points.h"
#include "psi4/libfock/cubature.h"
#include "psi4/psi4-dec.h"
#include "psi4/liboptions/liboptions.h"
#include "psi4/libpsio/psio.hpp"
#include "psi4/libmints/wavefunction.h"
#include "psi4/libmints/mintshelper.h"
#include "psi4/libmints/matrix.h"
#include "psi4/libmints/vector.h"
#include "psi4/libmints/basisset.h"
#include "psi4/libmints/molecule.h"
#include "psi4/lib3index/dftensor.h"
#include "psi4/libqt/qt.h"
// jk object
#include "psi4/libfock/jk.h"
// for dft
#include "psi4/libfock/v.h"
#include "psi4/libfunctional/superfunctional.h"
#include "mcpdft_solver.h"
// @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
// @ The four major conventions regarding to the principal variables used for @
// @ building exchange-correlation (XC) functionals are as follows: @
// @ @
// @ Convention (I) spin densities rho_a, rho_b and their gradients: EXC[rho_a, rho_b, rho_a', rho_b'] @
// @ Convention (II) total density, spin-magnetization density m and their gradients: EXC[rho, m, rho', m'] @
// @ Convention (III) total density, spin polarization and their gradients: EXC[rho, zeta, rho', zeta'] @
// @ Convention (IV) singlet and triplet charge densities @
// @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
namespace psi{ namespace mcpdft {
//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
//+++++++++++++++++++ Exchange functionals ++++++++++++++++++
// wPBE, Lh-BLYP, wB88 +
//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
double MCPDFTSolver::EX_wPBE_I(std::shared_ptr<Vector> RHO_A, std::shared_ptr<Vector> RHO_B,
std::shared_ptr<Vector> SIGMA_AA, std::shared_ptr<Vector> SIGMA_BB) {
const double OMEGA = options_.get_double("MCPDFT_OMEGA");
const double A_bar = 0.757211;
const double B = -0.106364;
const double C = -0.118649;
const double D = 0.609650;
const double E = -0.0477963;
const double a2 = 0.0159941;
const double a3 = 0.0852995;
const double a4 = -0.160368;
const double a5 = 0.152645;
const double a6 = -0.0971263;
const double a7 = 0.0422061;
const double b1 = 5.33319;
const double b2 = -12.4780;
const double b3 = 11.0988;
const double b4 = -5.11013;
const double b5 = 1.71468;
const double b6 = -0.610380;
const double b7 = 0.307555;
const double b8 = -0.0770547;
const double b9 = 0.0334840;
double * rho_ap = RHO_A->pointer();
double * rho_bp = RHO_B->pointer();
double * sigma_aap = SIGMA_AA->pointer();
double * sigma_bbp = SIGMA_BB->pointer();
auto kF = [](double RHO) -> double {
double dum = pow(3.0 * M_PI * M_PI * RHO ,1.0/3.0);
return dum;
};
auto S = [=](double RHO, double SIGMA) -> double {
double temp = sqrt(SIGMA) / (2.0 * kF(RHO) * RHO);
return temp;
};
auto H = [=](double RHO, double SIGMA) -> double {
double s1 = S(RHO,SIGMA);
double s2 = s1 * s1;
double s3 = s2 * s1;
double s4 = s3 * s1;
double s5 = s4 * s1;
double s6 = s5 * s1;
double s7 = s6 * s1;
double s8 = s7 * s1;
double s9 = s8 * s1;
double numerator = a2 * s2 + a3 * s3 + a4 * s4 + a5 * s5 + a6 * s6 + a7 * s7;
double denominator = 1.0 + b1 * s1 + b2 * s2 + b3 * s3 + b4 * s4 + b5 * s5 + b6 * s6 + b7 * s7 + b8 * s8 + b9 * s9;
double dum = numerator/denominator;
return dum;
};
auto Nu = [=](double RHO) -> double {
double dum = OMEGA / kF(RHO);
return dum;
};
auto ZETA = [=](double RHO, double SIGMA) -> double {
double dum = pow(S(RHO,SIGMA), 2.0) * H(RHO, SIGMA);
return dum;
};
auto ETA = [=](double RHO, double SIGMA) -> double {
double temp = A_bar + ZETA(RHO, SIGMA);
return temp;
};
auto LAMBDA = [=](double RHO, double SIGMA) -> double {
double temp = D + ZETA(RHO, SIGMA);
return temp;
};
auto Chi = [=](double RHO, double SIGMA) -> double {
double dum = Nu(RHO) / sqrt(LAMBDA(RHO,SIGMA) + pow(Nu(RHO),2.0));
return dum;
};
auto BG_LAMBDA = [=](double RHO, double SIGMA) -> double {
double temp = LAMBDA(RHO,SIGMA) / (1.0 - Chi(RHO,SIGMA));
return temp;
};
auto F_bar = [=](double RHO, double SIGMA) -> double {
double s0 = 2.0;
double s1 = S(RHO,SIGMA);
double s2 = s1 * s1;
double ze_v = ZETA(RHO,SIGMA);
double dum = 1.0 - (1.0/(27.0*C)) * (s2/(1.0 + (s2/pow(s0,2.0)))) - (1.0/(2.0*C)) * ze_v;
return dum;
};
auto G_bar = [=](double RHO, double SIGMA) -> double {
double ze_v = ZETA(RHO,SIGMA);
double et_v = ETA(RHO,SIGMA);
double lam_v = LAMBDA(RHO,SIGMA);
double lam_v2 = lam_v * lam_v;
double lam_v3 = lam_v2 * lam_v;
double lam_v72 = pow(lam_v,7.0/2.0);
double sq_ze = sqrt(ze_v);
double sq_et = sqrt(et_v);
double dum = -(2.0/5.0) * C * F_bar(RHO,SIGMA) * lam_v - (4.0/15.0) * B * lam_v2 - (6.0/5.0) * A_bar * lam_v3
- (4.0/5.0) * sqrt(M_PI) * lam_v72 - (12.0/5.0) * lam_v72 * (sq_ze - sq_et);
dum *= (1.0/E);
return dum;
};
auto eX = [=](double RHO) -> double {
double temp = -(3.0 * kF(RHO)) / (4.0 * M_PI);
return temp;
};
auto FX = [=](double RHO, double SIGMA) -> double {
double chi_v = Chi(RHO,SIGMA);
double chi_v2 = chi_v * chi_v;
double chi_v3 = chi_v2 * chi_v;
double chi_v5 = chi_v3 * chi_v2;
double nu_v = Nu(RHO);
double ze_v = ZETA(RHO,SIGMA);
double et_v = ETA(RHO,SIGMA);
double bg_lam_v = BG_LAMBDA(RHO,SIGMA);
double bg_lam_v2 = bg_lam_v * bg_lam_v;
double bg_lam_v3 = bg_lam_v2 * bg_lam_v;
double lam_v = LAMBDA(RHO,SIGMA);
double lam_v2 = lam_v * lam_v;
double lam_v3 = lam_v2 * lam_v;
double sq_ze_nu = sqrt(ze_v + nu_v*nu_v);
double sq_et_nu = sqrt(et_v + nu_v*nu_v);
double sq_la_nu = sqrt(lam_v + nu_v*nu_v);
double temp = A_bar * ( ze_v/( (sq_ze_nu + sq_et_nu) * (sq_ze_nu + nu_v) ) + et_v/( (sq_ze_nu + sq_et_nu) * (sq_et_nu + nu_v) ) )
- (4.0/9.0) * (B/bg_lam_v) - (4.0/9.0) * (C * F_bar(RHO,SIGMA) / bg_lam_v2) * (1.0 + (1.0/2.0) * chi_v )
- (8.0/9.0) * (E * G_bar(RHO,SIGMA) / bg_lam_v3) * (1.0 + (9.0/8.0) * chi_v + (3.0/8.0) * chi_v2)
+ 2.0 * ze_v * log( 1.0 - (lam_v - ze_v) / ( (nu_v + sq_la_nu) * (sq_la_nu + sq_ze_nu) ) )
- 2.0 * et_v * log( 1.0 - (lam_v - et_v) / ( (nu_v + sq_la_nu) * (sq_la_nu + sq_et_nu) ) );
return temp;
};
double exc = 0.0;
for (int p = 0; p < phi_points_; p++) {
double rhoa = rho_ap[p];
double rhob = rho_bp[p];
double rho = rhoa + rhob;
double sigmaaa = sigma_aap[p];
double sigmabb = sigma_bbp[p];
double sigma = 0.0;
double tol = 1.0e-20;
if ( rho > tol ) {
if ( rhoa < tol ){
rho = rhob;
sigmabb = std::max(0.0,sigmabb);
sigma = sigmabb;
double zk = eX(2.0 * rho) * FX(2.0 * rho, 4.0 * sigma);
exc += rho * zk * grid_w_->pointer()[p];
}else if ( rhob < tol ){
rho = rhoa;
sigmaaa = std::max(0.0,sigmaaa);
sigma = sigmaaa;
double zk = eX(2.0 * rho) * FX(2.0 * rho, 4.0 * sigma);
exc += rho * zk * grid_w_->pointer()[p];
}else {
double zka = rhoa * eX(2.0 * rhoa) * FX(2.0 * rhoa, 4.0 * sigmaaa);
double zkb = rhob * eX(2.0 * rhob) * FX(2.0 * rhob, 4.0 * sigmabb);
double zk = zka + zkb;
exc += zk * grid_w_->pointer()[p];
}
}else{
//double zk = 0.0;
exc += 0.0;
}
}
return exc;
}
double MCPDFTSolver::Lh_EX_B88_I(std::shared_ptr<Vector> RHO_A, std::shared_ptr<Vector> RHO_B,
std::shared_ptr<Vector> SIGMA_AA, std::shared_ptr<Vector> SIGMA_BB){
double tol = 1.0e-20;
const double Cx = 0.73855876638202240586;
const double beta = 0.0042;
const double c = pow(2.0,1.0/3.0) * Cx;
double * ex_exact_p = ex_exact_->pointer();
double * lmf_p = lmf_->pointer();
double * rho_ap = RHO_A->pointer();
double * rho_bp = RHO_B->pointer();
double * sigma_aap = SIGMA_AA->pointer();
double * sigma_bbp = SIGMA_BB->pointer();
double exc = 0.0;
for (int p = 0; p < phi_points_; p++) {
double rhoa = rho_ap[p];
double rhob = rho_bp[p];
double rho = rhoa + rhob;
double sigmaaa = sigma_aap[p];
double sigmabb = sigma_bbp[p];
double rhoa_43 = 0.0;
double rhob_43 = 0.0;
double Xa = 0.0;
double Xb = 0.0;
double Xa_2 = 0.0;
double Xb_2 = 0.0;
if ( rho > tol ) {
if ( rhoa < tol ){
rhoa = 0.0;
sigmabb = std::max(0.0,sigma_bbp[p]);
rhob_43 = pow(rhob, 4.0/3.0);
Xb = sqrt(sigma_bbp[p]) / rhob_43;
Xb_2 = Xb * Xb;
}else if ( rhob < tol ){
rhob = 0.0;
sigmaaa = std::max(0.0,sigma_aap[p]);
rhoa_43 = pow( rhoa, 4.0/3.0);
Xa = sqrt(sigma_aap[p]) / rhoa_43;
Xa_2 = Xa * Xa;
}else{
sigmaaa = std::max(0.0,sigma_aap[p]);
sigmabb = std::max(0.0,sigma_bbp[p]);
rhoa_43 = pow( rhoa, 4.0/3.0);
rhob_43 = pow( rhob, 4.0/3.0);
Xa = sqrt(sigma_aap[p]) / rhoa_43;
Xb = sqrt(sigma_bbp[p]) / rhob_43;
Xa_2 = Xa * Xa;
Xb_2 = Xb * Xb;
}
exc += -rhoa_43 * ( c + (beta * Xa_2) / (1.0 + 6.0 * beta * Xa * asinh(Xa)) ) * (1.0 - lmf_p[p]) * grid_w_->pointer()[p];
exc += -rhob_43 * ( c + (beta * Xb_2) / (1.0 + 6.0 * beta * Xb * asinh(Xb)) ) * (1.0 - lmf_p[p]) * grid_w_->pointer()[p];
exc += pow(rho,1.0/3.0) * ex_exact_p[p] * lmf_p[p] * grid_w_->pointer()[p];// TODO:Check the spin-polarized version as well
}else{
exc += 0.0;
}
}
return exc;
}
double MCPDFTSolver::EX_wB88_I(std::shared_ptr<Vector> RHO_A, std::shared_ptr<Vector> RHO_B,
std::shared_ptr<Vector> SIGMA_AA, std::shared_ptr<Vector> SIGMA_BB) {
const double OMEGA = options_.get_double("MCPDFT_OMEGA");
const double A_bar = 0.757211;
const double B = -0.106364;
const double C = -0.118649;
const double D = 0.609650;
const double E = -0.0477963;
const double a2 = 0.0253933;
const double a3 = -0.0673075;
const double a4 = 0.0891476;
const double a5 = -0.0454168;
const double a6 = -0.0076581;
const double a7 = 0.0142506;
const double b1 = -2.65060;
const double b2 = 3.91108;
const double b3 = -3.31509;
const double b4 = 1.54485;
const double b5 = -0.198386;
const double b6 = -0.136112;
const double b7 = 0.0647862;
const double b8 = 0.0159586;
const double b9 = -0.000245066;
double * rho_ap = RHO_A->pointer();
double * rho_bp = RHO_B->pointer();
double * sigma_aap = SIGMA_AA->pointer();
double * sigma_bbp = SIGMA_BB->pointer();
auto kF = [](double RHO) -> double {
double dum = pow(3.0 * M_PI * M_PI * RHO ,1.0/3.0);
return dum;
};
auto SS = [=](double RHO, double SIGMA) -> double {
double temp = sqrt(SIGMA) / (2.0 * kF(RHO) * RHO);
return temp;
};
auto S = [=](double RHO, double SIGMA) -> double {
double xi = 1.0 / (exp(20.0) - 1.0);
double temp = -log( ( exp(-SS(RHO,SIGMA)) + xi ) / (1.0 + xi) );
return temp;
};
auto H = [=](double RHO, double SIGMA) -> double {
double s1 = S(RHO,SIGMA);
double s2 = s1 * s1;
double s3 = s2 * s1;
double s4 = s3 * s1;
double s5 = s4 * s1;
double s6 = s5 * s1;
double s7 = s6 * s1;
double s8 = s7 * s1;
double s9 = s8 * s1;
double numerator = a2 * s2 + a3 * s3 + a4 * s4 + a5 * s5 + a6 * s6 + a7 * s7;
double denominator = 1.0 + b1 * s1 + b2 * s2 + b3 * s3 + b4 * s4 + b5 * s5 + b6 * s6 + b7 * s7 + b8 * s8 + b9 * s9;
double dum = numerator/denominator;
return dum;
};
auto Nu = [=](double RHO) -> double {
double dum = OMEGA / kF(RHO);
return dum;
};
auto ZETA = [=](double RHO, double SIGMA) -> double {
double dum = pow(S(RHO,SIGMA), 2.0) * H(RHO, SIGMA);
return dum;
};
auto ETA = [=](double RHO, double SIGMA) -> double {
double temp = A_bar + ZETA(RHO, SIGMA);
return temp;
};
auto LAMBDA = [=](double RHO, double SIGMA) -> double {
double temp = D + ZETA(RHO, SIGMA);
return temp;
};
auto Chi = [=](double RHO, double SIGMA) -> double {
double dum = Nu(RHO) / sqrt(LAMBDA(RHO,SIGMA) + pow(Nu(RHO),2.0));
return dum;
};
auto BG_LAMBDA = [=](double RHO, double SIGMA) -> double {
double temp = LAMBDA(RHO,SIGMA) / (1.0 - Chi(RHO,SIGMA));
return temp;
};
auto F_bar = [=](double RHO, double SIGMA) -> double {
double s0 = 2.0;
double s1 = S(RHO,SIGMA);
double s2 = s1 * s1;
double ze_v = ZETA(RHO,SIGMA);
double dum = 1.0 - (1.0/(27.0*C)) * (s2/(1.0 + (s2/pow(s0,2.0)))) - (1.0/(2.0*C)) * ze_v;
return dum;
};
auto G_bar = [=](double RHO, double SIGMA) -> double {
double ze_v = ZETA(RHO,SIGMA);
double et_v = ETA(RHO,SIGMA);
double lam_v = LAMBDA(RHO,SIGMA);
double lam_v2 = lam_v * lam_v;
double lam_v3 = lam_v2 * lam_v;
double lam_v72 = pow(lam_v,7.0/2.0);
double sq_ze = sqrt(ze_v);
double sq_et = sqrt(et_v);
double dum = -(2.0/5.0) * C * F_bar(RHO,SIGMA) * lam_v - (4.0/15.0) * B * lam_v2 - (6.0/5.0) * A_bar * lam_v3
- (4.0/5.0) * sqrt(M_PI) * lam_v72 - (12.0/5.0) * lam_v72 * (sq_ze - sq_et);
dum *= (1.0/E);
return dum;
};
auto eX = [=](double RHO) -> double {
double temp = -(3.0 * kF(RHO)) / (4.0 * M_PI);
return temp;
};
auto FX = [=](double RHO, double SIGMA) -> double {
double chi_v = Chi(RHO,SIGMA);
double chi_v2 = chi_v * chi_v;
double chi_v3 = chi_v2 * chi_v;
double chi_v5 = chi_v3 * chi_v2;
double nu_v = Nu(RHO);
double ze_v = ZETA(RHO,SIGMA);
double et_v = ETA(RHO,SIGMA);
double bg_lam_v = BG_LAMBDA(RHO,SIGMA);
double bg_lam_v2 = bg_lam_v * bg_lam_v;
double bg_lam_v3 = bg_lam_v2 * bg_lam_v;
double lam_v = LAMBDA(RHO,SIGMA);
double lam_v2 = lam_v * lam_v;
double lam_v3 = lam_v2 * lam_v;
double sq_ze_nu = sqrt(ze_v + nu_v*nu_v);
double sq_et_nu = sqrt(et_v + nu_v*nu_v);
double sq_la_nu = sqrt(lam_v + nu_v*nu_v);
double temp = A_bar * ( ze_v/( (sq_ze_nu + sq_et_nu) * (sq_ze_nu + nu_v) ) + et_v/( (sq_ze_nu + sq_et_nu) * (sq_et_nu + nu_v) ) )
- (4.0/9.0) * (B/bg_lam_v) - (4.0/9.0) * (C * F_bar(RHO,SIGMA) / bg_lam_v2) * (1.0 + (1.0/2.0) * chi_v )
- (8.0/9.0) * (E * G_bar(RHO,SIGMA) / bg_lam_v3) * (1.0 + (9.0/8.0) * chi_v + (3.0/8.0) * chi_v2)
+ 2.0 * ze_v * log( 1.0 - (lam_v - ze_v) / ( (nu_v + sq_la_nu) * (sq_la_nu + sq_ze_nu) ) )
- 2.0 * et_v * log( 1.0 - (lam_v - et_v) / ( (nu_v + sq_la_nu) * (sq_la_nu + sq_et_nu) ) );
return temp;
};
double exc = 0.0;
for (int p = 0; p < phi_points_; p++) {
double rhoa = rho_ap[p];
double rhob = rho_bp[p];
double rho = rhoa + rhob;
double sigmaaa = sigma_aap[p];
double sigmabb = sigma_bbp[p];
double sigma = 0.0;
double tol = 1.0e-20;
if ( rho > tol ) {
if ( rhoa < tol ){
rho = rhob;
sigmabb = std::max(0.0,sigmabb);
sigma = sigmabb;
double zk = eX(2.0 * rho) * FX(2.0 * rho, 4.0 * sigma);
exc += rho * zk * grid_w_->pointer()[p];
}else if ( rhob < tol ){
rho = rhoa;
sigmaaa = std::max(0.0,sigmaaa);
sigma = sigmaaa;
double zk = eX(2.0 * rho) * FX(2.0 * rho, 4.0 * sigma);
exc += rho * zk * grid_w_->pointer()[p];
}else {
double zka = rhoa * eX(2.0 * rhoa) * FX(2.0 * rhoa, 4.0 * sigmaaa);
double zkb = rhob * eX(2.0 * rhob) * FX(2.0 * rhob, 4.0 * sigmabb);
double zk = zka + zkb;
exc += zk * grid_w_->pointer()[p];
}
}else{
//double zk = 0.0;
exc += 0.0;
}
}
return exc;
}
//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
//+++++++++++++++++ Correlation Functionals +++++++++++++++++
// +
//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
}} // End namespaces