mirror of https://gitlab.com/QEF/q-e.git
127 lines
3.6 KiB
Fortran
127 lines
3.6 KiB
Fortran
!
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! Copyright (C) 2003 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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function dmxc (rho)
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!-----------------------------------------------------------------------
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!
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! derivative of the xc potential with respect to the local density
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!
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USE kinds, only : DP
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use funct
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implicit none
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! I/O variables
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real(kind=DP) :: rho, dmxc
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! input: the charge density ( positive )
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! output: the derivative of the xc potential
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real(kind=DP) :: dr, vxp, vcp, vxm, vcm, ex, ec
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! delta rrho for numerical derivatives
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! the potentials for + charge
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! the potentials for - charge
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! the energy
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! DFT functional
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! auxiliary variables
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real(kind=DP) :: vx, rs, dpz
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integer :: iflg
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! parameters
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real(kind=DP) :: small, e2, pi34, third
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parameter (small = 1.d-30, e2 = 2.d0)
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parameter (pi34 = 0.75d0 / 3.141592653589793d+00, third = 1.d0 / &
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3.d0)
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dmxc = 0.d0
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if (rho.le.small) then
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return
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endif
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!
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! first case: analytical derivatives available
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!
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if (iexch.eq.1.and.icorr.eq.1) then
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rs = (pi34 / rho) **third
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!..exchange
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call slater (rs, ex, vx)
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dmxc = vx / (3.d0 * rho)
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!..correlation
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iflg = 2
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if (rs.lt.1.0d0) iflg = 1
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dmxc = dmxc + dpz (rs, iflg)
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else
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!
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! second case: numerical derivatives
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!
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dr = min (1.d-6, 1.d-4 * rho)
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call xc (rho + dr, ex, ec, vxp, vcp)
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call xc (rho - dr, ex, ec, vxm, vcm)
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dmxc = (vxp + vcp - vxm - vcm) / (2.d0 * dr)
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endif
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!
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! scales to rydberg units
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!
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dmxc = e2 * dmxc
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return
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end function dmxc
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!-----------------------------------------------------------------------
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function dpz (rs, iflg)
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!-----------------------------------------------------------------------
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! derivative of the correlation potential with respect to the local den
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! Perdew and Zunger parameterization of the C.A. functional
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!
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USE kinds, only : DP
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implicit none
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real(kind=DP) :: rs, dpz
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! input : the value of rs
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! output: the derivative of the corr. poten
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integer :: iflg
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! input : flag to choose the functional for
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real(kind=DP) :: b1, b2, a1, a2, gc, a, b, c, d, pi, fpi
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!\
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! \
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! \
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! \
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! parameter which define the functional
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!
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!
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!
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! /
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! /
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!/
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parameter (a = 0.0311d0, b = - 0.048d0, c = 0.0020d0, d = - &
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0.0116d0, gc = - 0.1423d0, b1 = 1.0529d0, b2 = 0.3334d0, a1 = &
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7.0d0 * b1 / 6.d0, a2 = 4.d0 * b2 / 3.d0, pi = 3.14159265358979d0, &
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fpi = 4.d0 * pi)
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real(kind=DP) :: x, den, dmx, dmrs
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! auxiliary variable
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! auxiliary variable
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! auxiliary variable
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! auxiliary variable
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if (iflg.eq.1) then
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dmrs = a / rs + 2.d0 / 3.d0 * c * (log (rs) + 1.d0) + (2.d0 * &
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d-c) / 3.d0
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else
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x = sqrt (rs)
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den = 1.d0 + x * (b1 + x * b2)
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dmx = gc * ( (a1 + 2.d0 * a2 * x) * den - 2.d0 * (b1 + 2.d0 * &
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b2 * x) * (1.d0 + x * (a1 + x * a2) ) ) / den**3
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dmrs = 0.5d0 * dmx / x
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endif
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!
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dpz = - fpi * rs**4.d0 / 9.d0 * dmrs
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return
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end function dpz
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