mirror of https://gitlab.com/QEF/q-e.git
95 lines
2.5 KiB
Fortran
95 lines
2.5 KiB
Fortran
!
|
|
! Copyright (C) 2001 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 .
|
|
!
|
|
!-----------------------------------------------------------------------
|
|
function w1gauss (x, n)
|
|
!-----------------------------------------------------------------------
|
|
!
|
|
! w1gauss(x,n) = \int_{-\infty}^x y delta(y) dy
|
|
! where delta(x) is the current approximation for the delta function,
|
|
! as obtained from w0gauss(x,n)
|
|
!
|
|
! --> (n>=0) : Methfessel-Paxton case
|
|
!
|
|
! --> (n=-1): Cold smearing (Marzari-Vanderbilt-DeVita-Payne)
|
|
! w1gauss = 1/sqrt(2*pi)*(x-1/sqrt(2))*exp(-(x-1/sqrt(2))**2)
|
|
!
|
|
! --> (n=-99): Fermi-Dirac case. In this case w1gauss corresponds
|
|
! to the negative of the electronic entropy.
|
|
!
|
|
!
|
|
USE kinds, ONLY : DP
|
|
USE constants, ONLY : pi
|
|
implicit none
|
|
real(DP) :: w1gauss, x
|
|
! output: the value of the function
|
|
! input: the point where to compute the function
|
|
|
|
integer :: n
|
|
! input: the order of the smearing function
|
|
!
|
|
! here the local variables
|
|
!
|
|
|
|
real(DP) :: a, hp, arg, hpm1, hd, f, onemf, xp
|
|
! the coefficients a_n
|
|
! the hermite function
|
|
! the argument of the exponential
|
|
! the hermite function
|
|
! the hermite function
|
|
! Fermi-Dirac occupation number
|
|
! 1 - f
|
|
! auxiliary variable (cold smearing)
|
|
|
|
integer :: i, ni
|
|
! counter on n values
|
|
! counter on 2n values
|
|
|
|
! Fermi-Dirac smearing
|
|
if (n.eq. - 99) then
|
|
if (abs (x) .le.36.0) then
|
|
f = 1.0d0 / (1.0d0 + exp ( - x) )
|
|
onemf = 1.0d0 - f
|
|
w1gauss = f * log (f) + onemf * log (onemf)
|
|
! in order to avoid problems for large values of x
|
|
else
|
|
! neglect w1gauss when abs(w1gauss) < 1.0d-14
|
|
w1gauss = 0.0d0
|
|
endif
|
|
return
|
|
|
|
endif
|
|
! Cold smearing
|
|
if (n.eq. - 1) then
|
|
xp = x - 1.0d0 / sqrt (2.0d0)
|
|
arg = min (200.d0, xp**2)
|
|
w1gauss = 1.0d0 / sqrt (2.0d0 * pi) * xp * exp ( - arg)
|
|
return
|
|
|
|
endif
|
|
! Methfessel-Paxton
|
|
arg = min (200.d0, x**2)
|
|
w1gauss = - 0.5d0 * exp ( - arg) / sqrt (pi)
|
|
if (n.eq.0) return
|
|
hd = 0.d0
|
|
hp = exp ( - arg)
|
|
ni = 0
|
|
a = 1.d0 / sqrt (pi)
|
|
do i = 1, n
|
|
hd = 2.0d0 * x * hp - 2.0d0 * DBLE (ni) * hd
|
|
ni = ni + 1
|
|
hpm1 = hp
|
|
hp = 2.0d0 * x * hd-2.0d0 * DBLE (ni) * hp
|
|
ni = ni + 1
|
|
a = - a / (DBLE (i) * 4.0d0)
|
|
w1gauss = w1gauss - a * (0.5d0 * hp + DBLE (ni) * hpm1)
|
|
enddo
|
|
return
|
|
|
|
|
|
end function w1gauss
|