/****************************************
Function name : paw_bound_state_test
Description :
Return type : int
Argument : int n
Argument : int l
Argument : double *v
Author : Marat Valiev
Date & Time : 3/31/99 3:02:14 PM
****************************************/
int paw_bound_state_test(int l, double *v)
{
int i;
int Ngrid;
double L2,r2;
double Emin;
double *r;
Ngrid = paw_N_LogGrid();
r = (double *) paw_r_LogGrid();
L2 = ((double) (l*(l+1)));
Emin = 0;
for (i=0; i<Ngrid; ++i)
{
r2 = r[i];
r2 = r2*r2;
Emin = Min(Emin, (v[i] + 0.5*L2/r2));
}
if (Emin>=0)
{
return 0;
}
else
{
return 1;
}
}
/****************************************
Function name : paw_print_loggrid_information
Description :
Return type : void
Argument : FILE *fp
Author : Marat Valiev
Date & Time : 3/31/99 3:00:49 PM
****************************************/
void paw_print_loggrid_information(FILE *fp)
{
fprintf(fp,"\n");
fprintf(fp," Logarithmic grid information ( r(i)=r0*pow(a,i) ):\n");
fprintf(fp,"\n");
fprintf(fp," a = %le\n", paw_amesh_LogGrid());
fprintf(fp," N = %d\n", paw_N_LogGrid());
fprintf(fp," r0 = %le\n",paw_r0_LogGrid());
fprintf(fp," rmax = %le\n",paw_r_LogGrid()[paw_N_LogGrid()-1]);
fprintf(fp,"\n");
}
/****************************************
Function name : paw_solve_pseudo_orbitals
Description :
Return type : void
Author : Marat Valiev
Date & Time : 5/15/00
****************************************/
void paw_solve_pseudo_orbitals()
{
int i;
int k;
int i_end_point;
int Ngrid;
double scale;
double *rgrid;
Ngrid = paw_N_LogGrid();
rgrid = paw_r_LogGrid();
for (i=0;i<= nbasis-1;i++)
{
i_end_point = paw_get_grid_index(1.2*r_orbital[i]);
paw_solve_paw_scattering(orb_l[i], 3*r_orbital[i], e_ps[i], psi_ps[i],psi_ps_prime[i]);
if (paw_debug())
printf("%d%s log derivative %le %le \n",prin_n[i],paw_spd_Name(orb_l[i]),
psi_ps_prime[i][i_end_point]/(psi_ps[i][i_end_point]*rgrid[i_end_point]*paw_log_amesh_LogGrid()),
phi0_prime[i][i_end_point]/(phi0[i][i_end_point]*rgrid[i_end_point]*paw_log_amesh_LogGrid()));
/*rescale the orbitals*/
scale = phi_ps0[i][i_r_orbital[i]]/psi_ps[i][i_r_orbital[i]];
for (k=0;k<=i_end_point;++k)
{
psi_ps[i][k] = psi_ps[i][k]*scale;
psi_ps_prime[i][k] = psi_ps_prime[i][k]*scale;
}
for (k=i_end_point+1;k<=Ngrid-1;++k)
{
psi_ps[i][k] = phi_ps0[i][k];
psi_ps_prime[i][k] = phi_ps0_prime[i][k];
}
}
}
/****************************************
Function name : paw_init_ion(double Z)
Description :
****************************************/
void paw_init_ion(double Z)
{
int i;
int Ngrid;
double *rgrid;
Ngrid = paw_N_LogGrid();
rgrid = paw_r_LogGrid();
Zion = Z;
Vion = paw_alloc_LogGrid();
for (i=0; i<Ngrid; ++i)
Vion[i] = -Z/rgrid[i];
}
/****************************************
Function name : paw_get_core_density
Description :
Return type : void
Argument : double** rho
Author : Marat Valiev
Date & Time : 3/31/99 3:35:46 PM
****************************************/
void paw_generate_density(double* rho)
{
int i;
int k;
int Ngrid;
double* rgrid;
Ngrid = paw_N_LogGrid();
rgrid = paw_r_LogGrid();
paw_Zero_LogGrid(rho);
for (i=0; i<=Nvalence-1; ++i)
{
for (k=0; k<Ngrid; ++k)
rho[k] += fill[i]*pow((psi[i][k]/rgrid[k]),2.0);
}
}
void paw_generate_projectors_vanderbilt()
{
int i;
int j;
int k;
int Ngrid;
double norm;
double max_prj;
double max_phi;
double max_phi_ps;
double tmp_prj;
double *V_ref;
double *V;
double *rgrid;
double **b;
double **prj_ps0;
char output[300];
FILE *fp;
/*make sure the pseudo orbitalas were found*/
if (! pseudo_orbitals_done)
{
printf("cannot calculate projectors\n");
printf("pseudo basis is not ready\n");
exit(1);
}
Ngrid = paw_N_LogGrid();
rgrid = paw_r_LogGrid();
b = paw_alloc_2d_array(nbasis,nbasis);
prj_ps0 = paw_alloc_2d_array(nbasis,Ngrid);
/*obtain the ref potential*/
V_ref = paw_get_ref_pot();
/*form initial guess for projectors as in Blochl*/
for (i = 0; i < nbasis; ++i)
{
V = paw_get_paw_potential(i);
for (k = 0; k < Ngrid; ++k)
prj_ps[i][k] = (V_ref[k] - V[k])*phi_ps[i][k];
if (paw_debug())
{
sprintf(output, "%s%s_%d%d", paw_sdir(),"p",prin_n[i],orb_l[i]);
fp = fopen(output, "w+");
for (k = 0; k < Ngrid; ++k)
{
fprintf(fp, "%le\t %le\t %le \n", rgrid[k], prj_ps[i][k],(V_ref[k] - V[k]));
}
fclose(fp);
}
}
/*check for accidental null projectors*/
for (i = 0; i < nbasis; ++i)
{
max_prj = 0.0;
for (k = 0; k < Ngrid; ++k)
{
tmp_prj = fabs(prj_ps[i][k]);
if (tmp_prj > max_prj)
max_prj = tmp_prj;
}
if (max_prj <0.000001)
{
printf("found null projectors, aborting the program ... \n");
exit(1);
}
}
for (i=0;i<=nbasis-1;i++)
{
for (j=0;j<=nbasis-1;j++)
{
if (orb_l[i] == orb_l[j] )
{
b[i][j] = paw_dot_product(phi_ps[j],prj_ps[i]);
}
else
{
b[i][j] = 0.0;
}
}
}
paw_get_inverse(b,nbasis);
for (i=0;i<=nbasis-1;i++)
{
for (k = 0; k <= Ngrid-1; k++)
prj_ps0[i][k] = prj_ps[i][k];
}
for (i=0;i<=nbasis-1;i++)
{
paw_Zero_LogGrid(prj_ps[i]);
}
for (i=0;i<=nbasis-1;i++)
{
for (j=0;j<=nbasis-1;j++)
{
for (k = 0; k <= Ngrid-1; k++)
prj_ps[i][k] = prj_ps[i][k] + b[i][j]*prj_ps0[j][k];
}
}
for (i=0;i<=nbasis-1;i++)
{
norm = paw_dot_product(prj_ps[i],phi_ps[i]);
if (fabs(norm) < SMALL)
{
printf("division by zero while normalizing prj_pss");
exit(99);
}
if (paw_debug()) printf("prj_ps norm=%le\n",norm);
for (k = 0; k < Ngrid; ++k)
prj_ps[i][k] = prj_ps[i][k]/norm;
}
/*rescale basis*/
for (i = 0; i <= nbasis-1; i++)
{
max_prj = 0.0;
max_phi = 0.0;
max_phi_ps = 0.0;
for (k = 0; k < i_r_orbital[i]; k++)
{
if (max_prj < fabs(prj_ps[i][k]))
max_prj = fabs(prj_ps[i][k]);
if (max_phi_ps < fabs(phi_ps[i][k]))
max_phi_ps = fabs(phi_ps[i][k]);
}
if (max_prj == 0.0 || max_phi_ps == 0.0)
{
printf("division by zero while rescaling basis\n");
exit(99);
}
norm = 0.75*sqrt(max_phi_ps/max_prj);
max_prj = 0.0;
max_phi = 0.0;
max_phi_ps = 0.0;
for (k = 0; k < Ngrid; ++k)
{
prj_ps[i][k] = prj_ps[i][k]*norm;
phi[i][k] = phi[i][k]/norm;
phi_ps[i][k] = phi_ps[i][k]/norm;
phi_prime[i][k] = phi_prime[i][k]/norm;
phi_ps_prime[i][k] = phi_ps_prime[i][k]/norm;
}
}
}
/****************************************
Function name : solve_pseudo_orbitals
Description :
Return type : void
Author : Marat Valiev
Date & Time : 4/7/99 2:31:16 PM
****************************************/
void paw_generate_pseudo_orbitals()
{
int i;
int k;
int Ngrid;
int max_iter;
int converged;
int iteration;
int match;
int status;
double log_amesh;
double f1,f2;
double *V;
double *rgrid;
double *f;
double norm;
char output[300];
FILE *fp;
Ngrid = paw_N_LogGrid();
rgrid = paw_r_LogGrid();
log_amesh = paw_log_amesh_LogGrid();
/*set maximum number of iterations*/
max_iter = 600;
for (i = 0; i <= nbasis-1; i++)
{
iteration = 0;
converged = False;
status = False;
match = i_r_orbital[i];
/*Start the selfconsistent loop over given ps state */
while ((iteration <= max_iter) && (!converged))
{
++iteration;
/* get pseudopotential*/
V = paw_get_paw_potential(i);
/*
if(orb_type[i]==bound || orb_type[i]==virt)
{
status = paw_R_Schrodinger(prin_n_ps[i],
orb_l[i],
V,
&e_ps[i],
phi_ps[i],
phi_ps_prime[i]);
}
else if(orb_type[i]==scattering)
{
status = paw_R_Schrodinger_Fixed_Logderiv(prin_n_ps[i],
orb_l[i],
V,
match,
log_deriv[i],
&e_ps[i],
phi_ps[i],
phi_ps_prime[i]);
}
else
{
printf("unknown orbital type\n");
exit(1);
}
*/
status = paw_R_Schrodinger_Fixed_Logderiv(prin_n_ps[i],
orb_l[i],
V,
match,
log_deriv[i],
&e_ps[i],
phi_ps[i],
phi_ps_prime[i]);
/*Update pseudopotential potential*/
paw_update_paw_potential(&converged, i, e[i], e_ps[i],phi_ps[i]);
}
/*report on convergence status*/
if (converged && (status))
{
if (paw_debug()) printf("\n%d%d pseudo orbital with the eigenvalue=%f has been found\n",
prin_n[i], orb_l[i], e_ps[i]);
}
else
{
if (paw_debug()) printf("Unable to find %d%d orbital\n ",
prin_n[i], orb_l[i]);
}
norm = phi[i][match]/phi_ps[i][match];
/*scale ps orbital */
for (k=0;k<=match;k++)
{
phi_ps[i][k]=phi_ps[i][k]*norm;
phi_ps_prime[i][k]=phi_ps_prime[i][k]*norm;
}
for (k=match+1;k<=Ngrid-1;k++)
{
phi_ps[i][k]=phi[i][k];
phi_ps_prime[i][k]=phi_prime[i][k];
}
}
if (paw_debug())
{
for (i = 0; i <= nbasis-1; ++i)
{
sprintf(output, "%s%s%d%d", paw_sdir(),"test",prin_n[i],orb_l[i]);
fp = fopen(output, "w+");
for (k = 0; k < Ngrid; k++)
{
fprintf(fp, "%f\t%f\t%f\n", rgrid[k], phi[i][k],phi_ps[i][k]);
}
fclose(fp);
}
}
pseudo_orbitals_done = True;
/* save original basis functions */
for (i=0;i<=nbasis-1;i++)
{
for (k = 0; k <= Ngrid-1; k++)
{
phi0[i][k] = phi[i][k];
phi0_prime[i][k] = phi_prime[i][k];
phi_ps0[i][k] = phi_ps[i][k];
phi_ps0_prime[i][k] = phi_ps_prime[i][k];
}
}
/* calculate densities */
paw_Zero_LogGrid(rho);
paw_Zero_LogGrid(rho_ps);
for (i = 0; i <= nbasis-1; i++)
{
for (k = 0; k <= Ngrid-1; k++)
{
rho[k] += fill[i]*pow((phi0[i][k]/rgrid[k]),2.0);
rho_ps[k] += fill[i]*pow((phi_ps0[i][k]/rgrid[k]),2.0);
}
}
/*calculate kinetic energy*/
ekin = paw_get_kinetic_energy(nbasis, orb_l, fill, phi, phi_prime);
f = paw_alloc_LogGrid();
for (i = 0; i <= nbasis-1; i++)
{
for (k=0; k<=Ngrid-1; k++)
{
f[k] = 0.5*phi_prime[i][k]/(rgrid[k]*log_amesh)*
phi_prime[i][k]/(rgrid[k]*log_amesh) -
0.5*phi_ps_prime[i][k]/(rgrid[k]*log_amesh)*
phi_ps_prime[i][k]/(rgrid[k]*log_amesh);
}
f1 = paw_Def_Integr(0.0,f,0.0,Ngrid-1);
for (k=0; k<=Ngrid-1; k++)
{
f[k] = 0.5*phi_prime[i][k]/(rgrid[k]*log_amesh)*
phi_prime[i][k]/(rgrid[k]*log_amesh);
}
f2 = paw_Def_Integr(0.0,f,0.0,Ngrid-1);
delta_ekin[i] = (int)(100*f1/f2);
if (paw_debug())
printf("kinetic energy of the %d%s orbital was reduced by %d%s\n",
prin_n[i],paw_spd_Name(orb_l[i]),delta_ekin[i],"%");
}
paw_dealloc_LogGrid(f);
}
/****************************************
Function name : paw_solve_pseudo_orbitals
Description :
Return type : void
Author : Marat Valiev
Date & Time : 5/15/00
****************************************/
void paw_scattering_test(double e1,double e2,int number_points ,int l, double r )
{
int i;
int k;
int i_end_point;
int Ngrid;
double *rgrid;
FILE *fp;
double *V_ks;
double *psi1;
double *psi1_prime;
double *psi;
double *psi_prime;
double *log_grid_ae;
double *log_grid_paw;
double de;
double* e3;
double e_test;
double log_amesh;
/*char output[30];*/
char data_filename[300];
char script_filename[300];
Ngrid = paw_N_LogGrid();
rgrid = paw_r_LogGrid();
log_amesh = paw_log_amesh_LogGrid();
psi1 = paw_alloc_LogGrid();
psi1_prime = paw_alloc_LogGrid();
psi = paw_alloc_LogGrid();
psi_prime = paw_alloc_LogGrid();
log_grid_ae = paw_alloc_1d_array(number_points);
log_grid_paw = paw_alloc_1d_array(number_points);
e3 = paw_alloc_1d_array(number_points);
de = (e2-e1)/number_points;
V_ks = paw_get_kohn_sham_potential();
i_end_point = paw_get_grid_index(r);
for (i=0;i<= number_points-1;i++)
{
e_test = e1+de*i;
e3[i] = e_test;
paw_solve_paw_scattering(l, r, e_test, psi,psi_prime);
paw_R_Schrodinger_Fixed_E(
l,
V_ks,
i_end_point,
e_test,
psi1,
psi1_prime
);
log_grid_ae[i] = psi1_prime[i_end_point-1]/(psi1[i_end_point-1]*rgrid[i_end_point-1]*log_amesh);
log_grid_paw[i] = psi_prime[i_end_point-1]/(psi[i_end_point-1]*rgrid[i_end_point-1]*log_amesh);
}
if (paw_debug())
{
sprintf(data_filename,"%s%s_%s_scat_test.dat", paw_sdir(),paw_get_atom_name(),paw_spd_Name(l));
fp = fopen(data_filename,"w+");
for (k=0; k<=number_points-1; k++)
{
fprintf(fp,"%le\t%le\t%le\n", e3[k],log_grid_ae[k],log_grid_paw[k]);
}
fclose(fp);
sprintf(script_filename,"%s%s_%s_scat_test.plt", paw_sdir(),paw_get_atom_name(),paw_spd_Name(l));
printf("script_filename: %s\n",script_filename);
fp = fopen(script_filename,"w+");
fprintf(fp,"set style data lines \n");
fprintf(fp,"set nolabel \n");
fprintf(fp,"set autoscale \n");
fprintf(fp,"set xr[%f:%f] \n",e1,e2);
fprintf(fp,"set grid \n");
fprintf(fp,"set nolabel \n");
fprintf(fp,"set xlabel \"e (Hartree)\" \n");
fprintf(fp,"set ylabel \"logarithmic derivative at r=%f\" \n",r);
fprintf(fp,"set title \" %s %s channel scattering test\n",paw_get_atom_name(),paw_spd_Name(l));
fprintf(fp,"plot \"%s\" using 1:2 title \"all electron\",",data_filename);
fprintf(fp,"\"\" using 1:3 title \"paw\" \n");
fprintf(fp,"\n");
fprintf(fp,"pause -1\n");
fclose(fp);
}
}
/****************************************
Function name : paw_print_basis_to_file
Description :
Return type : void
Author : Marat Valiev
Date & Time : 3/31/99 3:01:57 PM
****************************************/
void paw_print_basis_test_to_file(char* atom_name)
{
int i;
int j;
int k;
int Ngrid;
double *rgrid;
char data_filename[300];
char script_filename[300];
char nl_name[20];
char title[20];
FILE *fp;
Ngrid = paw_N_LogGrid();
rgrid = paw_r_LogGrid();
if (paw_debug())
{
sprintf(data_filename,"%s%s_test.dat",paw_sdir(),atom_name);
printf("data_filename: %s\n",data_filename);
fp = fopen(data_filename,"w+");
for (k=0; k<=Ngrid-1; k++)
{
fprintf(fp,"%le", rgrid[k]);
for (i=0; i<=nbasis-1; i++)
fprintf(fp,"\t%le \t%le",phi_ps0[i][k],psi_ps[i][k]);
fprintf(fp,"\n");
}
fclose(fp);
/*gnu script file */
for (i=0,j=2; i<=nbasis-1; i++,j=j+2)
{
sprintf(nl_name,"%d%s",prin_n[i],paw_spd_Name(orb_l[i]));
sprintf(script_filename,"%s%s_%s_test.plt",paw_sdir(),atom_name,nl_name);
printf("script_filename: %s \n",script_filename);
fp = fopen(script_filename,"w+");
fprintf(fp,"set style data lines \n");
fprintf(fp,"set nolabel \n");
fprintf(fp,"set autoscale \n");
fprintf(fp,"set xr[0:%f] \n",1.5*r_orbital[i]);
fprintf(fp,"set grid \n");
fprintf(fp,"set key \n");
fprintf(fp,"set nolabel \n");
fprintf(fp,"set xlabel \"r (a0)\" \n");
fprintf(fp,"set title \" %s paw_basis test for %s\\n (e=%f Hartree)\" \n",
nl_name,atom_name,e_ps[i]);
sprintf(title,"%s (%f)",nl_name,e_ps[i]);
fprintf(fp,"plot \"%s\" using 1:%d title \" original pseudo orbital \" , ",data_filename,j);
fprintf(fp,"\"%s\" using 1:%d title \" solution of PAW Hamiltonian \" with points\n",data_filename,j+1);
fprintf(fp,"\n");
fprintf(fp,"pause -1\n");
fclose(fp);
}
}
}
/****************************************
Function name : paw_print_basis_to_file
Description :
Return type : void
Author : Marat Valiev
Date & Time : 3/31/99 3:01:57 PM
****************************************/
void paw_print_basis_to_file(char* atom_name)
{
int i;
int j;
int k;
int Ngrid;
double *rgrid;
char data_filename[300];
char script_filename[300];
char nl_name[20];
char title[20];
FILE *fp;
Ngrid = paw_N_LogGrid();
rgrid = paw_r_LogGrid();
if (paw_debug())
{
sprintf(data_filename,"%s%s_paw.dat",paw_sdir(),atom_name);
fp = fopen(data_filename,"w+");
for (k=0; k<=Ngrid-1; k++)
{
fprintf(fp,"%le", rgrid[k]);
for (i=0; i<=nbasis-1; i++)
fprintf(fp,"\t%le \t%le \t%le ",phi[i][k],phi_ps[i][k],prj_ps[i][k]);
fprintf(fp,"\n");
}
fclose(fp);
/* individual orbitals gnu script file */
for (i=0,j=2; i<=nbasis-1; i++,j=j+3)
{
sprintf(nl_name,"%d%s",prin_n[i],paw_spd_Name(orb_l[i]));
sprintf(script_filename,"%s%s_%s_paw.plt",paw_sdir(),atom_name,nl_name);
fp = fopen(script_filename,"w+");
fprintf(fp,"set style data lines \n");
fprintf(fp,"set nolabel \n");
fprintf(fp,"set autoscale \n");
fprintf(fp,"set xr[0:%f] \n",1.5*r_orbital[i]);
fprintf(fp,"set grid \n");
fprintf(fp,"set key \n");
fprintf(fp,"set nolabel \n");
fprintf(fp,"set xlabel \"r (a0)\" \n");
fprintf(fp,"set title \" %s paw_basis for %s\\n (e=%f Hartree)\" \n",
nl_name,atom_name,e_ps[i]);
sprintf(title,"%s (%f)",nl_name,e_ps[i]);
fprintf(fp,"plot \"%s\" using 1:%d title \" all-electron orbital \" , ",data_filename,j);
fprintf(fp,"\"%s\" using 1:%d title \" pseudo orbital \" , ",data_filename,j+1);
fprintf(fp,"\"%s\" using 1:%d title \" projector \" \n",data_filename,j+2);
fprintf(fp,"\n");
fprintf(fp,"pause -1\n");
fclose(fp);
}
}
}
/****************************************
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);
}
/****************************************
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);
}
void paw_generate_basis_file(char *outfile)
{
char* atom_name;
FILE *fp;
int i;
int k;
double tmp;
double *Vpseudo;
double *rho_core;
double *rho_core_ps;
int nbasis;
int Ngrid;
double *rgrid;
int* prin_n;
int* prin_n_ps;
int *l;
double* e;
double** psi;
double** psi_ps0;
double** psi_prime;
double** psi_ps;
double** psi_ps_prime;
double** prj_ps;
double** prj_ps0;
Ngrid = paw_N_LogGrid();
rgrid = paw_r_LogGrid();
atom_name = paw_get_atom_name();
nbasis = paw_get_nbasis();
prin_n = paw_get_pointer_paw_n_array();
prin_n_ps = paw_get_pointer_paw_n_ps_array();
l = paw_get_pointer_paw_l_array();
e = paw_get_pointer_paw_e_array();
psi = paw_get_pointer_paw_psi_array();
psi_ps = paw_get_pointer_paw_psi_ps_array();
psi_prime = paw_get_pointer_paw_psi_prime_array();
psi_ps_prime = paw_get_pointer_paw_psi_ps_prime_array();
prj_ps = paw_get_pointer_paw_prj_ps_array();
prj_ps0 = paw_get_pointer_paw_prj_ps0_array();
rho_core = paw_get_pointer_core_density();
rho_core_ps = paw_get_pointer_ps_core_density();
Vpseudo = paw_get_pointer_pseudopotential();
psi_ps0 = paw_get_pointer_paw_psi_ps_unscr_array();
/* output the basis file */
/*sprintf(output, "%s_basis", atom_name);*/
if (paw_debug()) printf("paw basis file generated: %s\n",outfile);
fp = fopen(outfile, "w+");
fprintf(fp,"4\n"); /*dummy tag*/ /* new*/
fprintf(fp,"%s\n",atom_name); /* new*/
fprintf(fp,"%lf\n",paw_get_Zvalence()); /* new*/
fprintf(fp,"%15.11e\n",rgrid[0]);
fprintf(fp,"%15.11e\n",rgrid[Ngrid-1]);
fprintf(fp,"%d\n",Ngrid);
fprintf(fp,"%d\n",nbasis);
/* printout cutoff radii */ /* new*/
for (i=0; i<nbasis; ++i) fprintf(fp,"%le ",paw_get_r_orbital(i)); /* new*/
fprintf(fp,"\n"); /* new*/
fprintf(fp,"%d\n",paw_get_max_i_r_orbital());
fprintf(fp,"%s\n",paw_get_comment()); /* new*/
fprintf(fp,"%15.11e\n",paw_get_core_kinetic_energy());
for ( i = 0; i < nbasis; ++i)
fprintf(fp, "%d\t %15.11e\t %d\t %d\n",prin_n[i],e[i],prin_n_ps[i],l[i]);
for ( i = 0; i <= nbasis-1; i++)
{
for (k = 0; k <= Ngrid-1; k++)
fprintf(fp, "%15.11e \n",psi[i][k]);
}
for ( i = 0; i <= nbasis-1; i++)
{
for (k = 0; k <= Ngrid-1; k++)
{
tmp = psi_prime[i][k]/(rgrid[k]*paw_log_amesh_LogGrid());
fprintf(fp, "%15.11e \n",psi_prime[i][k]/(rgrid[k]*paw_log_amesh_LogGrid()));
}
}
for ( i = 0; i <= nbasis-1; i++)
{
for (k = 0; k <= Ngrid-1; k++)
fprintf(fp, "%15.11e \n",psi_ps[i][k]);
}
for ( i = 0; i <= nbasis-1; i++)
{
for (k = 0; k <= Ngrid-1; k++)
{
tmp = psi_ps_prime[i][k]/(rgrid[k]*paw_log_amesh_LogGrid());
fprintf(fp, "%15.11e \n",psi_ps_prime[i][k]/(rgrid[k]*paw_log_amesh_LogGrid()));
}
}
for ( i = 0; i <= nbasis-1; i++)
{
for (k = 0; k <= Ngrid-1; k++)
fprintf(fp, "%15.11e \n",prj_ps[i][k]);
}
for (k = 0; k <= Ngrid-1; k++)
{
fprintf(fp, "%15.11e \n",rho_core[k]/(4.0*PI));
}
for (k = 0; k <= Ngrid-1; k++)
{
fprintf(fp, "%15.11e \n",rho_core_ps[k]/(4.0*PI));
}
for (k = 0; k <= Ngrid-1; k++)
{
fprintf(fp, "%15.11e \n",Vpseudo[k]);
}
fprintf(fp,"%15.11e\n",paw_get_sigma_comp());
fprintf(fp,"%15.11e\n",paw_get_ion_charge());
for ( i = 0; i <= nbasis-1; i++)
{
for (k = 0; k <= Ngrid-1; k++)
fprintf(fp, "%15.11e \n",prj_ps0[i][k]);
}
fclose(fp);
}
/****************************************
Function name : paw_save_orbitals_to_file
Description :
Return type : void
Author : Marat Valiev
Date & Time : 3/31/99 3:01:57 PM
****************************************/
void paw_print_orbitals_to_file(char* atom_name)
{
int i;
int k;
int Ngrid;
double *rgrid;
char data_filename[300];
char script_filename[300];
char nl_name[20];
char title[20];
FILE *fp;
Ngrid = paw_N_LogGrid();
rgrid = paw_r_LogGrid();
if (paw_debug())
{
sprintf(data_filename,"%s%s_orb.dat",paw_sdir(),atom_name);
fp = fopen(data_filename,"w+");
for (k=0; k<=Ngrid-1; k++)
{
fprintf(fp,"%le", rgrid[k]);
for (i=0; i<=Ntotal-1; i++)
{
fprintf(fp,"\t%le",psi[i][k]);
}
fprintf(fp,"\n");
}
fclose(fp);
/* all orbitals gnu script file */
sprintf(script_filename,"%s%s_all_orb.plt",paw_sdir(),atom_name);
fp = fopen(script_filename,"w+");
fprintf(fp,
"set title \" Kohn-Sham bound states for %s \" \n",
atom_name);
fprintf(fp,"set nolabel \n");
fprintf(fp,"set key right top box\n");
fprintf(fp,"set grid \n");
fprintf(fp,"set xlabel \"r (a0)\" \n");
fprintf(fp,"set style data lines \n");
fprintf(fp,"set autoscale \n");
fprintf(fp,"set xr[0:5] \n");
i=0;
sprintf(nl_name,"%d%s",n[i],paw_spd_Name(l[i]));
sprintf(title,"%s (%f)",nl_name,eigenvalue[i]);
fprintf(fp,"plot \"%s\" using 1:2 title \"%s\" ",data_filename,title);
for (i=1; i<=Nbound-1; i++)
{
sprintf(nl_name,"%d%s",n[i],paw_spd_Name(l[i]));
sprintf(title,"%s (%f)",nl_name,eigenvalue[i]);
fprintf(fp,",\"\" using 1:%d title \"%s\" ",i+2,title);
}
fprintf(fp,"\n");
fprintf(fp,"pause -1\n");
fclose(fp);
/* individual orbitals gnu script file */
for (i=0; i<=Ntotal-1; i++)
{
sprintf(nl_name,"%d%s",n[i],paw_spd_Name(l[i]));
sprintf(script_filename,"%s%s_%s_orb.plt",paw_sdir(),atom_name,nl_name);
fp = fopen(script_filename,"w+");
fprintf(fp,"set style data lines \n");
fprintf(fp,"set nolabel \n");
fprintf(fp,"set autoscale \n");
fprintf(fp,"set xr[0:%d] \n",n[i]+l[i]);
fprintf(fp,"set xlabel \"r (a0)\" \n");
fprintf(fp,"set grid \n");
fprintf(fp,"set nokey \n");
fprintf(fp,"set title \" %s orbital for %s\\n (e=%f Hartree)\" \n",
nl_name,atom_name,eigenvalue[i]);
sprintf(title,"%s (%f)",nl_name,eigenvalue[i]);
fprintf(fp,"plot \"%s\" using 1:%d title \"%s\" ",data_filename,i+2,title);
fprintf(fp,"\n");
fprintf(fp,"pause -1\n");
fclose(fp);
}
}
}
int paw_R_Schrodinger_Fixed_Logderiv1(
int n,
int l,
double *v,
int match,
double u_logderiv,
double *Eig,
double *u,
double *uprime
)
{
int i;
int j;
int iteration;
int Ngrid;
double sum;
double E;
double de;
double Emax;
double Emin;
double log_amesh;
double log_amesh2;
double gamma;
double L2;
double r2;
double uout;
double upout;
double upin;
double *r;
double *f_upp;
double *upp;
/* define eigenvalues */
E = *Eig;
/* define power of the orbital near 0 */
gamma = ((double) (l+1));
/* define square of the angular momentum */
L2 = ((double) (l*(l+1)));
/* define log grid parameters */
Ngrid = paw_N_LogGrid();
log_amesh = paw_log_amesh_LogGrid();
log_amesh2 = log_amesh*log_amesh;
/* get pointer rgrid, and extra memory */
r = (double *) paw_r_LogGrid();
f_upp = (double *) paw_alloc_LogGrid();
upp = (double *) paw_alloc_LogGrid();
/* set up bounds for eigenvalue */
Emax = E + 10.0;
Emin = E - 10.0;
iteration = 0;
while (iteration < Max_Iterations)
{
++iteration;
/* define f_upp */
for (i=0; i<Ngrid; ++i)
{
r2 = r[i]*r[i];
f_upp[i] = log_amesh2*(L2 + 2.0*(v[i] - E)*r2);
}
/* set the boundry condition near zero */
for (i=0; i<4; ++i)
{
u[i] = pow(r[i],gamma);
uprime[i] = log_amesh*gamma*u[i];
upp[i] = log_amesh*uprime[i] + f_upp[i]*u[i];
}
/* integrate from 0 to match */
for (i=3; i<match; ++i)
{
/* predictors */
u[i+1] = paw_Predictor_Out(i,u,uprime);
uprime[i+1] = paw_Predictor_Out(i,uprime,upp);
/* correctors */
for (j=0; j<Corrector_Iterations; ++j)
{
upp[i+1] = log_amesh*uprime[i+1] + f_upp[i+1]*u[i+1];
uprime[i+1] = paw_Corrector_Out(i,uprime,upp);
u[i+1] = paw_Corrector_Out(i,u,uprime);
}
}
uout = u[match];
upout = uprime[match];
upin = u_logderiv*uout;
/* Find Integral(u^2) */
sum = paw_Norm_LogGrid(match,gamma,u);
sum = 1.0/sqrt(sum);
uout = sum*uout;
upout = sum*upout;
upin = sum*upin;
for (i=0; i<=match; ++i)
{
u[i] = sum*u[i];
uprime[i] = sum*uprime[i];
}
for (i=match+1; i<Ngrid; ++i)
{
u[i] = 0.0;
uprime[i] = 0.0;
}
/* figure out new eigenvalue */
de = 0.5*uout*(upout-upin)/(log_amesh*r[match]);
/* eigenvalue is converged, exit */
if (fabs(de) < (Max(fabs(E),0.2)*tolerance))
{
*Eig = E;
/* dealloc memory */
paw_dealloc_LogGrid(upp);
paw_dealloc_LogGrid(f_upp);
return True;
}
if (de > 0.0)
Emin = E;
else
Emax = E;
E = E + de;
if ( (E > Emax) || (E < Emin))
E = 0.5*(Emin+Emax);
} /* while */
printf("paw_Error R_Schrodinger_Fixed_Logderiv: More than %d iterations\n",
Max_Iterations);
*Eig = E;
/* dealloc memory */
paw_dealloc_LogGrid(upp);
paw_dealloc_LogGrid(f_upp);
return False;
} /* paw_R_Schrodinger_Fixed_LogDeriv */
/****************************************
Function name : paw_solve_scattering_orbitals
Description :
Return type : void
Author : Marat Valiev
Date & Time : 4/10/99 4:58:27 PM
****************************************/
void paw_solve_scattering_orbitals()
{
int i;
int j;
int k;
int i_match;
int Ngrid;
double sum;
double *V;
double *rgrid;
double r_sphere;
double Zion;
Ngrid = paw_N_LogGrid();
rgrid = paw_r_LogGrid();
Zion = paw_get_ion_charge();
/*normalization sphere radius*/
r_sphere = 2.0;
/*check if the occupied orbitals are done*/
if (!(occupied_orbitals_done))
{
printf("cannot calculate scattering orbitals\n");
printf("calculate occupied states first\n");
}
/*get Kohn-Sham potential*/
V = paw_get_kohn_sham_potential();
for (i=Nbound;i<Ntotal;i++)
{
/*set the end point*/
i_match = Ngrid-1;
if (Solver_Type==Schrodinger)
{
paw_R_Schrodinger_Fixed_E(l[i],V,i_match,eigenvalue[i],psi[i],psi_prime[i]);
}
else
{
paw_R_Pauli_Fixed_E(n[i],l[i],Zion,V,i_match,eigenvalue[i],psi[i],psi_prime[i]);
}
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*/
sum = paw_dot_product1(paw_get_grid_index(r_sphere),psi[i],psi[i]);
sum = 1.0/sqrt(sum);
for (k=0;k<Ngrid;++k)
{
psi[i][k] = psi[i][k]*sum;
psi_prime[i][k] = psi_prime[i][k]*sum;
}
}
/*debug
printf("orthogonality\n");
for(i=0;i<=Ntotal-1;i++)
{
for(j=0;j<=Ntotal-1;j++)
{
if(l[i]==l[j])
{
printf("%d\t %d\t %f\n",i,j, paw_dot_product(psi[i],psi[j]));
}
}
}
exit(1);
end debug */
}
/****************************************
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);
}
}
void paw_generate_projectors_blochl()
{
int i;
int j;
int k;
int Ngrid;
double norm;
double max_prj;
double max_phi;
double max_phi_ps;
double tmp_prj;
double *V_ref;
double *V;
double *rgrid;
double **b;
double **L;
double **U;
double **L_inv;
double **U_inv;
double **test_matrix;
char output[300];
FILE *fp;
/*make sure the pseudo orbitalas were found*/
if (! pseudo_orbitals_done)
{
printf("cannot calculate projectors\n");
printf("pseudo basis is not ready\n");
exit(1);
}
Ngrid = paw_N_LogGrid();
rgrid = paw_r_LogGrid();
b = paw_alloc_2d_array(nbasis,nbasis);
L = paw_alloc_2d_array(nbasis,nbasis);
L_inv = paw_alloc_2d_array(nbasis,nbasis);
U = paw_alloc_2d_array(nbasis,nbasis);
U_inv = paw_alloc_2d_array(nbasis,nbasis);
test_matrix = paw_alloc_2d_array(nbasis,nbasis);
/*obtain the ref potential*/
V_ref = paw_get_ref_pot();
/*form initial guess for projectors as in Blochl*/
for (i = 0; i < nbasis; ++i)
{
V = paw_get_paw_potential(i);
for (k = 0; k < Ngrid; ++k)
prj_ps[i][k] = (V_ref[k] - V[k])*phi_ps[i][k];
if (paw_debug())
{
sprintf(output, "%s%s_%d%d", paw_sdir(),"p",prin_n[i],orb_l[i]);
fp = fopen(output, "w+");
for (k = 0; k < Ngrid; ++k)
{
fprintf(fp, "%le\t %le\t %le \n", rgrid[k], prj_ps[i][k],(V_ref[k] - V[k]));
}
fclose(fp);
}
}
/*check for accidental null projectors*/
for (i = 0; i < nbasis; ++i)
{
max_prj = 0.0;
for (k = 0; k < Ngrid; ++k)
{
tmp_prj = fabs(prj_ps[i][k]);
if (tmp_prj > max_prj)
max_prj = tmp_prj;
}
if (max_prj <0.000001)
{
printf("found null projectors, aborting the program ... \n");
exit(1);
}
}
for (i=0;i<=nbasis-1;i++)
{
for (j=0;j<=nbasis-1;j++)
{
if (orb_l[i] == orb_l[j] )
{
b[i][j] = paw_dot_product(phi_ps[j],prj_ps[i]);
}
else
{
b[i][j] = 0.0;
}
}
}
paw_lu_decompose(nbasis, b, L, U);
paw_triang_matrix_inverse("l",nbasis,L,L_inv);
paw_triang_matrix_inverse("u",nbasis,U,U_inv);
for (i=0;i<=nbasis-1;i++)
{
for (k = 0; k <= Ngrid-1; k++)
prj_ps0[i][k] = prj_ps[i][k];
}
for (i=0;i<=nbasis-1;i++)
{
paw_Zero_LogGrid(prj_ps[i]);
paw_Zero_LogGrid(phi[i]);
paw_Zero_LogGrid(phi_ps[i]);
paw_Zero_LogGrid(phi_prime[i]);
paw_Zero_LogGrid(phi_ps_prime[i]);
}
for (i=0;i<=nbasis-1;i++)
{
for (j=0;j<=i;j++)
{
for (k = 0; k <= Ngrid-1; k++)
{
prj_ps[i][k] = prj_ps[i][k] + L_inv[i][j]*prj_ps0[j][k];
phi[i][k] = phi[i][k] + U_inv[j][i]*phi0[j][k];
phi_ps[i][k] = phi_ps[i][k] + U_inv[j][i]*phi_ps0[j][k];
phi_prime[i][k] = phi_prime[i][k] + U_inv[j][i]*phi0_prime[j][k];
phi_ps_prime[i][k] = phi_ps_prime[i][k] + U_inv[j][i]*phi_ps0_prime[j][k];
}
}
}
for (i=0;i<=nbasis-1;i++)
paw_Zero_LogGrid(prj_ps0[i]);
for (i=0;i<=nbasis-1;i++)
{
for (j=0;j<=nbasis-1;j++)
{
for (k = 0; k <= Ngrid-1; k++)
{
prj_ps0[i][k] = prj_ps0[i][k] + U_inv[i][j]*prj_ps[j][k];
}
}
}
/*rescale basis*/
for (i = 0; i <= nbasis-1; i++)
{
max_prj = 0.0;
max_phi = 0.0;
max_phi_ps = 0.0;
for (k = 0; k < i_r_orbital[i]; k++)
{
if (max_prj < fabs(prj_ps[i][k]))
max_prj = fabs(prj_ps[i][k]);
if (max_phi_ps < fabs(phi_ps[i][k]))
max_phi_ps = fabs(phi_ps[i][k]);
}
if (max_prj == 0.0 || max_phi_ps == 0.0)
{
printf("division by zero while rescaling basis\n");
exit(99);
}
norm = 0.75*sqrt(max_phi_ps/max_prj);
max_prj = 0.0;
max_phi = 0.0;
max_phi_ps = 0.0;
scaling_factor[i] = norm;
for (k = 0; k < Ngrid; ++k)
{
prj_ps[i][k] = prj_ps[i][k]*norm;
phi[i][k] = phi[i][k]/norm;
phi_ps[i][k] = phi_ps[i][k]/norm;
phi_prime[i][k] = phi_prime[i][k]/norm;
phi_ps_prime[i][k] = phi_ps_prime[i][k]/norm;
}
}
for (i = 0; i <= nbasis-1; i++)
{
for (j = 0; j <= nbasis-1; j++)
{
tr_matrix[i][j] = U_inv[i][j];
}
}
if (paw_debug())
printf("derivative=%f\n",phi_ps_prime[0][0]/(rgrid[0]*paw_log_amesh_LogGrid()));
}
/****************************************
Function name : paw_init_paw_orbitals
Description :
Return type : void
Argument : int a_nbasis
Argument : double *a_rc_orb
Argument : int *a_n
Argument : int *a_n_ps
Argument : int *a_l
Argument : int *a_s_z
Argument : double *a_e
Argument : double *a_fill
Author : Marat Valiev
Date & Time : 4/4/99 5:11:29 PM
****************************************/
void paw_init_paw_basis(
char* a_nodal_constraint,
char* a_projector_method,
int a_nbasis,
int *a_n,
int *a_l,
double *r_match
)
{
int i;
int k;
int i_match;
int Ngrid;
int index;
double *rgrid;
double *psi;
double *psi_prime;
Ngrid = paw_N_LogGrid();
rgrid = paw_r_LogGrid();
strcpy(nodal_constraint,a_nodal_constraint);
strcpy(projector_method,a_projector_method);
nbasis = a_nbasis;
/* prin_n = a_n; */
/* orb_l = a_l; */
/* r_orbital = r_match; */
/*maximum angular momentum in the basis*/
max_orb_l = 0;
for (i=0;i<=nbasis-1;i++)
{
if (max_orb_l < a_l[i])
max_orb_l = a_l[i];
}
delta_ekin = (int *) malloc( nbasis* sizeof(int));
orb_type = (int *) malloc( nbasis* sizeof(int));
prin_n_ps = (int *) malloc( nbasis* sizeof(int));
prin_n = (int *) malloc( nbasis* sizeof(int));
orb_l = (int *) malloc( nbasis* sizeof(int));
l_counter = (int *) malloc((max_orb_l+1)*sizeof(int));
i_r_orbital = (int *) malloc( nbasis* sizeof(int));
r_orbital = (double *) malloc( nbasis* sizeof(double));
fill = (double *) malloc( nbasis* sizeof(double));
e = (double *) malloc( nbasis* sizeof(double));
e_ps = (double *) malloc( nbasis* sizeof(double));
log_deriv = (double *) malloc( nbasis* sizeof(double));
rho = paw_alloc_LogGrid();
rho_ps = paw_alloc_LogGrid();
phi = (double **) malloc(nbasis * sizeof(double *));
phi0 = (double **) malloc(nbasis * sizeof(double *));
phi_prime = (double **) malloc(nbasis * sizeof(double *));
phi_ps0 = (double **) malloc(nbasis * sizeof(double *));
phi_ps0_prime= (double **) malloc(nbasis * sizeof(double *));
phi0_prime = (double **) malloc(nbasis * sizeof(double *));
phi_ps = (double **) malloc(nbasis * sizeof(double *));
phi_ps_prime = (double **) malloc(nbasis * sizeof(double *));
prj_ps = (double **) malloc(nbasis * sizeof(double *));
prj_ps0 = (double **) malloc(nbasis * sizeof(double *));
psi_ps = (double **) malloc(nbasis * sizeof(double *));
psi_ps_prime = (double **) malloc(nbasis * sizeof(double *));
for (i = 0; i < nbasis; ++i)
{
prin_n[i] = a_n[i];
orb_l[i] = a_l[i];
phi0[i] = paw_alloc_LogGrid();
phi[i] = paw_alloc_LogGrid();
phi_prime[i] = paw_alloc_LogGrid();
phi_ps0[i] = paw_alloc_LogGrid();
phi_ps[i] = paw_alloc_LogGrid();
phi_ps_prime[i] = paw_alloc_LogGrid();
phi_ps0_prime[i] = paw_alloc_LogGrid();
phi0_prime[i] = paw_alloc_LogGrid();
prj_ps[i] = paw_alloc_LogGrid();
prj_ps0[i] = paw_alloc_LogGrid();
psi_ps[i] = paw_alloc_LogGrid();
psi_ps_prime[i] = paw_alloc_LogGrid();
}
Zvalence = 0.0;
for (i=0;i<=nbasis-1;i++)
{
index = paw_get_orbital_index(prin_n[i],orb_l[i]);
fill[i] = paw_get_fill(index);
Zvalence += fill[i];
e[i] = paw_get_e(index);
e_ps[i] = e[i];
orb_type[i] = paw_get_orb_type(index);
psi = paw_get_psi(index);
for (k=0;k<=Ngrid-1;k++)
phi[i][k] = psi[k];
psi_prime = paw_get_psi_prime(index);
for (k=0;k<=Ngrid-1;k++)
phi_prime[i][k] = psi_prime[k];
}
/* set matching point for pseudoorbitals*/
for (i=0;i<=nbasis-1;i++)
{
i_r_orbital[i] = paw_get_grid_index(r_match[i]);
/*r_orbital[i] = rgrid[i_r_orbital[i]]; */
r_orbital[i] = r_match[i];
}
/*largest sphere in the basis*/
max_i_r_orbital = 0;
for (i=0;i<=nbasis-1;i++)
{
if (max_i_r_orbital < i_r_orbital[i])
max_i_r_orbital = i_r_orbital[i];
}
/*check if prin_n array is monotonically increasing*/
for (i=0;i<=nbasis-2;i++)
{
if (prin_n[i]>prin_n[i+1])
printf("please order your states according to increasing n");
}
/* counter for number of orbitals per angular momentum*/
for (i=0;i<(max_orb_l+1);++i)
l_counter[i] = 0;
if (strcmp(nodal_constraint,"off")==0)
{
for (i=0;i<nbasis;++i)
{
prin_n_ps[i] = orb_l[i] + 1;
}
}
else if (strcmp(nodal_constraint,"on")==0)
{
for (i=0;i<nbasis;++i)
{
prin_n_ps[i] = orb_l[i] + 1 + l_counter[orb_l[i]];
l_counter[orb_l[i]] = l_counter[orb_l[i]]+1;
}
}
else
{
printf("unknown value for the nodal_constraint\n");
exit(1);
}
for (i = 0; i < nbasis; ++i)
{
i_match = i_r_orbital[i];
if (fabs(phi[i][i_match]) < SMALL)
{
printf("error, your orbital matching sphere is to close to the node of %d%d orbital \n",
prin_n[i],orb_l[i]);
exit(1);
}
else
{
log_deriv[i] = phi_prime[i][i_match]/phi[i][i_match];
}
}
/*set all paw orbitals to scattering ***/
for (i = 0; i < nbasis; ++i)
{
orb_type[i]=scattering;
}
scaling_factor = paw_alloc_1d_array(nbasis);
tr_matrix = paw_alloc_2d_array(nbasis,nbasis);
}
/****************************************
Function name : paw_init_paw_potential
Description :
Return type : void
Argument : int a_nbasis
Argument : double a_r_sphere
Author : Marat Valiev
Date & Time : 4/11/99 4:11:34 PM
****************************************/
void paw_init_paw_potential(int a_nbasis,
double c0,
double a_r_ref,
double* a_r_potential,
double* V_ks)
{
int i;
int k;
int Ngrid;
int ic;
double rc;
double a,d,b;
double V_prime;
double *rgrid;
Ngrid = paw_N_LogGrid();
rgrid = paw_r_LogGrid();
nbasis = a_nbasis;
r_ref = a_r_ref;
rc_ref = paw_find_rc_pot(r_ref);
i_r_potential = (int *) malloc(nbasis * sizeof(int));
r_potential = (double *) malloc(nbasis * sizeof(double));
rc_pot = (double *) malloc(nbasis * sizeof(double));
c = (double *) malloc(nbasis * sizeof(double));
fcut = (double **) malloc(nbasis * sizeof(double *));
V_pseudo = paw_alloc_LogGrid();
V_ref = paw_alloc_LogGrid();
V_paw = (double **) malloc(nbasis * sizeof(double *));
for (i = 0; i <= nbasis-1; ++i)
{
V_paw[i] = paw_alloc_LogGrid();
fcut[i] = paw_alloc_LogGrid();
}
for (i=0; i <= nbasis-1;i++)
{
i_r_potential[i] = paw_get_grid_index(a_r_potential[i]);
/*r_potential[i] = rgrid[i_r_potential[i]];*/
r_potential[i] = a_r_potential[i];
rc_pot[i] = paw_find_rc_pot(r_potential[i]);
}
/* set ref potential
for (k = 0; k <= Ngrid-1; ++k)
V_ref[k] = V_ks[k]*(1 - exp(-pow((rgrid[k]/rc_ref),lambda)))+
c0*exp(-pow((rgrid[k]/rc_ref),lambda));
*/
ic = paw_get_grid_index(a_r_ref);
rc = rgrid[ic];
V_prime = 0.5*(V_ks[ic+1] - V_ks[ic-1])/(rc*paw_log_amesh_LogGrid());
a = c0;
d = (0.5*V_prime*rc + a - V_ks[ic])/(rc*rc*rc*rc);
b = (0.5*V_prime*rc - 2.0*d*rc*rc*rc*rc)/(rc*rc);
for (k=0;k<ic;++k)
V_ref[k] = a + b*rgrid[k]*rgrid[k] + d*rgrid[k]*rgrid[k]*rgrid[k]*rgrid[k];
for (k=ic;k<Ngrid;++k)
V_ref[k] = V_ks[k];
/* Form cutoff function for PS potential*/
for (i = 0; i <= nbasis-1; i++)
for (k = 0; k <= Ngrid-1; k++)
fcut[i][k] = exp(-pow((rgrid[k]/rc_pot[i]),lambda));
/*Initialize coefficients for the construction of PS potential*/
for (i=0; i<nbasis; ++i)
c[i] = V_ks[i_r_potential[i]];
/*
for (i = 0; i < nbasis; ++i)
c[i] = V_ks[paw_get_grid_index(r_potential[i])];
*/
/* set initial paw potential*/
for (i = 0; i < nbasis; ++i)
for (k = 0; k <= Ngrid-1; k++)
V_paw[i][k] = V_ref[k] + c[i] * fcut[i][k];
}
int paw_R_Schrodinger(int n,
int l,
double* v,
double *Eig,
double* u,
double* uprime)
{
int i,j,
iteration,
node,
match,
Ninf, Ngrid;
double E, de,
Emax,
Emin,
log_amesh,
log_amesh2,
gamma,
L2,
sum, a, scale, m1scale,
uout,upout,upin,
*r,
*f_upp,
*r2,
*upp;
/* define eigenvalues */
E = *Eig;
gamma = ((double) (l+1));
L2 = ((double) (l*(l+1)));
/* define log grid parameters */
Ngrid = paw_N_LogGrid();
log_amesh = paw_log_amesh_LogGrid();
log_amesh2 = log_amesh*log_amesh;
/* get pointer rgrid, and extra memory */
r = paw_r_LogGrid();
r2 = paw_r2_LogGrid();
f_upp = paw_alloc_LogGrid();
upp = paw_alloc_LogGrid();
/* set up bounds for eigenvalue */
Emin = 0.0;
Emax = v[Ngrid-1] + 0.5*L2/(r[Ngrid-1]*r[Ngrid-1]);
for (i=0; i <= Ngrid-1; i++)
Emin = Min(Emin, (v[i] + 0.5*L2/r2[i]));
if (E > Emax) E = 1.25*Emax;
if (E < Emin) E = 0.75*Emin;
if (E > Emax) E = 0.5*(Emax+Emin);
iteration = 0;
while (iteration < Max_Iterations)
{
++iteration;
/* define f_upp */
for (i=0; i<Ngrid; ++i)
f_upp[i] = log_amesh2*(L2 + 2.0*(v[i] - E)*r2[i]);
/* classical turning point is used for matching */
match = Ngrid-1;
while (f_upp[match-1]*f_upp[match] > 0.0)
{
match = match - 1;
if (match < 2)
{
printf("Error in paw_R_Schrodinger: no turning point\n");
return False;
}
}
/* set the boundry condition near zero */
m1scale = 1.0;
for (i=0; i<(n-l-1); ++i)
m1scale *= -1.0;
for (i=0; i<=3; i++)
{
u[i] = m1scale*pow(r[i],gamma);
uprime[i] = log_amesh*gamma*u[i];
upp[i] = log_amesh*uprime[i] + f_upp[i]*u[i];
}
/* integrate from 0 to match */
node = 0;
for (i=3; i <= match-1; i++)
{
/* predictors */
u[i+1] = paw_Predictor_Out(i,u,uprime);
uprime[i+1] = paw_Predictor_Out(i,uprime,upp);
/* correctors */
for (j=0; j<= Corrector_Iterations-1; j++)
{
upp[i+1] = log_amesh*uprime[i+1] + f_upp[i+1]*u[i+1];
uprime[i+1] = paw_Corrector_Out(i,uprime,upp);
u[i+1] = paw_Corrector_Out(i,u,uprime);
}
/* finding nodes */
if (u[i+1]*u[i] <= 0) node = node + 1;
}
uout = u[match];
upout = uprime[match];
/* not enough nodes in u */
if ((node-n+l+1) < 0)
{
Emin = E;
E = 0.5*(Emin+Emax);
}
/* too many nodes in u */
else if ((node-n+l+1) > 0)
{
Emax = E;
E = 0.5*(Emin+Emax);
}
/* number of nodes ok, start integration inward */
else
{
/* find infinity
*/
/* find infinity */
Ninf = match + floor(2.3/log_amesh);
if ((Ninf+5) > Ngrid) Ninf = Ngrid - 5;
/* define boundry near infinity */
a = sqrt( L2/(r[Ninf]*r[Ninf]) + 2.0*(v[Ninf]-E) );
for (i=Ninf; i<=(Ninf+4); i++)
{
u[i] = exp(-a*(r[i]-r[Ninf]));
uprime[i] = -r[i]*log_amesh*a*u[i];
upp[i] = log_amesh*uprime[i] + f_upp[i]*u[i];
}
/* integrate from infinity to match */
for (i=Ninf; i>=(match+1); --i)
{
/* predictors */
u[i-1] = paw_Predictor_In(i,u,uprime);
uprime[i-1] = paw_Predictor_In(i,uprime,upp);
/* Correctors */
for (j=0; j<Corrector_Iterations; ++j)
{
upp[i-1] = log_amesh*uprime[i-1] + f_upp[i-1]*u[i-1];
uprime[i-1] = paw_Corrector_In(i,uprime,upp);
u[i-1] = paw_Corrector_In(i,u,uprime);
}
}
/* make the outside u, match the inside u */
scale = uout/u[match];
for (i=match; i<= Ninf; i++)
{
u[i] = scale*u[i];
uprime[i] = scale*uprime[i];
}
upin = uprime[match];
/* Find Integral(u^2) */
sum = paw_Norm_LogGrid(Ninf,gamma,u);
sum = 1.0/sqrt(sum);
uout = sum*uout;
upout = sum*upout;
upin = sum*upin;
for (i=0; i<=Ninf; i++)
{
u[i] = sum*u[i];
uprime[i] = sum*uprime[i];
}
/* figure out new eigenvalue */
de = 0.5*uout*(upout-upin)/(log_amesh*r[match]);
/* eigenvalue is converged, exit */
if (fabs(de) < (Max(fabs(E),0.2)*tolerance))
{
*Eig = E;
for (i=Ninf+1; i<Ngrid; ++i)
{
u[i] = u[Ninf]*exp(-a*(r[i]-r[Ninf]));
uprime[i] = -r[i]*log_amesh*a*u[i];
}
/* dealloc memory */
paw_dealloc_LogGrid(upp);
paw_dealloc_LogGrid(f_upp);
return True;
}
if (de > 0.0)
Emin = E;
else
Emax = E;
E = E + de;
if (Emax<=Emin)
{
/* dealloc memory */
paw_dealloc_LogGrid(upp);
paw_dealloc_LogGrid(f_upp);
*Eig = E;
return False;
}
if ( (E > Emax) || (E < Emin))
E = 0.5*(Emin+Emax);
} /* nodes ok */
} /* while */
printf("Error paw_R_Schrodinger: More than %d iterations\n",Max_Iterations);
*Eig = E;
/* dealloc memory */
paw_dealloc_LogGrid(upp);
paw_dealloc_LogGrid(f_upp);
return False;
} /* paw_R_Schrodinger */
void paw_print_paw_potential_to_file(char* atom_name)
{
int i;
int j;
int k;
int Ngrid;
int *prin_n;
int * orb_l;
double *rgrid;
char data_filename[300];
char script_filename[300];
char nl_name[20];
FILE *fp;
if (paw_debug())
{
Ngrid = paw_N_LogGrid();
rgrid = paw_r_LogGrid();
prin_n = paw_get_pointer_paw_n_array();
orb_l = paw_get_pointer_paw_l_array();
sprintf(data_filename,"%s%s_pot.dat",paw_sdir(),atom_name);
fp = fopen(data_filename,"w+");
for (k=0; k<=Ngrid-1; k++)
{
fprintf(fp,"%le\t%le\t%le", rgrid[k], V_ref[k], V_pseudo[k]);
for (i=0; i<=nbasis-1; i++)
fprintf(fp,"\t%le ",V_paw[i][k]);
fprintf(fp,"\n");
}
fclose(fp);
sprintf(script_filename,"%s%s_ref_pot.plt",paw_sdir(),atom_name);
fp = fopen(script_filename,"w+");
fprintf(fp,"set data style lines \n");
fprintf(fp,"set nolabel \n");
fprintf(fp,"set autoscale \n");
fprintf(fp,"set xr[0:%f] \n",2*r_ref);
fprintf(fp,"set grid \n");
fprintf(fp,"set nokey \n");
fprintf(fp,"set nolabel \n");
fprintf(fp,"set xlabel \"r (a0)\" \n");
fprintf(fp,"set title \" %s reference potential\n",atom_name);
fprintf(fp,"plot \"%s\" using 1:2 \n",data_filename);
fprintf(fp,"\n");
fprintf(fp,"pause -1\n");
fclose(fp);
sprintf(script_filename,"%s%s_loc_pot.plt",paw_sdir(),atom_name);
fp = fopen(script_filename,"w+");
fprintf(fp,"set data style lines \n");
fprintf(fp,"set nolabel \n");
fprintf(fp,"set autoscale \n");
fprintf(fp,"set xr[0:%f] \n",2*r_ref);
fprintf(fp,"set grid \n");
fprintf(fp,"set nokey \n");
fprintf(fp,"set nolabel \n");
fprintf(fp,"set xlabel \"r (a0)\" \n");
fprintf(fp,"set title \" %s local potential\n",atom_name);
fprintf(fp,"plot \"%s\" using 1:3 \n",data_filename);
fprintf(fp,"\n");
fprintf(fp,"pause -1\n");
fclose(fp);
/*gnu script file */
for (i=0,j=4; i<=nbasis-1; i++,j=j+1)
{
sprintf(nl_name,"%d%s",prin_n[i],paw_spd_Name(orb_l[i]));
sprintf(script_filename,"%s%s_%s_pot.plt",paw_sdir(),atom_name,nl_name);
fp = fopen(script_filename,"w+");
fprintf(fp,"set data style lines \n");
fprintf(fp,"set nolabel \n");
fprintf(fp,"set autoscale \n");
fprintf(fp,"set xr[0:%f] \n",1.5*r_potential[i]);
fprintf(fp,"set grid \n");
fprintf(fp,"set nokey \n");
fprintf(fp,"set nolabel \n");
fprintf(fp,"set xlabel \"r (a0)\" \n");
fprintf(fp,"set title \" %s paw potential for %s orbital\" \n",
atom_name,nl_name);
fprintf(fp,"plot \"%s\" using 1:%d \n",data_filename,j);
fprintf(fp,"\n");
fprintf(fp,"pause -1\n");
fclose(fp);
}
}
}
void paw_R_Schrodinger_Fixed_E1(
int l,
double *v,
double *f,
int match,
double E,
double *u,
double *uprime
)
{
int i,j,
Ngrid;
double log_amesh,
log_amesh2,
gamma,
L2,
r2,
*r,
*f_upp,
*upp;
double max_u;
/*set maximum allowed value for u*/
max_u = 10000000;
/* define power of the orbital near 0 */
gamma = ((double) (l+1));
/* define square of the angular momentum */
L2 = ((double) (l*(l+1)));
/* define log grid parameters */
Ngrid = paw_N_LogGrid();
log_amesh = paw_log_amesh_LogGrid();
log_amesh2 = log_amesh*log_amesh;
if (match > Ngrid-1)
{
printf("match point is outside the allowed region\n");
printf("abborting the program\n");
exit(1);
}
/* get pointer rgrid, and extra memory */
r = (double *) paw_r_LogGrid();
f_upp = (double *) paw_alloc_LogGrid();
upp = (double *) paw_alloc_LogGrid();
for (i=0; i<=match; i++)
{
u[i] = 0.0;
uprime[i] = 0.0;
}
/* define f_upp */
for (i=0; i<match+1; ++i)
{
r2 = r[i]*r[i];
f_upp[i] = log_amesh2*(L2 + 2.0*(v[i] - E)*r2);
}
for (i=0; i<4; ++i)
{
u[i] = pow(r[i],gamma);
uprime[i] = log_amesh*gamma*u[i];
upp[i] = log_amesh*uprime[i] + f_upp[i]*u[i];
}
/* integrate from 0 to match */
i=3;
while (i<match && fabs(u[i])<max_u)
{
/* predictors */
u[i+1] = paw_Predictor_Out(i,u,uprime);
uprime[i+1] = paw_Predictor_Out(i,uprime,upp);
/* correctors */
for (j=0; j<Corrector_Iterations; ++j)
{
upp[i+1] = log_amesh*uprime[i+1] + f_upp[i+1]*u[i+1]- 2.0*log_amesh2*r[i+1]*r[i+1]*f[i+1];
uprime[i+1] = paw_Corrector_Out(i,uprime,upp);
u[i+1] = paw_Corrector_Out(i,u,uprime);
}
i = i+1;
}
/* dealloc memory */
paw_dealloc_LogGrid(upp);
paw_dealloc_LogGrid(f_upp);
return;
} /* paw_R_Schrodinger */