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QuAcK/src/eDFT/RGIC_lda_exchange_derivative_discontinuity.f90

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subroutine RGIC_lda_exchange_derivative_discontinuity(nEns,wEns,nGrid,weight,rhow,ExDD)
! Compute the restricted version of the GIC exchange individual energy
implicit none
include 'parameters.h'
! Input variables
integer,intent(in) :: nEns
double precision,intent(in) :: wEns(nEns)
integer,intent(in) :: nGrid
double precision,intent(in) :: weight(nGrid)
double precision,intent(in) :: rhow(nGrid)
! Local variables
integer :: iEns,jEns
integer :: iG
double precision :: r
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double precision,allocatable :: dExdw(:)
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double precision,external :: Kronecker_delta
double precision :: a,b,c,w
double precision :: dCxGICdw
! Output variables
double precision,intent(out) :: ExDD(nEns)
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! Memory allocation
allocate(dExdw(nEns))
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! Weight-dependent Cx coefficient for RMFL20 exchange functional
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! Parameters for H2 at equilibrium
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a = + 0.5739189000851961d0
b = - 0.0003469882157336496d0
c = - 0.2676338054343272d0
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! Parameters for stretch H2
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! a = + 0.01918229168254928d0
! b = - 0.01545313842512261d0
! c = - 0.012720073519142448d0
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! Parameters for He
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! a = 1.9015719148496788d0
! b = 2.5236598782764412d0
! c = 1.6652282199359842d0
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w = 0.5d0*wEns(2) + wEns(3)
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dCxGICdw = (0.5d0*b + (2d0*a + 0.5d0*c)*(w - 0.5d0) - (1d0 - w)*w*(3d0*b + 4d0*c*(w - 0.5d0)))
dCxGICdw = CxLDA*dCxGICdw
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dExdw(:) = 0d0
do iG=1,nGrid
r = max(0d0,rhow(iG))
if(r > threshold) then
dExdw(1) = 0d0
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dExdw(2) = dExdw(2) + 0.5d0*weight(iG)*dCxGICdw*r**(4d0/3d0)
dExdw(3) = dExdw(3) + 1.0d0*weight(iG)*dCxGICdw*r**(4d0/3d0)
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end if
end do
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ExDD(:) = 0d0
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do iEns=1,nEns
do jEns=2,nEns
ExDD(iEns) = ExDD(iEns) + (Kronecker_delta(iEns,jEns) - wEns(jEns))*dExdw(jEns)
end do
end do
end subroutine RGIC_lda_exchange_derivative_discontinuity