2020-10-19 02:16:45 +08:00
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!
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2020-12-17 06:10:07 +08:00
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! Copyright (C) 2020 Quantum ESPRESSO 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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2020-10-19 02:16:45 +08:00
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!
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2020-12-17 06:10:07 +08:00
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!========================================================================
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! GGA POTENTIAL DERIVATIVE DRIVERS
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!========================================================================
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!
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!------------------------------------------------------------------------
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2020-10-19 02:16:45 +08:00
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MODULE qe_drivers_d_gga
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2020-12-17 06:10:07 +08:00
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!----------------------------------------------------------------------
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!! Module with QE driver routines that calculates the derivatives of XC
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!! potential.
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2020-10-19 02:16:45 +08:00
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!
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2020-12-17 06:10:07 +08:00
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USE kind_l, ONLY: DP
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USE dft_par_mod, ONLY: igcx, igcc, is_libxc
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2020-10-19 02:16:45 +08:00
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!
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IMPLICIT NONE
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!
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SAVE
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!
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PRIVATE
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!
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PUBLIC :: dgcxc_unpol, dgcxc_spin, d3gcxc
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!
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!
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CONTAINS
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2020-06-09 23:30:39 +08:00
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!---------------------------------------------------------------------------
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2020-10-19 02:16:45 +08:00
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SUBROUTINE dgcxc_unpol( length, r_in, s2_in, vrrx, vsrx, vssx, vrrc, vsrc, vssc )
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2020-06-09 23:30:39 +08:00
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!-------------------------------------------------------------------------
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!! This routine computes the derivative of the exchange and correlation
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2020-12-17 06:10:07 +08:00
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!! potentials of GGA family.
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2020-06-09 23:30:39 +08:00
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!
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2020-10-19 02:16:45 +08:00
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USE qe_drivers_gga, ONLY: gcxc
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2020-06-09 23:30:39 +08:00
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!
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IMPLICIT NONE
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!
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INTEGER, INTENT(IN) :: length
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2020-12-17 06:10:07 +08:00
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!! Number of k-points
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REAL(DP), INTENT(IN), DIMENSION(length) :: r_in
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!! Charge density
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REAL(DP), INTENT(IN), DIMENSION(length) :: s2_in
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!! Square modulus of the density gradient for each k-point
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REAL(DP), INTENT(OUT), DIMENSION(length) :: vrrx
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!! V1x term of the derivative
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REAL(DP), INTENT(OUT), DIMENSION(length) :: vsrx
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!! Cross term for exchange
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REAL(DP), INTENT(OUT), DIMENSION(length) :: vssx
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!! V2x term
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REAL(DP), INTENT(OUT), DIMENSION(length) :: vrrc
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!! V1c term
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REAL(DP), INTENT(OUT), DIMENSION(length) :: vsrc
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!! Cross term for correlation
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REAL(DP), INTENT(OUT), DIMENSION(length) :: vssc
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!! V2c term
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2020-06-09 23:30:39 +08:00
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!
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! ... local variables
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!
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INTEGER :: i1, i2, i3, i4, f1, f2, f3, f4
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INTEGER :: igcx_, igcc_
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2020-06-09 23:30:39 +08:00
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REAL(DP), DIMENSION(length) :: dr, s, ds
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REAL(DP), DIMENSION(4*length) :: raux, s2aux
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REAL(DP), ALLOCATABLE :: v1x(:), v2x(:), v1c(:), v2c(:)
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REAL(DP), ALLOCATABLE :: sx(:), sc(:)
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REAL(DP), PARAMETER :: small = 1.E-30_DP
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!
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ALLOCATE( v1x(4*length), v2x(4*length), sx(4*length) )
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ALLOCATE( v1c(4*length), v2c(4*length), sc(4*length) )
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!
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2020-10-23 22:21:08 +08:00
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igcx_=igcx
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igcc_=igcc
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IF (is_libxc(3)) igcx=0
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IF (is_libxc(4)) igcc=0
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!
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2020-06-09 23:30:39 +08:00
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i1 = 1 ; f1 = length !4 blocks: [ rho+dr , grho2 ]
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i2 = f1+1 ; f2 = 2*length ! [ rho-dr , grho2 ]
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i3 = f2+1 ; f3 = 3*length ! [ rho , (grho+ds)^2 ]
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i4 = f3+1 ; f4 = 4*length ! [ rho , (grho-ds)^2 ]
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!
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s = SQRT(s2_in)
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dr = MIN(1.d-4, 1.d-2*r_in)
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ds = MIN(1.d-4, 1.d-2*s)
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!
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raux(i1:f1) = r_in+dr ; s2aux(i1:f1) = s2_in
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raux(i2:f2) = r_in-dr ; s2aux(i2:f2) = s2_in
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raux(i3:f3) = r_in ; s2aux(i3:f3) = (s+ds)**2
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raux(i4:f4) = r_in ; s2aux(i4:f4) = (s-ds)**2
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!
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2020-10-19 02:16:45 +08:00
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CALL gcxc( length*4, raux, s2aux, sx, sc, v1x, v2x, v1c, v2c )
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2020-06-09 23:30:39 +08:00
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!
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! ... to avoid NaN in the next operations
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WHERE( r_in<=small .OR. s2_in<=small )
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dr = 1._DP ; ds = 1._DP ; s = 1._DP
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END WHERE
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!
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vrrx = 0.5_DP * (v1x(i1:f1) - v1x(i2:f2)) / dr
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vrrc = 0.5_DP * (v1c(i1:f1) - v1c(i2:f2)) / dr
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!
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vsrx = 0.25_DP * ((v2x(i1:f1) - v2x(i2:f2)) / dr + &
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(v1x(i3:f3) - v1x(i4:f4)) / ds / s)
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vsrc = 0.25_DP * ((v2c(i1:f1) - v2c(i2:f2)) / dr + &
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(v1c(i3:f3) - v1c(i4:f4)) / ds / s)
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!
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vssx = 0.5_DP * (v2x(i3:f3) - v2x(i4:f4)) / ds / s
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vssc = 0.5_DP * (v2c(i3:f3) - v2c(i4:f4)) / ds / s
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!
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DEALLOCATE( v1x, v2x, sx )
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DEALLOCATE( v1c, v2c, sc )
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!
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2020-10-23 22:21:08 +08:00
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IF (is_libxc(3)) igcx=igcx_
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IF (is_libxc(4)) igcc=igcc_
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!
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2020-06-09 23:30:39 +08:00
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RETURN
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!
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2020-10-19 02:16:45 +08:00
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END SUBROUTINE dgcxc_unpol
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2020-06-09 23:30:39 +08:00
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!
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2020-06-10 00:20:03 +08:00
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!
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!--------------------------------------------------------------------------
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2020-10-19 02:16:45 +08:00
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SUBROUTINE dgcxc_spin( length, r_in, g_in, vrrx, vrsx, vssx, vrrc, vrsc, &
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2020-06-10 00:20:03 +08:00
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vssc, vrzc )
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!------------------------------------------------------------------------
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!! This routine computes the derivative of the exchange and correlation
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!! potentials in the spin-polarized case.
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!
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2020-10-19 02:16:45 +08:00
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USE qe_drivers_gga, ONLY: gcx_spin, gcc_spin
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2020-06-10 00:20:03 +08:00
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!
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IMPLICIT NONE
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!
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INTEGER, INTENT(IN) :: length
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2020-12-17 06:10:07 +08:00
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!! Number of k-points
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2020-06-10 00:20:03 +08:00
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REAL(DP), INTENT(IN), DIMENSION(length,2) :: r_in
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2020-12-17 06:10:07 +08:00
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!! Charge density up and down
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2020-06-10 00:20:03 +08:00
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REAL(DP), INTENT(IN), DIMENSION(length,3,2) :: g_in
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2020-12-17 06:10:07 +08:00
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!! Gradient of the charge density up and down
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REAL(DP), INTENT(OUT), DIMENSION(length,2) :: vrrx
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!! V1x term of the derivative
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REAL(DP), INTENT(OUT), DIMENSION(length,2) :: vrsx
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!! Cross term for exchange
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REAL(DP), INTENT(OUT), DIMENSION(length,2) :: vssx
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!! V2x term of the derivative
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REAL(DP), INTENT(OUT), DIMENSION(length,2) :: vrrc
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!! V1c term of the derivative
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REAL(DP), INTENT(OUT), DIMENSION(length,2) :: vrsc
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!! Cross term for correlation
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REAL(DP), INTENT(OUT), DIMENSION(length,2) :: vrzc
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!! Derivative of V1c with respect to zeta
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2020-06-10 00:20:03 +08:00
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REAL(DP), INTENT(OUT), DIMENSION(length) :: vssc
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2020-12-17 06:10:07 +08:00
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!! V2c term of the derivative
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2020-06-10 00:20:03 +08:00
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!
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! ... local variables
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!
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INTEGER :: i1, i2, i3, i4, i5, i6, i7, i8
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INTEGER :: f1, f2, f3, f4, f5, f6, f7, f8
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! block delimiters
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2020-10-23 22:21:08 +08:00
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INTEGER :: igcx_, igcc_
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2020-06-10 00:20:03 +08:00
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REAL(DP), DIMENSION(length,2) :: r, s, s2
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REAL(DP), DIMENSION(length,2) :: drup, drdw, dsup, dsdw
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REAL(DP), ALLOCATABLE :: sx(:), v1x(:,:), v2x(:,:)
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REAL(DP), ALLOCATABLE :: sc(:), v1c(:,:), v2c(:)
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REAL(DP), DIMENSION(length) :: rt, zeta, st, s2t
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REAL(DP), DIMENSION(length) :: dr, ds, dz
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REAL(DP), DIMENSION(length,2) :: null_v
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! used to set output values to zero when input values
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! are too small (e.g. rho<eps)
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!
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REAL(DP), ALLOCATABLE :: raux(:,:), s2aux(:,:)
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REAL(DP), ALLOCATABLE :: rtaux(:), s2taux(:), zetaux(:)
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! auxiliary arrays for gcx- and gcc- routines input
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!
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REAL(DP), PARAMETER :: eps = 1.D-6
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REAL(DP), PARAMETER :: rho_trash = 0.4_DP, zeta_trash = 0.2_DP, &
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s2_trash = 0.1_DP
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!
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2020-10-23 22:21:08 +08:00
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igcx_=igcx
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igcc_=igcc
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IF (is_libxc(3)) igcx=0
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IF (is_libxc(4)) igcc=0
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!
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2020-06-10 00:20:03 +08:00
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vrrx = 0.0_DP ; vrsx = 0.0_DP ; vssx = 0.0_DP
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vrrc = 0.0_DP ; vrsc = 0.0_DP ; vrzc = 0.0_DP
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vssc = 0.0_DP
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!
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! ... EXCHANGE
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!
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i1 = 1 ; f1 = length !8 blocks(x2): [ rho+drup , grho2 ]
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i2 = f1+1 ; f2 = 2*length ! [ rho-drup , grho2 ]
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i3 = f2+1 ; f3 = 3*length ! [ rho , (grho+dsup)^2 ]
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i4 = f3+1 ; f4 = 4*length ! [ rho , (grho-dsup)^2 ]
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i5 = f4+1 ; f5 = 5*length ! [ rho+drdw , grho2 ]
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i6 = f5+1 ; f6 = 6*length ! [ rho-drdw , grho2 ]
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i7 = f6+1 ; f7 = 7*length ! [ rho , (grho+dsdw)^2 ]
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i8 = f7+1 ; f8 = 8*length ! [ rho , (grho-dsdw)^2 ]
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!
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ALLOCATE( raux(length*8,2), s2aux(length*8,2) )
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ALLOCATE( sx(length*8), v1x(length*8,2), v2x(length*8,2) )
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!
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s2(:,1) = g_in(:,1,1)**2 + g_in(:,2,1)**2 + g_in(:,3,1)**2 !up
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s2(:,2) = g_in(:,1,2)**2 + g_in(:,2,2)**2 + g_in(:,3,2)**2 !down
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s = SQRT(s2)
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r = r_in
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!
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null_v = 1.0_DP
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!
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! ... thresholds
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WHERE ( r_in(:,1)<=eps .OR. s(:,1)<=eps )
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r(:,1) = rho_trash
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s2(:,1) = s2_trash ; s(:,1) = SQRT(s2_trash)
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null_v(:,1) = 0.0_DP
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END WHERE
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!
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WHERE ( r_in(:,2)<=eps .OR. s(:,2)<=eps )
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r(:,2) = rho_trash
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s2(:,2) = s2_trash ; s(:,2) = SQRT(s2_trash)
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null_v(:,2) = 0.0_DP
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END WHERE
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!
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drup = 0.0_DP ; drdw = 0.0_DP
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dsup = 0.0_DP ; dsdw = 0.0_DP
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!
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drup(:,1) = MIN(1.D-4, 1.D-2*r(:,1)) ; dsup(:,1) = MIN(1.D-4, 1.D-2*s(:,1))
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drdw(:,2) = MIN(1.D-4, 1.D-2*r(:,2)) ; dsdw(:,2) = MIN(1.D-4, 1.D-2*s(:,2))
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!
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! ... up
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raux(i1:f1,:) = r+drup ; s2aux(i1:f1,:) = s2
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raux(i2:f2,:) = r-drup ; s2aux(i2:f2,:) = s2
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raux(i3:f3,:) = r ; s2aux(i3:f3,:) = (s+dsup)**2
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raux(i4:f4,:) = r ; s2aux(i4:f4,:) = (s-dsup)**2
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! ... down
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raux(i5:f5,:) = r+drdw ; s2aux(i5:f5,:) = s2
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raux(i6:f6,:) = r-drdw ; s2aux(i6:f6,:) = s2
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raux(i7:f7,:) = r ; s2aux(i7:f7,:) = (s+dsdw)**2
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raux(i8:f8,:) = r ; s2aux(i8:f8,:) = (s-dsdw)**2
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!
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!
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2020-10-19 02:16:45 +08:00
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CALL gcx_spin( length*8, raux, s2aux, sx, v1x, v2x )
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2020-06-10 00:20:03 +08:00
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!
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! ... up
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vrrx(:,1) = 0.5_DP * (v1x(i1:f1,1) - v1x(i2:f2,1)) / drup(:,1)
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vrsx(:,1) = 0.25_DP * ((v2x(i1:f1,1) - v2x(i2:f2,1)) / drup(:,1) + &
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(v1x(i3:f3,1) - v1x(i4:f4,1)) / dsup(:,1) / s(:,1))
|
|
|
|
|
vssx(:,1) = 0.5_DP * (v2x(i3:f3,1) - v2x(i4:f4,1)) / dsup(:,1) / s(:,1)
|
|
|
|
|
! ... down
|
|
|
|
|
vrrx(:,2) = 0.5_DP * (v1x(i5:f5,2) - v1x(i6:f6,2)) / drdw(:,2)
|
|
|
|
|
vrsx(:,2) = 0.25_DP * ((v2x(i5:f5,2) - v2x(i6:f6,2)) / drdw(:,2) + &
|
|
|
|
|
(v1x(i7:f7,2) - v1x(i8:f8,2)) / dsdw(:,2) / s(:,2))
|
|
|
|
|
vssx(:,2) = 0.5_DP * (v2x(i7:f7,2) - v2x(i8:f8,2)) / dsdw(:,2) / s(:,2)
|
|
|
|
|
!
|
|
|
|
|
vrrx(:,1) = vrrx(:,1)*null_v(:,1) ; vrrx(:,2) = vrrx(:,2)*null_v(:,2)
|
|
|
|
|
vrsx(:,1) = vrsx(:,1)*null_v(:,1) ; vrsx(:,2) = vrsx(:,2)*null_v(:,2)
|
|
|
|
|
vssx(:,1) = vssx(:,1)*null_v(:,1) ; vssx(:,2) = vssx(:,2)*null_v(:,2)
|
|
|
|
|
!
|
|
|
|
|
DEALLOCATE( raux, s2aux )
|
|
|
|
|
DEALLOCATE( sx, v1x, v2x )
|
|
|
|
|
!
|
|
|
|
|
! ... CORRELATION
|
|
|
|
|
!
|
|
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|
|
i1 = 1 ; f1 = length !6 blocks: [ rt+dr , s2t , zeta ]
|
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|
|
|
i2 = f1+1 ; f2 = 2*length ! [ rt-dr , s2t , zeta ]
|
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|
i3 = f2+1 ; f3 = 3*length ! [ rt , (st+ds)^2 , zeta ]
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|
|
i4 = f3+1 ; f4 = 4*length ! [ rt , (st-ds)^2 , zeta ]
|
|
|
|
|
i5 = f4+1 ; f5 = 5*length ! [ rt , grho2 , zeta+dz ]
|
|
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|
|
i6 = f5+1 ; f6 = 6*length ! [ rt , grho2 , zeta-dz ]
|
|
|
|
|
!
|
|
|
|
|
ALLOCATE( rtaux(length*6), s2taux(length*6), zetaux(length*6) )
|
|
|
|
|
ALLOCATE( v1c(length*6,2), v2c(length*6), sc(length*6) )
|
|
|
|
|
!
|
|
|
|
|
rt(:) = r_in(:,1) + r_in(:,2)
|
|
|
|
|
!
|
|
|
|
|
null_v = 1.0_DP
|
|
|
|
|
!
|
|
|
|
|
WHERE (rt > eps)
|
|
|
|
|
zeta = (r_in(:,1) - r_in(:,2)) / rt(:)
|
|
|
|
|
ELSEWHERE
|
|
|
|
|
zeta = zeta_trash
|
|
|
|
|
null_v(:,1) = 0.0_DP
|
|
|
|
|
END WHERE
|
|
|
|
|
!
|
|
|
|
|
s2t = (g_in(:,1,1) + g_in(:,1,2))**2 + &
|
|
|
|
|
(g_in(:,2,1) + g_in(:,2,2))**2 + &
|
|
|
|
|
(g_in(:,3,1) + g_in(:,3,2))**2
|
|
|
|
|
st = SQRT(s2t)
|
|
|
|
|
!
|
|
|
|
|
WHERE (rt<eps .OR. ABS(zeta)>1._DP .OR. st<eps)
|
|
|
|
|
rt(:) = rho_trash
|
|
|
|
|
s2t(:) = s2_trash ; st = SQRT(s2_trash)
|
|
|
|
|
zeta(:) = zeta_trash
|
|
|
|
|
null_v(:,1) = 0.0_DP
|
|
|
|
|
END WHERE
|
|
|
|
|
!
|
|
|
|
|
dr = MIN(1.D-4, 1.D-2 * rt)
|
|
|
|
|
ds = MIN(1.D-4, 1.D-2 * st)
|
|
|
|
|
!dz = MIN(1.D-4, 1.D-2 * ABS(zeta) )
|
|
|
|
|
dz = 1.D-6
|
|
|
|
|
!
|
|
|
|
|
! ... If zeta is too close to +-1 the derivative is evaluated at a
|
|
|
|
|
! slightly smaller value.
|
|
|
|
|
zeta = SIGN( MIN(ABS(zeta), (1.0_DP - 2.0_DP*dz)), zeta )
|
|
|
|
|
!
|
|
|
|
|
rtaux(i1:f1) = rt+dr ; s2taux(i1:f1) = s2t ; zetaux(i1:f1) = zeta
|
|
|
|
|
rtaux(i2:f2) = rt-dr ; s2taux(i2:f2) = s2t ; zetaux(i2:f2) = zeta
|
|
|
|
|
rtaux(i3:f3) = rt ; s2taux(i3:f3) = (st+ds)**2 ; zetaux(i3:f3) = zeta
|
|
|
|
|
rtaux(i4:f4) = rt ; s2taux(i4:f4) = (st-ds)**2 ; zetaux(i4:f4) = zeta
|
|
|
|
|
rtaux(i5:f5) = rt ; s2taux(i5:f5) = s2t ; zetaux(i5:f5) = zeta+dz
|
|
|
|
|
rtaux(i6:f6) = rt ; s2taux(i6:f6) = s2t ; zetaux(i6:f6) = zeta-dz
|
|
|
|
|
!
|
2020-10-19 02:16:45 +08:00
|
|
|
CALL gcc_spin( length*6, rtaux, zetaux, s2taux, sc, v1c, v2c )
|
2020-06-10 00:20:03 +08:00
|
|
|
!
|
|
|
|
|
vrrc(:,1) = 0.5_DP * (v1c(i1:f1,1) - v1c(i2:f2,1)) / dr * null_v(:,1)
|
|
|
|
|
vrrc(:,2) = 0.5_DP * (v1c(i1:f1,2) - v1c(i2:f2,2)) / dr * null_v(:,1)
|
|
|
|
|
vrsc(:,1) = 0.5_DP * (v1c(i3:f3,1) - v1c(i4:f4,1)) / ds/st * null_v(:,1)
|
|
|
|
|
vrsc(:,2) = 0.5_DP * (v1c(i3:f3,2) - v1c(i4:f4,2)) / ds/st * null_v(:,1)
|
|
|
|
|
vssc(:) = 0.5_DP * (v2c(i3:f3) - v2c(i4:f4) ) / ds/st * null_v(:,1)
|
|
|
|
|
vrzc(:,1) = 0.5_DP * (v1c(i5:f5,1) - v1c(i6:f6,1)) / dz * null_v(:,1)
|
|
|
|
|
vrzc(:,2) = 0.5_DP * (v1c(i5:f5,2) - v1c(i6:f6,2)) / dz * null_v(:,1)
|
|
|
|
|
!
|
2020-10-23 22:21:08 +08:00
|
|
|
IF (is_libxc(3)) igcx=igcx_
|
|
|
|
|
IF (is_libxc(4)) igcc=igcc_
|
|
|
|
|
!
|
2020-06-10 00:20:03 +08:00
|
|
|
RETURN
|
|
|
|
|
!
|
2020-10-19 02:16:45 +08:00
|
|
|
END SUBROUTINE dgcxc_spin
|
2020-06-10 00:20:03 +08:00
|
|
|
!
|
|
|
|
|
!
|
|
|
|
|
!-----------------------------------------------------------------------
|
2020-10-19 02:16:45 +08:00
|
|
|
SUBROUTINE d3gcxc( r, s2, vrrrx, vsrrx, vssrx, vsssx, &
|
2020-06-10 00:20:03 +08:00
|
|
|
vrrrc, vsrrc, vssrc, vsssc )
|
|
|
|
|
!-----------------------------------------------------------------------
|
2020-12-17 06:10:07 +08:00
|
|
|
! wat20101006:
|
|
|
|
|
!! Calculates all derivatives of the exchange (x) and correlation (c)
|
|
|
|
|
!! potential in third order of the Exc.
|
2020-06-10 00:20:03 +08:00
|
|
|
!
|
|
|
|
|
! input: r = rho, s2=|\nabla rho|^2
|
|
|
|
|
! definition: E_xc = \int ( f_x(r,s2) + f_c(r,s2) ) dr
|
|
|
|
|
! output: vrrrx = d^3(f_x)/d(r)^3
|
|
|
|
|
! vsrrx = d^3(f_x)/d(|\nabla r|)d(r)^2 / |\nabla r|
|
|
|
|
|
! vssrx = d/d(|\nabla r|) [ &
|
|
|
|
|
! d^2(f_x)/d(|\nabla r|)d(r) / |\nabla r| ] &
|
|
|
|
|
! / |\nabla r|
|
|
|
|
|
! vsssx = d/d(|\nabla r|) [ &
|
|
|
|
|
! d/d(|\nabla r|) [ &
|
|
|
|
|
! d(f_x)/d(|\nabla r|) / |\nabla r| ] &
|
|
|
|
|
! / |\nabla r| ] &
|
|
|
|
|
! / |\nabla r|
|
|
|
|
|
! same for (c)
|
|
|
|
|
!
|
|
|
|
|
IMPLICIT NONE
|
|
|
|
|
!
|
|
|
|
|
REAL(DP) :: r, s2
|
|
|
|
|
REAL(DP) :: vrrrx, vsrrx, vssrx, vsssx, vrrrc, vsrrc, vssrc, vsssc
|
|
|
|
|
!
|
|
|
|
|
! ... local variables
|
|
|
|
|
!
|
|
|
|
|
REAL(DP) :: dr, s, ds
|
|
|
|
|
REAL(DP), DIMENSION(4) :: raux, s2aux
|
|
|
|
|
REAL(DP), DIMENSION(4) :: vrrx_rs, vsrx_rs, vssx_rs, vrrc_rs, &
|
|
|
|
|
vsrc_rs, vssc_rs
|
|
|
|
|
!
|
|
|
|
|
s = SQRT(s2)
|
|
|
|
|
dr = MIN(1.d-4, 1.d-2 * r)
|
|
|
|
|
ds = MIN(1.d-4, 1.d-2 * s)
|
|
|
|
|
!
|
|
|
|
|
raux(1) = r+dr ; s2aux(1) = s2 !4 blocks: [ rho+dr , grho2 ]
|
|
|
|
|
raux(2) = r-dr ; s2aux(2) = s2 ! [ rho-dr , grho2 ]
|
|
|
|
|
raux(3) = r ; s2aux(3) = (s+ds)**2 ! [ rho , (grho+ds)^2 ]
|
|
|
|
|
raux(4) = r ; s2aux(4) = (s-ds)**2 ! [ rho , (grho-ds)^2 ]
|
|
|
|
|
!
|
2020-10-19 02:16:45 +08:00
|
|
|
CALL dgcxc_unpol( 4, raux, s2aux, vrrx_rs, vsrx_rs, vssx_rs, vrrc_rs, vsrc_rs, vssc_rs )
|
2020-06-10 00:20:03 +08:00
|
|
|
!
|
|
|
|
|
vrrrx = 0.5d0 * (vrrx_rs(1) - vrrx_rs(2)) / dr
|
|
|
|
|
vsrrx = 0.25d0 * ((vsrx_rs(1) - vsrx_rs(2)) / dr &
|
|
|
|
|
+(vrrx_rs(3) - vrrx_rs(4)) / ds / s)
|
|
|
|
|
vssrx = 0.25d0 * ((vssx_rs(1) - vssx_rs(2)) / dr &
|
|
|
|
|
+(vsrx_rs(3) - vsrx_rs(4)) / ds / s)
|
|
|
|
|
vsssx = 0.5d0 * (vssx_rs(3) - vssx_rs(4)) / ds / s
|
|
|
|
|
!
|
|
|
|
|
vrrrc = 0.5d0 * (vrrc_rs(1) - vrrc_rs(2)) / dr
|
|
|
|
|
vsrrc = 0.25d0 * ((vsrc_rs(1) - vsrc_rs(2)) / dr &
|
|
|
|
|
+(vrrc_rs(3) - vrrc_rs(4)) / ds / s)
|
|
|
|
|
vssrc = 0.25d0 * ((vssc_rs(1) - vssc_rs(2)) / dr &
|
|
|
|
|
+(vsrc_rs(3) - vsrc_rs(4)) / ds / s)
|
|
|
|
|
vsssc = 0.5d0 * (vssc_rs(3) - vssc_rs(4)) / ds / s
|
|
|
|
|
!
|
|
|
|
|
RETURN
|
|
|
|
|
!
|
2020-10-19 02:16:45 +08:00
|
|
|
END SUBROUTINE d3gcxc
|
|
|
|
|
!
|
|
|
|
|
END MODULE qe_drivers_d_gga
|
2020-06-10 00:20:03 +08:00
|
|
|
|
