./41_xc_lowlevel/xctfw.F90

ABINIT/xctfw

ABINIT/xctfw [ Functions ]

NAME

 xctfw

FUNCTION

 Add gradient part of the Thomas-Fermi-Weizsacker functional
 Perrot F.,Phys. Rev. A20,586-594 (1979)

 Copyright (C) 1998-2018 ABINIT group (JFD,LK)
 This file is distributed under the terms of the
 GNU General Public License, see ~abinit/COPYING
 or http://www.gnu.org/copyleft/gpl.txt .
 For the initials of contributors, see ~abinit/doc/developers/contributors .

INPUTS

  ndvxcdgr= size of dvxcdgr(npts,ndvxcdgr)
  ngr2= size of grho2_updn(npts,ngr2)
  npts= number of points to be computed
  nspden=number if spin density component (necessarily 1 here)
  grho2_updn(npts,ngr2)=square of the gradient of the spin-up,
     and, if nspden==2, spin-down, and total density (Hartree/Bohr**2),
     only used if gradient corrected functional (option=2,-2,-4 and 4 or beyond)
  rho_updn(npts,nspden)=spin-up and spin-down density (Hartree/bohr**3)
  temp= electronic temperature
  usefxc=1 if free energy fxc is used

SIDE EFFECTS

  The following arrays are modified (gradient correction added):
  dvxcdgr(npts,3)=partial derivative of the XC energy divided by the norm of the gradient
  exci(npts)=exchange-correlation energy density
  fxci(npts)=free energy energy density
  vxci(npts,nspden)=exchange-correlation potential

PARENTS

      rhotoxc

CHILDREN

      invcb

SOURCE

 43 !!$#if defined HAVE_CONFIG_H
 44 !!$#include "config.h"
 45 !!$#endif
 46 
 47 #if defined HAVE_CONFIG_H
 48 #include "config.h"
 49 #endif
 50 
 51 #include "abi_common.h"
 52 
 53 subroutine xctfw(temp,exci,fxci,usefxc,rho_updn,vxci,npts,nspden,dvxcdgr,ndvxcdgr,grho2_updn,ngr2)
 54 
 55  use defs_basis
 56  use m_profiling_abi
 57  use m_errors
 58 
 59 !This section has been created automatically by the script Abilint (TD).
 60 !Do not modify the following lines by hand.
 61 #undef ABI_FUNC
 62 #define ABI_FUNC 'xctfw'
 63  use interfaces_41_xc_lowlevel, except_this_one => xctfw
 64 !End of the abilint section
 65 
 66  implicit none
 67 
 68 !Arguments ------------------------------------
 69 !scalars
 70  integer,intent(in) :: ndvxcdgr,ngr2,npts,nspden,usefxc
 71  real(dp),intent(in) :: temp
 72 !arrays
 73  real(dp),intent(in) :: grho2_updn(npts,ngr2),rho_updn(npts,nspden)
 74  real(dp),intent(inout) :: dvxcdgr(npts,ndvxcdgr),fxci(npts*usefxc),exci(npts),vxci(npts,nspden)
 75 
 76 !Local variables-------------------------------
 77 !scalars
 78  integer :: iperrot,ipts
 79  logical :: has_fxc,has_dvxcdgr
 80  real(dp) :: etfw,rho,rho_inv,rhomot,yperrot0,vtfw
 81  real(dp) :: yperrot,uperrot,dyperrotdn,duperrotdyperrot
 82  real(dp) :: hperrot,dhperrotdyperrot,dhperrotdn,dhperrotduperrot
 83 !arrays
 84  real(dp) :: wpy(0:7), wpu(0:7)
 85  real(dp),allocatable :: rho_updnm1_3(:,:)
 86 
 87 ! *************************************************************************
 88 
 89 !DBG_ENTER('COLL')
 90 
 91  has_fxc=(usefxc/=0)
 92  has_dvxcdgr=(ndvxcdgr/=0)
 93 
 94  yperrot0=1.666081101_dp
 95 
 96  wpy(0)=0.5_dp; wpy(1)=-0.1999176316_dp
 97  wpy(2)=0.09765615709_dp; wpy(3)=-0.06237609924_dp
 98  wpy(4)=0.05801466322_dp; wpy(5)=-0.04449287774_dp
 99  wpy(6)=0.01903211697_dp; wpy(7)=-0.003284096926_dp
100 
101  wpu(0)=one/6._dp; wpu(1)=0.311590799_dp
102  wpu(2)=3.295662439_dp; wpu(3)=-29.22038326_dp
103  wpu(4)=116.1084531_dp; wpu(5)=-250.4543147_dp
104  wpu(6)=281.433688_dp; wpu(7)=-128.8784806_dp
105 
106  ABI_ALLOCATE(rho_updnm1_3,(npts,2))
107 
108  call invcb(rho_updn(:,1),rho_updnm1_3(:,1),npts)
109 
110  do ipts=1,npts
111 
112    rho   =rho_updn(ipts,1)
113    rhomot=rho_updnm1_3(ipts,1)
114    rho_inv=rhomot*rhomot*rhomot
115 
116    yperrot=pi*pi/sqrt2/temp**1.5*two*rho
117    uperrot=yperrot**(2./3.)
118 
119    dyperrotdn=pi*pi/sqrt2/temp**1.5*2.0_dp
120 
121    hperrot=zero
122    dhperrotdyperrot=zero
123    dhperrotduperrot=zero
124    if(yperrot<=yperrot0)then
125      do iperrot=0,7
126        hperrot=hperrot+wpy(iperrot)*yperrot**iperrot
127        dhperrotdyperrot=dhperrotdyperrot+iperrot*wpy(iperrot)*yperrot**(iperrot-1)
128      end do
129      hperrot=one/12.0_dp*hperrot
130      dhperrotdyperrot=one/12.0_dp*dhperrotdyperrot
131      dhperrotdn=dhperrotdyperrot*dyperrotdn
132    else
133      do iperrot=0,7
134        hperrot=hperrot+wpu(iperrot)/uperrot**(2*iperrot)
135        dhperrotduperrot=dhperrotduperrot-2.*iperrot*wpu(iperrot)/uperrot**(2*iperrot+1)
136      end do
137      hperrot=one/12.0_dp*hperrot
138      dhperrotduperrot=one/12.0_dp*dhperrotduperrot
139      duperrotdyperrot=two/3._dp/yperrot**(1./3.)
140      dhperrotdn=dhperrotduperrot*duperrotdyperrot*dyperrotdn
141    end if
142 
143    etfw=hperrot*grho2_updn(ipts,1)*rho_inv*rho_inv
144    vtfw=-etfw + rho/hperrot*dhperrotdn*etfw
145 
146    if(yperrot<=yperrot0)then
147      exci(ipts)   = exci(ipts) + etfw + 1.5_dp*yperrot*dhperrotdyperrot*grho2_updn(ipts,1)*rho_inv*rho_inv
148    else
149      exci(ipts)   = exci(ipts) + etfw + uperrot*dhperrotduperrot*grho2_updn(ipts,1)*rho_inv*rho_inv
150    end if
151    vxci(ipts,1) = vxci(ipts,1)  + vtfw
152    if (has_fxc) fxci(ipts)   = fxci(ipts) + etfw
153    if (has_dvxcdgr) dvxcdgr(ipts,1)= dvxcdgr(ipts,1)+two*hperrot*rho_inv
154 
155  end do
156 
157  ABI_DEALLOCATE(rho_updnm1_3)
158 
159 !DBG_EXIT('COLL')
160 
161 end subroutine xctfw

TABLE OF CONTENTS

ABINIT/xctfw [ Functions ]