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/**********************************************************************
AtomicDenF.c:
AtomicDenF.c is a subroutine to calculate the atomic charge
density of one atom specified "Gensi" at R.
Log of AtomicDenF.c:
22/Nov/2001 Released by T.Ozaki
***********************************************************************/
#include <stdio.h>
#include <math.h>
#include "openmx_common.h"
double AtomicDenF(int spe, double R)
{
int mp_min,mp_max,m;
double h1,h2,h3,f1,f2,f3,f4;
double g1,g2,x1,x2,y1,y2,f,df;
double rm,y12,y22,a,b;
double result;
mp_min = 0;
mp_max = Spe_Num_Mesh_PAO[spe] - 1;
if (Spe_PAO_RV[spe][Spe_Num_Mesh_PAO[spe]-1]<R){
result = 0.0;
}
else if (R<Spe_PAO_RV[spe][0]){
m = 4;
rm = Spe_PAO_RV[spe][m];
h1 = Spe_PAO_RV[spe][m-1] - Spe_PAO_RV[spe][m-2];
h2 = Spe_PAO_RV[spe][m] - Spe_PAO_RV[spe][m-1];
h3 = Spe_PAO_RV[spe][m+1] - Spe_PAO_RV[spe][m];
f1 = Spe_Atomic_Den[spe][m-2];
f2 = Spe_Atomic_Den[spe][m-1];
f3 = Spe_Atomic_Den[spe][m];
f4 = Spe_Atomic_Den[spe][m+1];
g1 = ((f3-f2)*h1/h2 + (f2-f1)*h2/h1)/(h1+h2);
g2 = ((f4-f3)*h2/h3 + (f3-f2)*h3/h2)/(h2+h3);
x1 = rm - Spe_PAO_RV[spe][m-1];
x2 = rm - Spe_PAO_RV[spe][m];
y1 = x1/h2;
y2 = x2/h2;
y12 = y1*y1;
y22 = y2*y2;
f = y22*(3.0*f2 + h2*g1 + (2.0*f2 + h2*g1)*y2)
+ y12*(3.0*f3 - h2*g2 - (2.0*f3 - h2*g2)*y1);
df = 2.0*y2/h2*(3.0*f2 + h2*g1 + (2.0*f2 + h2*g1)*y2)
+ y22*(2.0*f2 + h2*g1)/h2
+ 2.0*y1/h2*(3.0*f3 - h2*g2 - (2.0*f3 - h2*g2)*y1)
- y12*(2.0*f3 - h2*g2)/h2;
a = 0.5*df/rm;
b = f - a*rm*rm;
result = a*R*R + b;
}
else{
do{
m = (mp_min + mp_max)/2;
if (Spe_PAO_RV[spe][m]<R)
mp_min = m;
else
mp_max = m;
}
while((mp_max-mp_min)!=1);
m = mp_max;
if (m<2)
m = 2;
else if (Spe_Num_Mesh_PAO[spe]<=m)
m = Spe_Num_Mesh_PAO[spe] - 2;
/****************************************************
Spline like interpolation
****************************************************/
if (m==1){
h2 = Spe_PAO_RV[spe][m] - Spe_PAO_RV[spe][m-1];
h3 = Spe_PAO_RV[spe][m+1] - Spe_PAO_RV[spe][m];
f2 = Spe_Atomic_Den[spe][m-1];
f3 = Spe_Atomic_Den[spe][m];
f4 = Spe_Atomic_Den[spe][m+1];
h1 = -(h2+h3);
f1 = f4;
}
else if (m==(Spe_Num_Mesh_PAO[spe]-1)){
h1 = Spe_PAO_RV[spe][m-1] - Spe_PAO_RV[spe][m-2];
h2 = Spe_PAO_RV[spe][m] - Spe_PAO_RV[spe][m-1];
f1 = Spe_Atomic_Den[spe][m-2];
f2 = Spe_Atomic_Den[spe][m-1];
f3 = Spe_Atomic_Den[spe][m];
h3 = -(h1+h2);
f4 = f1;
}
else{
h1 = Spe_PAO_RV[spe][m-1] - Spe_PAO_RV[spe][m-2];
h2 = Spe_PAO_RV[spe][m] - Spe_PAO_RV[spe][m-1];
h3 = Spe_PAO_RV[spe][m+1] - Spe_PAO_RV[spe][m];
f1 = Spe_Atomic_Den[spe][m-2];
f2 = Spe_Atomic_Den[spe][m-1];
f3 = Spe_Atomic_Den[spe][m];
f4 = Spe_Atomic_Den[spe][m+1];
}
/****************************************************
Calculate the value at R
****************************************************/
g1 = ((f3-f2)*h1/h2 + (f2-f1)*h2/h1)/(h1+h2);
g2 = ((f4-f3)*h2/h3 + (f3-f2)*h3/h2)/(h2+h3);
x1 = R - Spe_PAO_RV[spe][m-1];
x2 = R - Spe_PAO_RV[spe][m];
y1 = x1/h2;
y2 = x2/h2;
result = y2*y2*(3.0*f2 + h2*g1 + (2.0*f2 + h2*g1)*y2)
+ y1*y1*(3.0*f3 - h2*g2 - (2.0*f3 - h2*g2)*y1);
}
return fabs(result);
}
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