mirror of
https://github.com/pfloos/quack
synced 2024-11-19 12:32:36 +01:00
132 lines
3.5 KiB
Fortran
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
|