mirror of
https://github.com/pfloos/quack
synced 2024-08-14 16:48:35 +02:00
173 lines
4.4 KiB
Fortran
173 lines
4.4 KiB
Fortran
|
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
|