mirror of https://gitlab.com/QEF/q-e.git
65 lines
2.1 KiB
Fortran
65 lines
2.1 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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!-----------------------------------------------------------------------
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function d2mxc (rho)
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!-----------------------------------------------------------------------
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!
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! second derivative of the xc potential with respect to the local densi
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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) :: rho, d2mxc
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! input: the charge density ( positive )
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! output: the second derivative of the xc potent
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real (kind = dp) :: b1, b2, gc, a, b, c, d, pi, thofpi_3, fpioth_3, &
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thopi_3, tm1, tm2, tm3, tm4, tm5, tm6
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! _ parameters defining the functionals
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! /
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! pi
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! (3/4/pi)^0.333
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! (4*pi/3)^0.333
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! (3/pi)^0.333
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! 35.d0*b1,
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! 76.d0*b1*b1 + 64.d0*b2
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! 35.d0*b1*b1*b1 + 234.d0*b1*b2
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! 140.d0*b2*b1*b1 + 176.d0*b2*b2
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! 175.d0*b1*b2*b2
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! 64.d0*b2*b2*b2
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parameter (b1 = 1.0529d0, b2 = 0.3334d0, gc = - 0.1423d0, a = &
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0.0311d0, b = - 0.0480d0, c = 0.0020d0, d = - 0.0116d0, pi = &
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3.14159265358979d0, fpioth_3 = 1.61199195401647d0, thofpi_3 = &
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0.620350490899400d0, thopi_3 = 0.98474502184270d0, tm1 = &
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36.85150d0, tm2 = 105.59107916d0, tm3 = 122.996139546115d0, tm4 = &
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71.30831794516d0, tm5 = 20.4812455967d0, tm6 = 2.371792877056d0)
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real (kind = dp) :: rs, x, den
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rs = thofpi_3 * (1.d0 / rho) **0.3333333333333333d0
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if (rs.ge.1.d0) then
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x = sqrt (rs)
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den = 1.d0 + x * b1 + b2 * x**2
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d2mxc = - gc * (tm1 * x + tm2 * x**2 + tm3 * x**3 + tm4 * x**4 &
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+ tm5 * x**5 + tm6 * x**6) / ( (rho**2) * (den**4) * 216.d0)
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else
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d2mxc = (9.d0 * a + (6.d0 * c + 8.d0 * d) * rs + 8.d0 * c * rs &
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* log (rs) ) / (rho**2) / 27.d0
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endif
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rs = rs * fpioth_3
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d2mxc = d2mxc + (2.d0 / 9.d0 * thopi_3 * rs**5)
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d2mxc = 2.d0 * d2mxc
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return
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end function d2mxc
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