/****************************************
Function name : generate_projectors
Description :
Return type : void
Author : Marat Valiev
Date & Time : 4/7/99 2:31:54 PM
****************************************/
void paw_generate_projectors()
{
int i;
int j;
double norm;
double norm_error;
if (strcmp(projector_method,"vanderbilt")==0)
{
paw_generate_projectors_vanderbilt();
}
else if (strcmp(projector_method,"blochl")==0)
{
paw_generate_projectors_blochl();
}
else
{
printf("error, unknown projector_method in generate_projectors \n");
exit(1);
}
/*Check paw basis orthogonality*/
norm_error = 0.0;
for (i = 0; i <= nbasis-1; i++)
{
for (j = 0; j <= nbasis-1; j++)
{
if (orb_l[i] == orb_l[j])
{
norm = paw_dot_product(prj_ps[i],phi_ps[j]);
if (i==j) norm = norm - 1.0;
if (fabs(norm) > norm_error) norm_error=fabs(norm);
}
}
}
if (paw_debug())
printf("paw basis is orthogonal to within %le \n",norm_error);
projectors_done = True;
}
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()));
}
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 : 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);
}
}
/****************************************
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);
}
