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/*
Copyright (C) 2006-2008 M.A.L. Marques
This Source Code Form is subject to the terms of the Mozilla Public
License, v. 2.0. If a copy of the MPL was not distributed with this
file, You can obtain one at http://mozilla.org/MPL/2.0/.
*/
/************************************************************************
This file is to be included in meta GGA exchange functionals. As often these
functionals are written as a function of s = |grad n|/n^(4/3) and tau, this
routine performs the necessary conversions between a functional of s and tau
and of rho.
************************************************************************/
/* WARNING Kinetic energy functionals are still not working */
#ifndef XC_DIMENSIONS
# define XC_DIMENSIONS 3
#endif
static void
#ifdef XC_KINETIC_FUNCTIONAL
work_mgga_k
#else
work_mgga_x
#endif
(const xc_func_type *p, int np,
const double *rho, const double *sigma, const double *lapl, const double *tau,
double *zk, double *vrho, double *vsigma, double *vlapl, double *vtau,
double *v2rho2, double *v2sigma2, double *v2lapl2, double *v2tau2,
double *v2rhosigma, double *v2rholapl, double *v2rhotau,
double *v2sigmalapl, double *v2sigmatau, double *v2lapltau)
{
xc_mgga_work_x_t r;
double sfact, sfact2, x_factor_c, beta, dens;
double min_grad = p->dens_threshold;
int is, ip;
/* WARNING: derivatives are _not_ OK for 2 dimensions */
#if XC_DIMENSIONS == 2
const double cnst_rs = 1.0/M_SQRTPI;
x_factor_c = X_FACTOR_2D_C;
#else /* three dimensions */
const double cnst_rs = RS_FACTOR;
x_factor_c = X_FACTOR_C;
#endif
/* initialize everything to zero */
memset(&r, 0, sizeof(r));
r.order = -1;
if(zk != NULL) r.order = 0;
if(vrho != NULL) r.order = 1;
if(v2rho2 != NULL) r.order = 2;
if(r.order < 0) return;
sfact = (p->nspin == XC_POLARIZED) ? 1.0 : 2.0;
sfact2 = sfact*sfact;
for(ip = 0; ip < np; ip++){
xc_rho2dzeta(p->nspin, rho, &dens, &r.zeta);
if(dens < p->dens_threshold) goto end_ip_loop;
r.rs = cnst_rs*pow(dens, -1.0/XC_DIMENSIONS);
for(is=0; is<p->nspin; is++){
double lrho, rho1D, rho2pD_D, lsigma, gdm, lnr2, ltau;
int js = (is == 0) ? 0 : 2;
int ls = (is == 0) ? 0 : 3;
int ks = (is == 0) ? 0 : 5;
if (rho[is] < p->dens_threshold) continue;
lsigma= max(sigma[js]/sfact2, min_grad*min_grad);
gdm = sqrt(lsigma);
lrho = rho[is]/sfact;
rho1D = pow(lrho, 1.0/XC_DIMENSIONS);
rho2pD_D = lrho*rho1D*rho1D;
r.x = gdm/(lrho*rho1D);
ltau = tau[is]/sfact;
r.t = ltau/rho2pD_D; /* tau/rho^((2+D)/D) */
if(p->info->flags & XC_FLAGS_NEEDS_LAPLACIAN){
lnr2 = lapl[is]/sfact; /* this can be negative */
r.u = lnr2/rho2pD_D; /* lapl/rho^((2+D)/D) */
}
func(p, &r);
if(zk != NULL && (p->info->flags & XC_FLAGS_HAVE_EXC))
*zk += -sfact*x_factor_c*(lrho*rho1D)*r.f;
if(vrho != NULL && (p->info->flags & XC_FLAGS_HAVE_VXC)){
vrho[is] = -x_factor_c*rho1D*(-r.rs*r.dfdrs + 4.0/3.0*(r.f - r.dfdx*r.x) - 5.0/3.0*(r.dfdt*r.t + r.dfdu*r.u));
vtau[is] = -x_factor_c*r.dfdt/rho1D;
if(p->info->flags & XC_FLAGS_NEEDS_LAPLACIAN)
vlapl[is] = -x_factor_c*r.dfdu/rho1D;
if(gdm>min_grad)
vsigma[js] = -x_factor_c*(rho1D*lrho)*r.dfdx*r.x/(2.0*sfact*lsigma);
}
/* WARNING: terms with rs not implemented yet */
if(v2rho2 != NULL && (p->info->flags & XC_FLAGS_HAVE_FXC)){
v2rho2[js] = -x_factor_c/(9.0*sfact*rho1D*rho1D)*
(4.0*r.f - 4.0*r.x*r.dfdx + 4.0*4.0*r.x*r.x*r.d2fdx2 + 5.0*5.0*r.t*r.t*r.d2fdt2 + 5.0*5.0*r.u*r.u*r.d2fdu2 +
2.0*5.0*(4.0*r.x*r.t*r.d2fdxt + 4.0*r.x*r.u*r.d2fdxu + 5.0*r.t*r.u*r.d2fdtu));
v2tau2[js] = -x_factor_c*r.d2fdt2/(sfact*rho1D*rho2pD_D);
if(p->info->flags & XC_FLAGS_NEEDS_LAPLACIAN){
v2lapl2[js] = -x_factor_c*r.d2fdu2/(sfact*rho1D*rho2pD_D);
v2rholapl[ls] = -x_factor_c*rho1D/(3.0*sfact*rho2pD_D)*
(4.0*r.dfdu - 4.0*r.x*r.d2fdxu - 5.0*r.t*r.d2fdtu - 5.0*(r.dfdu + r.u*r.d2fdu2));
v2lapltau[ls] = -x_factor_c*r.d2fdtu/(rho1D*rho2pD_D);
}
v2rhotau[ls] = -x_factor_c*rho1D/(3.0*sfact*rho2pD_D)*
(4.0*r.dfdt - 4.0*r.x*r.d2fdxt - 5.0*r.u*r.d2fdtu - 5.0*(r.dfdt + r.t*r.d2fdt2));
if(gdm > min_grad){
v2sigma2[ks] = -x_factor_c*(rho1D*lrho)/(4.0*sfact2*sfact*lsigma*lsigma)*
(r.d2fdx2*r.x*r.x - r.dfdx*r.x);
v2rhosigma[ks] = -x_factor_c*rho1D*r.x/(3.0*2.0*sfact2*lsigma)*
(-4.0*r.x*r.d2fdx2 - 5.0*r.t*r.d2fdxt - 5.0*r.u*r.d2fdxu);
if(p->info->flags & XC_FLAGS_NEEDS_LAPLACIAN)
v2sigmalapl[ks] = -x_factor_c*r.x/(2.0*sfact2*lsigma*rho1D)*r.d2fdxu;
v2sigmatau[ks] = -x_factor_c*r.x/(2.0*sfact2*lsigma*rho1D)*r.d2fdxt;
}
}
}
if(zk != NULL)
*zk /= dens; /* we want energy per particle */
end_ip_loop:
/* increment pointers */
rho += p->n_rho;
sigma += p->n_sigma;
tau += p->n_tau;
lapl += p->n_lapl;
if(zk != NULL)
zk += p->n_zk;
if(vrho != NULL){
vrho += p->n_vrho;
vsigma += p->n_vsigma;
vtau += p->n_vtau;
vlapl += p->n_vlapl;
}
if(v2rho2 != NULL){
v2rho2 += p->n_v2rho2;
v2sigma2 += p->n_v2sigma2;
v2tau2 += p->n_v2tau2;
v2lapl2 += p->n_v2lapl2;
v2rhosigma += p->n_v2rhosigma;
v2rhotau += p->n_v2rhotau;
v2rholapl += p->n_v2rholapl;
v2sigmatau += p->n_v2sigmatau;
v2sigmalapl += p->n_v2sigmalapl;
v2lapltau += p->n_v2lapltau;
}
}
}
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