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quantum-espresso/Gamma/dgradcorr.f90

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!
! Copyright (C) 2003 PWSCF group
! This file is distributed under the terms of the
! GNU General Public License. See the file `License'
! in the root directory of the present distribution,
! or http://www.gnu.org/copyleft/gpl.txt .
!
!--------------------------------------------------------------------
subroutine dgradcor1 (rho, grho, dvxc_rr, dvxc_sr, dvxc_ss, dvxc_s, &
drho, drhoc, nr1, nr2, nr3, nrx1, nrx2, nrx3, nrxx, nspin, &
nl, nlm, ngm, g, alat, omega, dvxc)
! ===================
!--------------------------------------------------------------------
! ADD Gradient Correction contibution to screening potential
! phonon calculation, half G-vectors
#include "f_defs.h"
USE kinds, only : DP
implicit none
!
integer :: nr1, nr2, nr3, nrx1, nrx2, nrx3, nrxx, ngm, nspin, &
nl (ngm), nlm(ngm)
real(DP) :: rho (nrxx, nspin), grho (3, nrxx, nspin), &
dvxc_rr(nrxx, nspin, nspin), dvxc_sr (nrxx, nspin, nspin), &
dvxc_ss (nrxx,nspin, nspin), dvxc_s (nrxx, nspin, nspin),&
drho (nrxx,nspin), g (3, ngm), alat, omega
complex(DP) :: drhoc(nrxx, nspin), dvxc (nrxx, nspin)
integer :: k, ipol, is, js, ks, ls
real(DP) :: epsr, epsg, grho2
complex(DP) :: s1
complex(DP) :: a (2, 2, 2), b (2, 2, 2, 2), c (2, 2, 2), &
ps (2, 2), ps1 (3, 2, 2), ps2 (3, 2, 2, 2)
real(DP), allocatable :: gdrho (:,:,:)
complex(DP), allocatable :: h (:,:,:), dh (:)
parameter (epsr = 1.0d-6, epsg = 1.0d-10)
allocate (gdrho( 3, nrxx , nspin))
allocate (h( 3, nrxx , nspin))
allocate (dh( nrxx))
h (:,:,:) = (0.d0, 0.d0)
do is = 1, nspin
call gradient1 (nrx1, nrx2, nrx3, nr1, nr2, nr3, nrxx, &
drhoc(1, is), ngm, g, nl, nlm, alat, gdrho (1, 1, is) )
enddo
do k = 1, nrxx
grho2 = grho(1, k, 1)**2 + grho(2, k, 1)**2 + grho(3, k, 1)**2
if (nspin.eq.1) then
!
! LDA case
!
if (abs (rho (k, 1) ) .gt.epsr.and.grho2.gt.epsg) then
s1 = grho (1, k, 1) * gdrho (1, k, 1) + &
grho (2, k, 1) * gdrho (2, k, 1) + &
grho (3, k, 1) * gdrho (3, k, 1)
!
! linear variation of the first term
!
dvxc (k, 1) = dvxc (k, 1) + dvxc_rr (k, 1, 1) * drho (k, 1) &
+ dvxc_sr (k, 1, 1) * s1
do ipol = 1, 3
h (ipol, k, 1) = (dvxc_sr(k, 1, 1) * drho(k, 1) + &
dvxc_ss(k, 1, 1) * s1 )*grho(ipol, k, 1) + &
dvxc_s (k, 1, 1) * gdrho (ipol, k, 1)
enddo
else
do ipol = 1, 3
h (ipol, k, 1) = (0.d0, 0.d0)
enddo
endif
else
!
! LSDA case
!
ps (:,:) = (0.d0, 0.d0)
do is = 1, nspin
do js = 1, nspin
do ipol = 1, 3
ps1(ipol, is, js) = drho (k, is) * grho (ipol, k, js)
ps(is, js) = ps(is, js) + grho(ipol,k,is)*gdrho(ipol,k,js)
enddo
do ks = 1, nspin
if (is.eq.js.and.js.eq.ks) then
a (is, js, ks) = dvxc_sr (k, is, is)
c (is, js, ks) = dvxc_sr (k, is, is)
else
if (is.eq.1) then
a (is, js, ks) = dvxc_sr (k, 1, 2)
else
a (is, js, ks) = dvxc_sr (k, 2, 1)
endif
if (js.eq.1) then
c (is, js, ks) = dvxc_sr (k, 1, 2)
else
c (is, js, ks) = dvxc_sr (k, 2, 1)
endif
endif
do ipol = 1, 3
ps2 (ipol, is, js, ks) = ps (is, js) * grho (ipol, k, ks)
enddo
do ls = 1, nspin
if (is.eq.js.and.js.eq.ks.and.ks.eq.ls) then
b (is, js, ks, ls) = dvxc_ss (k, is, is)
else
if (is.eq.1) then
b (is, js, ks, ls) = dvxc_ss (k, 1, 2)
else
b (is, js, ks, ls) = dvxc_ss (k, 2, 1)
endif
endif
enddo
enddo
enddo
enddo
do is = 1, nspin
do js = 1, nspin
dvxc (k, is) = dvxc (k, is) + dvxc_rr (k, is, js) * drho (k, &
js)
do ipol = 1, 3
h (ipol, k, is) = h (ipol, k, is) + &
dvxc_s (k, is, js) * gdrho(ipol, k, js)
enddo
do ks = 1, nspin
dvxc (k, is) = dvxc (k, is) + a (is, js, ks) * ps (js, ks)
do ipol = 1, 3
h (ipol, k, is) = h (ipol, k, is) + &
c (is, js, ks) * ps1 (ipol, js, ks)
enddo
do ls = 1, nspin
do ipol = 1, 3
h (ipol, k, is) = h (ipol, k, is) + &
b (is, js, ks, ls) * ps2 (ipol, js, ks, ls)
enddo
enddo
enddo
enddo
enddo
endif
enddo
! linear variation of the second term
do is = 1, nspin
call grad_dot1 (nrx1, nrx2, nrx3, nr1, nr2, nr3, nrxx, &
h (1, 1, is), ngm, g, nl, nlm, alat, dh)
do k = 1, nrxx
dvxc (k, is) = dvxc (k, is) - dh (k)
enddo
enddo
deallocate (dh)
deallocate (h)
deallocate (gdrho)
return
end subroutine dgradcor1
!
!--------------------------------------------------------------------
subroutine gradient1(nrx1, nrx2, nrx3, nr1, nr2, nr3, nrxx, &
a, ngm, g, nl, nlm, alat, ga)
!--------------------------------------------------------------------
! Calculates ga = \grad a in R-space (a is G-space)
USE kinds, only : DP
USE constants, ONLY : tpi
implicit none
integer :: nrx1, nrx2, nrx3, nr1, nr2, nr3, nrxx, ngm, nl (ngm), &
nlm(ngm)
complex(DP) :: a (nrxx)
real(DP) :: ga (3, nrxx), g (3, ngm), alat
integer :: n, ipol
real(DP) :: tpiba
complex(DP), allocatable :: gaux (:)
allocate (gaux( nrxx))
tpiba = tpi / alat
! a(G) multiply by i(q+G) to get (\grad_ipol a)(q+G) ...
! do ipol = 1, 3
! x, y
ipol=1
do n = 1, nrxx
gaux (n) = (0.d0, 0.d0)
enddo
do n = 1, ngm
gaux(nl (n)) = CMPLX(0.d0, g(ipol , n))* a (nl(n)) - &
g(ipol+1, n) * a (nl(n))
gaux(nlm(n)) = CMPLX(0.d0, - g(ipol , n))* CONJG(a (nl(n))) + &
g(ipol+1, n) * CONJG(a (nl(n)))
enddo
! bring back to R-space, (\grad_ipol a)(r) ...
call cft3 (gaux, nr1, nr2, nr3, nrx1, nrx2, nrx3, 1)
! ...and add the factor 2\pi/a missing in the definition of q+G
do n = 1, nrxx
ga (ipol , n) = DBLE(gaux (n)) * tpiba
ga (ipol+1, n) = AIMAG(gaux (n)) * tpiba
enddo
! z
ipol=3
do n = 1, nrxx
gaux (n) = (0.d0, 0.d0)
enddo
do n = 1, ngm
gaux(nl (n)) = CMPLX(0.d0, g(ipol, n)) * a (nl(n))
gaux(nlm(n)) = CONJG(gaux(nl(n)))
enddo
! bring back to R-space, (\grad_ipol a)(r) ...
call cft3 (gaux, nr1, nr2, nr3, nrx1, nrx2, nrx3, 1)
! ...and add the factor 2\pi/a missing in the definition of q+G
do n = 1, nrxx
ga (ipol, n) = DBLE(gaux (n)) * tpiba
enddo
! enddo
deallocate (gaux)
return
end subroutine gradient1
!--------------------------------------------------------------------
subroutine grad_dot1 (nrx1, nrx2, nrx3, nr1, nr2, nr3, nrxx, &
a, ngm, g, nl, nlm, alat, da)
!--------------------------------------------------------------------
! Calculates da = \sum_i \grad_i a_i in R-space
USE kinds, only : DP
USE constants, ONLY : tpi
implicit none
integer :: nrx1, nrx2, nrx3, nr1, nr2, nr3, nrxx, ngm, nl (ngm), &
nlm(ngm)
complex(DP) :: a (3, nrxx), da (nrxx)
real(DP) :: g (3, ngm), alat
integer :: n, ipol
real(DP) :: tpiba
complex(DP), allocatable :: aux (:)
complex(DP) :: fp, fm, aux1, aux2
allocate (aux ( nrxx))
tpiba = tpi / alat
do n = 1, nrxx
da(n) = (0.d0, 0.d0)
enddo
!!! do ipol = 1, 3
! x, y
ipol=1
! copy a(ipol,r) to a complex array...
do n = 1, nrxx
aux (n) = CMPLX( DBLE(a(ipol, n)), DBLE(a(ipol+1, n)))
enddo
! bring a(ipol,r) to G-space, a(G) ...
call cft3 (aux, nr1, nr2, nr3, nrx1, nrx2, nrx3, - 1)
! multiply by i(q+G) to get (\grad_ipol a)(q+G) ...
do n = 1, ngm
fp = (aux(nl (n)) + aux (nlm(n)))*0.5d0
fm = (aux(nl (n)) - aux (nlm(n)))*0.5d0
aux1 = CMPLX( DBLE(fp), AIMAG(fm))
aux2 = CMPLX(AIMAG(fp),- DBLE(fm))
da (nl(n)) = da (nl(n)) + CMPLX(0.d0, g(ipol , n)) * aux1 + &
CMPLX(0.d0, g(ipol+1, n)) * aux2
end do
! z
ipol=3
! copy a(ipol,r) to a complex array...
do n = 1, nrxx
aux (n) = a(ipol, n)
enddo
! bring a(ipol,r) to G-space, a(G) ...
call cft3 (aux, nr1, nr2, nr3, nrx1, nrx2, nrx3, - 1)
! multiply by i(q+G) to get (\grad_ipol a)(q+G) ...
do n = 1, ngm
da (nl(n)) = da (nl(n)) + CMPLX(0.d0, g(ipol, n)) * aux(nl(n))
enddo
!!! enddo
do n = 1, ngm
da(nlm(n)) = CONJG(da(nl(n)))
enddo
! bring back to R-space, (\grad_ipol a)(r) ...
call cft3 (da, nr1, nr2, nr3, nrx1, nrx2, nrx3, 1)
! ...add the factor 2\pi/a missing in the definition of q+G and sum
do n = 1, nrxx
da (n) = da (n) * tpiba
enddo
deallocate (aux)
return
end subroutine grad_dot1
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