2021-02-12 16:47:40 +01:00
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subroutine ULYP_gga_correlation_potential(nGrid,weight,nBas,AO,dAO,rho,drho,Fc)
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! Compute LYP correlation potential
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implicit none
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include 'parameters.h'
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! Input variables
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integer,intent(in) :: nGrid
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double precision,intent(in) :: weight(nGrid)
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integer,intent(in) :: nBas
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double precision,intent(in) :: AO(nBas,nGrid)
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double precision,intent(in) :: dAO(ncart,nBas,nGrid)
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double precision,intent(in) :: rho(nGrid,nspin)
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double precision,intent(in) :: drho(ncart,nGrid,nspin)
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! Local variables
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integer :: mu,nu,iG
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double precision :: vAO,gaAO,gbAO
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double precision :: ra,rb,r
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double precision :: ga,gab,gb,g
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2021-02-12 22:34:20 +01:00
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double precision :: dfdra,dfdrb
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2021-02-13 16:06:38 +01:00
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double precision :: dfdga,dfdgab,dfdgb
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double precision :: dodra,dodrb,dddra,dddrb
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2021-02-12 16:47:40 +01:00
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double precision :: a,b,c,d
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double precision :: Cf,omega,delta
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! Output variables
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2021-02-12 22:34:20 +01:00
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double precision,intent(out) :: Fc(nBas,nBas,nspin)
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2021-02-12 16:47:40 +01:00
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! Prameter of the functional
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a = 0.04918d0
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b = 0.132d0
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c = 0.2533d0
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d = 0.349d0
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Cf = 3d0/10d0*(3d0*pi**2)**(2d0/3d0)
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! Compute matrix elements in the AO basis
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2021-02-12 22:34:20 +01:00
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Fc(:,:,:) = 0d0
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2021-02-12 16:47:40 +01:00
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do mu=1,nBas
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do nu=1,nBas
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do iG=1,nGrid
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ra = max(0d0,rho(iG,1))
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rb = max(0d0,rho(iG,2))
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r = ra + rb
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if(r > threshold) then
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2021-02-13 22:31:46 +01:00
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ga = drho(1,iG,1)*drho(1,iG,1) + drho(2,iG,1)*drho(2,iG,1) + drho(3,iG,1)*drho(3,iG,1)
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gb = drho(1,iG,2)*drho(1,iG,2) + drho(2,iG,2)*drho(2,iG,2) + drho(3,iG,2)*drho(3,iG,2)
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2021-02-12 16:47:40 +01:00
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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)
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g = ga + 2d0*gab + gb
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2021-02-12 16:47:40 +01:00
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omega = exp(-c*r**(-1d0/3d0))/(1d0 + d*r**(-1d0/3d0))*r**(-11d0/3d0)
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delta = c*r**(-1d0/3d0) + d*r**(-1d0/3d0)/(1d0 + d*r**(-1d0/3d0))
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vAO = weight(iG)*AO(mu,iG)*AO(nu,iG)
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2021-02-13 22:31:46 +01:00
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dodra = (d/(3d0*r**(4d0/3d0)*(1d0 + d*r**(-1d0/3d0))) + c/(3d0*r**(4d0/3d0)) - 11d0/(3d0*r))*omega
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dodrb = dodra
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2021-02-12 22:34:20 +01:00
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2021-02-13 16:06:38 +01:00
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dddra = - c/3d0*r**(-4d0/3d0) &
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+ d**2/(3d0*(1d0 + d*r**(-1d0/3d0))**2)*r**(-5d0/3d0) &
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2021-02-13 22:31:46 +01:00
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- d/(3d0*(1d0 + d*r**(-1d0/3d0)))*r**(-4d0/3d0)
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2021-02-13 16:06:38 +01:00
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dddrb = dddra
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dfdra = - 4d0*a/(1d0 + d*r**(-1d0/3d0))*rb/r &
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- 4d0/3d0*a*d/(1d0 + d*r**(-1d0/3d0))**2*ra*rb/r**(7d0/3d0) &
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+ 4d0*a/(1d0 + d*r**(-1d0/3d0))*ra*rb/r**2 &
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- a*b*omega*rb*( &
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+ 2d0**(11d0/3d0)*Cf*(ra**(8d0/3d0) + rb**(8d0/3d0)) &
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+ (47d0/18d0 - 7d0*delta/18d0)*g &
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- (5d0/2d0 - delta/18d0)*(ga + gb) &
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- (delta - 11d0)/9d0*(ra/r*ga + rb/r*gb) &
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- 4d0/3d0*r/rb*g &
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+ (4d0/3d0*r/rb - 2d0*ra/rb)*gb &
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+ 4d0/3d0*r/rb*ga ) &
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- a*b*omega*ra*rb*( &
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+ 8d0/3d0*2d0**(11d0/3d0)*Cf*ra**(5d0/3d0) &
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- 7d0*dddra/18d0*g &
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+ dddra/18d0*(ga + gb) &
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- dddra/9d0*(ra/r*ga + rb/r*gb) &
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- (delta - 11d0)/(9d0*r)*(-ra/r*ga - rb/r*gb + ga) ) &
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- a*b*dodra*ra*rb*( &
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+ 2d0**(11d0/3d0)*Cf*(ra**(8d0/3d0) + rb**(8d0/3d0)) &
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+ (47d0/18d0 - 7d0*delta/18d0)*g &
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- (5d0/2d0 - delta/18d0)*(ga + gb) &
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- (delta - 11d0)/9d0*(ra/r*ga + rb/r*gb) ) &
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- a*b*dodra*( &
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- 2d0*r**2/3d0*g &
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+ (2d0*r**2/3d0 - ra**2)*gb &
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+ (2d0*r**2/3d0 - rb**2)*ga )
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dfdrb = - 4d0*a/(1d0 + d*r**(-1d0/3d0))*ra/r &
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- 4d0/3d0*a*d/(1d0 + d*r**(-1d0/3d0))**2*ra*rb/r**(7d0/3d0) &
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+ 4d0*a/(1d0 + d*r**(-1d0/3d0))*ra*rb/r**2 &
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- a*b*omega*ra*( &
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+ 2d0**(11d0/3d0)*Cf*(ra**(8d0/3d0) + rb**(8d0/3d0)) &
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+ (47d0/18d0 - 7d0*delta/18d0)*g &
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- (5d0/2d0 - delta/18d0)*(ga + gb) &
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- (delta - 11d0)/9d0*(ra/r*ga + rb/r*gb) &
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- 4d0/3d0*r/ra*g &
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+ (4d0/3d0*r/ra - 2d0*rb/ra)*ga &
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+ 4d0/3d0*r/ra*gb ) &
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- a*b*omega*ra*rb*( &
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+ 8d0/3d0*2d0**(11d0/3d0)*Cf*rb**(5d0/3d0) &
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- 7d0*dddrb/18d0*g &
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+ dddrb/18d0*(ga + gb) &
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- dddrb/9d0*(ra/r*ga + rb/r*gb) &
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- (delta - 11d0)/(9d0*r)*(-ra/r*ga - rb/r*gb + gb) ) &
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- a*b*dodrb*ra*rb*( &
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+ 2d0**(11d0/3d0)*Cf*(ra**(8d0/3d0) + rb**(8d0/3d0)) &
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+ (47d0/18d0 - 7d0*delta/18d0)*g &
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- (5d0/2d0 - delta/18d0)*(ga + gb) &
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- (delta - 11d0)/9d0*(ra/r*ga + rb/r*gb) ) &
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- a*b*dodrb*( &
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- 2d0*r**2/3d0*g &
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+ (2d0*r**2/3d0 - ra**2)*gb &
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+ (2d0*r**2/3d0 - rb**2)*ga )
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2021-02-12 22:34:20 +01:00
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Fc(mu,nu,1) = Fc(mu,nu,1) + vAO*dfdra
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Fc(mu,nu,2) = Fc(mu,nu,2) + vAO*dfdrb
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2021-02-12 16:47:40 +01:00
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gaAO = drho(1,iG,1)*(dAO(1,mu,iG)*AO(nu,iG) + AO(mu,iG)*dAO(1,nu,iG)) &
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+ drho(2,iG,1)*(dAO(2,mu,iG)*AO(nu,iG) + AO(mu,iG)*dAO(2,nu,iG)) &
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+ drho(3,iG,1)*(dAO(3,mu,iG)*AO(nu,iG) + AO(mu,iG)*dAO(3,nu,iG))
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gaAO = weight(iG)*gaAO
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gbAO = drho(1,iG,2)*(dAO(1,mu,iG)*AO(nu,iG) + AO(mu,iG)*dAO(1,nu,iG)) &
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+ drho(2,iG,2)*(dAO(2,mu,iG)*AO(nu,iG) + AO(mu,iG)*dAO(2,nu,iG)) &
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+ drho(3,iG,2)*(dAO(3,mu,iG)*AO(nu,iG) + AO(mu,iG)*dAO(3,nu,iG))
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gbAO = weight(iG)*gbAO
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2021-02-12 22:34:20 +01:00
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2021-02-13 16:06:38 +01:00
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dfdga = -a*b*omega*(-rb**2 + ra*rb*(1d0/9d0 - (delta-11d0)/9d0*ra/r - delta/3d0))
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dfdgab = -a*b*omega*(-4d0/3d0*r**2 + 2d0*ra*rb*(47d0/18d0 - 7d0*delta/18d0))
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2021-02-13 16:06:38 +01:00
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dfdgb = -a*b*omega*(-ra**2 + ra*rb*(1d0/9d0 - (delta-11d0)/9d0*rb/r - delta/3d0))
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2021-02-12 16:47:40 +01:00
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2021-02-13 16:06:38 +01:00
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Fc(mu,nu,1) = Fc(mu,nu,1) + 2d0*gaAO*dfdga + gbAO*dfdgab
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Fc(mu,nu,2) = Fc(mu,nu,2) + 2d0*gbAO*dfdgb + gaAO*dfdgab
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2021-02-12 16:47:40 +01:00
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end if
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end do
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end do
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end do
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end subroutine ULYP_gga_correlation_potential
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