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UPBE
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172
src/eDFT/UPBE_gga_correlation_energy.f90
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172
src/eDFT/UPBE_gga_correlation_energy.f90
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subroutine UPBE_gga_correlation_energy(nGrid,weight,rho,drho,Ec)
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! Compute unrestricted PBE GGA correlation energy
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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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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 :: iG
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double precision :: ra,rb,r,rs,z
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double precision :: ga,gab,gb,g
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double precision :: a,b,c,d
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double precision :: gam,beta
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double precision :: A_p,a1_p,b1_p,b2_p,b3_p,b4_p
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double precision :: A_f,a1_f,b1_f,b2_f,b3_f,b4_f
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double precision :: A_a,a1_a,b1_a,b2_a,b3_a,b4_a
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double precision :: ec_z,ec_p,ec_f,ec_a
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double precision :: fz,d2fz
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double precision :: H,kf,ks,t,phi
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! Output variables
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double precision :: Ec(nsp)
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! Parameters for PW92
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A_p = 0.031091d0
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a1_p = 0.21370d0
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b1_p = 7.5957d0
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b2_p = 3.5876d0
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b3_p = 1.6382d0
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b4_p = 0.49294d0
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A_f = 0.015545d0
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a1_f = 0.20548d0
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b1_f = 14.1189d0
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b2_f = 6.1977d0
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b3_f = 3.3662d0
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b4_f = 0.62517d0
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A_a = 0.016887d0
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a1_a = 0.11125d0
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b1_a = 10.357d0
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b2_a = 3.6231d0
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b3_a = 0.88026d0
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b4_a = 0.49671d0
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! Parameters PBE
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gam = (1d0 - log(2d0))/pi**2
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beta = 0.066725d0
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! Initialization
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Ec(:) = 0d0
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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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z = (ra - rb)/r
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! alpha-alpha contribution
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if(ra > threshold) then
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rs = (4d0*pi*ra/3d0)**(-1d0/3d0)
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ec_f = b1_f*sqrt(rs) + b2_f*rs + b3_f*rs**(3d0/2d0) + b4_f*rs**2
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ec_f = -2d0*A_f*(1d0 + a1_f*rs)*log(1d0 + 1d0/(2d0*A_f*ec_f))
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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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kf = (3d0*pi**2*ra)**(1d0/3d0)
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ks = sqrt(4d0*kf/pi)
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phi = 1d0
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t = sqrt(ga)/(2d0*phi*ks*ra)
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A = beta/gam/(exp(-ec_f/(gam*phi**3)) - 1d0)
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H = gam*phi**3*log(1d0 + beta/gam*t**2*((1d0 + A*t**2)/(1d0 + A*t**2 + A**2*t**4)))
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Ec(1) = Ec(1) + weight(iG)*(ec_f + H)*ra
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end if
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r = ra + rb
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! alpha-beta contribution
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if(r > threshold) then
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rs = (4d0*pi*r/3d0)**(-1d0/3d0)
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fz = (1d0 + z)**(4d0/3d0) + (1d0 - z)**(4d0/3d0) - 2d0
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fz = fz/(2d0*(2d0**(1d0/3d0) - 1d0))
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d2fz = 4d0/(9d0*(2**(1d0/3d0) - 1d0))
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ec_p = b1_p*sqrt(rs) + b2_p*rs + b3_p*rs**(3d0/2d0) + b4_p*rs**2
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ec_p = -2d0*A_p*(1d0 + a1_p*rs)*log(1d0 + 1d0/(2d0*A_p*ec_p))
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ec_f = b1_f*sqrt(rs) + b2_f*rs + b3_f*rs**(3d0/2d0) + b4_f*rs**2
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ec_f = -2d0*A_f*(1d0 + a1_f*rs)*log(1d0 + 1d0/(2d0*A_f*ec_f))
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ec_a = b1_a*sqrt(rs) + b2_a*rs + b3_a*rs**(3d0/2d0) + b4_a*rs**2
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ec_a = +2d0*A_a*(1d0 + a1_a*rs)*log(1d0 + 1d0/(2d0*A_a*ec_a))
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ec_z = ec_p + ec_a*fz/d2fz*(1d0-z**4) + (ec_f - ec_p)*fz*z**4
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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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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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rs = (4d0*pi*r/3d0)**(-1d0/3d0)
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kf = (3d0*pi**2*r)**(1d0/3d0)
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ks = sqrt(4d0*kf/pi)
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phi = ((1d0 + z)**(2d0/3d0) + (1d0 - z)**(2d0/3d0))/2d0
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t = sqrt(g)/(2d0*phi*ks*r)
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A = beta/gam/(exp(-ec_p/(gam*phi**3)) - 1d0)
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H = gam*phi**3*log(1d0 + beta/gam*t**2*((1d0 + A*t**2)/(1d0 + A*t**2 + A**2*t**4)))
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Ec(2) = Ec(2) - weight(iG)*(ec_p + H)*r
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end if
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! beta-beta contribution
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if(rb > threshold) then
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rs = (4d0*pi*rb/3d0)**(-1d0/3d0)
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ec_f = b1_f*sqrt(rs) + b2_f*rs + b3_f*rs**(3d0/2d0) + b4_f*rs**2
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ec_f = -2d0*A_f*(1d0 + a1_f*rs)*log(1d0 + 1d0/(2d0*A_f*ec_f))
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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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kf = (3d0*pi**2*rb)**(1d0/3d0)
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ks = sqrt(4d0*kf/pi)
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phi = 1d0
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t = sqrt(gb)/(2d0*phi*ks*rb)
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A = beta/gam/(exp(-ec_f/(gam*phi**3)) - 1d0)
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H = gam*phi**3*log(1d0 + beta/gam*t**2*((1d0 + A*t**2)/(1d0 + A*t**2 + A**2*t**4)))
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Ec(3) = Ec(3) + weight(iG)*(ec_f + H)*rb
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end if
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end do
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Ec(2) = Ec(2) - Ec(1) - Ec(3)
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end subroutine UPBE_gga_correlation_energy
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88
src/eDFT/UPBE_gga_correlation_potential.f90
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88
src/eDFT/UPBE_gga_correlation_potential.f90
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@ -0,0 +1,88 @@
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subroutine UPBE_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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double precision :: dfdra,dfdrb
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double precision :: dfdga,dfdgab,dfdgb
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double precision :: dodra,dodrb,dddra,dddrb
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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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double precision,intent(out) :: Fc(nBas,nBas,nspin)
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! Prameter of the functional
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! Compute matrix elements in the AO basis
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call UPW92_lda_correlation_potential(nGrid,weight,nBas,AO,rho,Fc)
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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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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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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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vAO = weight(iG)*AO(mu,iG)*AO(nu,iG)
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dfdra = 0d0
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dfdrb = 0d0
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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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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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dfdga = 0d0
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dfdgab = 0d0
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dfdgb = 0d0
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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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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 UPBE_gga_correlation_potential
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