TABLE OF CONTENTS

ABINIT/fexsGamma [ Functions ]

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NAME

 fexsGamma

FUNCTION

 Free energy for the IIT finite temperautre XC functional

INPUTS

 Gamma= ?
 t=temperature

OUTPUT

 fexsGamma=free energy

SOURCE

137  function fexsGamma(Gamma,t)
138 
139 !Arguments ------------------------------------
140  real(dp) :: fexsGamma
141  real(dp),intent(in) :: Gamma,t
142 !Local variables-------------------------------
143  real(dp) :: lambda
144  real(dp) :: tanht,tanhst
145  real(dp) :: a,b,c,d,e
146  real(dp) :: bmcdse,amcse,sqrt4emd2
147 
148 ! *************************************************************************
149 
150    lambda=(4.0_dp/(9.0_dp*pi))**(one/3.0_dp)
151    tanht=tanh(one/t)
152    tanhst=tanh(one/sqrt(t))
153 
154    a=one/(pi*lambda)*(0.75_dp+3.04363_dp*t**2-0.09227_dp*t**3+1.7035_dp*t**4)/(one+8.31051_dp*t**2+5.1105_dp*t**4)*tanht
155    b=(0.341308_dp+12.070873_dp*t**2+1.148889_dp*t**4)/(one+10.495346_dp*t**2+1.326623_dp*t**4)*sqrt(t)*tanhst
156    e=(0.539409_dp+2.522206_dp*t**2+0.178484_dp*t**4)/(one+2.555501_dp*t**2+0.146319_dp*t**4)*t*tanht
157    c=(0.872496_dp+0.025248_dp*exp(-1./t))*e
158    d=(0.614925_dp+16.996055_dp*t**2+1.489056_dp*t**4)/(one+10.10935_dp*t**2+1.22184_dp*t**4)*sqrt(t)*tanhst
159 
160    bmcdse=b-c*d/e
161    amcse=a-c/e
162    sqrt4emd2=sqrt(4.0_dp*e-d**2)
163 
164    fexsGamma=-one/Gamma*(c/e*Gamma+2.0_dp/e*bmcdse*sqrt(Gamma)+one/e*(amcse-d/e*bmcdse)*log(e*Gamma+d*sqrt(Gamma)+one)- &
165 &   2.0_dp/(e*sqrt4emd2)*(d*amcse+(2.0_dp-d**2/e)*bmcdse)*(atan((2.0_dp*e*sqrt(Gamma)+d)/sqrt4emd2)-atan(d/sqrt4emd2)))
166 
167  end function fexsGamma

ABINIT/Fxc_iit [ Functions ]

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NAME

 Fxc_iit

FUNCTION

 Auxiliary function for the IIT finite temperature XC functional

INPUTS

 deltavxc= ?
 rs=Wigner-Seitz radius
 t=temperature

OUTPUT

 Fxc_iit=auxiliary function

SOURCE

188  function Fxc_iit(rs,t,deltavxc)
189 
190 !Arguments ------------------------------------
191  real(dp) :: Fxc_iit
192  real(dp),intent(in) :: rs,t,deltavxc
193 !Local variables-------------------------------
194  real(dp) :: newrs,newt,newGamma
195 
196 ! *************************************************************************
197 
198    newrs=rs/(one+deltavxc)**(one/3.0_dp)
199    newt=t/(one+deltavxc)**(2.0_dp/3.0_dp)
200    newGamma=2.0_dp*(4.0_dp/(9.0_dp*pi))**(2.0_dp/3.0_dp)*newrs/newt
201    Fxc_iit=3.0_dp/(4.0_dp*pi)*fexsGamma(newGamma,newt)/newrs**4
202 
203  end function Fxc_iit

ABINIT/m_xciit [ Modules ]

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NAME

  m_xciit

FUNCTION

 Exchange-correlation at finite temperature of an electron gas
 Ichimaru S., Iyetomi H., Tanaka S., Phys. Rep. 149, 91-205 (1987) [[cite:Ichimaru1987]]

COPYRIGHT

  Copyright (C) 2002-2024 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 .

SOURCE

17 #if defined HAVE_CONFIG_H
18 #include "config.h"
19 #endif
20 
21 #include "abi_common.h"
22 
23 module m_xciit
24 
25  use defs_basis
26  use m_errors
27 
28  implicit none
29 
30  private

ABINIT/tdexcsdtiit [ Functions ]

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NAME

 tdexcsdtiit

FUNCTION

 Auxiliary function for the IIT finite temperature XC functional

INPUTS

 rs=Wigner-Seitz radius
 t=temperature

OUTPUT

 tdexcsdtiit=auxiliary function

SOURCE

223  function tdexcsdtiit(rs,t)
224 
225 !Arguments ------------------------------------
226  real(dp) :: tdexcsdtiit
227  real(dp),intent(in) :: rs,t
228 !Local variables-------------------------------
229  real(dp) :: ef,Gamma
230  real(dp) :: deltat=1.0d-2
231 
232 ! *************************************************************************
233 
234    ef=half*(9.0_dp*pi/4.0_dp)**(2.0_dp/3.0_dp)/rs**2
235    Gamma=one/(t*ef)/rs
236    tdexcsdtiit=8.0_dp*(fexsGamma(Gamma/(one+deltat),(one+deltat)*t) &
237 &   -fexsGamma(Gamma/(one-deltat),(one-deltat)*t)) &
238 &   -(fexsGamma(Gamma/(one+2.0_dp*deltat),(one+2.0_dp*deltat)*t) &
239 &   -fexsGamma(Gamma/(one-2.0_dp*deltat),(one-2.0_dp*deltat)*t))
240    tdexcsdtiit=t*tdexcsdtiit/(12.0_dp*deltat*t)/rs
241 
242  end function tdexcsdtiit

ABINIT/xciit [ Functions ]

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NAME

  xciit

FUNCTION

 Exchange-correlation at finite temperature of an electron gas
 Ichimaru S., Iyetomi H., Tanaka S., Phys. Rep. 149, 91-205 (1987) [[cite:Ichimaru1987]]

INPUTS

  temp= (electronic) temperature
  npt=number of real space points
  order=gives the maximal derivative of Exc computed.
  rspts(npt)=Wigner-Seitz radii at each point

OUTPUT

  exc(npt)=exchange-correlation energy density
  fxc(npt)=exchange-correlation free energy at finite temperature
  vxc(npt)=exchange-correlation potential
  --- optional output ---
  [dvxc(npt)]=partial second derivatives of the xc energy

SOURCE

 62 subroutine xciit(exc,fxc,npt,order,rspts,temp,vxc, &
 63 &                dvxc)!Optional argument
 64 
 65 !Arguments ------------------------------------
 66 !scalars
 67  integer,intent(in) :: npt,order
 68  real(dp),intent(in) :: temp
 69 !arrays
 70  real(dp),intent(in) :: rspts(npt)
 71  real(dp),intent(out) :: exc(npt),fxc(npt),vxc(npt)
 72  real(dp),intent(out),optional :: dvxc(npt)
 73 
 74 !Local variables-------------------------------
 75 !scalars
 76  integer :: ipt
 77  real(dp) :: ef,deltavxc,Gamma,rs,rsm1,tt
 78  character(len=500) :: msg
 79 
 80 ! *************************************************************************
 81 
 82 !Checks the values of order
 83  if(order<0.or.order>2)then
 84    write(msg, '(4a,i3,a)' ) ch10,&
 85 &   'With Ishimaru-Iyetomi-Tanka xc functional, the only',ch10,&
 86 &   'allowed values for order are 0, 1 or 2, while it is found to be ',order,'.'
 87    ABI_BUG(msg)
 88  end if
 89 
 90 !Loop over grid points
 91  do ipt=1,npt
 92 
 93    rs=rspts(ipt)
 94    rsm1=one/rs
 95 !  Step for the Vxc computation
 96    deltavxc=0.01_dp
 97 !  Compute ef
 98    ef=0.5_dp*(9.0_dp*pi/4.0_dp)**(2.0_dp/3.0_dp)*rsm1**2
 99 !  Compute temperature
100    tt=max(temp/ef,tol12)
101 !  Compute Gamma
102    Gamma=one/(tt*ef)/rs
103 
104 !  Exchange-correlation of Ichimaru functional
105    fxc(ipt)= fexsGamma(Gamma,tt)*rsm1
106    exc(ipt)=fxc(ipt) - tdexcsdtiit(rs,tt);
107    vxc(ipt)=(8.0_dp*(Fxc_iit(rs,tt,deltavxc)-Fxc_iit(rs,tt,-deltavxc)) &
108 &   -(Fxc_iit(rs,tt,two*deltavxc)-Fxc_iit(rs,tt,-two*deltavxc)))/ &
109 &   (12.0_dp*deltavxc*3.0_dp/(4.0_dp*pi)/rs**3)
110    if (order==2) then
111      dvxc(ipt)=(-30.0_dp*Fxc_iit(rs,tt,zero)+16.0_dp*(Fxc_iit(rs,tt,deltavxc)+Fxc_iit(rs,tt,-deltavxc)) &
112 &     -(Fxc_iit(rs,tt,two*deltavxc)+Fxc_iit(rs,tt,two*deltavxc)))/ &
113 &     (12.0_dp*(deltavxc*3.0_dp/(4.0_dp*pi)/rs**3)**2)
114    end if
115  end do
116 
117  CONTAINS