subroutine UPW92_lda_correlation_energy(nGrid,weight,rho,Ec) ! Compute unrestricted PW92 LDA correlation energy implicit none include 'parameters.h' ! Input variables integer,intent(in) :: nGrid double precision,intent(in) :: weight(nGrid) double precision,intent(in) :: rho(nGrid,nspin) ! Local variables integer :: iG double precision :: ra,rb,r,rs,x,z 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 :: ec_z,ec_p,ec_f,ec_a double precision :: fz,d2fz ! Output variables double precision :: Ec(nsp) ! 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 Ec(:) = 0d0 do iG=1,nGrid ra = max(0d0,rho(iG,1)) rb = max(0d0,rho(iG,2)) ! alpha-alpha contribution if(ra > threshold) then rs = (4d0*pi*ra/3d0)**(-1d0/3d0) 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(1) = Ec(1) + weight(iG)*ec_f*ra end if ! alpha-beta contribution if(ra > threshold .or. rb > threshold) then r = ra + rb rs = (4d0*pi*r/3d0)**(-1d0/3d0) z = (ra - rb)/r x = sqrt(rs) 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 Ec(2) = Ec(2) + weight(iG)*ec_z*r end if ! beta-beta contribution if(rb > threshold) then rs = (4d0*pi*rb/3d0)**(-1d0/3d0) x = sqrt(rs) 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(3) = Ec(3) + weight(iG)*ec_f*rb end if end do Ec(2) = Ec(2) - Ec(1) - Ec(3) end subroutine UPW92_lda_correlation_energy