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quack/src/eDFT/UC16_lda_correlation_potential.f90
2020-07-02 14:27:38 +02:00

132 lines
3.5 KiB
Fortran

subroutine UC16_lda_correlation_potential(nGrid,weight,nBas,AO,rho,Fc)
! Compute unrestricted LDA correlation potential
implicit none
include 'parameters.h'
! Input variables
integer,intent(in) :: nGrid
double precision,intent(in) :: weight(nGrid)
integer,intent(in) :: nBas
double precision,intent(in) :: AO(nBas,nGrid)
double precision,intent(in) :: rho(nGrid,nspin)
! Local variables
integer :: mu,nu,iG
double precision :: ra,rb,r,rs
double precision :: a_p,b_p,ec_p,decdrs_p,decdra_p,decdrb_p
double precision :: a_f,b_f,ec_f,decdrs_f,decdra_f,decdrb_f
double precision :: ec_z,decdra_z,decdrb_z
double precision :: z,dzdra,dzdrb,fz,dfzdz,dfzdra,dfzdrb
double precision :: drsdra,drsdrb,dFcdra,dFcdrb
! Output variables
double precision,intent(out) :: Fc(nBas,nBas,nspin)
! Coefficients for Chachiyo's LDA correlation
a_p = (log(2d0) - 1d0)/(2d0*pi**2)
b_p = 20.4562557d0
a_f = (log(2d0) - 1d0)/(4d0*pi**2)
b_f = 27.4203609d0
! Compute LDA correlation matrix in the AO basis
Fc(:,:,:) = 0d0
do mu=1,nBas
do nu=1,nBas
do iG=1,nGrid
! Spin-up and spin-down densities
ra = max(0d0,rho(iG,1))
rb = max(0d0,rho(iG,2))
! Total density
r = ra + rb
! Spin-up part contribution
if(ra > threshold) then
rs = (4d0*pi*r/3d0)**(-1d0/3d0)
ec_p = a_p*log(1d0 + b_p/rs + b_p/rs**2)
ec_f = a_f*log(1d0 + b_f/rs + b_f/rs**2)
z = (ra-rb)/r
fz = (1d0 + z)**(4d0/3d0) + (1d0 - z)**(4d0/3d0) - 2d0
fz = fz/(2d0*(2d0**(1d0/3d0) - 1d0))
ec_z = ec_p + (ec_f - ec_p)*fz
dzdra = (1d0 - z)/r
dfzdz = (4d0/3d0)*((1d0 + z)**(1d0/3d0) - (1d0 - z)**(1d0/3d0))/(2d0*(2d0**(1d0/3d0) - 1d0))
dfzdra = dzdra*dfzdz
drsdra = - (36d0*pi)**(-1d0/3d0)*r**(-4d0/3d0)
decdrs_p = - a_p/rs**2*(b_p + 2d0*b_p/rs)/(1d0 + b_p/rs + b_p/rs**2)
decdrs_f = - a_f/rs**2*(b_f + 2d0*b_f/rs)/(1d0 + b_f/rs + b_f/rs**2)
decdra_p = drsdra*decdrs_p
decdra_f = drsdra*decdrs_f
decdra_z = decdra_p + (decdra_f - decdra_p)*fz + (ec_f - ec_p)*dfzdra
dFcdra = decdra_z*r + ec_z
Fc(mu,nu,1) = Fc(mu,nu,1) + weight(iG)*AO(mu,iG)*AO(nu,iG)*dFcdra
endif
! Spin-down part contribution
if(rb > threshold) then
rs = (4d0*pi*r/3d0)**(-1d0/3d0)
ec_p = a_p*log(1d0 + b_p/rs + b_p/rs**2)
ec_f = a_f*log(1d0 + b_f/rs + b_f/rs**2)
z = (ra-rb)/r
fz = (1d0 + z)**(4d0/3d0) + (1d0 - z)**(4d0/3d0) - 2d0
fz = fz/(2d0*(2d0**(1d0/3d0) - 1d0))
ec_z = ec_p + (ec_f - ec_p)*fz
dzdrb = - (1d0 + z)/r
dfzdz = (4d0/3d0)*((1d0 + z)**(1d0/3d0) - (1d0 - z)**(1d0/3d0))/(2d0*(2d0**(1d0/3d0) - 1d0))
dfzdrb = dzdrb*dfzdz
drsdrb = - (36d0*pi)**(-1d0/3d0)*r**(-4d0/3d0)
decdrs_p = - a_p/rs**2*(b_p + 2d0*b_p/rs)/(1d0 + b_p/rs + b_p/rs**2)
decdrs_f = - a_f/rs**2*(b_f + 2d0*b_f/rs)/(1d0 + b_f/rs + b_f/rs**2)
decdrb_p = drsdrb*decdrs_p
decdrb_f = drsdrb*decdrs_f
decdrb_z = decdrb_p + (decdrb_f - decdrb_p)*fz + (ec_f - ec_p)*dfzdrb
dFcdrb = decdrb_z*r + ec_z
Fc(mu,nu,2) = Fc(mu,nu,2) + weight(iG)*AO(mu,iG)*AO(nu,iG)*dFcdrb
endif
enddo
enddo
enddo
end subroutine UC16_lda_correlation_potential