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PW92
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122
src/eDFT/UPW92_lda_correlation_energy.f90
Normal file
122
src/eDFT/UPW92_lda_correlation_energy.f90
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@ -0,0 +1,122 @@
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subroutine UPW92_lda_correlation_energy(nGrid,weight,rho,Ec)
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! Compute unrestricted PW92 LDA 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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! Local variables
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integer :: iG
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double precision :: ra,rb,r,rs,x,z
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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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! Output variables
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double precision :: Ec(nsp)
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! Parameters of the functional
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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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! 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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! 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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Ec(1) = Ec(1) + weight(iG)*ec_f*ra
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end if
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! alpha-beta contribution
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if(ra > threshold .or. rb > threshold) then
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r = ra + rb
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rs = (4d0*pi*r/3d0)**(-1d0/3d0)
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z = (ra - rb)/r
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x = sqrt(rs)
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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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Ec(2) = Ec(2) + weight(iG)*ec_z*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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x = sqrt(rs)
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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(3) = Ec(3) + weight(iG)*ec_f*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 UPW92_lda_correlation_energy
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184
src/eDFT/UPW92_lda_correlation_potential.f90
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184
src/eDFT/UPW92_lda_correlation_potential.f90
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@ -0,0 +1,184 @@
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subroutine UPW92_lda_correlation_potential(nGrid,weight,nBas,AO,rho,Fc)
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! Compute unrestricted PW92 LDA 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) :: rho(nGrid,nspin)
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! Local variables
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integer :: mu,nu,iG
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double precision :: ra,rb,r,rs,z,t,dt
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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 :: dfzdz,decdrs_p,decdrs_f,decdrs_a
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double precision :: dzdra,dfzdra,drsdra,decdra_p,decdra_f,decdra_a,decdra
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double precision :: dzdrb,dfzdrb,drsdrb,decdrb_p,decdrb_f,decdrb_a,decdrb
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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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! Output variables
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double precision :: Fc(nBas,nBas,nspin)
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! Parameters of the functional
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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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! Initialization
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Fc(:,:,:) = 0d0
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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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! spin-up contribution
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if(ra > threshold) then
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r = ra + rb
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rs = (4d0*pi*r/3d0)**(-1d0/3d0)
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z = (ra - rb)/r
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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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dzdra = (1d0 - z)/r
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dfzdz = (4d0/3d0)*((1d0 + z)**(1d0/3d0) - (1d0 - z)**(1d0/3d0))/(2d0*(2d0**(1d0/3d0) - 1d0))
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dfzdra = dzdra*dfzdz
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drsdra = - (36d0*pi)**(-1d0/3d0)*r**(-4d0/3d0)
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t = b1_p*sqrt(rs) + b2_p*rs + b3_p*rs**(3d0/2d0) + b4_p*rs**2
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dt = 0.5d0*b1_p*sqrt(rs) + b2_p*rs + 1.5d0*b3_p*rs**(3d0/2d0) + 2d0*b4_p*rs**2
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decdrs_p = (1d0 + a1_p*rs)/rs*dt/(t**2*(1d0 + 1d0/(2d0*A_p*t))) &
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- 2d0*A_p*a1_p*log(1d0 + 1d0/(2d0*A_p*t))
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t = b1_f*sqrt(rs) + b2_f*rs + b3_f*rs**(3d0/2d0) + b4_f*rs**2
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dt = 0.5d0*b1_f*sqrt(rs) + b2_f*rs + 1.5d0*b3_f*rs**(3d0/2d0) + 2d0*b4_f*rs**2
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decdrs_f = (1d0 + a1_f*rs)/rs*dt/(t**2*(1d0 + 1d0/(2d0*A_f*t))) &
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- 2d0*A_f*a1_f*log(1d0 + 1d0/(2d0*A_f*t))
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t = b1_a*sqrt(rs) + b2_a*rs + b3_a*rs**(3d0/2d0) + b4_a*rs**2
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dt = 0.5d0*b1_a*sqrt(rs) + b2_a*rs + 1.5d0*b3_a*rs**(3d0/2d0) + 2d0*b4_a*rs**2
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decdrs_a = (1d0 + a1_a*rs)/rs*dt/(t**2*(1d0 + 1d0/(2d0*A_a*t))) &
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- 2d0*A_a*a1_a*log(1d0 + 1d0/(2d0*A_a*t))
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decdra_p = drsdra*decdrs_p
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decdra_f = drsdra*decdrs_f
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decdra_a = drsdra*decdrs_a
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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 &
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+ (decdra_f - decdra_p)*fz*z**4 + (ec_f - ec_p)*dfzdra*z**4 + 4d0*(ec_f - ec_p)*fz*dzdra*z**3
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Fc(mu,nu,1) = Fc(mu,nu,1) + weight(iG)*AO(mu,iG)*AO(nu,iG)*(ec_z + decdra*r)
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end if
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! spin-down contribution
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if(rb > threshold) then
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r = ra + rb
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rs = (4d0*pi*r/3d0)**(-1d0/3d0)
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z = (ra - rb)/r
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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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dzdrb = - (1d0 + z)/r
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dfzdz = (4d0/3d0)*((1d0 + z)**(1d0/3d0) - (1d0 - z)**(1d0/3d0))/(2d0*(2d0**(1d0/3d0) - 1d0))
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dfzdrb = dzdrb*dfzdz
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drsdrb = - (36d0*pi)**(-1d0/3d0)*r**(-4d0/3d0)
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t = b1_p*sqrt(rs) + b2_p*rs + b3_p*rs**(3d0/2d0) + b4_p*rs**2
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dt = 0.5d0*b1_p*sqrt(rs) + b2_p*rs + 1.5d0*b3_p*rs**(3d0/2d0) + 2d0*b4_p*rs**2
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decdrs_p = (1d0 + a1_p*rs)/rs*dt/(t**2*(1d0 + 1d0/(2d0*A_p*t))) &
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- 2d0*A_p*a1_p*log(1d0 + 1d0/(2d0*A_p*t))
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t = b1_f*sqrt(rs) + b2_f*rs + b3_f*rs**(3d0/2d0) + b4_f*rs**2
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dt = 0.5d0*b1_f*sqrt(rs) + b2_f*rs + 1.5d0*b3_f*rs**(3d0/2d0) + 2d0*b4_f*rs**2
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decdrs_f = (1d0 + a1_f*rs)/rs*dt/(t**2*(1d0 + 1d0/(2d0*A_f*t))) &
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- 2d0*A_f*a1_f*log(1d0 + 1d0/(2d0*A_f*t))
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t = b1_a*sqrt(rs) + b2_a*rs + b3_a*rs**(3d0/2d0) + b4_a*rs**2
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dt = 0.5d0*b1_a*sqrt(rs) + b2_a*rs + 1.5d0*b3_a*rs**(3d0/2d0) + 2d0*b4_a*rs**2
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decdrs_a = (1d0 + a1_a*rs)/rs*dt/(t**2*(1d0 + 1d0/(2d0*A_a*t))) &
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- 2d0*A_a*a1_a*log(1d0 + 1d0/(2d0*A_a*t))
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decdrb_p = drsdrb*decdrs_p
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decdrb_f = drsdrb*decdrs_f
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decdrb_a = drsdrb*decdrs_a
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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 &
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+ (decdrb_f - decdrb_p)*fz*z**4 + (ec_f - ec_p)*dfzdrb*z**4 + 4d0*(ec_f - ec_p)*fz*dzdrb*z**3
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Fc(mu,nu,2) = Fc(mu,nu,2) + weight(iG)*AO(mu,iG)*AO(nu,iG)*(ec_z + decdrb*r)
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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 UPW92_lda_correlation_potential
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