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quack/src/eDFT/ULYP_gga_correlation_potential.f90

158 lines
7.4 KiB
Fortran
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OK with GGA exchange functionals
2021-02-12 16:47:40 +01:00
subroutine ULYP_gga_correlation_potential(nGrid,weight,nBas,AO,dAO,rho,drho,Fc)
! Compute LYP 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) :: dAO(ncart,nBas,nGrid)
double precision,intent(in) :: rho(nGrid,nspin)
double precision,intent(in) :: drho(ncart,nGrid,nspin)
! Local variables
integer :: mu,nu,iG
double precision :: vAO,gaAO,gbAO
double precision :: ra,rb,r
double precision :: ga,gab,gb,g
working on LYP potential
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double precision :: dfdra,dfdrb
potential for LYP done
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double precision :: dfdga,dfdgab,dfdgb
double precision :: dodra,dodrb,dddra,dddrb
OK with GGA exchange functionals
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double precision :: a,b,c,d
double precision :: Cf,omega,delta
! Output variables
working on LYP potential
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double precision,intent(out) :: Fc(nBas,nBas,nspin)
OK with GGA exchange functionals
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! Prameter of the functional
a = 0.04918d0
b = 0.132d0
c = 0.2533d0
d = 0.349d0
Cf = 3d0/10d0*(3d0*pi**2)**(2d0/3d0)
! Compute matrix elements in the AO basis
working on LYP potential
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Fc(:,:,:) = 0d0
OK with GGA exchange functionals
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do mu=1,nBas
do nu=1,nBas
do iG=1,nGrid
ra = max(0d0,rho(iG,1))
rb = max(0d0,rho(iG,2))
r = ra + rb
if(r > threshold) then
ga = drho(1,iG,1)**2 + drho(2,iG,1)**2 + drho(3,iG,1)**2
gb = drho(1,iG,2)**2 + drho(2,iG,2)**2 + drho(3,iG,2)**2
gab = drho(1,iG,1)*drho(1,iG,2) + drho(2,iG,1)*drho(2,iG,2) + drho(3,iG,1)*drho(3,iG,2)
g = ga + gab + gb
omega = exp(-c*r**(-1d0/3d0))/(1d0 + d*r**(-1d0/3d0))*r**(-11d0/3d0)
delta = c*r**(-1d0/3d0) + d*r**(-1d0/3d0)/(1d0 + d*r**(-1d0/3d0))
vAO = weight(iG)*AO(mu,iG)*AO(nu,iG)
potential for LYP done
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dodra = (d/(3d0*r**(4d0/3d0)*(1d0 + d*r**(-1d0/3d0)) + c/(3d0*r**(4d0/3d0)) - 11d0/(3d0*r)))*omega
dodrb = dodra
working on LYP potential
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potential for LYP done
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dddra = - c/3d0*r**(-4d0/3d0) &
+ d**2/(3d0*(1d0 + d*r**(-1d0/3d0))**2)*r**(-5d0/3d0) &
- d/(3d0*(1d0 + d*r**(-1d0/3d0))*r**(-4d0/3d0))
dddrb = dddra
dfdra = - 4d0*a/(1d0 + d*r**(-1d0/3d0))*rb/r &
- 4d0/3d0*a*d/(1d0 + d*r**(-1d0/3d0))**2*ra*rb/r**(7d0/3d0) &
+ 4d0*a/(1d0 + d*r**(-1d0/3d0))*ra*rb/r &
- a*b*omega*rb*( &
+ 2d0**(11d0/3d0)*Cf*(ra**(8d0/3d0) + rb**(8d0/3d0)) &
+ (47d0/18d0 - 7d0*delta/18d0)*g &
- (5d0/2d0 - delta/18d0)*(ga + gb) &
- (delta - 11d0)/9d0*(ra/r*ga + rb/r*gb) &
- 4d0/3d0*r/rb*g &
+ (4d0/3d0*r/rb - 2d0*ra/rb)*gb &
+ 4d0/3d0*r/rb*ga ) &
- a*b*omega*ra*rb*( &
+ 8d0/3d0*2d0**(11d0/3d0)*Cf*ra**(5d0/3d0) &
- 7d0*dddra/18d0*g &
+ dddra/18d0*(ga + gb) &
- dddra/9d0*(ra/r*ga + rb/r*gb) &
- (delta - 11d0)/(9d0*r)*(-ra/r*ga - rb/r*gb + ga) ) &
- a*b*dodra*ra*rb*( &
+ 2d0**(11d0/3d0)*Cf*(ra**(8d0/3d0) + rb**(8d0/3d0)) &
+ (47d0/18d0 - 7d0*delta/18d0)*g &
- (5d0/2d0 - delta/18d0)*(ga + gb) &
- (delta - 11d0)/9d0*(ra/r*ga + rb/r*gb) ) &
- a*b*dodra*( &
- 2d0*r**2/3d0*g &
+ (2d0*r**2/3d0 - ra**2)*gb &
+ (2d0*r**2/3d0 - rb**2)*ga )
dfdrb = - 4d0*a/(1d0 + d*r**(-1d0/3d0))*ra/r &
- 4d0/3d0*a*d/(1d0 + d*r**(-1d0/3d0))**2*ra*rb/r**(7d0/3d0) &
+ 4d0*a/(1d0 + d*r**(-1d0/3d0))*ra*rb/r &
- a*b*omega*ra*( &
+ 2d0**(11d0/3d0)*Cf*(ra**(8d0/3d0) + rb**(8d0/3d0)) &
+ (47d0/18d0 - 7d0*delta/18d0)*g &
- (5d0/2d0 - delta/18d0)*(ga + gb) &
- (delta - 11d0)/9d0*(ra/r*ga + rb/r*gb) &
- 4d0/3d0*r/ra*g &
+ (4d0/3d0*r/ra - 2d0*ra/rb)*ga &
+ 4d0/3d0*r/ra*gb ) &
- a*b*omega*ra*rb*( &
+ 8d0/3d0*2d0**(11d0/3d0)*Cf*rb**(5d0/3d0) &
- 7d0*dddrb/18d0*g &
+ dddrb/18d0*(ga + gb) &
- dddrb/9d0*(ra/r*ga + rb/r*gb) &
- (delta - 11d0)/(9d0*r)*(-ra/r*ga - rb/r*gb + gb) ) &
- a*b*dodrb*ra*rb*( &
+ 2d0**(11d0/3d0)*Cf*(ra**(8d0/3d0) + rb**(8d0/3d0)) &
+ (47d0/18d0 - 7d0*delta/18d0)*g &
- (5d0/2d0 - delta/18d0)*(ga + gb) &
- (delta - 11d0)/9d0*(ra/r*ga + rb/r*gb) ) &
- a*b*dodrb*( &
- 2d0*r**2/3d0*g &
+ (2d0*r**2/3d0 - ra**2)*gb &
+ (2d0*r**2/3d0 - rb**2)*ga )
working on LYP potential
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Fc(mu,nu,1) = Fc(mu,nu,1) + vAO*dfdra
Fc(mu,nu,2) = Fc(mu,nu,2) + vAO*dfdrb
OK with GGA exchange functionals
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gaAO = drho(1,iG,1)*(dAO(1,mu,iG)*AO(nu,iG) + AO(mu,iG)*dAO(1,nu,iG)) &
+ drho(2,iG,1)*(dAO(2,mu,iG)*AO(nu,iG) + AO(mu,iG)*dAO(2,nu,iG)) &
+ drho(3,iG,1)*(dAO(3,mu,iG)*AO(nu,iG) + AO(mu,iG)*dAO(3,nu,iG))
gaAO = weight(iG)*gaAO
gbAO = drho(1,iG,2)*(dAO(1,mu,iG)*AO(nu,iG) + AO(mu,iG)*dAO(1,nu,iG)) &
+ drho(2,iG,2)*(dAO(2,mu,iG)*AO(nu,iG) + AO(mu,iG)*dAO(2,nu,iG)) &
+ drho(3,iG,2)*(dAO(3,mu,iG)*AO(nu,iG) + AO(mu,iG)*dAO(3,nu,iG))
gbAO = weight(iG)*gbAO
working on LYP potential
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potential for LYP done
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dfdga = -a*b*omega*(-rb**2 + ra*rb*(1d0/9d0 - (delta-11d0)/9d0*ra/r - delta/3d0))
dfdgab = -a*b*omega*(-2d0/3d0*r**2 + ra*rb*(47d0/18d0 - 7d0*delta/18d0))
dfdgb = -a*b*omega*(-ra**2 + ra*rb*(1d0/9d0 - (delta-11d0)/9d0*rb/r - delta/3d0))
OK with GGA exchange functionals
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potential for LYP done
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Fc(mu,nu,1) = Fc(mu,nu,1) + 2d0*gaAO*dfdga + gbAO*dfdgab
Fc(mu,nu,2) = Fc(mu,nu,2) + 2d0*gbAO*dfdgb + gaAO*dfdgab
OK with GGA exchange functionals
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end if
end do
end do
end do
end subroutine ULYP_gga_correlation_potential
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