/****************************************
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_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];
}
/****************************************
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_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_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 */
}
