diff --git a/src/eDFT/UPBE_gga_correlation_energy.f90 b/src/eDFT/UPBE_gga_correlation_energy.f90 new file mode 100644 index 0000000..461e2bb --- /dev/null +++ b/src/eDFT/UPBE_gga_correlation_energy.f90 @@ -0,0 +1,172 @@ +subroutine UPBE_gga_correlation_energy(nGrid,weight,rho,drho,Ec) + +! Compute unrestricted PBE GGA 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) + double precision,intent(in) :: drho(ncart,nGrid,nspin) + +! Local variables + + integer :: iG + double precision :: ra,rb,r,rs,z + double precision :: ga,gab,gb,g + + double precision :: a,b,c,d + double precision :: gam,beta + + 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 + + double precision :: H,kf,ks,t,phi + +! Output variables + + double precision :: Ec(nsp) + +! Parameters for PW92 + + 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 + +! Parameters PBE + + gam = (1d0 - log(2d0))/pi**2 + beta = 0.066725d0 + +! Initialization + + Ec(:) = 0d0 + + do iG=1,nGrid + + ra = max(0d0,rho(iG,1)) + rb = max(0d0,rho(iG,2)) + r = ra + rb + z = (ra - rb)/r + +! 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)) + + 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) + + kf = (3d0*pi**2*ra)**(1d0/3d0) + ks = sqrt(4d0*kf/pi) + phi = 1d0 + t = sqrt(ga)/(2d0*phi*ks*ra) + + A = beta/gam/(exp(-ec_f/(gam*phi**3)) - 1d0) + + H = gam*phi**3*log(1d0 + beta/gam*t**2*((1d0 + A*t**2)/(1d0 + A*t**2 + A**2*t**4))) + + Ec(1) = Ec(1) + weight(iG)*(ec_f + H)*ra + + end if + + r = ra + rb + +! alpha-beta contribution + + if(r > threshold) then + + rs = (4d0*pi*r/3d0)**(-1d0/3d0) + + 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 + + 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) + 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) + 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 + 2d0*gab + gb + + rs = (4d0*pi*r/3d0)**(-1d0/3d0) + kf = (3d0*pi**2*r)**(1d0/3d0) + ks = sqrt(4d0*kf/pi) + phi = ((1d0 + z)**(2d0/3d0) + (1d0 - z)**(2d0/3d0))/2d0 + t = sqrt(g)/(2d0*phi*ks*r) + + A = beta/gam/(exp(-ec_p/(gam*phi**3)) - 1d0) + + H = gam*phi**3*log(1d0 + beta/gam*t**2*((1d0 + A*t**2)/(1d0 + A*t**2 + A**2*t**4))) + + Ec(2) = Ec(2) - weight(iG)*(ec_p + H)*r + + end if + +! beta-beta contribution + + if(rb > threshold) then + + rs = (4d0*pi*rb/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)) + + 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) + + kf = (3d0*pi**2*rb)**(1d0/3d0) + ks = sqrt(4d0*kf/pi) + phi = 1d0 + t = sqrt(gb)/(2d0*phi*ks*rb) + + A = beta/gam/(exp(-ec_f/(gam*phi**3)) - 1d0) + + H = gam*phi**3*log(1d0 + beta/gam*t**2*((1d0 + A*t**2)/(1d0 + A*t**2 + A**2*t**4))) + + Ec(3) = Ec(3) + weight(iG)*(ec_f + H)*rb + + end if + + end do + + Ec(2) = Ec(2) - Ec(1) - Ec(3) + + +end subroutine UPBE_gga_correlation_energy diff --git a/src/eDFT/UPBE_gga_correlation_potential.f90 b/src/eDFT/UPBE_gga_correlation_potential.f90 new file mode 100644 index 0000000..af8794a --- /dev/null +++ b/src/eDFT/UPBE_gga_correlation_potential.f90 @@ -0,0 +1,88 @@ +subroutine UPBE_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 + double precision :: dfdra,dfdrb + double precision :: dfdga,dfdgab,dfdgb + double precision :: dodra,dodrb,dddra,dddrb + + double precision :: a,b,c,d + double precision :: Cf,omega,delta + +! Output variables + + double precision,intent(out) :: Fc(nBas,nBas,nspin) + +! Prameter of the functional + +! Compute matrix elements in the AO basis + + call UPW92_lda_correlation_potential(nGrid,weight,nBas,AO,rho,Fc) + + 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)*drho(1,iG,1) + drho(2,iG,1)*drho(2,iG,1) + drho(3,iG,1)*drho(3,iG,1) + 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) + 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 + 2d0*gab + gb + + vAO = weight(iG)*AO(mu,iG)*AO(nu,iG) + + dfdra = 0d0 + dfdrb = 0d0 + + Fc(mu,nu,1) = Fc(mu,nu,1) + vAO*dfdra + Fc(mu,nu,2) = Fc(mu,nu,2) + vAO*dfdrb + + 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 + + dfdga = 0d0 + dfdgab = 0d0 + dfdgb = 0d0 + + + 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 + + end if + + end do + end do + end do + +end subroutine UPBE_gga_correlation_potential