subroutine UPW92_lda_correlation_potential(nGrid,weight,nBas,AO,rho,Fc) ! Compute unrestricted PW92 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,z,t,dt double precision :: A_p,a1_p,b1_p,b2_p,b3_p,b4_p double precision :: A_f,a1_f,b1_f,b2_f,b3_f,b4_f double precision :: A_a,a1_a,b1_a,b2_a,b3_a,b4_a double precision :: dfzdz,decdrs_p,decdrs_f,decdrs_a double precision :: dzdra,dfzdra,drsdra,decdra_p,decdra_f,decdra_a,decdra double precision :: dzdrb,dfzdrb,drsdrb,decdrb_p,decdrb_f,decdrb_a,decdrb double precision :: ec_z,ec_p,ec_f,ec_a double precision :: fz,d2fz ! Output variables double precision :: Fc(nBas,nBas,nspin) ! Parameters of the functional A_p = 0.031091d0 a1_p = 0.21370d0 b1_p = 7.5957d0 b2_p = 3.5876d0 b3_p = 1.6382d0 b4_p = 0.49294d0 A_f = 0.015545d0 a1_f = 0.20548d0 b1_f = 14.1189d0 b2_f = 6.1977d0 b3_f = 3.3662d0 b4_f = 0.62517d0 A_a = 0.016887d0 a1_a = 0.11125d0 b1_a = 10.357d0 b2_a = 3.6231d0 b3_a = 0.88026d0 b4_a = 0.49671d0 ! Initialization Fc(:,:,:) = 0d0 do mu=1,nBas do nu=1,nBas do iG=1,nGrid ra = max(0d0,rho(iG,1)) rb = max(0d0,rho(iG,2)) ! spin-up contribution if(ra > threshold) then r = ra + rb rs = (4d0*pi*r/3d0)**(-1d0/3d0) z = (ra - rb)/r fz = (1d0 + z)**(4d0/3d0) + (1d0 - z)**(4d0/3d0) - 2d0 fz = fz/(2d0*(2d0**(1d0/3d0) - 1d0)) d2fz = 4d0/(9d0*(2**(1d0/3d0) - 1d0)) ec_p = b1_p*sqrt(rs) + b2_p*rs + b3_p*rs**(3d0/2d0) + b4_p*rs**2 ec_p = -2d0*A_p*(1d0 + a1_p*rs)*log(1d0 + 1d0/(2d0*A_p*ec_p)) ec_f = b1_f*sqrt(rs) + b2_f*rs + b3_f*rs**(3d0/2d0) + b4_f*rs**2 ec_f = -2d0*A_f*(1d0 + a1_f*rs)*log(1d0 + 1d0/(2d0*A_f*ec_f)) ec_a = b1_a*sqrt(rs) + b2_a*rs + b3_a*rs**(3d0/2d0) + b4_a*rs**2 ec_a = +2d0*A_a*(1d0 + a1_a*rs)*log(1d0 + 1d0/(2d0*A_a*ec_a)) ec_z = ec_p + ec_a*fz/d2fz*(1d0-z**4) + (ec_f - ec_p)*fz*z**4 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) t = b1_p*sqrt(rs) + b2_p*rs + b3_p*rs**(3d0/2d0) + b4_p*rs**2 dt = 0.5d0*b1_p*sqrt(rs) + b2_p*rs + 1.5d0*b3_p*rs**(3d0/2d0) + 2d0*b4_p*rs**2 decdrs_p = (1d0 + a1_p*rs)/rs*dt/(t**2*(1d0 + 1d0/(2d0*A_p*t))) & - 2d0*A_p*a1_p*log(1d0 + 1d0/(2d0*A_p*t)) t = b1_f*sqrt(rs) + b2_f*rs + b3_f*rs**(3d0/2d0) + b4_f*rs**2 dt = 0.5d0*b1_f*sqrt(rs) + b2_f*rs + 1.5d0*b3_f*rs**(3d0/2d0) + 2d0*b4_f*rs**2 decdrs_f = (1d0 + a1_f*rs)/rs*dt/(t**2*(1d0 + 1d0/(2d0*A_f*t))) & - 2d0*A_f*a1_f*log(1d0 + 1d0/(2d0*A_f*t)) t = b1_a*sqrt(rs) + b2_a*rs + b3_a*rs**(3d0/2d0) + b4_a*rs**2 dt = 0.5d0*b1_a*sqrt(rs) + b2_a*rs + 1.5d0*b3_a*rs**(3d0/2d0) + 2d0*b4_a*rs**2 decdrs_a = (1d0 + a1_a*rs)/rs*dt/(t**2*(1d0 + 1d0/(2d0*A_a*t))) & - 2d0*A_a*a1_a*log(1d0 + 1d0/(2d0*A_a*t)) decdra_p = drsdra*decdrs_p decdra_f = drsdra*decdrs_f decdra_a = drsdra*decdrs_a decdra = decdra_p + decdra_a*fz/d2fz*(1d0-z**4) + ec_a*dfzdra/d2fz*(1d0-z**4) - 4d0*ec_a*fz/d2fz*dzdra*z**3 & + (decdra_f - decdra_p)*fz*z**4 + (ec_f - ec_p)*dfzdra*z**4 + 4d0*(ec_f - ec_p)*fz*dzdra*z**3 Fc(mu,nu,1) = Fc(mu,nu,1) + weight(iG)*AO(mu,iG)*AO(nu,iG)*(ec_z + decdra*r) end if ! spin-down contribution if(rb > threshold) then r = ra + rb rs = (4d0*pi*r/3d0)**(-1d0/3d0) z = (ra - rb)/r fz = (1d0 + z)**(4d0/3d0) + (1d0 - z)**(4d0/3d0) - 2d0 fz = fz/(2d0*(2d0**(1d0/3d0) - 1d0)) d2fz = 4d0/(9d0*(2**(1d0/3d0) - 1d0)) ec_p = b1_p*sqrt(rs) + b2_p*rs + b3_p*rs**(3d0/2d0) + b4_p*rs**2 ec_p = -2d0*A_p*(1d0 + a1_p*rs)*log(1d0 + 1d0/(2d0*A_p*ec_p)) ec_f = b1_f*sqrt(rs) + b2_f*rs + b3_f*rs**(3d0/2d0) + b4_f*rs**2 ec_f = -2d0*A_f*(1d0 + a1_f*rs)*log(1d0 + 1d0/(2d0*A_f*ec_f)) ec_a = b1_a*sqrt(rs) + b2_a*rs + b3_a*rs**(3d0/2d0) + b4_a*rs**2 ec_a = +2d0*A_a*(1d0 + a1_a*rs)*log(1d0 + 1d0/(2d0*A_a*ec_a)) ec_z = ec_p + ec_a*fz/d2fz*(1d0-z**4) + (ec_f - ec_p)*fz*z**4 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) t = b1_p*sqrt(rs) + b2_p*rs + b3_p*rs**(3d0/2d0) + b4_p*rs**2 dt = 0.5d0*b1_p*sqrt(rs) + b2_p*rs + 1.5d0*b3_p*rs**(3d0/2d0) + 2d0*b4_p*rs**2 decdrs_p = (1d0 + a1_p*rs)/rs*dt/(t**2*(1d0 + 1d0/(2d0*A_p*t))) & - 2d0*A_p*a1_p*log(1d0 + 1d0/(2d0*A_p*t)) t = b1_f*sqrt(rs) + b2_f*rs + b3_f*rs**(3d0/2d0) + b4_f*rs**2 dt = 0.5d0*b1_f*sqrt(rs) + b2_f*rs + 1.5d0*b3_f*rs**(3d0/2d0) + 2d0*b4_f*rs**2 decdrs_f = (1d0 + a1_f*rs)/rs*dt/(t**2*(1d0 + 1d0/(2d0*A_f*t))) & - 2d0*A_f*a1_f*log(1d0 + 1d0/(2d0*A_f*t)) t = b1_a*sqrt(rs) + b2_a*rs + b3_a*rs**(3d0/2d0) + b4_a*rs**2 dt = 0.5d0*b1_a*sqrt(rs) + b2_a*rs + 1.5d0*b3_a*rs**(3d0/2d0) + 2d0*b4_a*rs**2 decdrs_a = (1d0 + a1_a*rs)/rs*dt/(t**2*(1d0 + 1d0/(2d0*A_a*t))) & - 2d0*A_a*a1_a*log(1d0 + 1d0/(2d0*A_a*t)) decdrb_p = drsdrb*decdrs_p decdrb_f = drsdrb*decdrs_f decdrb_a = drsdrb*decdrs_a decdrb = decdrb_p + decdrb_a*fz/d2fz*(1d0-z**4) + ec_a*dfzdrb/d2fz*(1d0-z**4) - 4d0*ec_a*fz/d2fz*dzdrb*z**3 & + (decdrb_f - decdrb_p)*fz*z**4 + (ec_f - ec_p)*dfzdrb*z**4 + 4d0*(ec_f - ec_p)*fz*dzdrb*z**3 Fc(mu,nu,2) = Fc(mu,nu,2) + weight(iG)*AO(mu,iG)*AO(nu,iG)*(ec_z + decdrb*r) end if end do end do end do end subroutine UPW92_lda_correlation_potential