/****************************************
Function name : paw_get_correlation_energy_LDA(double *rho)
****************************************/
double paw_get_correlation_energy_LDA(double *rho)
{
int i;
double rs,n;
double x,xxp;
double ec_p;
double Ec;
double *tmp;
/* loggrid variables */
int Ngrid;
/* access the loggrid variables */
Ngrid = paw_N_LogGrid();
tmp = paw_scratch_LogGrid();
/* allocate temporary memory */
tmp = paw_alloc_LogGrid();
ec_functional = paw_alloc_LogGrid();
for (i=0; i<= Ngrid-1; i++)
{
n = rho[i]/(4.0*PI);
rs = rs_scale/pow(n,onethird);
x = sqrt(rs);
xxp = rs + bp*x + cp;
ec_p = cp1*log(rs/xxp) + cp2*log( (x+cp3)*(x+cp3)/xxp)
+ cp4*atan(cp5/(x+cp6));
ec_functional[i] = ec_p;
} /*for i*/
for (i=0; i<= Ngrid-1; i++)
tmp[i] = rho[i]*ec_functional[i];
Ec = paw_Integrate_LogGrid(tmp);
return Ec;
}
/****************************************
Function name : paw_get_ion_energy
Description :
Return type : double
Argument : double *dn
Author : Marat Valiev
Date & Time : 3/31/99 2:12:25 PM
****************************************/
double paw_get_ion_energy(double *dn)
{
int k;
int Ngrid;
double *tmp;
Ngrid = paw_N_LogGrid();
tmp = paw_scratch_LogGrid();
for (k=0; k<Ngrid; ++k)
{
tmp[k] = Vion[k]*dn[k];
}
Eion = paw_Integrate_LogGrid(tmp);
return Eion;
}
/****************************************
Function name : paw_get_exchange_energy_LDA(double *rho)
Description :
****************************************/
double paw_get_exchange_energy_LDA(double *rho)
{
int i;
double n;
double n_onethird;
double ex_p;
double Ex;
double *tmp;
/* loggrid variables */
int Ngrid;
/* access the loggrid variables */
Ngrid = paw_N_LogGrid();
tmp = paw_scratch_LogGrid();
for (i=0; i<Ngrid; ++i)
{
n = rho[i]/(4.0*PI);
n_onethird = pow((3.0*n/PI),onethird);
ex_p = -(9.0/8.0)*alpha*n_onethird;
ex_functional[i] = ex_p;
} /*for i*/
for (i=0; i<Ngrid; ++i)
tmp[i] = rho[i]*ex_functional[i];
Ex = paw_Integrate_LogGrid(tmp);
return Ex;
}
/****************************************
Function name : paw_generate_pseudopot
Description :
Return type : void
Author : Marat Valiev
Date & Time : 4/10/99 7:40:00 PM
****************************************/
void paw_generate_pseudopot()
{
int k;
int Ngrid;
double charge;
double ps_charge;
double Z;
double *Vh;
double *Vx;
double *Vc;
double *rho;
double *rho_ps;
double *rho_core;
double *rho_core_ps;
double *full_density;
double *full_ps_density;
double* V_comp;
double *rgrid;
FILE *fp;
char data_filename[300];
if ( !(paw_projectors_are_done()) )
{
printf("error, pseudopotential cannot be generated ");
printf(" because projectors have not been yet \n");
exit(1);
}
Ngrid = paw_N_LogGrid();
rgrid = paw_r_LogGrid();
Vh = paw_alloc_LogGrid();
Vx = paw_alloc_LogGrid();
Vc = paw_alloc_LogGrid();
full_density = paw_alloc_LogGrid();
full_ps_density = paw_alloc_LogGrid();
Z = paw_get_ion_charge();
paw_set_core();
/*get densities*/
rho = paw_get_pointer_paw_density();
rho_ps = paw_get_pointer_paw_ps_density();
rho_core = paw_get_pointer_core_density();
rho_core_ps = paw_get_pointer_ps_core_density();
paw_Zero_LogGrid(full_density);
paw_Zero_LogGrid(full_ps_density);
for (k=0;k<=Ngrid-1;k++)
{
full_density[k] = rho[k] + rho_core[k];
full_ps_density[k] = rho_ps[k] + rho_core_ps[k];
}
charge = paw_Integrate_LogGrid(full_density);
ps_charge = paw_Integrate_LogGrid(full_ps_density);
V_comp = paw_find_comp_charge_potential(Z,charge,ps_charge);
paw_generate_hartree_pot(full_ps_density);
Vh = paw_get_hartree_pot();
paw_generate_exchange_pot_LDA(full_ps_density);
Vx = paw_get_exchange_potential();
paw_generate_corr_pot_LDA(full_ps_density);
Vc = paw_get_corr_pot_LDA();
/*form pseudopotential*/
for (k=0;k<=Ngrid-1;k++)
{
V_pseudo[k] = V_ref[k] - Vh[k]- V_comp[k]- Vc[k] - Vx[k];
}
if (paw_debug())
{
sprintf(data_filename,"%sdensity",paw_sdir());
fp = fopen(data_filename,"w");
for (k=0;k<Ngrid;++k)
fprintf(fp,"%f %f %f\n",rgrid[k],rho[k] - rho_ps[k],V_pseudo[k]);
fclose(fp);
}
paw_dealloc_LogGrid(full_density);
paw_dealloc_LogGrid(full_ps_density);
}
/****************************************
Function name : paw_solve_unoccupied_orbitals
Description :
Return type : void
Author : Marat Valiev
Date & Time : 4/10/99 6:13:39 PM
****************************************/
void paw_solve_unoccupied_orbitals()
{
int i;
int j;
int k;
int state;
int Ngrid;
int status;
double sum;
double *V;
double *rgrid;
double Zion;
Ngrid = paw_N_LogGrid();
rgrid = paw_r_LogGrid();
Zion = paw_get_ion_charge();
/*check if the occupied orbitals are done*/
if (!(occupied_orbitals_done))
{
printf("cannot calculate unoccupied states\n");
printf("calculate occupied states first\n");
}
/*get Kohn-Sham potential*/
V = paw_get_kohn_sham_potential();
for (i=Nvalence; i<= Nbound-1; i++)
{
state=paw_bound_state_test(l[i],V);
if (state==0)
{
printf("This potential has no bound states with n=%d l=%d\n",n[i],l[i]);
printf("please change your input file\n");
exit(1);
}
else
{
if (Solver_Type==Schrodinger)
{
status = paw_R_Schrodinger(n[i],l[i],V,
&eigenvalue[i],psi[i],psi_prime[i]);
}
else
{
status = paw_R_Pauli(n[i],l[i],Zion,V,
&eigenvalue[i],psi[i],psi_prime[i]);
}
}
if (!(status))
{
printf("This potential has no bound states with n=%d l=%d\n",n[i],l[i]);
printf("please change your input file\n");
exit(1);
}
/*orthogonalize to lower orbitals*/
for (j=0;j<=i-1;j++)
{
if (l[i]==l[j])
{
sum = paw_dot_product(psi[i],psi[j]);
for (k=0;k<=Ngrid-1;k++)
psi[i][k] = psi[i][k] - sum*psi[j][k];
}
}
for (k=0;k<=Ngrid-1;k++)
psi_tmp[k] = pow((psi[i][k]/rgrid[k]),2.0);
sum = paw_Integrate_LogGrid(psi_tmp);
for (k=0;k<=Ngrid-1;k++)
psi[i][k]=psi[i][k]/pow(sum,0.5);
}
}
/****************************************
Function name : paw_solve_occupied_orbitals
Description :
Return type : void
Author : Marat Valiev
Date & Time : 4/10/99 6:13:22 PM
****************************************/
void paw_solve_occupied_orbitals()
{
int i;
int j;
int k;
int it;
int converged;
int Ngrid;
int max_iter;
double sum;
double Etmp;
double thl;
double sn;
double sd;
double dr;
double rl0;
double rl1;
double vn;
double Zion;
double *Vo;
double *Vo1;
double *Vi1;
double *Vi;
double *rgrid;
max_iter = 100;
Ngrid = paw_N_LogGrid();
rgrid = paw_r_LogGrid();
/* allocate temporary grids */
Vi = paw_alloc_LogGrid();
Vo1 = paw_alloc_LogGrid();
Vi1 = paw_alloc_LogGrid();
/* set initial guess for KS potential as Thomas-Fermi*/
Zion = paw_get_ion_charge();
paw_Thomas_Fermi(Zion,Vi);
/*initial guess for the eigenvalues*/
paw_guess_eigenvalues(Zion,Vi);
it = 0;
converged = False;
while ((!converged) && (it < max_iter))
{
it = it + 1;
converged = True;
/* solve for each of the eigenstates */
for (i=0; i<= Nvalence-1; i++)
{
Etmp = eigenvalue[i];
if (Solver_Type==Schrodinger)
{
paw_R_Schrodinger(n[i],l[i],Vi,
&Etmp,psi[i],psi_prime[i]);
}
else
{
paw_R_Pauli(n[i],l[i],Zion,Vi,
&Etmp,psi[i],psi_prime[i]);
}
if (fabs(eigenvalue[i] - Etmp) >1.0e-10)
converged = False;
eigenvalue[i]=Etmp;
/*orthogonalize to lower orbitals*/
for (j=0;j<=i-1;j++)
{
if (l[i]==l[j])
{
sum = paw_dot_product(psi[i],psi[j]);
for (k=0;k<Ngrid;++k)
psi[i][k] = psi[i][k] - sum*psi[j][k];
}
}
/*normalize the orbital*/
for (k=0; k<=Ngrid-1; k++)
psi_tmp[k] = pow((psi[i][k]/rgrid[k]),2.0);
sum = paw_Integrate_LogGrid(psi_tmp);
for (k=0; k<=Ngrid-1; k++)
psi[i][k]=psi[i][k]/pow(sum,0.5);
}
/*get new density*/
paw_generate_density(rho);
/*get new potential*/
paw_set_kohn_sham_potential(rho);
Vo = paw_get_kohn_sham_potential();
/*****************************************/
/* Generate the next iteration potential */
/* using D.G. Anderson method */
/*****************************************/
thl = 0.0;
if (it > 1)
{
sn = 0.0;
sd = 0.0;
for (k=0; k<Ngrid; ++k)
{
rl0 = Vo[k] - Vi[k];
rl1 = Vo1[k] - Vi1[k];
dr = rl0 - rl1;
sn = sn + rl0*dr*(rgrid[k]*rgrid[k]);
sd = sd + dr*dr*(rgrid[k]*rgrid[k]);
}
thl = sn/sd;
}
for (k=0; k<=Ngrid-1; k++)
{
vn = (1.0-0.5)*( (1.0-thl)*Vi[k] + thl*Vi1[k] )
+ 0.5 *( (1.0-thl)*Vo[k] + thl*Vo1[k] );
Vi1[k] = Vi[k];
Vo1[k] = Vo[k];
Vi[k] = vn;
}
} /* end while */
if (!converged)
{
printf("Not Converged\n");
exit(1);
}
occupied_orbitals_done = True;
paw_generate_density(rho);
paw_set_kohn_sham_potential(rho);
/* free up temporary memory */
paw_dealloc_LogGrid(Vi);
paw_dealloc_LogGrid(Vo1);
paw_dealloc_LogGrid(Vi1);
}
