mirror of https://gitlab.com/QEF/q-e.git
265 lines
8.0 KiB
Fortran
265 lines
8.0 KiB
Fortran
!
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! Copyright (C) 2001 PWSCF group
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! This file is distributed under the terms of the
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! GNU General Public License. See the file `License'
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! in the root directory of the present distribution,
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! or http://www.gnu.org/copyleft/gpl.txt .
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!
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!--------------------------------------------------------------------
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subroutine gradcorr (rho, rho_core, nr1, nr2, nr3, nrx1, nrx2, &
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nrx3, nrxx, nl, ngm, g, alat, omega, nspin, etxc, vtxc, v)
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! ===================
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!--------------------------------------------------------------------
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#include "machine.h"
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use parameters
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use funct
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implicit none
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!
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integer :: nr1, nr2, nr3, nrx1, nrx2, nrx3, nrxx, ngm, nl (ngm), &
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nspin
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real(kind=DP) :: rho (nrxx, nspin), rho_core (nrxx), v (nrxx, nspin), &
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g (3, ngm), vtxc, etxc, alat, omega, zeta, rh, grh2
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integer :: k, ipol, is
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real(kind=DP), allocatable :: grho (:,:,:), h (:,:,:), dh (:)
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real(kind=DP) :: grho2 (2), sx, sc, v1x, v2x, v1c, v2c, v1xup, v1xdw, &
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v2xup, v2xdw, v1cup, v1cdw , etxcgc, vtxcgc, segno, arho, fac
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real(kind=DP), parameter :: e2 = 2.d0, epsr = 1.0d-6, epsg = 1.0d-10
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if (igcx == 0 .and. igcc == 0) return
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etxcgc = 0.d0
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vtxcgc = 0.d0
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allocate (h( 3, nrxx, nspin))
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allocate (grho( 3, nrxx, nspin))
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! calculate the gradient of rho+rho_core in real space
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fac = 1.d0 / float (nspin)
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do is = 1, nspin
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call DAXPY (nrxx, fac, rho_core, 1, rho (1, is), 1)
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call gradient (nrx1, nrx2, nrx3, nr1, nr2, nr3, nrxx, rho (1, is), &
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ngm, g, nl, alat, grho (1, 1, is) )
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enddo
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do k = 1, nrxx
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do is = 1, nspin
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grho2 (is) = grho(1, k, is)**2 + grho(2, k, is)**2 + grho(3, k, is)**2
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enddo
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if (nspin == 1) then
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!
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! This is the spin-unpolarised case
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!
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arho = abs (rho (k, 1) )
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segno = sign (1.d0, rho (k, 1) )
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if (arho.gt.epsr.and.grho2 (1) .gt.epsg) then
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call gcxc (arho, grho2, sx, sc, v1x, v2x, v1c, v2c)
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!
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! first term of the gradient correction : D(rho*Exc)/D(rho)
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v (k, 1) = v (k, 1) + e2 * (v1x + v1c)
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! h contains D(rho*Exc)/D(|grad rho|) * (grad rho) / |grad rho|
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do ipol = 1, 3
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h (ipol, k, 1) = e2 * (v2x + v2c) * grho (ipol, k, 1)
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enddo
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vtxcgc = vtxcgc + e2 * (v1x + v1c) * (rho (k, 1) - rho_core(k) )
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etxcgc = etxcgc + e2 * (sx + sc) * segno
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else
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do ipol = 1, 3
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h (ipol, k, 1) = 0.d0
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enddo
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endif
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else
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!
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! spin-polarised case
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!
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call gcx_spin (rho (k, 1), rho (k, 2), grho2 (1), grho2 (2), &
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sx, v1xup, v1xdw, v2xup, v2xdw)
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rh = rho (k, 1) + rho (k, 2)
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if (rh.gt.epsr) then
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zeta = (rho (k, 1) - rho (k, 2) ) / rh
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grh2 = (grho (1, k, 1) + grho (1, k, 2) ) **2 + &
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(grho (2, k, 1) + grho (2, k, 2) ) **2 + &
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(grho (3, k, 1) + grho (3, k, 2) ) **2
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call gcc_spin (rh, zeta, grh2, sc, v1cup, v1cdw, v2c)
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else
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sc = 0.d0
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v1cup = 0.d0
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v1cdw = 0.d0
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v2c = 0.d0
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endif
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!
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! first term of the gradient correction : D(rho*Exc)/D(rho)
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!
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v (k, 1) = v (k, 1) + e2 * (v1xup + v1cup)
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v (k, 2) = v (k, 2) + e2 * (v1xdw + v1cdw)
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!
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! h contains D(rho*Exc)/D(|grad rho|) * (grad rho) / |grad rho|
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!
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do ipol = 1, 3
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h (ipol, k, 1) = e2 * ( (v2xup + v2c) * grho (ipol, k, 1) &
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+ v2c * grho (ipol, k, 2) )
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h (ipol, k, 2) = e2 * ( (v2xdw + v2c) * grho (ipol, k, 2) &
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+ v2c * grho (ipol, k, 1) )
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enddo
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vtxcgc = vtxcgc + e2 * (v1xup + v1cup) * (rho (k, 1) - &
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rho_core (k) * fac)
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vtxcgc = vtxcgc + e2 * (v1xdw + v1cdw) * (rho (k, 2) - &
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rho_core (k) * fac)
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etxcgc = etxcgc + e2 * (sx + sc)
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endif
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enddo
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do is = 1, nspin
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call DAXPY (nrxx, - fac, rho_core, 1, rho (1, is), 1)
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enddo
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deallocate(grho)
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allocate (dh( nrxx))
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!
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! second term of the gradient correction :
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! \sum_alpha (D / D r_alpha) ( D(rho*Exc)/D(grad_alpha rho) )
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!
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do is = 1, nspin
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call grad_dot (nrx1, nrx2, nrx3, nr1, nr2, nr3, nrxx, h (1, 1, is), &
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ngm, g, nl, alat, dh)
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do k = 1, nrxx
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v (k, is) = v (k, is) - dh (k)
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vtxcgc = vtxcgc - dh (k) * rho (k, is)
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enddo
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enddo
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vtxc = vtxc + omega * vtxcgc / (nr1 * nr2 * nr3)
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etxc = etxc + omega * etxcgc / (nr1 * nr2 * nr3)
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deallocate (dh)
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deallocate (h)
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return
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end subroutine gradcorr
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!--------------------------------------------------------------------
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subroutine gradient (nrx1, nrx2, nrx3, nr1, nr2, nr3, nrxx, a, &
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ngm, g, nl, alat, ga)
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!--------------------------------------------------------------------
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!
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! Calculates ga = \grad a in R-space (a is also in R-space)
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use parameters
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use gvect, only: nlm
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use wvfct, only: gamma_only
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implicit none
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integer :: nrx1, nrx2, nrx3, nr1, nr2, nr3, nrxx, ngm, nl (ngm)
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real(kind=DP) :: a (nrxx), g (3, ngm), ga (3, nrxx), alat
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integer :: n, ipol
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real(kind=DP), allocatable :: aux (:,:), gaux (:,:)
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real(kind=DP) :: tpi, tpiba
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parameter (tpi = 2.d0 * 3.14159265358979d0)
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allocate (aux( 2,nrxx))
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allocate (gaux(2,nrxx))
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tpiba = tpi / alat
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!
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! copy a(r) to complex array...
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!
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aux(2,:) = 0.d0
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call DCOPY (nrxx, a, 1, aux, 2)
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!
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! bring a(r) to G-space, a(G) ...
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!
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call cft3 (aux, nr1, nr2, nr3, nrx1, nrx2, nrx3, - 1)
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!
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! multiply by (iG) to get (\grad_ipol a)(G) ...
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!
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ga(:,:) = 0.d0
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do ipol = 1, 3
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gaux(:,:) = 0.d0
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do n = 1, ngm
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gaux (1, nl (n) ) = - g (ipol, n) * aux (2, nl (n) )
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gaux (2, nl (n) ) = g (ipol, n) * aux (1, nl (n) )
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enddo
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if (gamma_only) then
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do n = 1, ngm
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gaux (1, nlm(n) ) = gaux (1, nl(n) )
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gaux (2, nlm(n) ) = - gaux (2, nl(n) )
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enddo
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end if
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!
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! bring back to R-space, (\grad_ipol a)(r) ...
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!
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call cft3 (gaux, nr1, nr2, nr3, nrx1, nrx2, nrx3, 1)
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!
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! ...and add the factor 2\pi/a missing in the definition of G
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!
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call DAXPY (nrxx, tpiba, gaux, 2, ga (ipol, 1), 3)
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enddo
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deallocate (gaux)
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deallocate (aux)
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return
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end subroutine gradient
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!--------------------------------------------------------------------
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subroutine grad_dot (nrx1, nrx2, nrx3, nr1, nr2, nr3, nrxx, a, &
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ngm, g, nl, alat, da)
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!--------------------------------------------------------------------
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!
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! Calculates da = \sum_i \grad_i a_i in R-space
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use parameters
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use gvect, only: nlm
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use wvfct, only: gamma_only
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implicit none
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integer :: nrx1, nrx2, nrx3, nr1, nr2, nr3, nrxx, ngm, nl (ngm)
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real(kind=DP) :: a (3, nrxx), g (3, ngm), da (nrxx), alat
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integer :: n, ipol
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real(kind=DP), allocatable :: aux (:,:), gaux (:,:)
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real(kind=DP) :: tpi, tpiba
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parameter (tpi = 2.d0 * 3.14159265358979d0)
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allocate (aux( 2,nrxx))
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allocate (gaux(2,nrxx))
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gaux(:,:) = 0.d0
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do ipol = 1, 3
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!
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! copy a(ipol,r) to a complex array...
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!
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aux(2,:) = 0.d0
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call DCOPY (nrxx, a (ipol, 1), 3, aux, 2)
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!
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! bring a(ipol,r) to G-space, a(G) ...
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!
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call cft3 (aux, nr1, nr2, nr3, nrx1, nrx2, nrx3, - 1)
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!
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! multiply by (iG) to get (\grad_ipol a)(G) ...
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!
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do n = 1, ngm
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gaux (1, nl (n) ) = gaux (1, nl (n) ) - g (ipol, n) * aux (2,nl(n))
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gaux (2, nl (n) ) = gaux (2, nl (n) ) + g (ipol, n) * aux (1,nl(n))
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enddo
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enddo
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if (gamma_only) then
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do n = 1, ngm
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gaux (1, nlm(n) ) = gaux (1, nl (n) )
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gaux (2, nlm(n) ) = - gaux (2, nl (n) )
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enddo
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end if
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!
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! bring back to R-space, (\grad_ipol a)(r) ...
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!
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call cft3 (gaux, nr1, nr2, nr3, nrx1, nrx2, nrx3, 1)
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!
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! ...add the factor 2\pi/a missing in the definition of G and sum
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!
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tpiba = tpi / alat
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do n=1,nrxx
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da(n) = gaux(1,n)*tpiba
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end do
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!
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deallocate (gaux)
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deallocate (aux)
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return
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end subroutine grad_dot
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