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

128  function fexsGamma(Gamma,t)
129 
130 
131 !This section has been created automatically by the script Abilint (TD).
132 !Do not modify the following lines by hand.
133 #undef ABI_FUNC
134 #define ABI_FUNC 'fexsGamma'
135 !End of the abilint section
136 
137  implicit none
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 
191 !This section has been created automatically by the script Abilint (TD).
192 !Do not modify the following lines by hand.
193 #undef ABI_FUNC
194 #define ABI_FUNC 'Fxc_iit'
195 !End of the abilint section
196 
197  implicit none
198  
199 !Arguments ------------------------------------
200  real(dp) :: Fxc_iit
201  real(dp),intent(in) :: rs,t,deltavxc
202 !Local variables-------------------------------
203  real(dp) :: newrs,newt,newGamma
204 
205 ! *************************************************************************
206 
207    newrs=rs/(one+deltavxc)**(one/3.0_dp)
208    newt=t/(one+deltavxc)**(2.0_dp/3.0_dp)
209    newGamma=2.0_dp*(4.0_dp/(9.0_dp*pi))**(2.0_dp/3.0_dp)*newrs/newt
210    Fxc_iit=3.0_dp/(4.0_dp*pi)*fexsGamma(newGamma,newt)/newrs**4
211 
212  end function Fxc_iit

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

232  function tdexcsdtiit(rs,t)
233 
234 
235 !This section has been created automatically by the script Abilint (TD).
236 !Do not modify the following lines by hand.
237 #undef ABI_FUNC
238 #define ABI_FUNC 'tdexcsdtiit'
239 !End of the abilint section
240 
241  implicit none
242 
243 !Arguments ------------------------------------
244  real(dp) :: tdexcsdtiit
245  real(dp),intent(in) :: rs,t
246 !Local variables-------------------------------
247  real(dp) :: ef,Gamma
248  real(dp) :: deltat=1.0d-2
249 
250 ! *************************************************************************
251 
252    ef=half*(9.0_dp*pi/4.0_dp)**(2.0_dp/3.0_dp)/rs**2
253    Gamma=one/(t*ef)/rs
254    tdexcsdtiit=8.0_dp*(fexsGamma(Gamma/(one+deltat),(one+deltat)*t) &
255 &   -fexsGamma(Gamma/(one-deltat),(one-deltat)*t)) &
256 &   -(fexsGamma(Gamma/(one+2.0_dp*deltat),(one+2.0_dp*deltat)*t) &
257 &   -fexsGamma(Gamma/(one-2.0_dp*deltat),(one-2.0_dp*deltat)*t))
258    tdexcsdtiit=t*tdexcsdtiit/(12.0_dp*deltat*t)/rs
259 
260  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)

COPYRIGHT

 Copyright (C) 2002-2018 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 .

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

PARENTS

      drivexc

CHILDREN

SOURCE

 36 #if defined HAVE_CONFIG_H
 37 #include "config.h"
 38 #endif
 39 
 40 #include "abi_common.h"
 41 
 42 subroutine xciit(exc,fxc,npt,order,rspts,temp,vxc, &
 43 &                dvxc)!Optional argument
 44 
 45  use defs_basis
 46  use m_errors
 47 
 48 !This section has been created automatically by the script Abilint (TD).
 49 !Do not modify the following lines by hand.
 50 #undef ABI_FUNC
 51 #define ABI_FUNC 'xciit'
 52 !End of the abilint section
 53 
 54  implicit none
 55 
 56 !Arguments ------------------------------------
 57 !scalars
 58  integer,intent(in) :: npt,order
 59  real(dp),intent(in) :: temp
 60 !arrays
 61  real(dp),intent(in) :: rspts(npt)
 62  real(dp),intent(out) :: exc(npt),fxc(npt),vxc(npt)
 63  real(dp),intent(out),optional :: dvxc(npt)
 64 
 65 !Local variables-------------------------------
 66 !scalars
 67  integer :: ipt
 68  real(dp) :: ef,deltavxc,Gamma,rs,rsm1,tt
 69  character(len=500) :: msg
 70 
 71 ! *************************************************************************
 72 
 73 !Checks the values of order
 74  if(order<0.or.order>2)then
 75    write(msg, '(4a,i3,a)' ) ch10,&
 76 &   'With Ishimaru-Iyetomi-Tanka xc functional, the only',ch10,&
 77 &   'allowed values for order are 0, 1 or 2, while it is found to be ',order,'.'
 78    MSG_BUG(msg)
 79  end if
 80 
 81 !Loop over grid points
 82  do ipt=1,npt
 83 
 84    rs=rspts(ipt)
 85    rsm1=one/rs
 86 !  Step for the Vxc computation
 87    deltavxc=0.01_dp
 88 !  Compute ef
 89    ef=0.5_dp*(9.0_dp*pi/4.0_dp)**(2.0_dp/3.0_dp)*rsm1**2
 90 !  Compute temperature
 91    tt=max(temp/ef,tol12)
 92 !  Compute Gamma
 93    Gamma=one/(tt*ef)/rs
 94 
 95 !  Exchange-correlation of Ichimaru functionnal
 96    fxc(ipt)= fexsGamma(Gamma,tt)*rsm1
 97    exc(ipt)=fxc(ipt) - tdexcsdtiit(rs,tt);
 98    vxc(ipt)=(8.0_dp*(Fxc_iit(rs,tt,deltavxc)-Fxc_iit(rs,tt,-deltavxc)) &
 99 &   -(Fxc_iit(rs,tt,two*deltavxc)-Fxc_iit(rs,tt,-two*deltavxc)))/ &
100 &   (12.0_dp*deltavxc*3.0_dp/(4.0_dp*pi)/rs**3)
101    if (order==2) then
102      dvxc(ipt)=(-30.0_dp*Fxc_iit(rs,tt,zero)+16.0_dp*(Fxc_iit(rs,tt,deltavxc)+Fxc_iit(rs,tt,-deltavxc)) &
103 &     -(Fxc_iit(rs,tt,two*deltavxc)+Fxc_iit(rs,tt,two*deltavxc)))/ &
104 &     (12.0_dp*(deltavxc*3.0_dp/(4.0_dp*pi)/rs**3)**2)
105    end if
106  end do
107 
108  CONTAINS