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/**********************************************************************
XC_PW91C.c:
XC_PW91C.c is a subroutine to calculate the correlation
potential developed by Perdew and Wang (Ref: J.P.Perdew
and Y.Wang, PRB, 45, 13244 (1992)) for given densities
up (dens[0]) and down (dens[1]).
This routine was written by T.Ozaki, based on the original fortran
code provided by the SIESTA group through their website.
Thanks to them.
Log of PW91C.c:
22/Nov/2001 Released by T.Ozaki
***********************************************************************/
#include <stdio.h>
#include <math.h>
#include <stdlib.h>
#include "openmx_common.h"
#define den_min 1.0e-15
#define den_min_half 0.5*1.0e-15
void XC_PW91C(double dens[2], double Ec[1], double Vc[2])
{
int i;
double dtot,rs,srs,zeta,coe;
double dum,dum1,dum2,b,c,dbdrs,dcdrs;
double tmp0,tmp1,tmp2,tmp12,tmp14,tmp22,tmp24;
double fpp0,f,dfdz;
double G[3],dGdrs[3];
double dEcdd[2];
double dEcdrs,dEcdz;
double drsdd,dzdd[2];
/****************************************************
parameters from Table I of
Perdew and Wang, PRB, 45, 13244 (92)
****************************************************/
double p[3] = {1.0000000, 1.0000000, 1.0000000};
double A[3] = {0.0310910, 0.0155450, 0.0168870};
double alpha1[3] = {0.2137000, 0.2054800, 0.1112500};
double beta1[3] = {7.5957000, 14.1189000, 10.3570000};
double beta2[3] = {3.5876000, 6.1977000, 3.6231000};
double beta3[3] = {1.6382000, 3.3662000, 0.8802600};
double beta4[3] = {0.4929400, 0.6251700, 0.4967100};
/****************************************************
zeta and rs
****************************************************/
coe = 0.6203504908994; /* pow(3.0/4.0/PI,1.0/3.0); */
dtot = dens[0] + dens[1];
if (dtot<=den_min){
rs = 6203.504908994; /* coe*pow(1.0e-12,-1.0/3.0); */
dens[0] = den_min_half;
dens[1] = den_min_half;
dtot = den_min;
}
else
rs = coe*pow(dtot,-0.33333333333333333333333);
tmp0 = 1.0/dtot;
zeta = tmp0*(dens[0] - dens[1]);
if (1.0<zeta) zeta = 1.0 - den_min;
if (zeta<-1.0) zeta = -1.0 + den_min;
drsdd = -0.3333333333333333333333*rs*tmp0;
dzdd[0] = tmp0*( 1.0 - zeta);
dzdd[1] = tmp0*(-1.0 - zeta);
/****************************************************
eps_c(rs,0)=G(0)
eps_c(rs,1)=G(1)
-alpha_c(rs)=G(2)
using eq.(10) in
Perdew and Wang, PRB, 45, 13244 (1992))
****************************************************/
srs = sqrt(rs);
for (i=0; i<=2; i++){
b = beta1[i]*srs + rs*(beta2[i] + beta3[i]*srs + beta4[i]*rs);
dbdrs = beta1[i]*0.50/srs
+ beta2[i]
+ beta3[i]*1.50*srs
+ beta4[i]*2.0*rs;
c = 1.0 + 1.0/(2.0*A[i]*b);
dcdrs = -(c - 1.0)*dbdrs/b;
dum = log(c);
dum1 = 1.0 + alpha1[i]*rs;
G[i] = -2.0*A[i]*dum1*dum;
dGdrs[i] = -2.0*A[i]*(alpha1[i]*dum + dum1*dcdrs/c);
}
/****************************************************
f''(0) and f(zeta) from eq.(9)
****************************************************/
c = 1.92366105093154; /* 1/(2*(2^{1/3}-1)) */
fpp0 = 1.70992093416137;
dum1 = 1.0 + zeta;
dum2 = 1.0 - zeta;
tmp1 = pow(dum1,0.333333333333333333);
tmp2 = pow(dum2,0.333333333333333333);
tmp12 = tmp1*tmp1;
tmp22 = tmp2*tmp2;
tmp14 = tmp12*tmp12;
tmp24 = tmp22*tmp22;
f = (tmp14 + tmp24 - 2.0)*c;
dfdz = 1.333333333333333333*(tmp1 - tmp2)*c;
/****************************************************
eps_c(rs,zeta) from eq.(8)
****************************************************/
dum1 = zeta*zeta*zeta;
dum = dum1*zeta;
Ec[0] = G[0] - G[2]*f/fpp0*(1.0 - dum) + (G[1] - G[0])*f*dum;
dEcdrs = dGdrs[0] - dGdrs[2]*f/fpp0*(1.0 - dum)
+ (dGdrs[1] - dGdrs[0])*f*dum;
dEcdz = - G[2]/fpp0*(dfdz*(1.0 - dum) - f*4.0*dum1)
+ (G[1] - G[0])*(dfdz*dum + f*4.0*dum1);
/*
printf("rs = %18.15f\n",rs);
printf("zeta = %18.15f\n",zeta);
printf("Ec = %18.15f\n",Ec[0]);
printf("Ec2 = %18.15f %18.15f\n",
-G[2]*f/fpp0*(1.0 - dum),-dGdrs[2]*f/fpp0*(1.0 - dum));
printf("Ec3 = %18.15f %18.15f\n",
(G[1] - G[0])*f*dum,(dGdrs[1] - dGdrs[0])*f*dum);
printf("G0 dGdrs0 = %18.15f %18.15f\n",G[0],dGdrs[0]);
printf("G1 dGdrs1 = %18.15f %18.15f\n",G[1],dGdrs[1]);
printf("G2 dGdrs2 = %18.15f %18.15f\n",G[2],dGdrs[2]);
printf("dEcdrs = %18.15f\n",dEcdrs);
printf("dEcdz = %18.15f\n",dEcdz);
*/
/****************************************************
Find correlation potential
****************************************************/
dum = dEcdrs*drsdd;
dEcdd[0] = dum + dEcdz*dzdd[0];
dEcdd[1] = dum + dEcdz*dzdd[1];
Vc[0] = Ec[0] + dtot*dEcdd[0];
Vc[1] = Ec[0] + dtot*dEcdd[1];
}
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