void dp_xpansion(double dp[])
{
int i;
double r1,r2,r3,r5,r7,r9,r11;
double *r;
r = r_LogGrid();
/* generate (d/dr)p(r) */
for (i=0; i<=match; ++i)
{
r1 = r[i];
r2 = r1*r1;
r3 = r1*r2;
r5 = r3*r2;
r7 = r5*r2;
r9 = r7*r2;
r11 = r9*r2;
dp[i] = 2.0 *c[1]*r1
+ 4.0 *c[2]*r3
+ 6.0 *c[3]*r5
+ 8.0 *c[4]*r7
+ 10.0*c[5]*r9
+ 12.0*c[6]*r11;
}
} /* dp_xpansion */
void ddp_xpansion(double ddp[])
{
int i;
double r1,r2,r4,r6,r8,r10;
double *r;
r = r_LogGrid();
/* generate (d/dr)(d/dr) p(r) */
for (i=0; i<=match; ++i)
{
r1 = r[i];
r2 = r1*r1;
r4 = r2*r2;
r6 = r4*r2;
r8 = r6*r2;
r10 = r8*r2;
ddp[i] = 2.0 *c[1]
+ 12.0 *c[2]*r2
+ 30.0 *c[3]*r4
+ 56.0 *c[4]*r6
+ 90.0 *c[5]*r8
+ 132.0*c[6]*r10;
}
} /* ddp_xpansion */
void p_xpansion(double p[])
{
int i;
double r1,r2,r4,r6,r8,r10,r12;
double *r;
r = r_LogGrid();
/* generate p(r) */
for (i=0; i<=match; ++i)
{
r1 = r[i];
r2 = r1*r1;
r4 = r2*r2;
r6 = r4*r2;
r8 = r6*r2;
r10 = r8*r2;
r12 = r10*r2;
p[i] = c[0]
+ c[1]*r2
+ c[2]*r4
+ c[3]*r6
+ c[4]*r8
+ c[5]*r10
+ c[6]*r12;
}
} /* p_xpansion */
void psp_xpansion()
{
int i,Ngrid;
double *r,*dp,*ddp;
Ngrid = N_LogGrid();
r = r_LogGrid();
dp = alloc_LogGrid();
ddp = alloc_LogGrid();
dp_xpansion(dp);
ddp_xpansion(ddp);
for (i=0; i<=match; ++i)
{
Vl[i] = el + dp[i]*(l+1.0)/r[i]
+ 0.5*ddp[i] + 0.5*dp[i]*dp[i];
}
for (i=(match+1); i<Ngrid; ++i)
Vl[i] = Vall[i];
dealloc_LogGrid(dp);
dealloc_LogGrid(ddp);
} /* psp_xpansion */
void dpsi_xpansion()
{
int i,Ngrid;
double al;
double *r,*p,*dp;
Ngrid = N_LogGrid();
r = r_LogGrid();
al = log_amesh_LogGrid();
p = alloc_LogGrid();
dp = alloc_LogGrid();
p_xpansion(p);
dp_xpansion(dp);
/* wl_prime = (d/di)wl */
for (i=0; i<=match; ++i)
wl_prime[i] = (al*r[i])*( (l+1.0) + r[i]*dp[i] )*pow(r[i],l)*exp(p[i]);
for (i=(match+1); i<Ngrid; ++i)
wl_prime[i] = ul_prime[i];
dealloc_LogGrid(p);
dealloc_LogGrid(dp);
} /* dpsi_xpansion */
void chi_xpansion2()
{
int i,Ngrid;
double *r,*dp,*ddp;
Ngrid = N_LogGrid();
r = r_LogGrid();
dp = alloc_LogGrid();
ddp = alloc_LogGrid();
dp_xpansion2(dp);
ddp_xpansion2(ddp);
for (i=0; i<=match; ++i)
{
Vl[i] = el + dp[i]*(l+1.0)/r[i]
+ 0.5*ddp[i] + 0.5*dp[i]*dp[i];
}
for (i=(match+1); i<Ngrid; ++i)
Vl[i] = Vall[i];
/* make it a projector rather than a potential */
for (i=0; i<Ngrid; ++i)
Vl[i] = Vl[i]*wl[i];
dealloc_LogGrid(dp);
dealloc_LogGrid(ddp);
} /* chi_xpansion2 */
void R_Screening_Cut(double * Vx)
{
int k,NN,n0,n1=0;
double r0,r1=0.0,v0,v1=0.0,m,b;
double *r;
if (screening_cut>0.0)
{
r = r_LogGrid();
NN = index_r_LogGrid(screening_cut) + 5;
for (k=0; k<NN; ++k)
if (r[k] < screening_cut)
{ n0=n1; r0=r1; v0=v1; n1=k; r1=r[k]; v1=Vx[k]; }
m = (v1-v0)/(r1-r0);
b = v1 - m*r1;
for (k=0; k<n1; ++k)
Vx[k] = m*r[k] + b;
}
}
void psi_xpansion()
{
int i,Ngrid;
double *r,*p;
Ngrid = N_LogGrid();
r = r_LogGrid();
p = alloc_LogGrid();
p_xpansion(p);
for (i=0; i<=match; ++i)
wl[i] = pow(r[i],l+1.0)*exp(p[i]);
for (i=(match+1); i<Ngrid; ++i)
wl[i] = ul[i];
dealloc_LogGrid(p);
} /* psi_xpansion */
void
solve_RelPsp ()
{
int p, k, Ngrid;
double *rgrid;
/* get loggrid variables */
Ngrid = N_LogGrid ();
rgrid = r_LogGrid ();
if (Solver_Type==Troullier) {
solve_RelTroullier(Nvalence, n, l, spin, eigenvalue, fill, rcut,
r_psi, r_psi_prime, rho, rho_semicore, V_psp,
&Total_E,
&E_Hartree, &P_Hartree,
&E_exchange, &P_exchange, &E_correlation, &P_correlation);
}else{
solve_RelHamann(Nvalence, n, l, spin, eigenvalue, fill, rcut,
r_psi, r_psi_prime, rho, rho_semicore, V_psp,
&Total_E,
&E_Hartree, &P_Hartree,
&E_exchange, &P_exchange, &E_correlation, &P_correlation);
}
/******************************************************/
/* find the outermost peak of the pseudowavefunctions */
/******************************************************/
for (p = 0; p < Nvalence; ++p)
{
if (fill[p] != 0.0)
{
k = Ngrid - 2;
while ((r_psi_prime[p][k] * r_psi_prime[p][k + 1] >= 0.0)
&& (k >= 0))
--k;
peak[p] = rgrid[k];
}
else
peak[p] = rgrid[Ngrid - 1];
}
} /* solve_RelPsp */
void ddddp_xpansion2(double ddddp[])
{
int i;
double r1,r2,r4,r6,r8;
double *r;
r = r_LogGrid();
/* generate (d/dr)**4 p(r) */
for (i=0; i<=match; ++i)
{
r1 = r[i];
r2 = r1*r1;
r4 = r2*r2;
r6 = r4*r2;
r8 = r6*r2;
ddddp[i] = 24.0 *c[2]
+ 360.0 *c[3]*r2
+ 1680.0 *c[4]*r4
+ 5040.0 *c[5]*r6;
}
} /* ddddp_xpansion2 */
void dddp_xpansion2(double dddp[])
{
int i;
double r1,r2,r3,r5,r7,r9;
double *r;
r = r_LogGrid();
/* generate (d/dr)**3 p(r) */
for (i=0; i<=match; ++i)
{
r1 = r[i];
r2 = r1*r1;
r3 = r1*r2;
r5 = r3*r2;
r7 = r5*r2;
r9 = r7*r2;
dddp[i] = 24.0 *c[2]*r1
+ 120.0 *c[3]*r3
+ 336.0 *c[4]*r5
+ 720.0 *c[5]*r7;
}
} /* dddp_xpansion2 */
void
solve_RelTroullier (int num_psp,
int *n_psp,
int *l_psp,
int *s_psp,
double *e_psp,
double *fill_psp,
double *rcut_psp,
double **r_psi_psp,
double **r_psi_prime_psp,
double *rho_psp,
double *rho_semicore,
double **V_psp, double *eall_psp,
double *eh_psp, double *ph_psp,
double *ex_psp, double *px_psp,
double *ec_psp, double *pc_psp)
{
int istate, i, l, k, p, s2, match, mch, Ngrid;
double al, amesh, rmax, Zion;
double gamma, gpr, nu0;
double ldpsi_match;
double el, eeig=0.0;
double ph, px, pc, eh, ex, ec;
double *ul, *ul_prime;
double *wl, *wl_prime;
double *r, *Vh, *Vx, *Vc, *rho_total, *Vall, *Vl;
/* Allocate Grids */
Vall = Vall_Atom ();
r = r_LogGrid ();
Ngrid = N_LogGrid ();
al = log_amesh_LogGrid ();
amesh = amesh_LogGrid ();
Zion = 0.0;
for (k = 0; k < Ngrid; ++k)
rho_psp[k] = 0.0;
if (debug_print ())
{
printf ("\n\nRelTroullier pseudopotential check\n\n");
printf
("l\trcore rmatch E in E psp norm test slope test\n");
}
for (p = 0; p < (num_psp); ++p)
{
l = l_psp[p];
s2 = s_psp[p];
wl = r_psi_psp[p];
wl_prime = r_psi_prime_psp[p];
Vl = V_psp[p];
/*******************************************/
/* Solve for scattering state if necessary */
/*******************************************/
if (fill_psp[p] < 1.e-15)
{
rmax = 10.0;
solve_Scattering_State_Atom (n_psp[p], l_psp[p], e_psp[p], rmax);
/* scattering state saved at the end of the atom list */
istate = Nvalence_Atom () + Ncore_Atom ();
if (s2 < 0)
istate += 1;
mch = (int) rint (log (rmax / r[0]) / al);
ul = r_psi_Atom (istate);
ul_prime = r_psi_prime_Atom (istate);
nu0 = Norm_LogGrid (mch, (l + 1.0), ul);
nu0 = 1.0 / sqrt (nu0);
for (i = 0; i < Ngrid; ++i)
{
ul[i] = ul[i] * nu0;
ul_prime[i] = ul_prime[i] * nu0;
}
}
/*******************************************/
/* find state of all-electron wavefunction */
/*******************************************/
else
istate = state_RelAtom (n_psp[p], l_psp[p], s_psp[p]);
/*************************************/
/* get the all-electron wavefunction */
/*************************************/
ul = r_psi_Atom (istate);
ul_prime = r_psi_prime_Atom (istate);
el = e_psp[p];
/*****************************/
/* find matching point stuff */
/*****************************/
match = (int) rint (log (rcut_psp[p] / r[0]) / al);
ldpsi_match = ul_prime[match] / ul[match];
/* make sure that wavefunctions are non-negative at the matching point */
if (ul[match] < 0.0)
{
nu0 = -1.0;
for (i = 0; i < Ngrid; ++i)
{
ul[i] = ul[i] * nu0;
ul_prime[i] = ul_prime[i] * nu0;
}
}
/**************************************/
/* generate troullier pseudopotential */
/**************************************/
init_xpansion (l, match, fill_psp[p], el, Vall, ul, ul_prime, Vl, wl,
wl_prime);
psi_xpansion ();
dpsi_xpansion ();
psp_xpansion ();
/******************/
/* verify psp Vl */
/******************/
/*******************/
/* psp bound state */
/*******************/
if (fill_psp[p] > 1.e-14)
{
R_Schrodinger (l_psp[p] + 1, l_psp[p], Vl, &mch, &el, wl, wl_prime);
}
/* scattering state */
else
{
R_Schrodinger_Fixed_Logderiv (l_psp[p] + 1, l_psp[p], Vl, match,
ldpsi_match, &el, wl, wl_prime);
R_Schrodinger_Fixed_E (l_psp[p] + 1, l_psp[p], Vl,
Ngrid - 1, el, wl, wl_prime);
/* normalize the scattering state to mch = 10.0 a.u. */
rmax = 10.0;
mch = rint (log (rmax / r[0]) / al);
nu0 = Norm_LogGrid (mch, (l + 1.0), wl);
nu0 = 1.0 / sqrt (nu0);
for (i = 0; i < Ngrid; ++i)
{
wl[i] = wl[i] * nu0;
wl_prime[i] = wl_prime[i] * nu0;
}
}
gamma = fabs (ul[match] / wl[match]);
gpr = fabs (ul_prime[match] / wl_prime[match]);
if (debug_print ())
{
/*printf("ul[match] wl[match]: %lf %lf\n",ul[match],wl[match]); */
printf ("%d\t%lf %lf %lf %lf %lf %lf\n", l_psp[p],
rcut_psp[p], r[match], e_psp[p], el, gamma, gpr);
}
/* Use the analytic form of pseudopotential */
el = e_psp[p];
psi_xpansion ();
dpsi_xpansion ();
psp_xpansion ();
if (fill_psp[p] > 1.e-14)
{
eeig += fill_psp[p] * el;
/* accumulate charges */
Zion += fill_psp[p];
for (k = 0; k < Ngrid; ++k)
rho_psp[k] += fill_psp[p] * pow (wl[k] / r[k], 2.0);
}
} /* for p */
/***************************************/
/* get the hartree potential an energy */
/* get the exchange potential and energy */
/* get the correlation potential and energy */
/***************************************/
Vh = alloc_LogGrid ();
Vx = alloc_LogGrid ();
Vc = alloc_LogGrid ();
ph = R_Hartree_DFT (rho_psp, Zion, Vh);
eh = 0.5 * ph;
rho_total = alloc_LogGrid ();
for (k = 0; k < Ngrid; ++k)
rho_total[k] = rho_psp[k] + rho_semicore[k];
R_Exchange_DFT (rho_total, Vx, &ex, &px);
R_Correlation_DFT (rho_total, Vc, &ec, &pc);
/* recalculate px and pc */
for (k = 0; k < Ngrid; ++k)
rho_total[k] = (rho_psp[k]) * Vx[k];
px = Integrate_LogGrid (rho_total);
for (k = 0; k < Ngrid; ++k)
rho_total[k] = (rho_psp[k]) * Vc[k];
pc = Integrate_LogGrid (rho_total);
*eall_psp = eeig + eh + ex + ec - ph - px - pc;
*eh_psp = eh;
*ph_psp = ph;
*ex_psp = ex;
*px_psp = px;
*ec_psp = ec;
*pc_psp = pc;
for (p = 0; p < num_psp; ++p)
for (k = 0; k < Ngrid; ++k)
V_psp[p][k] = V_psp[p][k] - Vh[k] - Vx[k] - Vc[k];
/* deallocate memory */
dealloc_LogGrid (Vh);
dealloc_LogGrid (Vx);
dealloc_LogGrid (Vc);
dealloc_LogGrid (rho_total);
} /* solve_Troullier */
void
init_Atom (char *filename)
{
int i, Ngrid, nx, lx, ncvh;
double *rgrid, fillx;
char *w;
FILE *fp;
/* set the solver type first */
fp = fopen (filename, "r+");
w = get_word (fp);
while ((w != NIL) && (strcmp ("<solver>", w) != 0))
w = get_word (fp);
if (w != NIL)
{
w = get_word (fp);
if (strcmp ("schrodinger", w) == 0)
Solver_Type = Schrodinger;
if (strcmp ("pauli", w) == 0)
Solver_Type = Pauli;
if (strcmp ("dirac", w) == 0)
Solver_Type = Dirac;
if (strcmp ("zora", w) == 0)
Solver_Type = ZORA;
}
fclose (fp);
/* open data file */
fp = fopen (filename, "r+");
/* move to <atom> section of data file */
w = get_word (fp);
while ((w != NIL) && (strcmp ("<atom>", w) != 0))
w = get_word (fp);
/* Error occured */
if (w == NIL)
{
printf ("Error: <atom> section not found\n");
fclose (fp);
exit (99);
}
/* set the name of the atom */
fscanf (fp, "%s", atom_name);
/* read in atom info. from the stream */
fscanf (fp, "%le", &Zion);
fscanf (fp, "%le", &amass);
fscanf (fp, "%d %d", &Ncore, &Nvalence);
if (Solver_Type != Dirac && Solver_Type!=ZORA)
{
Ncv = Ncore + Nvalence;
/* allocate the necessary memory for eigenvalues */
n = (int *) malloc ((Ncv + 1) * sizeof (int));
l = (int *) malloc ((Ncv + 1) * sizeof (int));
s2 = (int *) malloc ((Ncv + 1) * sizeof (int));
fill = (double *) malloc ((Ncv + 1) * sizeof (double));
/* allocate memory for outer peak and turning_point positions */
turning_point = (int *) malloc ((Ncv + 1) * sizeof (int));
peak = (double *) malloc ((Ncv + 1) * sizeof (double));
/* set eigenvalue arrays */
lmax = 0;
for (i = 0; i < Ncv; ++i)
{
fscanf (fp, "%d %d %le", &n[i], &l[i], &fill[i]);
if (l[i] > lmax)
lmax = l[i];
}
/* set up logarithmic grid */
init_LogGrid (Zion);
Ngrid = N_LogGrid ();
rgrid = r_LogGrid ();
/* allocate the necessary memory */
eigenvalue = (double *) malloc ((Ncv + 1) * sizeof (double));
r_psi = (double **) malloc ((Ncv + 1) * sizeof (double *));
r_psi_prime = (double **) malloc ((Ncv + 1) * sizeof (double *));
for (i = 0; i < (Ncv + 1); ++i)
{
r_psi[i] = alloc_LogGrid ();
r_psi_prime[i] = alloc_LogGrid ();
}
}
else
{
Ncore = 2 * Ncore;
Nvalence = 2 * Nvalence;
Ncv = Ncore + Nvalence;
/* allocate the necessary memory for eigenvalues */
n = (int *) malloc ((Ncv + 2) * sizeof (int));
l = (int *) malloc ((Ncv + 2) * sizeof (int));
s2 = (int *) malloc ((Ncv + 2) * sizeof (int));
fill = (double *) malloc ((Ncv + 2) * sizeof (double));
/* allocate memory for outer peak and turning_point positions */
turning_point = (int *) malloc ((Ncv + 2) * sizeof (int));
peak = (double *) malloc ((Ncv + 2) * sizeof (double));
/* set eigenvalue arrays */
lmax = 0;
ncvh = Ncv / 2;
for (i = 0; i < ncvh; ++i)
{
fscanf (fp, "%d %d %le", &nx, &lx, &fillx);
lmax=(lmax>lx)?lmax:lx;
n[2 * i] = nx;
n[2 * i + 1] = nx;
l[2 * i] = lx;
l[2 * i + 1] = lx;
s2[2 * i] = -1;
s2[2 * i + 1] = 1;
/****************************************************************
* fill in the j=l+0.5 and j=l-0.5 states with the proper
* occupancy. A simple divide will give the wrong occupancies.
****************************************************************/
if (!lx)
{
fill[2 * i] = fillx * 0.5;
fill[2 * i + 1] = fillx * 0.5;
}
else
{
fill[2 * i] = (2.0 * lx) * (fillx * 0.5 / (2. * lx + 1.));
fill[2 * i + 1] = (2.0 * lx+ 2.0) *
(fillx * 0.5 / (2. * lx + 1.));
}
}
/* set up logarithmic grid */
init_LogGrid (Zion);
Ngrid = N_LogGrid ();
rgrid = r_LogGrid ();
/* allocate the necessary memory */
eigenvalue = (double *) malloc ((Ncv + 2) * sizeof (double));
r_psi = (double **) malloc ((Ncv + 2) * sizeof (double *));
r_psi_prime = (double **) malloc ((Ncv + 2) * sizeof (double *));
for (i = 0; i < (Ncv + 2); ++i)
{
r_psi[i] = alloc_LogGrid ();
r_psi_prime[i] = alloc_LogGrid ();
}
}
rho = alloc_LogGrid ();
rho_core = alloc_LogGrid ();
rho_valence = alloc_LogGrid ();
Vion = alloc_LogGrid ();
Vall = alloc_LogGrid ();
/* set Vion */
for (i = 0; i < Ngrid; ++i)
Vion[i] = -Zion / rgrid[i];
fclose (fp);
/* initialize DFT stuff */
init_DFT (filename);
}
void FATR rpspsolve_
#if defined(USE_FCD)
(Integer * print_ptr,
Integer * debug_ptr,
Integer * lmax_ptr,
Integer * locp_ptr,
double *rlocal_ptr,
const _fcd fcd_sdir_name,
Integer * n9,
const _fcd fcd_dir_name,
Integer * n0,
const _fcd fcd_in_filename,
Integer * n1, const _fcd fcd_out_filename, Integer * n2)
{
char *sdir_name = _fcdtocp (fcd_sdir_name);
char *dir_name = _fcdtocp (fcd_dir_name);
char *in_filename = _fcdtocp (fcd_in_filename);
char *out_filename = _fcdtocp (fcd_out_filename);
#else
(print_ptr, debug_ptr, lmax_ptr, locp_ptr, rlocal_ptr,
sdir_name, n9, dir_name, n0, in_filename, n1, out_filename, n2)
Integer *print_ptr;
Integer *debug_ptr;
Integer *lmax_ptr;
Integer *locp_ptr;
double *rlocal_ptr;
char sdir_name[];
Integer *n9;
char dir_name[];
Integer *n0;
char in_filename[];
Integer *n1;
char out_filename[];
Integer *n2;
{
#endif
int i, j, k, l, p, Nlinear, Nvalence;
int debug, print;
double *rl, *rhol, **psil, **pspl;
double over_fourpi, c, x, y;
int Ngrid;
double *vall, *rgrid;
char name[255];
int lmax_out, locp_out, nvh;
double rlocal_out, vx;
FILE *fp;
int m9 = ((int) (*n9));
int m0 = ((int) (*n0));
int m1 = ((int) (*n1));
int m2 = ((int) (*n2));
char *infile = (char *) malloc (m9 + m1 + 5);
char *outfile = (char *) malloc (m0 + m2 + 5);
char *soutfile = (char *) malloc (m0 + m2 + 9);
char *full_filename = (char *) malloc (m9 + 25 + 5);
print = *print_ptr;
debug = *debug_ptr;
lmax_out = *lmax_ptr;
locp_out = *locp_ptr;
rlocal_out = *rlocal_ptr;
(void) strncpy (infile, sdir_name, m9);
infile[m9] = '\0';
strcat (infile, "/");
infile[m9 + 1] = '\0';
strncat (infile, in_filename, m1);
infile[m9 + m1 + 1] = '\0';
(void) strncpy (outfile, dir_name, m0);
outfile[m0] = '\0';
strcat (outfile, "/");
outfile[m0 + 1] = '\0';
strncat (outfile, out_filename, m2);
outfile[m0 + m2 + 1] = '\0';
over_fourpi = 0.25/M_PI;
/********************
* we have already solved for the Relativsitic AE wavefunctions using atom
* in the call to pspsolve
*******************/
set_debug_print (debug);
init_RelPsp (infile);
solve_RelPsp ();
if (debug)
print_RelPsp (stdout);
init_Linear (infile);
/* allocate linear meshes */
Nvalence = Nvalence_RelPsp ();
Nlinear = nrl_Linear ();
psil = (double **) malloc (Nvalence * sizeof (double *));
pspl = (double **) malloc (Nvalence * sizeof (double *));
for (p = 0; p < Nvalence; ++p)
{
psil[p] = (double *) malloc (Nlinear * sizeof (double));
pspl[p] = (double *) malloc (Nlinear * sizeof (double));
}
rl = (double *) malloc (Nlinear * sizeof (double));
rhol = (double *) malloc (Nlinear * sizeof (double));
/* Norm-conserving output */
for (p = 0; p < Nvalence; ++p)
{
Log_to_Linear (r_psi_RelPsp (p), rl, psil[p]);
Log_to_Linear_zero (V_RelPsp (p), rl, pspl[p]);
/* normalize scattering state */
if (fill_RelPsp (p) == 0.0)
{
normalize_Linear (psil[p]);
}
}
Log_to_Linear (rho_RelPsp (), rl, rhol);
if (debug)
{
/* output pseudowavefunctions argv[1].psw */
strcpy (name, name_Atom ());
strcat (name, ".psw.plt");
full_filename[0] = '\0';
strncpy (full_filename, sdir_name, m9);
full_filename[m9] = '\0';
strcat (full_filename, "/");
full_filename[m9 + 1] = '\0';
strcat (full_filename, name);
printf ("Outputing pseudowavefunctions: %s\n", full_filename);
fp = fopen (full_filename, "w+");
for (k = 0; k < Nlinear; ++k)
{
fprintf (fp, "%12.8lf", rl[k]);
for (p = 0; p < Nvalence; ++p)
fprintf (fp, " %12.8lf", psil[p][k]);
fprintf (fp, "\n");
}
fclose (fp);
/* output pseudopotentials argv[1].psp.plt */
strcpy (name, name_Atom ());
strcat (name, ".psp.plt");
full_filename[0] = '\0';
strncpy (full_filename, sdir_name, m9);
full_filename[m9] = '\0';
strcat (full_filename, "/");
full_filename[m9 + 1] = '\0';
strcat (full_filename, name);
printf ("Outputing pseudopotentials: %s\n", full_filename);
fp = fopen (full_filename, "w+");
for (k = 0; k < Nlinear; ++k)
{
fprintf (fp, "%12.8lf", rl[k]);
for (p = 0; p < Nvalence; ++p)
fprintf (fp, " %12.8lf", pspl[p][k]);
fprintf (fp, "\n");
}
fclose (fp);
/* output pseudodensity infile.psd.plt */
strcpy (name, name_Atom ());
strcat (name, ".psd.plt");
full_filename[0] = '\0';
strncpy (full_filename, sdir_name, m9);
full_filename[m9] = '\0';
strcat (full_filename, "/");
full_filename[m9 + 1] = '\0';
strcat (full_filename, name);
fp = fopen (full_filename, "w+");
for (k = 0; k < Nlinear; ++k)
fprintf (fp, "%12.8lf %12.8lf\n", rl[k], rhol[k]);
fclose (fp);
}
/* output datafile to be used for Kleinman-Bylander input, argv[1].psp */
if (print)
{
printf (" Creating datafile for Kleinman-Bylander input: %s\n",
outfile);
}
fp = fopen (outfile, "w+");
fprintf (fp, "7 %s\n", name_Atom ());
fprintf (fp, "%lf %lf %d %d %d %lf\n", Zion_RelPsp (), Amass_Atom (),
lmax_RelPsp (), lmax_out, locp_out, rlocal_out);
for (p = 0; p <= lmax_RelPsp (); ++p)
fprintf (fp, "%lf ", rcut_RelPsp (p));
fprintf (fp, "\n");
fprintf (fp, "%d %lf\n", nrl_Linear (), drl_Linear ());
fprintf (fp, "%s\n", comment_RelPsp ());
if (print)
{
printf (" + Appending pseudopotentials: %s thru %s\n",
spd_Name (0), spd_Name (lmax_RelPsp ()));
}
nvh=Nvalence/2;
for (k = 0; k < Nlinear; ++k)
{
fprintf (fp, "%12.8lf", rl[k]);
for (p = 0; p < nvh; ++p)
{
/**************************************************************
* Here we output the v average
* v_avg(l,r)=((l*v(l-1/2) + (l+1)*v(l+1/2))/(2*l+1)
*************************************************************/
vx = ((p) * pspl[2 * p][k] + (p+1) * pspl[2 * p + 1][k])/(p+p+1);
fprintf (fp, " %12.8lf", vx);
}
fprintf (fp, "\n");
}
if (print)
{
printf (" + Appending pseudowavefunctions: %s thru %s\n",
spd_Name (0), spd_Name (lmax_RelPsp ()));
}
for (k = 0; k < Nlinear; ++k)
{
fprintf (fp, "%12.8lf ", rl[k]);
for (p = 0; p < Nvalence; ++p)
fprintf (fp, " %12.8lf", psil[p][k]);
fprintf (fp, "\n");
}
/* output spin-orbit datafile to be used for Kleinman-Bylander input, argv[1].dat */
if (print)
{
printf
(" Creating spin-orbit datafile for Kleinman-Bylander input: %s\n",
outfile);
}
if (print)
{
printf (" + Appending Spin-Orbit pseudopotentials: %s thru %s\n",
spd_Name (0), spd_Name (lmax_RelPsp ()));
}
for (k = 0; k < Nlinear; ++k)
{
fprintf (fp, "%12.8lf", rl[k]);
/**************************************************************
* Here we output the v spin orbit
* v_spin_orbit(l,r)=2*(v(l+1/2) - v(l-1/2))/(2*l+1)
*
* so that V_spin_orbit|Psi>= -1/2(1+kappa)*v_spin_orbit|Psi>
* its confusing because L*S -> - (1+kappa)/2
*************************************************************/
for (p = 1; p < nvh;++p)
{
vx = (pspl[2*p+1][k] - pspl[2*p][k]);
vx *= 2. / (2. * p + 1.);
fprintf (fp, " %15.8lf", vx);
}
fprintf (fp, "\n");
}
/* append semicore corrections */
if (r_semicore_RelPsp () != 0.0)
{
if (print)
{
printf (" + Appending semicore density\n");
}
Log_to_Linear (rho_semicore_RelPsp (), rl, rhol);
fprintf (fp, "%lf\n", r_semicore_RelPsp ());
for (k = 0; k < Nlinear; ++k)
fprintf (fp, "%12.8lf %12.8lf\n", rl[k],
fabs (rhol[k] * over_fourpi));
if (print)
{
printf (" + Appending semicore density gradient\n");
}
Log_to_Linear (drho_semicore_RelPsp (), rl, rhol);
for (k = 0; k < Nlinear; ++k)
fprintf (fp, "%12.8lf %12.8lf\n", rl[k], (rhol[k] * over_fourpi));
}
fclose (fp);
/******************************************************************/
/******************* output AE information ************************/
/******************************************************************/
if (debug)
{
/* output all-electron wavefunctions */
printf ("Outputing all-electron wavefunctions:");
Ngrid = N_LogGrid ();
rgrid = r_LogGrid ();
for (p = 0; p < (Ncore_Atom () + Nvalence_Atom ()); ++p)
{
sprintf (name, "%s.%1d%s%s", name_Atom (), n_Atom (p),
spd_Name (l_Atom (p)), spin_Name (p));
full_filename[0] = '\0';
strncpy (full_filename, sdir_name, m9);
full_filename[m9] = '\0';
strcat (full_filename, "/");
full_filename[m9 + 1] = '\0';
strcat (full_filename, name);
printf (" %s", full_filename);
fp = fopen (full_filename, "w+");
for (k = 0; k < Ngrid; ++k)
fprintf (fp, "%12.8lf %12.8lf\n", rgrid[k], r_psi_Atom (p)[k]);
fclose (fp);
}
printf ("\n");
/* output density argv[1].dns */
Ngrid = N_LogGrid ();
rgrid = r_LogGrid ();
strcpy (name, name_Atom ());
strcat (name, ".dns.plt");
full_filename[0] = '\0';
strncpy (full_filename, sdir_name, m9);
full_filename[m9] = '\0';
strcat (full_filename, "/");
full_filename[m9 + 1] = '\0';
strcat (full_filename, name);
printf ("Outputing atom density: %s\n", full_filename);
fp = fopen (full_filename, "w+");
for (k = 0; k < Ngrid; ++k)
fprintf (fp, "%12.8lf %12.8lf\n", rgrid[k], rho_Atom ()[k]);
fclose (fp);
/* output core density argv[1].cdns */
Ngrid = N_LogGrid ();
rgrid = r_LogGrid ();
strcpy (name, name_Atom ());
strcat (name, ".cdns.plt");
full_filename[0] = '\0';
strncpy (full_filename, sdir_name, m9);
full_filename[m9] = '\0';
strcat (full_filename, "/");
full_filename[m9 + 1] = '\0';
strcat (full_filename, name);
printf ("Outputing core density: %s\n", full_filename);
fp = fopen (full_filename, "w+");
for (k = 0; k < Ngrid; ++k)
fprintf (fp, "%12.8lf %12.8lf\n", rgrid[k], rho_core_Atom ()[k]);
fclose (fp);
/* output core density gradient argv[1].cddns */
vall = alloc_LogGrid ();
Derivative_LogGrid (rho_core_Atom (), vall);
Ngrid = N_LogGrid ();
rgrid = r_LogGrid ();
strcpy (name, name_Atom ());
strcat (name, ".cddns.plt");
full_filename[0] = '\0';
strncpy (full_filename, sdir_name, m9);
full_filename[m9] = '\0';
strcat (full_filename, "/");
full_filename[m9 + 1] = '\0';
strcat (full_filename, name);
printf ("Outputing core density gradient: %s\n", full_filename);
fp = fopen (full_filename, "w+");
for (k = 0; k < Ngrid; ++k)
fprintf (fp, "%12.8lf %12.8lf\n", rgrid[k], vall[k]);
fclose (fp);
dealloc_LogGrid (vall);
/* output semicore density infile.sdns */
Ngrid = N_LogGrid ();
rgrid = r_LogGrid ();
strcpy (name, name_Atom ());
strcat (name, ".sdns.plt");
full_filename[0] = '\0';
strncpy (full_filename, sdir_name, m9);
full_filename[m9] = '\0';
strcat (full_filename, "/");
full_filename[m9 + 1] = '\0';
strcat (full_filename, name);
printf ("Outputing semicore density: %s\n", full_filename);
fp = fopen (full_filename, "w+");
for (k = 0; k < Ngrid; ++k)
fprintf (fp, "%12.8lf %12.8lf\n", rgrid[k], rho_semicore_RelPsp ()[k]);
fclose (fp);
/* output semicore density gradient infile.sddns */
Ngrid = N_LogGrid ();
rgrid = r_LogGrid ();
strcpy (name, name_Atom ());
strcat (name, ".sddns.plt");
full_filename[0] = '\0';
strncpy (full_filename, sdir_name, m9);
full_filename[m9] = '\0';
strcat (full_filename, "/");
full_filename[m9 + 1] = '\0';
strcat (full_filename, name);
printf ("Outputing semicore density gradient: %s\n", full_filename);
fp = fopen (full_filename, "w+");
for (k = 0; k < Ngrid; ++k)
{
vx=drho_semicore_RelPsp()[k];
fprintf (fp, "%12.8lf %12.8lf\n", rgrid[k], vx);
}
fclose (fp);
/* output all-electron potential infile.pot */
vall = Vall_Atom ();
Ngrid = N_LogGrid ();
rgrid = r_LogGrid ();
strcpy (name, name_Atom ());
strcat (name, ".pot.plt");
full_filename[0] = '\0';
strncpy (full_filename, sdir_name, m9);
full_filename[m9] = '\0';
strcat (full_filename, "/");
full_filename[m9 + 1] = '\0';
strcat (full_filename, name);
printf ("Outputing all-electron potential(non-screened): %s\n",
full_filename);
fp = fopen (full_filename, "w+");
c = 0.0;
for (k = 0; k < Ngrid; ++k)
{
x = rgrid[k] / rcut_RelPsp (0);
x = pow (x, 3.5);
x = exp (-x);
y = 1.0 - x;
fprintf (fp, "%12.8lf %12.8lf %12.8lf\n", rgrid[k], vall[k],
y * vall[k] + c * x);
}
fclose (fp);
}
/* free malloc memory */
free (infile);
free (outfile);
free (full_filename);
for (p = 0; p < Nvalence; ++p)
{
free (psil[p]);
free (pspl[p]);
}
free (psil);
free (pspl);
free (rl);
free (rhol);
end_Linear ();
fflush (stdout);
return;
}
void init_xpansion(int l_in,
int match_in,
double occupation_in,
double el_in,
double *Vall_in,
double *ul_in,
double *ul_prime_in,
double *Vl_in,
double *wl_in,
double *wl_prime_in)
{
int i,iteration;
double gamma,gamma_mid,dgamma;
double constraint1,constraint2,constraint_mid;
double gamma1,gamma2;
double Vall_match, dVall_match,ddVall_match;
double al;
double *r;
r = r_LogGrid();
al = log_amesh_LogGrid();
l = l_in;
match = match_in;
occupation = occupation_in;
el = el_in;
Vall = Vall_in;
ul = ul_in;
ul_prime = ul_prime_in;
Vl = Vl_in;
wl = wl_in;
wl_prime = wl_prime_in;
/* fix ul_prime = (d/dr)ul, rather then (d/di)ul */
ldpsi = ul_prime[match]/(al*r[match]*ul[match]);
Vall_match = Vall[match];
dVall_match = (1.0/(al*r[match]))*Derivative7_4(match,Vall);
ddVall_match = (-1.0/(r[match]*r[match]*al)) *Derivative7_4(match,Vall)
+ (+1.0/(r[match]*r[match]*al*al))*Laplacian7_4(match,Vall);
rc[0] = 1.0;
rc[1] = r[match];
for (i=2; i<13; ++i)
rc[i] = rc[1]*rc[i-1];
/******************************************/
/* Calculate the all-electron core charge */
/******************************************/
ae_core_charge = Norm_LogGrid(match,(l+1.0),ul);
/**************************************************************/
/* define p(rcl), p'(rcl), p''(rcl), p'''(rcl) and p''''(rcl) */
/**************************************************************/
poly[0] = log(ul[match]/pow(rc[1],(l+1.0)));
poly[1] = ldpsi - (l+1.0)/rc[1];
poly[2] = 2.0*Vall_match
- 2.0*el
- (2.0*(l+1.0)/rc[1])*poly[1]
- poly[1]*poly[1];
poly[3] = 2.0*dVall_match
+ (2.0*(l+1.0)/rc[2])*poly[1]
- (2.0*(l+1.0)/rc[1])*poly[2]
- 2.0*poly[1]*poly[2];
poly[4] = 2.0*ddVall_match
- (4.0*(l+1.0)/rc[3])*poly[1]
+ (4.0*(l+1.0)/rc[2])*poly[2]
- (2.0*(l+1.0)/rc[1])*poly[3]
- 2.0*poly[2]*poly[2]
- 2.0*poly[1]*poly[3];
/* get initial guess for gamma */
get_c0_c10();
/* Bracket gamma, so that constraint==0 can be found */
gamma1 = c[1];
gamma2 = -c[1];
constraint1 = get_c0_c12(gamma1);
constraint2 = get_c0_c12(gamma2);
iteration = 0;
while ((constraint1*constraint2 > 0.0) && (iteration <=50))
{
++iteration;
if (fabs(constraint1) < fabs(constraint2))
{
gamma1 = gamma1 + 1.6*(gamma1-gamma2);
constraint1 = get_c0_c12(gamma1);
}
else
{
gamma2 = gamma2 + 1.6*(gamma2-gamma1);
constraint2 = get_c0_c12(gamma2);
}
}
/* perform bisection of gamma1 and gamma2 until constraint==0 */
constraint1 = get_c0_c12(gamma1);
constraint2 = get_c0_c12(gamma2);
if (constraint1 < 0.0)
{
gamma = gamma1;
dgamma = (gamma2-gamma1);
}
else
{
gamma = gamma2;
dgamma = (gamma1-gamma2);
}
iteration = 0;
constraint_mid = 1.0;
while ((fabs(dgamma) > SMALL) && (constraint_mid != 0.0) && (iteration<=80))
{
++iteration;
dgamma = 0.5*dgamma;
gamma_mid = gamma+dgamma;
constraint_mid = get_c0_c12(gamma_mid);
if (constraint_mid < 0.0)
gamma = gamma_mid;
}
} /*init_xpansion */
int init_xpansion2(int l_in,
int match_in,
double el_in,
double *Vall_in,
double *ul_in,
double *ul_prime_in,
double *Vl_in,
double *wl_in,
double *wl_prime_in)
{
int i;
double Vall_match, dVall_match,ddVall_match;
double al;
double *r;
r = r_LogGrid();
al = log_amesh_LogGrid();
l = l_in;
match = match_in;
el = el_in;
Vall = Vall_in;
ul = ul_in;
ul_prime = ul_prime_in;
Vl = Vl_in;
wl = wl_in;
wl_prime = wl_prime_in;
/* fix ul_prime = (d/dr)ul, rather then (d/di)ul */
ldpsi = ul_prime[match]/(al*r[match]*ul[match]);
Vall_match = Vall[match];
dVall_match = (1.0/(al*r[match]))*Derivative7_4(match,Vall);
ddVall_match = (-1.0/(r[match]*r[match]*al)) *Derivative7_4(match,Vall)
+ (+1.0/(r[match]*r[match]*al*al))*Laplacian7_4(match,Vall);
rc[0] = 1.0;
rc[1] = r[match];
for (i=2; i<13; ++i)
rc[i] = rc[1]*rc[i-1];
/**************************************************************/
/* define p(rcl), p'(rcl), p''(rcl), p'''(rcl) and p''''(rcl) */
/**************************************************************/
poly[0] = log(ul[match]/pow(rc[1],(l+1.0)));
poly[1] = ldpsi - (l+1.0)/rc[1];
poly[2] = 2.0*Vall_match
- 2.0*el
- (2.0*(l+1.0)/rc[1])*poly[1]
- poly[1]*poly[1];
poly[3] = 2.0*dVall_match
+ (2.0*(l+1.0)/rc[2])*poly[1]
- (2.0*(l+1.0)/rc[1])*poly[2]
- 2.0*poly[1]*poly[2];
poly[4] = 2.0*ddVall_match
- (4.0*(l+1.0)/rc[3])*poly[1]
+ (4.0*(l+1.0)/rc[2])*poly[2]
- (2.0*(l+1.0)/rc[1])*poly[3]
- 2.0*poly[2]*poly[2]
- 2.0*poly[1]*poly[3];
/* generate trouulier-Martin expansion, if possible */
return get_c0_c10_xpansion2();
} /*init_xpansion2 */