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/* Calculate Madelung constant and leading term in correction for
* charged cells */
#include<stdio.h>
#include<stdlib.h>
#include<math.h>
#include "c2xsf.h"
double madelung(struct unit_cell *c){
double M, M_real,M_recip,M_self,M_charged;
double E_real,E_recip,E_self,E_charged;
double dist,disp[3];
double sigma;
int i,j,k,ii,jj,kk,m;
sigma=M_PI*pow(0.7/(c->vol*c->vol),1.0/3.0);
fprintf(stderr,"sigma=%f\n",sigma);
/* Real space sum */
M_real=0.0;
/* erfc(x) is approx exp(-x*x),
* we don't care about terms smaller than 1e-16,
* which is exp(-6*6) */
ii=1+6.0/sqrt(sigma)/sqrt(vmod2(c->basis[0]));
jj=1+6.0/sqrt(sigma)/sqrt(vmod2(c->basis[1]));
kk=1+6.0/sqrt(sigma)/sqrt(vmod2(c->basis[2]));
if (debug>1)
fprintf(stderr,"Real space Ewald grid=%dx%dx%d\n",2*ii+1,2*jj+1,2*kk+1);
for(i=-ii;i<=ii;i++){
for(j=-jj;j<=jj;j++){
for(k=-kk;k<=kk;k++){
if ((i==0)&&(j==0)&&(k==0)) continue;
for(m=0;m<3;m++) disp[m]=c->basis[0][m]*i+
c->basis[1][m]*j+c->basis[2][m]*k;
dist=sqrt(vmod2(disp));
M_real+=(1.0/dist)*erfc(dist*sqrt(sigma));
}
}
}
M_self=-2.0*sqrt(sigma/M_PI);
E_real=M_real/(4*M_PI*EPS0);
E_self=M_self/(4*M_PI*EPS0);
ii=1+sqrt(4*sigma)/sqrt(vmod2(c->recip[0]));
jj=1+sqrt(4*sigma)/sqrt(vmod2(c->recip[1]));
kk=1+sqrt(4*sigma)/sqrt(vmod2(c->recip[2]));
if (debug>1)
fprintf(stderr,"Rec space Ewald grid=%dx%dx%d\n",2*ii+1,2*jj+1,2*kk+1);
M_recip=0.0;
for(i=-ii;i<=ii;i++){
for(j=-jj;j<=jj;j++){
for(k=-kk;k<=kk;k++){
if ((i==0)&&(j==0)&&(k==0)) continue;
for(m=0;m<3;m++) disp[m]=c->recip[0][m]*i+
c->recip[1][m]*j+c->recip[2][m]*k;
dist=4*M_PI*M_PI*vmod2(disp);
M_recip+=exp(-0.25*dist/sigma)/dist;
}
}
}
M_recip*=4*M_PI/c->vol;
E_recip=M_recip/(4*M_PI*EPS0);
M_charged=-M_PI/(c->vol*sigma);
E_charged=M_charged/(4*M_PI*EPS0);
if(debug>2){
/* For comparison with pymatgen */
fprintf(stderr,"Volume: %f\n",c->vol);
fprintf(stderr,"Real space: %f\n",E_real);
fprintf(stderr,"Recip space: %f\n",E_recip);
fprintf(stderr,"Self: %f\n",E_self);
fprintf(stderr,"Charged: %f\n",E_charged);
fprintf(stderr,"Total: %f\n",E_real+E_recip+E_self+E_charged);
}
M=M_real+M_recip+M_self+M_charged;
M=-M*sqrt(vmod2(c->basis[0]));
if (debug) fprintf(stderr,"Madelung constant of lattice: %f\n",M);
return M;
}
double quadrupole(struct unit_cell *c, struct contents *m,
struct grid *g, double *ctr){
double q,Q_e,Q_i,vec[3],*ptr;
int i,ii[3],j;
double rvec[3],disp2,scale;
scale=c->vol/(g->size[0]*g->size[1]*g->size[2]);
Q_e=Q_i=0;
q=0;
ptr=g->data;
if (!ptr) return 0;
for(i=0;i<m->n;i++){
for(j=0;j<3;j++){
rvec[j]=m->atoms[i].frac[j]-ctr[j];
rvec[j]=fmod(rvec[j]+0.5,1.0);
if (rvec[j]<0) rvec[j]+=1;
rvec[j]-=0.5;
}
for(j=0;j<3;j++)
vec[j]=rvec[0]*c->basis[0][j]+
rvec[1]*c->basis[1][j]+rvec[2]*c->basis[2][j];
disp2=vmod2(vec);
Q_i+=m->atoms[i].chg*disp2;
}
if (debug) fprintf(stderr,"Ionic quadrupole: Q %f eA^2\n",Q_i);
for(ii[0]=0;ii[0]<g->size[0];ii[0]++){
for(ii[1]=0;ii[1]<g->size[1];ii[1]++){
for(ii[2]=0;ii[2]<g->size[2];ii[2]++){
for(i=0;i<3;i++){
rvec[i]=(double)ii[i]/g->size[i]-ctr[i]; /* BUG!!! */
/* force disp to range 0.5<=disp<=0.5 */
rvec[i]=fmod(rvec[i]+0.5,1.0);
if (rvec[i]<0) rvec[i]+=1;
rvec[i]-=0.5;
}
for(i=0;i<3;i++)
vec[i]=rvec[0]*c->basis[0][i]+
rvec[1]*c->basis[1][i]+rvec[2]*c->basis[2][i];
disp2=vmod2(vec);
q-=scale*(*ptr);
Q_e-=scale*(*ptr)*disp2;
ptr++;
}
}
}
if (debug) fprintf(stderr,"Electric quadrupole: q=%fe, Q %f eA^2\n",q,Q_e);
if (debug) fprintf(stderr,"Total quadrupole: %f eA^2\n",Q_e+Q_i);
return Q_e+Q_i;
}
double quadrupole_ii(struct unit_cell *c, struct contents *m,
struct grid *g, double *ctr, int dir){
double q,Q_e,Q_i,vec[3],*ptr;
int i,ii[3],j;
double rvec[3],disp2,scale;
scale=c->vol/(g->size[0]*g->size[1]*g->size[2]);
Q_e=Q_i=0;
q=0;
ptr=g->data;
if (!ptr) return 0;
for(i=0;i<m->n;i++){
for(j=0;j<3;j++){
rvec[j]=m->atoms[i].frac[j]-ctr[j];
rvec[j]=fmod(rvec[j]+0.5,1.0);
if (rvec[j]<0) rvec[j]+=1;
rvec[j]-=0.5;
}
for(j=0;j<3;j++)
vec[j]=rvec[0]*c->basis[0][j]+
rvec[1]*c->basis[1][j]+rvec[2]*c->basis[2][j];
disp2=vec[dir]*vec[dir];
Q_i+=m->atoms[i].chg*disp2;
}
if (debug) fprintf(stderr,"Ionic quadrupole_%c%c: Q %f eA^2\n",
dir+'a',dir+'a',Q_i);
for(ii[0]=0;ii[0]<g->size[0];ii[0]++){
for(ii[1]=0;ii[1]<g->size[1];ii[1]++){
for(ii[2]=0;ii[2]<g->size[2];ii[2]++){
for(i=0;i<3;i++){
rvec[i]=(double)ii[i]/g->size[i]-ctr[i]; /* BUG!!! */
/* force disp to range 0.5<=disp<=0.5 */
rvec[i]=fmod(rvec[i]+0.5,1.0);
if (rvec[i]<0) rvec[i]+=1;
rvec[i]-=0.5;
}
for(i=0;i<3;i++)
vec[i]=rvec[0]*c->basis[0][i]+
rvec[1]*c->basis[1][i]+rvec[2]*c->basis[2][i];
disp2=vec[dir]*vec[dir];
q-=scale*(*ptr);
Q_e-=scale*(*ptr)*disp2;
ptr++;
}
}
}
if (debug) fprintf(stderr,"Electric quadrupole_%c%c: q=%fe, Q %f eA^2\n",
dir+'a',dir+'a',q,Q_e);
if (debug) fprintf(stderr,"Total quadrupole_%c%c: %f eA^2\n",
dir+'a',dir+'a',Q_e+Q_i);
return Q_e+Q_i;
}
void charge_corr(struct unit_cell *c, struct contents *m,
struct grid *g, struct es *elect){
double charge,alpha,energy,quad,ctr[3];
double i_charge,e_charge;
double abc[6],a,dpole[3],dpole_frac[3];
int i,j,n_grid_points,dir;
if ((!g)||(!g->data)){
fprintf(stderr,
"Unable to correct for charge as no electron density read\n");
return;
}
if (elect->charge) charge=*elect->charge;
else{ /* Need to calculate charge in cell */
i_charge=0;
for(i=0;i<m->n;i++) i_charge+=m->atoms[i].chg;
if (!g->data){
fprintf(stderr,"Cannot calculate charge correction as net charge "
"not available\nDid you mean to read a density too?");
return;
}
e_charge=0;
n_grid_points=g->size[0]*g->size[1]*g->size[2];
for(i=0;i<n_grid_points;i++) e_charge+=g->data[i];
e_charge*=c->vol/n_grid_points;
if (debug>1) fprintf(stderr,"Ionic charge: %f\nElectronic charge: %f\n",
i_charge,e_charge);
charge=i_charge-e_charge;
}
if (*elect->dip_corr_dir=='m'){ /* 3D to 0D correction */
alpha=madelung(c);
energy=charge*charge*alpha/(8*M_PI*EPS0*sqrt(vmod2(c->basis[0])));
if (debug) fprintf(stderr,"Total charge: %f\n",charge);
fprintf(stderr,"Madelung energy correction: %12.6f eV\n",energy);
if (elect->energy){
fprintf(stderr,"Original energy: %12.6f eV\n",*elect->energy);
fprintf(stderr,"Corrected energy: %12.6f eV\n",
*elect->energy+energy);
}
ctr[0]=ctr[1]=ctr[2]=0.5;
cart2abc(c,NULL,abc,NULL,0);
dipole_calc(c,m,g,ctr,dpole);
for(i=0;i<3;i++){
if (fabs(dpole[i])>fabs(charge*abc[i])){
fprintf(stderr,"Charge too small / dipole too large for next term\n");
return;
}
dpole_frac[i]=0;
for(j=0;j<3;j++)
dpole_frac[i]+=dpole[i]*c->recip[i][j];
ctr[i]=ctr[i]+dpole_frac[i]/charge;
}
quad=quadrupole(c,m,g,ctr);
fprintf(stderr,"Quadrupole correction: %.6f eV\n",
charge*quad/(6*EPS0*c->vol));
fprintf(stderr,"Final corrected energy: %.6f eV\n",
*elect->energy+energy-charge*quad/(6*EPS0*c->vol));
}
else{ /* 3D to 2D slab correction */
cart2abc(c,NULL,abc,NULL,0);
dir=*elect->dip_corr_dir-'a';
for(i=0;i<3;i++){
if ((!aeq(abc[3+i],90))&&(dir!=i)){
fprintf(stderr,"Warning: charge correction axis not perpendicular "
"to other axes\n");
}
}
a=abc[(dir+1)%3]*abc[(dir+2)%3]*sin(abc[3+dir]*M_PI/180);
energy=-charge*charge*abc[dir]/(24*EPS0*a);
if (debug) fprintf(stderr,"Total charge: %f\n",charge);
fprintf(stderr,"Charged slab correction: %12.6f eV\n",energy);
if (elect->energy){
fprintf(stderr,"Original energy: %12.6f eV\n",*elect->energy);
fprintf(stderr,"Corrected energy: %12.6f eV\n",
*elect->energy+energy);
ctr[0]=ctr[1]=ctr[2]=0.5;
dipole_calc(c,m,g,ctr,dpole);
if (fabs(dpole[dir])>fabs(charge*abc[dir])){
fprintf(stderr,"Charge too small / dipole too large for next term\n");
return;
}
ctr[dir]=ctr[dir]+dpole[dir]/(charge*abc[dir]);
if (debug) fprintf(stderr,"Centre for quadrupole: (%f,%f,%f)\n",
ctr[0],ctr[1],ctr[2]);
quad=quadrupole_ii(c,m,g,ctr,dir);
quad=-quad*charge/(2*EPS0*c->vol);
fprintf(stderr,"Quadrupole correction: %12.6f eV\n",quad);
fprintf(stderr,"Final corrected energy: %12.6f eV\n",
*elect->energy+energy+quad);
}
}
}
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