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|
/* Ergo, version 3.8, a program for linear scaling electronic structure
* calculations.
* Copyright (C) 2019 Elias Rudberg, Emanuel H. Rubensson, Pawel Salek,
* and Anastasia Kruchinina.
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*
* Primary academic reference:
* Ergo: An open-source program for linear-scaling electronic structure
* calculations,
* Elias Rudberg, Emanuel H. Rubensson, Pawel Salek, and Anastasia
* Kruchinina,
* SoftwareX 7, 107 (2018),
* <http://dx.doi.org/10.1016/j.softx.2018.03.005>
*
* For further information about Ergo, see <http://www.ergoscf.org>.
*/
/* -*-mode:c; c-style:bsd; c-basic-offset:4;indent-tabs-mode:nil; -*- */
/** @file fun-vwn.c
implementation of VWN functional and its derivatives.
(c), Pawel Salek, pawsa@theochem.kth.se, sep 2001, nov 2002
*/
#include <math.h>
#include <stddef.h>
#include <stdlib.h>
#define __CVERSION__
#include "functionals.h"
/* INTERFACE PART */
static int vwn_isgga(void) { return 0; }
static int vwn_read(const char* conf_line);
static real vwn3_energy(const FunDensProp* dp);
static void vwn3_first(FunFirstFuncDrv *ds, real factor, const FunDensProp* dp);
static void vwn3_second(FunSecondFuncDrv *ds, real factor, const FunDensProp* dp);
static void vwn3_third(FunThirdFuncDrv *ds, real factor, const FunDensProp* dp);
static real vwn_energy(const FunDensProp* dp);
static void vwn_first(FunFirstFuncDrv *ds, real factor, const FunDensProp* dp);
static void vwn_second(FunSecondFuncDrv *ds, real factor, const FunDensProp* dp);
static void vwn_third(FunThirdFuncDrv *ds, real factor, const FunDensProp* dp);
static void vwn_fourth(FunFourthFuncDrv *ds, real factor,
const FunDensProp* dp);
static real vwni_energy(const FunDensProp* dp);
static void vwni_first(FunFirstFuncDrv *ds, real factor, const FunDensProp* dp);
static void vwni_second(FunSecondFuncDrv *ds, real factor, const FunDensProp* dp);
static void vwni_third(FunThirdFuncDrv *ds, real factor, const FunDensProp* dp);
static real vwn3i_energy(const FunDensProp* dp);
static void vwn3i_first(FunFirstFuncDrv *ds, real factor, const FunDensProp* dp);
static void vwn3i_second(FunSecondFuncDrv *ds, real factor, const FunDensProp* dp);
static void vwn3i_third(FunThirdFuncDrv *ds, real factor, const FunDensProp* dp);
/* VWN3 is a Gaussian version of the VWN functional based on suboptimal
* set of parameters */
Functional VWN3Functional = {
"VWN3", /* name */
vwn_isgga, /* gga-corrected */
vwn_read, /* no extra input expected, just set the common block */
NULL,
vwn3_energy,
vwn3_first,
vwn3_second,
vwn3_third
};
Functional VWN5Functional = {
"VWN5", /* name */
vwn_isgga, /* gga-corrected */
vwn_read, /* no extra input expected, just set the common block */
NULL,
vwn_energy,
vwn_first,
vwn_second,
vwn_third,
vwn_fourth
};
/* VWN is used for backward compatibility only */
Functional VWNFunctional = {
"VWN", /* name */
vwn_isgga, /* gga-corrected */
vwn_read, /* no extra input expected, just set the common block */
NULL,
vwn_energy,
vwn_first,
vwn_second,
vwn_third,
vwn_fourth
};
/* VWNIFunctional is a variant of VWN5 functional with another spin
polarization dependence:
F(r,zeta) = (E_p + f(zeta)*(E_f - E_p))*rho
*/
Functional VWNIFunctional = {
"VWNI", /* name */
vwn_isgga, /* gga-corrected */
vwn_read, /* no extra input expected, just set the common block */
NULL,
vwni_energy,
vwni_first,
vwni_second,
vwni_third
};
/* VWN3IFunctional is a variant of VWN3 functional with another spin
polarization dependence:
F(r,zeta) = (E_p + f(zeta)*(E_f - E_p))*rho
*/
Functional VWN3IFunctional = {
"VWN3I", /* name */
vwn_isgga, /* gga-corrected */
vwn_read, /* no extra input expected, just set the common block */
NULL,
vwn3i_energy,
vwn3i_first,
vwn3i_second,
vwn3i_third
};
/* IMPLEMENTATION PART */
#define VWN_ZERO 1e-35
static int
vwn_read(const char* conf_line)
{
fun_set_hf_weight(0);
return 1;
}
/* vwn_params contains two sets of parameters for paramagnetic and
ferromagnetic cases. See Table 5 in VWN paper.
*/
static const struct vwn_params {
real X0, A, B, C;
} vwn_paramagnetic = { -0.1049800, 0.0621814, 3.72744, 12.9352 },
vwn_ferromagnetic = { -0.3250000, 0.0310907, 7.06042, 18.0578 },
vwn_interp = { -0.0047584,-0.0337737, 1.13107, 13.0045 },
vwn3_paramagnetic = { -0.4092860, 0.0621814, 13.0720, 42.7198 },
vwn3_ferromagnetic= { -0.7432940, 0.0310907, 20.1231, 101.578 };
static const real SPINPOLF = 1.92366105093154; /* 1/(2(2^(1/3)-1)) */
static const real THREEFTHRD2 = 0.584822305543806;/* hm? 4.5/(4*SPINPOLF) */
static const real FOURTHREE = 1.333333333333333;
/* vwn_en_pot:
returns "order" numbers in enpot array
enpot[0]: energy of given type p E = rho F - THIS IS AN EXCEPTION!
DO NOT BLAME IT ON ME.
enpot[1]: E'=enpot[0] + rho*F'
enpot[2]: E''
enpot[3]: E'''
*/
static void
vwn_en_pot(real* enpot, real rho, int order, const struct vwn_params* p)
{
const real
AI = p->A,
BI = p->B,
CI = p->C,
X0I = p->X0;
const real
Q = SQRT(4*CI - BI*BI),
XF0I = X0I*X0I + BI*X0I + CI,
YF0I = Q/(BI + 2*X0I),
DCRS = POW(3.0/(4*M_PI),1.0/6.0),
B = X0I/XF0I,
C = XF0I*YF0I,
ACON = B*BI - 1.0,
BCON = 2*ACON + 2.0,
CCON = 2*BI*(1.0/Q - X0I/C);
real rho13 = POW(rho,1.0/3.0);
real x = DCRS/SQRT(rho13);
real xrho = -DCRS*POW(rho,-7.0/6.0)/6.0;
real xxrho = +DCRS*POW(rho,-13.0/6.0)*7.0/36.0;
real xf = x*x + BI*x+CI;
real xfx = 2*x + BI;
real yf = Q/xfx;
real e1, ex1, exx1, exxx1;
real xf_p2, xf_p3, xf_p4, xfx_p2, xfx_p4;
real xrho_p2, xrho_p3, xrho_p4, xxrho_p2, xxxrho, xxxxrho;
real Q_p2, exxxx1;
real x_p4;
e1 = 2*LOG(x)
+ ACON*LOG(xf)
- BCON*LOG(x - X0I)
+ CCON*ATAN(yf);
enpot[0] = 0.5*AI*e1;
if(order<1) return;
ex1 = 2.0/x
+ ACON*xfx/xf
- BCON/(x - X0I)
- CCON*(2*yf/xfx)/(1.0 + yf*yf);
enpot[1] = 0.5*AI*(e1 + rho*ex1*xrho);
if(order<2) return;
exx1= -2.0/(x*x)
+ ACON*(2.0/xf - xfx*xfx/(xf*xf))
+ BCON/((x - X0I)*(x - X0I))
+ CCON*8*Q*xfx/((Q*Q + xfx*xfx)*(Q*Q + xfx*xfx));
enpot[2] = 0.5*AI*xrho*(2*ex1 + rho*exx1*xrho - ex1*7.0/6.0);
if(order<3) return;
exxx1= 4.0/(x*x*x)
+ ACON*(2.0*xfx/(xf*xf))*(xfx*xfx/xf-3.0)
- BCON*2.0/POW(x - X0I,3.0)
+ CCON*16.0*Q*(Q*Q-3.0*xfx*xfx)/POW(Q*Q + xfx*xfx,3.0);
enpot[3] = 0.5*AI*xxrho*(2*ex1 + rho*exx1*xrho - 7.0/6.0*ex1)
+ 0.5*AI*xrho*(2*exx1*xrho
+exx1*xrho + rho*(exxx1*xrho*xrho+exx1*xxrho)
-7.0/6.0*exx1*xrho);
if(order<4) return;
x_p4 = POW(x,4.0);
xf_p2 = xf*xf;
xf_p3 = xf_p2*xf;
xf_p4 = xf_p2*xf_p2;
xfx_p2 = xfx*xfx;
xfx_p4 = xfx_p2*xfx_p2;
xrho_p2 = xrho*xrho;
xrho_p3 = xrho_p2*xrho;
xrho_p4 = xrho_p2*xrho_p2;
xxrho_p2 = xxrho*xxrho;
xxxrho = (-91.0/216.0)*DCRS/POW(rho,19.0/6.0);
xxxxrho = (1729.0/1296.0)*DCRS/POW(rho,25.0/6.0);
Q_p2 = Q*Q;
exxxx1 = 6*((-2*ACON)/xf_p2 + (4*xfx_p2*ACON)/xf_p3 -
(xfx_p4*ACON)/xf_p4 + (64*xfx*CCON*(xfx - Q)*Q*(xfx + Q))/
POW((xfx_p2 + Q_p2),4.0) - 2/x_p4 + BCON/POW((x - X0I),4.0));
enpot[4] = 0.5*AI*(4*exxx1*xrho_p3 + exxxx1*rho*xrho_p4 +
6*exxx1*rho*xrho_p2*xxrho +
3*exx1*rho*xxrho_p2 +
4*exx1*xrho*(3*xxrho + rho*xxxrho) +
ex1*(4*xxxrho + rho*xxxxrho));
/* for fourth derivatives we need also
first derivative of enpot[0] with respect to rho.
It is stored in enpot[5] (what a mess!) */
enpot[5] = 0.5*AI*ex1*xrho;
}
static real
par_energy(const FunDensProp* dp, const struct vwn_params* para,
const struct vwn_params* ferro)
{
real ep_p[2], ep_f[2], ep_i[2], zeta, zeta4, f_zeta, delta;
real rhoa = dp->rhoa, rhob = dp->rhob, rho;
if(rhoa<VWN_ZERO) rhoa = VWN_ZERO;
if(rhob<VWN_ZERO) rhob = VWN_ZERO;
rho = rhoa + rhob;
vwn_en_pot(ep_p, rho, 0, para);
if(FABS(dp->rhoa-dp->rhob)<VWN_ZERO) return ep_p[0]*rho;
vwn_en_pot(ep_f, rho, 0, ferro);
vwn_en_pot(ep_i, rho, 0, &vwn_interp);
zeta = (dp->rhoa-dp->rhob)/rho;
zeta4 = POW(zeta,4.0);
f_zeta = SPINPOLF*(POW(1+zeta,FOURTHREE)+POW(1-zeta,FOURTHREE)-2.0);
delta = f_zeta*((ep_f[0]-ep_p[0])*zeta4 + ep_i[0]*(1-zeta4)*THREEFTHRD2);
return (ep_p[0]+ delta)*rho;
}
static void
par_first(FunFirstFuncDrv *ds, real factor, const FunDensProp* dp,
const struct vwn_params* para, const struct vwn_params* ferro)
{
real zeta, zeta3,zeta4, f_zeta, f_zet1, e_f,acp, dacp, vcfp, g_f;
real delta, ep_p[2], ep_f[2], ep_i[2];
real rhoa = dp->rhoa, rhob = dp->rhob, rho;
if(rhoa<VWN_ZERO) rhoa = VWN_ZERO;
if(rhob<VWN_ZERO) rhob = VWN_ZERO;
rho = rhoa + rhob;
vwn_en_pot(ep_p, rho, 1, para);
ds->df1000 += ep_p[1]*factor;
ds->df0100 += ep_p[1]*factor;
if(FABS(dp->rhoa-dp->rhob)<VWN_ZERO) return;
/* contribution from spin-polarized case; first order */
zeta = (dp->rhoa-dp->rhob)/rho;
zeta3 = POW(zeta,3.0);
zeta4 = zeta3*zeta;
f_zeta = SPINPOLF*(POW(1+zeta,FOURTHREE)+POW(1-zeta,FOURTHREE)-2.0);
f_zet1 = SPINPOLF*4.0/3.0*(POW(1+zeta,1.0/3.0)-POW(1-zeta,1.0/3.0));
vwn_en_pot(ep_f, rho, 1, ferro);
e_f = ep_f[0] - ep_p[0];
g_f = ep_f[1] - ep_p[1];
vwn_en_pot(ep_i, rho, 1, &vwn_interp);
acp = ep_i[0]*THREEFTHRD2;
dacp = ep_i[1]*THREEFTHRD2;
vcfp = f_zeta*(g_f*zeta4 + dacp*(1-zeta4));
delta= (f_zet1*(e_f*zeta4 + acp*(1-zeta4)) +
4*f_zeta*(e_f - acp)*zeta3);
/* the final section: begin */
ds->df1000 += (vcfp + delta*(1-zeta))*factor;
ds->df0100 += (vcfp - delta*(1+zeta))*factor;
/* the final section: end */
}
/* vwn_second:
CAUTION: may raise zeros to a negative power!
*/
static void
par_second(FunSecondFuncDrv *ds, real factor, const FunDensProp* dp,
const struct vwn_params* para, const struct vwn_params* ferro)
{
real zeta, zeta2, zeta3,zeta4, f_zeta, f_zet1, f_zet2, vcfp;
real delta, ep_p[3], ep_f[3], ep_i[3];
real vcfp1, ef0, ef1, ef2, ei0, ei1, ei2, bterm, cterm, dterm;
real spA, spB;
real rhoa = dp->rhoa, rhob = dp->rhob, rho = dp->rhoa + dp->rhob;
real rho2 = rho*rho;
real dAA, dAB, dBB;
vwn_en_pot(ep_p, rho, 2, para);
ds->df1000 += ep_p[1]*factor;
ds->df0100 += ep_p[1]*factor;
ds->df2000 += ep_p[2]*factor;
ds->df0200 += ep_p[2]*factor;
ds->df1100 += ep_p[2]*factor;
/* if(0&&dp->rhoa==dp->rhob) return; */
/* contribution from spin-polarized case; second order */
zeta = (dp->rhoa-dp->rhob)/rho;
zeta2 = zeta*zeta;
zeta3 = zeta2*zeta;
zeta4 = zeta3*zeta;
f_zeta = SPINPOLF*(POW(1+zeta,FOURTHREE)+POW(1-zeta,FOURTHREE)-2.0);
f_zet1 = SPINPOLF*4.0/3.0*(POW(1+zeta,1.0/3.0)-POW(1-zeta,1.0/3.0));
/* CAUTION: may raise 0 to negative power! */
f_zet2 = SPINPOLF*4.0/9.0*(POW(1+zeta,-2.0/3.0)+POW(1-zeta,-2.0/3.0));
vwn_en_pot(ep_f, rho, 2, ferro);
ef0 = ep_f[0] - ep_p[0];
ef1 = ep_f[1] - ep_p[1];
ef2 = ep_f[2] - ep_p[2];
vwn_en_pot(ep_i, rho, 2, &vwn_interp);
ei0 = ep_i[0]*THREEFTHRD2;
ei1 = ep_i[1]*THREEFTHRD2;
ei2 = ep_i[2]*THREEFTHRD2;
bterm = ef1*zeta4 + ei1*(1-zeta4);
vcfp = f_zeta*bterm;
delta = (f_zet1*(ef0*zeta4 + ei0*(1-zeta4))
+ 4*f_zeta*(ef0 - ei0)*zeta3);
spA = 2*rhob/rho2; /* = 2(1-zeta)/rho */
spB =-2*rhoa/rho2; /* = -2(1+zeta)/rho */
/* contribution from spin-polarized case; second order */
/* spin independent part of vcfp */
vcfp1 = f_zeta*(ef2*zeta4 + ei2*(1-zeta4));
/* spin dependent part of vcfp */
cterm = 4*f_zeta*(ef1-ei1)*zeta3 + bterm*f_zet1 - delta;
/* spin dependent part of delta */
dterm = (f_zet2*(ef0*zeta4+ei0*(1-zeta4))
+8*f_zet1*(ef0-ei0)*zeta3
+12*f_zeta*(ef0-ei0)*zeta2)*rho;
dAA = dterm*spA*spA;
dAB = dterm*spA*spB;
dBB = dterm*spB*spB;
/* the final section: begin */
ds->df1000 += (vcfp + delta*(1-zeta))*factor;
ds->df0100 += (vcfp - delta*(1+zeta))*factor;
ds->df2000 += (vcfp1+ cterm*(spA+spA) + dAA)*factor;
ds->df1100 += (vcfp1+ cterm*(spA+spB) + dAB)*factor;
ds->df0200 += (vcfp1+ cterm*(spB+spB) + dBB)*factor;
/* the final section: end */
}
/* third not tested for open-shell! */
static void
par_third(FunThirdFuncDrv *ds, real factor, const FunDensProp* dp,
const struct vwn_params* para, const struct vwn_params* ferro)
{
real zeta, zeta2, zeta3,zeta4, f_zeta, f_zet1, f_zet2, f_zet3, vcfp;
real delta, ep_p[4], ep_f[4], ep_i[4];
real vcfp1, vcfp2, ef0, ef1, ef2, ef3, ei0, ei1, ei2, ei3;
real bterm, cterm, dterm, eterm, ctrm1, ctrm2, dtrm1, dtrm2;
real ef2bi, ei2bi;
real spA, spB, spAA, spAB, spBB;
real rhoa = dp->rhoa, rhob = dp->rhob, rho, rho2, rho3;
if(rhoa<VWN_ZERO) rhoa = VWN_ZERO;
if(rhob<VWN_ZERO) rhob = VWN_ZERO;
rho = rhoa + rhob;
rho2 = rho*rho; rho3 = rho2*rho;
vwn_en_pot(ep_p, rho, 3, para);
ds->df1000 += ep_p[1]*factor;
ds->df0100 += ep_p[1]*factor;
ds->df2000 += ep_p[2]*factor;
ds->df0200 += ep_p[2]*factor;
ds->df1100 += ep_p[2]*factor;
ds->df3000 += ep_p[3]*factor;
ds->df2100 += ep_p[3]*factor;
ds->df1200 += ep_p[3]*factor;
ds->df0300 += ep_p[3]*factor;
/* if(0&&dp->rhoa==dp->rhob) return; */
/* contribution from spin-polarized case; second order */
zeta = (dp->rhoa-dp->rhob)/rho;
zeta2 = zeta*zeta;
zeta3 = zeta2*zeta;
zeta4 = zeta3*zeta;
f_zeta = SPINPOLF* (POW(1+zeta,FOURTHREE)+POW(1-zeta,FOURTHREE)-2.0);
f_zet1 = SPINPOLF*4.0/3.0 *(POW(1+zeta, 1.0/3.0)-POW(1-zeta, 1.0/3.0));
f_zet2 = SPINPOLF*4.0/9.0 *(POW(1+zeta,-2.0/3.0)+POW(1-zeta,-2.0/3.0));
f_zet3 =-SPINPOLF*8.0/27.0*(POW(1+zeta,-5.0/3.0)-POW(1-zeta,-5.0/3.0));
vwn_en_pot(ep_f, rho, 3, ferro);
ef0 = ep_f[0] - ep_p[0];
ef1 = ep_f[1] - ep_p[1];
ef2 = ep_f[2] - ep_p[2];
ef3 = ep_f[3] - ep_p[3];
vwn_en_pot(ep_i, rho, 3,&vwn_interp);
ei0 = ep_i[0]*THREEFTHRD2;
ei1 = ep_i[1]*THREEFTHRD2;
ei2 = ep_i[2]*THREEFTHRD2;
ei3 = ep_i[3]*THREEFTHRD2;
bterm = ef1*zeta4 + ei1*(1-zeta4);
vcfp = f_zeta*bterm;
delta = (f_zet1*(ef0*zeta4 + ei0*(1-zeta4))
+ 4*f_zeta*(ef0 - ei0)*zeta3);
spA = 2*rhob/rho2; /* = 2(1-zeta)/rho */
spB =-2*rhoa/rho2; /* = -2(1+zeta)/rho */
spAA = -4*rhob/rho3;
spAB = 2*(rho-2*rhob)/rho3;
spBB = 4*rhoa/rho3;
/* contribution from spin-polarized case; second order */
/* spin independent part of vcfp */
vcfp1 = f_zeta*(ef2*zeta4 + ei2*(1-zeta4));
/* spin dependent part of vcfp */
cterm = 4*f_zeta*(ef1-ei1)*zeta3 + bterm*f_zet1 - delta;
/* spin dependent part of delta */
dterm = (f_zet2*(ef0*zeta4+ei0*(1-zeta4))
+8*f_zet1*(ef0-ei0)*zeta3
+12*f_zeta*(ef0-ei0)*zeta2)*rho;
/* third order terms */
vcfp2 = f_zeta*(ef3*zeta4+ei3*(1-zeta4));
eterm = f_zet1*(ef2*zeta4 + ei2*(1-zeta4)) + f_zeta*(ef2-ei2)*4*zeta3;
ef2bi = ef2-(ef1-ef0)/rho;
ei2bi = ei2-(ei1-ei0)/rho;
ctrm1 = 4*f_zeta*(ef2bi-ei2bi)*zeta3 +f_zet1*(ef2bi*zeta4+ei2bi*(1-zeta4));
ctrm2 = (ef1-ei1-ef0+ei0)*(8*f_zet1*zeta3+12*f_zeta*zeta2)
+f_zet2*(bterm-(ef0*zeta4 + ei0*(1-zeta4)));
dtrm1 = f_zet2*((ef1-ef0)*zeta4+(ei1-ei0)*(1-zeta4))
+(8*f_zet1*zeta3+12*f_zeta*zeta2)*(ef1-ei1-ef0+ei0)
+dterm/rho;
dtrm2 = ((12*f_zet2*zeta3 + 36*f_zet1*zeta2 + 24*f_zeta*zeta)*(ef0-ei0)+
f_zet3*(ef0*zeta4+ei0*(1-zeta4)))*rho;
/* the final section: begin */
ds->df1000 += (vcfp + delta*(1-zeta))*factor;
ds->df0100 += (vcfp - delta*(1+zeta))*factor;
ds->df2000 += (vcfp1+ cterm*(spA+spA) + dterm*spA*spA)*factor;
ds->df1100 += (vcfp1+ cterm*(spA+spB) + dterm*spA*spB)*factor;
ds->df0200 += (vcfp1+ cterm*(spB+spB) + dterm*spB*spB)*factor;
ds->df3000 += (vcfp2+ eterm*spA +
ctrm1*(spA+spA)+ ctrm2*spA*(spA+spA) + cterm*(spAA+spAA) +
dtrm1*(spA*spA)+ dtrm2*spA*spA*spA + dterm*(2*spAA*spA)
)*factor;
ds->df2100 += (vcfp2+ eterm*spB +
ctrm1*(spA+spA)+ ctrm2*spB*(spA+spA) + cterm*(spAB+spAB) +
dtrm1*(spA*spA)+ dtrm2*spA*spA*spB + dterm*(2*spAB*spA)
)*factor;
ds->df1200 += (vcfp2+ eterm*spA +
ctrm1*(spB+spB)+ ctrm2*spA*(spB+spB) + cterm*(spAB+spAB) +
dtrm1*(spB*spB)+ dtrm2*spB*spB*spA + dterm*(2*spAB*spB)
)*factor;
ds->df0300 += (vcfp2+ eterm*spB +
ctrm1*(spB+spB)+ ctrm2*spB*(spB+spB) + cterm*(spBB+spBB) +
dtrm1*(spB*spB)+ dtrm2*spB*spB*spB + dterm*(2*spBB*spB)
)*factor;
/* the final section: end */
}
/* The dispatch part of the functional implementation */
static real
vwn3_energy(const FunDensProp* dp)
{
return par_energy(dp, &vwn3_paramagnetic, &vwn3_ferromagnetic);
}
static void
vwn3_first(FunFirstFuncDrv *ds, real factor, const FunDensProp* dp)
{
par_first(ds, factor, dp, &vwn3_paramagnetic, &vwn3_ferromagnetic);
}
static void
vwn3_second(FunSecondFuncDrv *ds, real factor, const FunDensProp* dp)
{
par_second(ds, factor, dp, &vwn3_paramagnetic, &vwn3_ferromagnetic);
}
static void
vwn3_third(FunThirdFuncDrv *ds, real factor, const FunDensProp* dp)
{
par_third(ds, factor, dp, &vwn3_paramagnetic, &vwn3_ferromagnetic);
}
static real
vwn_energy(const FunDensProp* dp)
{
return par_energy(dp, &vwn_paramagnetic, &vwn_ferromagnetic);
}
static void
vwn_first(FunFirstFuncDrv *ds, real factor, const FunDensProp* dp)
{
par_first(ds, factor, dp, &vwn_paramagnetic, &vwn_ferromagnetic);
}
static void
vwn_second(FunSecondFuncDrv *ds, real factor, const FunDensProp* dp)
{
par_second(ds, factor, dp, &vwn_paramagnetic, &vwn_ferromagnetic);
}
static void
vwn_third(FunThirdFuncDrv *ds, real factor, const FunDensProp* dp)
{
par_third(ds, factor, dp, &vwn_paramagnetic, &vwn_ferromagnetic);
}
static void
vwn_fourth(FunFourthFuncDrv *ds, real factor, const FunDensProp* dp)
{
real zeta, zeta2, zeta3,zeta4, f_zeta, f_zet1, f_zet2, f_zet3, vcfp;
real delta, ep_p[6], ep_f[6], ep_i[6], d_ef0, d_ei0;
real vcfp1, vcfp2, ef0, ef1, ef2, ef3, ei0, ei1, ei2, ei3;
real bterm, cterm, dterm, eterm, ctrm1, ctrm2, dtrm1, dtrm2;
real ef2bi, ei2bi;
real spA, spB, spAA, spAB, spBB;
real rhoa = dp->rhoa, rhob = dp->rhob, rho = dp->rhoa + dp->rhob;
real rho2 = rho*rho;
real rho3 = rho2*rho;
real rho4 = rho2*rho2;
real f_zet4;
real ef4, ei4;
real spAAA, spBBB, spAAB, spABB;
real d_ef2bi, d_ei2bi, d_bterm_indep, d_bterm_dep, d_delta_indep,
d_delta_dep, d_vcfp2_indep, d_vcfp2_dep, d_eterm_indep,
d_eterm_dep, d_ctrm1_indep, d_ctrm1_dep, d_ctrm2_indep,
d_ctrm2_dep, d_cterm_indep, d_cterm_dep, d_dterm_indep,
d_dterm_dep, d_dtrm1_indep, d_dtrm1_dep, d_dtrm2_indep,
d_dtrm2_dep;
vwn_en_pot(ep_p, rho, 4, &vwn_paramagnetic);
ds->df1000 += ep_p[1]*factor;
ds->df0100 += ep_p[1]*factor;
ds->df2000 += ep_p[2]*factor;
ds->df0200 += ep_p[2]*factor;
ds->df1100 += ep_p[2]*factor;
ds->df3000 += ep_p[3]*factor;
ds->df2100 += ep_p[3]*factor;
ds->df1200 += ep_p[3]*factor;
ds->df0300 += ep_p[3]*factor;
ds->df4000 += ep_p[4]*factor;
ds->df3100 += ep_p[4]*factor;
ds->df2200 += ep_p[4]*factor;
ds->df1300 += ep_p[4]*factor;
ds->df0400 += ep_p[4]*factor;
/* if(dp->rhoa==dp->rhob) return; */
/* contribution from spin-polarized case; second order */
zeta = (dp->rhoa-dp->rhob)/rho;
zeta2 = zeta*zeta;
zeta3 = zeta2*zeta;
zeta4 = zeta3*zeta;
f_zeta = SPINPOLF* (POW(1+zeta,FOURTHREE)+POW(1-zeta,FOURTHREE)-2.0);
f_zet1 = SPINPOLF*4.0/3.0 *(POW(1+zeta, 1.0/3.0)-POW(1-zeta, 1.0/3.0));
f_zet2 = SPINPOLF*4.0/9.0 *(POW(1+zeta,-2.0/3.0)+POW(1-zeta,-2.0/3.0));
f_zet3 =-SPINPOLF*8.0/27.0*(POW(1+zeta,-5.0/3.0)-POW(1-zeta,-5.0/3.0));
f_zet4 = SPINPOLF*(40.0/81.0)*(POW(1-zeta,-8.0/3.0)+POW(1+zeta,-8.0/3.0));
vwn_en_pot(ep_f, rho, 4,&vwn_ferromagnetic);
ef0 = ep_f[0] - ep_p[0];
ef1 = ep_f[1] - ep_p[1];
ef2 = ep_f[2] - ep_p[2];
ef3 = ep_f[3] - ep_p[3];
ef4 = ep_f[4] - ep_p[4];
d_ef0 = ep_f[5] - ep_p[5];
vwn_en_pot(ep_i, rho, 4,&vwn_interp);
ei0 = ep_i[0]*THREEFTHRD2;
ei1 = ep_i[1]*THREEFTHRD2;
ei2 = ep_i[2]*THREEFTHRD2;
ei3 = ep_i[3]*THREEFTHRD2;
ei4 = ep_i[4]*THREEFTHRD2;
d_ei0 = ep_i[5]*THREEFTHRD2;
bterm = ef1*zeta4 + ei1*(1-zeta4);
vcfp = f_zeta*bterm;
delta = (f_zet1*(ef0*zeta4 + ei0*(1-zeta4))
+ 4*f_zeta*(ef0 - ei0)*zeta3);
spA = 2*rhob/rho2; /* = 2(1-zeta)/rho */
spB =-2*rhoa/rho2; /* = -2(1+zeta)/rho */
spAA = -4*rhob/rho3;
spAB = 2*(rho-2*rhob)/rho3;
spBB = 4*rhoa/rho3;
spAAA = 12*rhob/rho4;
spAAB = -4*(rhoa - 2* rhob)/rho4;
spABB = (-8*rhoa + 4*rhob)/rho4;
spBBB = -12*rhoa/rho4;
/* contribution from spin-polarized case; second order */
/* spin independent part of vcfp */
vcfp1 = f_zeta*(ef2*zeta4 + ei2*(1-zeta4));
/* spin dependent part of vcfp */
cterm = 4*f_zeta*(ef1-ei1)*zeta3 + bterm*f_zet1 - delta;
/* spin dependent part of delta */
dterm = (f_zet2*(ef0*zeta4+ei0*(1-zeta4))
+8*f_zet1*(ef0-ei0)*zeta3
+12*f_zeta*(ef0-ei0)*zeta2)*rho;
/* third order terms */
vcfp2 = f_zeta*(ef3*zeta4+ei3*(1-zeta4));
eterm = f_zet1*(ef2*zeta4 + ei2*(1-zeta4)) + f_zeta*(ef2-ei2)*4*zeta3;
ef2bi = ef2-(ef1-ef0)/rho;
ei2bi = ei2-(ei1-ei0)/rho;
ctrm1 = 4*f_zeta*(ef2bi-ei2bi)*zeta3 +f_zet1*(ef2bi*zeta4+ei2bi*(1-zeta4));
ctrm2 = (ef1-ei1-ef0+ei0)*(8*f_zet1*zeta3+12*f_zeta*zeta2)
+f_zet2*(bterm-(ef0*zeta4 + ei0*(1-zeta4)));
dtrm1 = f_zet2*((ef1-ef0)*zeta4+(ei1-ei0)*(1-zeta4))
+(8*f_zet1*zeta3+12*f_zeta*zeta2)*(ef1-ei1-ef0+ei0)
+dterm/rho;
dtrm2 = ((12*f_zet2*zeta3 + 36*f_zet1*zeta2 + 24*f_zeta*zeta)*(ef0-ei0)+
f_zet3*(ef0*zeta4+ei0*(1-zeta4)))*rho;
/* the final section: begin */
ds->df1000 += (vcfp + delta*(1-zeta))*factor;
ds->df0100 += (vcfp - delta*(1+zeta))*factor;
ds->df2000 += (vcfp1+ cterm*(spA+spA) + dterm*spA*spA)*factor;
ds->df1100 += (vcfp1+ cterm*(spA+spB) + dterm*spA*spB)*factor;
ds->df0200 += (vcfp1+ cterm*(spB+spB) + dterm*spB*spB)*factor;
ds->df3000 += (vcfp2+ eterm*spA +
ctrm1*(spA+spA)+ ctrm2*spA*(spA+spA) + cterm*(spAA+spAA) +
dtrm1*(spA*spA)+ dtrm2*spA*spA*spA + dterm*(2*spAA*spA)
)*factor;
ds->df2100 += (vcfp2+ eterm*spB +
ctrm1*(spA+spA)+ ctrm2*spB*(spA+spA) + cterm*(spAB+spAB) +
dtrm1*(spA*spA)+ dtrm2*spA*spA*spB + dterm*(2*spAB*spA)
)*factor;
ds->df1200 += (vcfp2+ eterm*spA +
ctrm1*(spB+spB)+ ctrm2*spA*(spB+spB) + cterm*(spAB+spAB) +
dtrm1*(spB*spB)+ dtrm2*spB*spB*spA + dterm*(2*spAB*spB)
)*factor;
ds->df0300 += (vcfp2+ eterm*spB +
ctrm1*(spB+spB)+ ctrm2*spB*(spB+spB) + cterm*(spBB+spBB) +
dtrm1*(spB*spB)+ dtrm2*spB*spB*spB + dterm*(2*spBB*spB)
)*factor;
d_ef2bi = ef3 + (-ef0 + ef1)/rho2 - (-d_ef0 + ef2)/rho;
d_ei2bi = ei3 + (-ei0 + ei1)/rho2 - (-d_ei0 + ei2)/rho;
d_bterm_indep = ei2*(1 - zeta4) + ef2*zeta4;
d_bterm_dep = (4*ef1*zeta3 - 4*ei1*zeta3);
d_delta_indep = 4*(d_ef0 - d_ei0)*f_zeta*zeta3 +
d_ei0*f_zet1*(1 - zeta4) + d_ef0*f_zet1*zeta4;
d_delta_dep = (12*(ef0 - ei0)*f_zeta*zeta2 + 4*ef0*f_zet1*zeta3 +
4*(ef0 - ei0)*f_zet1*zeta3 - 4*ei0*f_zet1*zeta3 +
f_zet2*(ei0*(1 - zeta4) + ef0*zeta4));
d_vcfp2_indep = ei4*f_zeta*(1 - zeta4) + ef4*f_zeta*zeta4;
d_vcfp2_dep = (4*ef3*f_zeta*zeta3 - 4*ei3*f_zeta*zeta3 +
f_zet1*(ei3*(1 - zeta4) + ef3*zeta4));
d_eterm_indep = 4*(ef3 - ei3)*f_zeta*zeta3 + ei3*f_zet1*(1 - zeta4) +
ef3*f_zet1*zeta4;
d_eterm_dep = (12*(ef2 - ei2)*f_zeta*zeta2 +
4*ef2*f_zet1*zeta3 + 4*(ef2 - ei2)*f_zet1*zeta3 -
4*ei2*f_zet1*zeta3 + f_zet2*(ei2*(1 - zeta4) +
ef2*zeta4));
d_ctrm1_indep = 4*(d_ef2bi - d_ei2bi)*f_zeta*zeta3 +
d_ei2bi*f_zet1*(1 - zeta4) + d_ef2bi*f_zet1*zeta4;
d_ctrm1_dep = (12*(ef2bi - ei2bi)*f_zeta*zeta2 +
4*ef2bi*f_zet1*zeta3 + 4*(ef2bi - ei2bi)*f_zet1*zeta3 -
4*ei2bi*f_zet1*zeta3 + f_zet2*(ei2bi*(1 - zeta4) +
ef2bi*zeta4));
d_ctrm2_indep = d_bterm_indep*f_zet2 + (-d_ef0 + d_ei0 + ef2 - ei2)*
(12*f_zeta*zeta2 + 8*f_zet1*zeta3) +
d_ei0*f_zet2*(-1 + zeta4) - d_ef0*f_zet2*zeta4;
d_ctrm2_dep = d_bterm_dep*f_zet2 +
(4*(-ef0 + ei0)*f_zet2*zeta3 -
4*(ef0 - ef1 - ei0 + ei1)*(6*f_zeta*zeta +
9*f_zet1*zeta2 + 2*f_zet2*zeta3) +
f_zet3*(bterm + ei0*(-1 + zeta4) - ef0*zeta4));
d_cterm_indep = -d_delta_indep + d_bterm_indep*f_zet1 +
4*(ef2 - ei2)*f_zeta*zeta3;
d_cterm_dep = -d_delta_dep + d_bterm_dep*f_zet1 +
(bterm*f_zet2 + 12*(ef1 - ei1)*f_zeta*
zeta2 + 4*(ef1 - ei1)*f_zet1*zeta3);
d_dterm_indep = 12*(ef0 - ei0)*f_zeta*zeta2 + 12*d_ef0*f_zeta*rho*
zeta2 + 8*(ef0 - ei0)*f_zet1*zeta3 +
8*d_ef0*f_zet1*rho*zeta3 + d_ef0*f_zet2*rho*zeta4 +
f_zet2*(ei0 + ef0*zeta4 - ei0*zeta4) +
d_ei0*rho*(f_zet2 - 12*f_zeta*zeta2 - 8*f_zet1*zeta3 -
f_zet2*zeta4);
d_dterm_dep = (24*ef0*f_zeta*rho*zeta +
36*ef0*f_zet1*rho*zeta2 + 12*ef0*f_zet2*rho*zeta3 -
ei0*rho*(12*(2*f_zeta*zeta + 3*f_zet1*zeta2 +
f_zet2*zeta3) + f_zet3*(-1 + zeta4)) +
ef0*f_zet3*rho*zeta4);
d_dtrm1_indep = -(d_ei0*f_zet2) + ei2*f_zet2 +
(-d_ef0 + d_ei0 + ef2 - ei2)*(12*f_zeta*zeta2 +
8*f_zet1*zeta3) - d_ef0*f_zet2*zeta4 +
(d_ei0 + ef2 - ei2)*f_zet2*zeta4 -
dterm/rho2 + d_dterm_indep/rho;
d_dtrm1_dep = (4*(-ef0 + ef1 + ei0 - ei1)*f_zet2*zeta3 -
4*(ef0 - ef1 - ei0 + ei1)*(6*f_zeta*zeta +
9*f_zet1*zeta2 + 2*f_zet2*zeta3)
+
f_zet3*(ei1 + ei0*(-1 + zeta4) - (ef0 - ef1 + ei1)*zeta4))
+ d_dterm_dep/rho;
d_dtrm2_indep = d_ei0*f_zet3*rho + 12*(ef0 - ei0)*
(2*f_zeta*zeta + 3*f_zet1*zeta2 + f_zet2*zeta3) +
12*(d_ef0 - d_ei0)*rho*(2*f_zeta*zeta + 3*f_zet1*zeta2 +
f_zet2*zeta3) + d_ef0*f_zet3*rho*zeta4 -
d_ei0*f_zet3*rho*zeta4 + f_zet3*(ei0 + ef0*zeta4 -
ei0*zeta4);
d_dtrm2_dep = (4*(ef0 - ei0)*f_zet3*rho*zeta3 +
12*(ef0 - ei0)*rho*(2*f_zeta + 8*f_zet1*zeta +
6*f_zet2*zeta2 + f_zet3*zeta3)
+ f_zet4*rho*(ei0 + ef0*zeta4 - ei0*zeta4));
ds->df4000 += ( d_vcfp2_indep + 2*d_ctrm1_indep*spA + d_eterm_indep*spA +
d_vcfp2_dep*spA + 2*d_ctrm1_dep*spA*spA +
2*d_ctrm2_indep*spA*spA + d_dtrm1_indep*spA*spA +
d_eterm_dep*spA*spA + 2*d_ctrm2_dep*spA*spA*spA +
d_dtrm1_dep*spA*spA*spA + d_dtrm2_indep*spA*spA*spA +
d_dtrm2_dep*spA*spA*spA*spA + 2*d_cterm_indep*spAA +
2*d_cterm_dep*spA*spAA + 2*d_dterm_indep*spA*spAA +
2*d_dterm_dep*spA*spA*spAA + 2*spAAA*cterm +
2*spAA*ctrm1 + 4*spA*spAA*ctrm2 +
2*spAA*spAA*dterm + 2*spA*spAAA*dterm +
2*spA*spAA*dtrm1 + 3*spA*spA*spAA*dtrm2 +
spAA*eterm
)*factor;
ds->df3100 += ( d_vcfp2_indep + 2*d_ctrm1_indep*spA + d_eterm_indep*spA +
2*d_ctrm2_indep*spA*spA + d_dtrm1_indep*spA*spA +
d_dtrm2_indep*spA*spA*spA + 2*d_cterm_indep*spAA +
2*d_dterm_indep*spA*spAA + d_vcfp2_dep*spB +
2*d_ctrm1_dep*spA*spB + d_eterm_dep*spA*spB +
2*d_ctrm2_dep*spA*spA*spB + d_dtrm1_dep*spA*spA*spB +
d_dtrm2_dep*spA*spA*spA*spB + 2*d_cterm_dep*spAA*spB +
2*d_dterm_dep*spA*spAA*spB + 2*spAAB*cterm +
2*spAB*ctrm1 + 4*spA*spAB*ctrm2 +
2*spA*spAAB*dterm + 2*spAA*spAB*dterm +
2*spA*spAB*dtrm1 + 3*spA*spA*spAB*dtrm2 +
spAB*eterm
)*factor;
ds->df2200 += (d_vcfp2_indep + 2*d_ctrm1_indep*spA +
d_dtrm1_indep*spA*spA + 2*d_cterm_indep*spAB +
2*d_dterm_indep*spA*spAB + d_eterm_indep*spB +
d_vcfp2_dep*spB + 2*d_ctrm1_dep*spA*spB +
2*d_ctrm2_indep*spA*spB + d_dtrm1_dep*spA*spA*spB +
d_dtrm2_indep*spA*spA*spB + 2*d_cterm_dep*spAB*spB +
2*d_dterm_dep*spA*spAB*spB + d_eterm_dep*spB*spB +
2*d_ctrm2_dep*spA*spB*spB + d_dtrm2_dep*spA*spA*spB*spB +
2*spABB*cterm + 2*spAB*ctrm1 +
2*spAB*spB*ctrm2 + 2*spA*spBB*ctrm2 +
2*spAB*spAB*dterm + 2*spA*spABB*dterm +
2*spA*spAB*dtrm1 + 2*spA*spAB*spB*dtrm2 +
spA*spA*spBB*dtrm2 + spBB*eterm
)*factor;
ds->df1300 += ( d_vcfp2_indep + 2*d_ctrm1_indep*spB + d_eterm_indep*spB +
2*d_ctrm2_indep*spB*spB + d_dtrm1_indep*spB*spB +
d_dtrm2_indep*spB*spB*spB + 2*d_cterm_indep*spBB +
2*d_dterm_indep*spB*spBB + d_vcfp2_dep*spA +
2*d_ctrm1_dep*spB*spA + d_eterm_dep*spB*spA +
2*d_ctrm2_dep*spB*spB*spA + d_dtrm1_dep*spB*spB*spA +
d_dtrm2_dep*spB*spB*spB*spA + 2*d_cterm_dep*spBB*spA +
2*d_dterm_dep*spB*spBB*spA + 2*spABB*cterm +
2*spAB*ctrm1 + 4*spB*spAB*ctrm2 +
2*spB*spABB*dterm + 2*spBB*spAB*dterm +
2*spB*spAB*dtrm1 + 3*spB*spB*spAB*dtrm2 +
spAB*eterm
)*factor;
ds->df0400 += ( d_vcfp2_indep + 2*d_ctrm1_indep*spB + d_eterm_indep*spB +
d_vcfp2_dep*spB + 2*d_ctrm1_dep*spB*spB +
2*d_ctrm2_indep*spB*spB + d_dtrm1_indep*spB*spB +
d_eterm_dep*spB*spB + 2*d_ctrm2_dep*spB*spB*spB +
d_dtrm1_dep*spB*spB*spB + d_dtrm2_indep*spB*spB*spB +
d_dtrm2_dep*spB*spB*spB*spB + 2*d_cterm_indep*spBB +
2*d_cterm_dep*spB*spBB + 2*d_dterm_indep*spB*spBB +
2*d_dterm_dep*spB*spB*spBB + 2*spBBB*cterm +
2*spBB*ctrm1 + 4*spB*spBB*ctrm2 +
2*spBB*spBB*dterm + 2*spB*spBBB*dterm +
2*spB*spBB*dtrm1 + 3*spB*spB*spBB*dtrm2 +
spBB*eterm
)*factor;
/* the final section: end */
}
/* Other spin interpolation scheme */
static real
spni_energy(const FunDensProp* dp, const struct vwn_params* para,
const struct vwn_params* ferro)
{
real ep_p[2], ep_f[2], ep_i[2], zeta, f_zeta, delta;
real rhoa = dp->rhoa, rhob = dp->rhob, rho;
if(rhoa<VWN_ZERO) rhoa = 1e-40;
if(rhob<VWN_ZERO) rhob = 1e-40;
rho = rhoa + rhob;
vwn_en_pot(ep_p, rho, 0, para);
if( FABS(dp->rhoa - dp->rhob)<VWN_ZERO) return ep_p[0]*rho;
vwn_en_pot(ep_f, rho, 0, ferro);
vwn_en_pot(ep_i, rho, 0, &vwn_interp);
zeta = (dp->rhoa-dp->rhob)/rho;
f_zeta = SPINPOLF*(POW(1+zeta,FOURTHREE)+POW(1-zeta,FOURTHREE)-2.0);
delta = f_zeta*(ep_f[0]-ep_p[0]);
return (ep_p[0]+ delta)*rho;
}
static void
spni_first(FunFirstFuncDrv *ds, real factor, const FunDensProp* dp,
const struct vwn_params* para, const struct vwn_params* ferro)
{
real zeta, f_zeta, f_zet1, vcfp;
real delta, ep_p[2], ep_f[2];
real rhoa = dp->rhoa, rhob = dp->rhob, rho;
if(rhoa<VWN_ZERO) rhoa = 1e-40;
if(rhob<VWN_ZERO) rhob = 1e-40;
rho = rhoa + rhob;
vwn_en_pot(ep_p, rho, 1, para);
ds->df1000 += ep_p[1]*factor;
ds->df0100 += ep_p[1]*factor;
/* if(dp->rhoa==dp->rhob) return; */
/* contribution from spin-polarized case; first order */
zeta = (dp->rhoa-dp->rhob)/rho;
f_zeta = SPINPOLF*(POW(1+zeta,FOURTHREE)+POW(1-zeta,FOURTHREE)-2.0);
f_zet1 = SPINPOLF*4.0/3.0*(POW(1+zeta,1.0/3.0)-POW(1-zeta,1.0/3.0));
vwn_en_pot(ep_f, rho, 1, ferro);
vcfp = f_zeta*(ep_f[1] - ep_p[1]);
delta= f_zet1*(ep_f[0] - ep_p[0]);
/* the final section: begin */
ds->df1000 += (vcfp + delta*(1-zeta))*factor;
ds->df0100 += (vcfp - delta*(1+zeta))*factor;
/* the final section: end */
}
static void
spni_second(FunSecondFuncDrv *ds, real factor, const FunDensProp* dp,
const struct vwn_params* para, const struct vwn_params* ferro)
{
real zeta, f_zeta, f_zet1, f_zet2, vcfp;
real delta, ep_p[3], ep_f[3];
real rhoa = dp->rhoa, rhob = dp->rhob, rho = dp->rhoa + dp->rhob;
real rho2 = rho*rho;
real vcf2, fac2, vap2, ef0, ef1, ef2;
real zA, zB, zAAr, zABr, zBBr;
vwn_en_pot(ep_p, rho, 2, para);
ds->df1000 += ep_p[1]*factor;
ds->df0100 += ep_p[1]*factor;
ds->df2000 += ep_p[2]*factor;
ds->df1100 += ep_p[2]*factor;
ds->df0200 += ep_p[2]*factor;
/* if( fabs(rhoa - rhob)<VWN_ZERO) return; */
/* contribution from spin-polarized case; first order */
zeta = (rhoa - rhob)/rho;
f_zeta = SPINPOLF*(POW(1+zeta,FOURTHREE)+POW(1-zeta,FOURTHREE)-2.0);
f_zet1 = SPINPOLF*4.0/3.0*(POW(1+zeta, 1.0/3.0)-POW(1-zeta, 1.0/3.0));
f_zet2 = SPINPOLF*4.0/9.0*(POW(1+zeta,-2.0/3.0)+POW(1-zeta,-2.0/3.0));
vwn_en_pot(ep_f, rho, 2, ferro);
ef0 = ep_f[0] - ep_p[0];
ef1 = ep_f[1] - ep_p[1];
ef2 = ep_f[2] - ep_p[2];
vcfp = f_zeta*ef1;
delta= f_zet1*ef0;
vcf2 = f_zeta*ef2;
vap2 = f_zet1*ef1;
fac2 = f_zet2*ef0*rho;
zA = 2*rhob/rho2;
zB = -2*rhoa/rho2;
zAAr = -4*rhob/rho2;
zABr = 2*zeta/rho;
zBBr = 4*rhoa/rho2;
/* the final section: begin */
ds->df1000 += (vcfp + delta*rho*zA)*factor;
ds->df0100 += (vcfp - delta*(1+zeta))*factor;
ds->df2000 += (vcf2 + vap2*(zA+zA) + fac2*zA*zA + delta*zAAr)*factor;
ds->df1100 += (vcf2 + vap2*(zA+zB) +fac2*zA*zB + delta*zABr)*factor;
ds->df0200 += (vcf2 + vap2*(zB+zB) + fac2*zB*zB + delta*zBBr)*factor;
/* the final section: end */
}
static real
vwni_energy(const FunDensProp* dp)
{
return spni_energy(dp, &vwn_paramagnetic, &vwn_ferromagnetic);
}
static void
vwni_first(FunFirstFuncDrv *ds, real factor, const FunDensProp* dp)
{
spni_first(ds, factor, dp, &vwn_paramagnetic, &vwn_ferromagnetic);
}
static void
vwni_second(FunSecondFuncDrv *ds, real factor, const FunDensProp* dp)
{
spni_second(ds, factor, dp, &vwn_paramagnetic, &vwn_ferromagnetic);
}
static void
vwni_third(FunThirdFuncDrv *ds, real factor, const FunDensProp* dp)
{
fun_printf("vwni_third not implemented."); exit(1);
}
static real
vwn3i_energy(const FunDensProp* dp)
{
return spni_energy(dp, &vwn3_paramagnetic, &vwn3_ferromagnetic);
}
static void
vwn3i_first(FunFirstFuncDrv *ds, real factor, const FunDensProp* dp)
{
spni_first(ds, factor, dp, &vwn3_paramagnetic, &vwn3_ferromagnetic);
}
static void
vwn3i_second(FunSecondFuncDrv *ds, real factor, const FunDensProp* dp)
{
spni_second(ds, factor, dp, &vwn3_paramagnetic, &vwn3_ferromagnetic);
}
static void
vwn3i_third(FunThirdFuncDrv *ds, real factor, const FunDensProp* dp)
{
fun_printf("vwni_third not implemented."); exit(1);
}
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