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/* Ergo, version 3.8.2, a program for linear scaling electronic structure
* calculations.
* Copyright (C) 2023 Elias Rudberg, Emanuel H. Rubensson, Pawel Salek,
* and Anastasia Kruchinina.
*
* 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/>.
*
* Primary academic reference:
* Ergo: An open-source program for linear-scaling electronic structure
* calculations,
* Elias Rudberg, Emanuel H. Rubensson, Pawel Salek, and Anastasia
* Kruchinina,
* SoftwareX 7, 107 (2018),
* <http://dx.doi.org/10.1016/j.softx.2018.03.005>
*
* For further information about Ergo, see <http://www.ergoscf.org>.
*/
/** @file fun-pw86x.c
The PW86 exchange functional and its derivative.
Contributed by Olav Fossgaard, olav@chem.uit.no, May 2002
Reference: Phys. Rev. B 33. 8800 (1986)
*/
#include <math.h>
#include <stdio.h>
#define __CVERSION__
#include "functionals.h"
/* INTERFACE PART */
static int pw86x_isgga(void) { return 1; }
static int pw86x_read(const char* conf_line);
static real pw86x_energy(const FunDensProp* dp);
static void pw86x_first (FunFirstFuncDrv *ds, real factor, const FunDensProp*dp);
Functional PW86xFunctional = {
"PW86x", /* name */
pw86x_isgga, /* gga-corrected */
pw86x_read,
NULL,
pw86x_energy,
pw86x_first,
NULL,
NULL
};
/* IMPLEMENTATION PART */
static int
pw86x_read(const char* conf_line)
{
fun_set_hf_weight(0);
return 1;
}
static real
pw86x_energy(const FunDensProp* dp)
{
/* Use density functional form. In case of spin polarization,
this function will have to be called twice with arguments
rho=2rhoa and rho=2rhob, respectively. The total energy is then
half the sum of the returned values.
*/
const real a = 1.0;
const real b = 1.296;
const real c = 14.0;
const real d = 0.20;
/* Closed shell (See eq. (25) in reference) */
real rho = dp->rhoa+dp->rhob, grad = dp->grada+dp->gradb;
const real Ax = -POW(3.0/M_PI,1.0/3.0)*3.0/4.0;
const real kf = POW(3.0*POW(M_PI,2.0)*rho,1.0/3.0);
real s = grad/(2.0*kf*rho);
real F = POW(a+b*POW(s,2.0)+c*POW(s,4.0)+d*POW(s,6.0),1.0/15.0);
return Ax*POW(rho,4.0/3.0)*F;
}
static void
pw86x_first(FunFirstFuncDrv *ds, real factor, const FunDensProp* dp)
{
/* The energy expression is the integral int(Ax*rho**(4/3)*F). We first
calculate d(F)/d(rho) and d(F)/d(grad_rho) and differentiate the
product in the last step.
*/
const real a = 1.0;
const real b = 1.296;
const real c = 14.0;
const real d = 0.20;
/* Closed shell (See eq. (25) in reference) */
real rho = dp->rhoa+dp->rhob, grad = dp->grada+dp->gradb;
const real Ax= -POW(3.0/M_PI,1.0/3.0)*3.0/4.0;
const real kf= POW(3.0*M_PI*M_PI*rho,1.0/3.0);
real s = grad/(2.0*kf*rho);
real F = POW(a+b*POW(s,2.0)+c*POW(s,4.0)+d*POW(s,6.0),1.0/15.0);
real F1 = 1.0/15.0*POW(a+b*POW(s,2.0)+c*POW(s,4.0)+d*POW(s,6.0),-14.0/15.0)
*(2.0*b*s+4.0*c*POW(s,3.0)+6.0*d*POW(s,5.0)); /* dF/ds */
real s1 = -4.0*s/(3.0*rho); /* ds/d(rho) */
real s2 = 1.0/(2.0*kf*rho); /* d(s)/d(grad) */
real G1 = F1*s1; /* dF/d(rho) */
real G2 = F1*s2; /* dF/d(grad) */
ds->df1000 += Ax*((4.0/3.0)*POW(rho,1.0/3.0)*F + POW(rho,4.0/3.0)*G1 )*factor;
ds->df0010 += Ax*POW(rho,4.0/3.0)*G2*factor;
}
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