153 lines
5.0 KiB
Fortran
153 lines
5.0 KiB
Fortran
!****************************************************************************
|
|
subroutine ESRC_MD_LDAERF (mu,rho_a,rho_b,dospin,e)
|
|
!*****************************************************************************
|
|
! Short-range spin-dependent LDA correlation functional with multideterminant reference
|
|
! for OEP calculations from Section V of
|
|
! Paziani, Moroni, Gori-Giorgi and Bachelet, PRB 73, 155111 (2006)
|
|
!
|
|
! Input: rhot : total density
|
|
! rhos : spin density
|
|
! mu : Interation parameter
|
|
! dospin : use spin density
|
|
!
|
|
! Ouput: e : energy
|
|
!
|
|
! Created: 26-08-11, J. Toulouse
|
|
!*****************************************************************************
|
|
implicit none
|
|
|
|
double precision, intent(in) :: rho_a,rho_b,mu
|
|
logical, intent(in) :: dospin
|
|
double precision, intent(out):: e
|
|
|
|
double precision :: e1
|
|
double precision :: rhoa,rhob
|
|
double precision :: rhot, rhos
|
|
rhoa=max(rho_a,1.0d-15)
|
|
rhob=max(rho_b,1.0d-15)
|
|
rhot = rhoa + rhob
|
|
rhos = rhoa - rhob
|
|
|
|
call ec_only_lda_sr(mu,rho_a,rho_b,e1)
|
|
if(isnan(e1))then
|
|
print*,'e1 is NaN'
|
|
print*,mu,rho_a,rho_b
|
|
stop
|
|
endif
|
|
call DELTA_LRSR_LDAERF (rhot,rhos,mu,dospin,e)
|
|
if(isnan(e))then
|
|
print*,'e is NaN'
|
|
print*,mu,rhot,rhos
|
|
stop
|
|
endif
|
|
e = e1 + e
|
|
|
|
end
|
|
|
|
!****************************************************************************
|
|
subroutine DELTA_LRSR_LDAERF (rhot,rhos,mu,dospin,e)
|
|
!*****************************************************************************
|
|
! LDA approximation to term Delta_(LR-SR) from Eq. 42 of
|
|
! Paziani, Moroni, Gori-Giorgi and Bachelet, PRB 73, 155111 (2006)
|
|
!
|
|
! Input: rhot : total density
|
|
! rhos : spin density
|
|
! mu : Interation parameter
|
|
! dospin : use spin density
|
|
!
|
|
! Ouput: e : energy
|
|
!
|
|
! Warning: not tested for z != 0
|
|
!
|
|
! Created: 26-08-11, J. Toulouse
|
|
!*****************************************************************************
|
|
implicit none
|
|
|
|
double precision rhot, rhos, mu
|
|
logical dospin
|
|
double precision e
|
|
|
|
double precision f13, f83, pi, rsfac, alpha2
|
|
double precision rs, rs2, rs3
|
|
|
|
double precision rhoa, rhob, z, z2, onepz, onemz, zp, zm, phi8
|
|
double precision g0f, g0s
|
|
double precision bd2, bd3
|
|
double precision c45, c4, c5
|
|
double precision bc2, bc4, bc3t, bc5t, d0
|
|
double precision delta2,delta3,delta4,delta5,delta6
|
|
double precision delta
|
|
|
|
parameter(f13 = 0.333333333333333d0)
|
|
parameter(f83 = 2.6666666666666665d0)
|
|
parameter(pi = 3.141592653589793d0)
|
|
parameter(rsfac = 0.620350490899400d0)
|
|
parameter(alpha2 = 0.2715053589826032d0)
|
|
|
|
rs = rsfac/(rhot**f13)
|
|
rs2 = rs*rs
|
|
rs3 = rs2*rs
|
|
|
|
! Spin-unpolarized case
|
|
if (.not.dospin) then
|
|
z = 0.d0
|
|
|
|
! Spin-polarized case
|
|
else
|
|
rhoa=max((rhot+rhos)*.5d0,1.0d-15)
|
|
rhob=max((rhot-rhos)*.5d0,1.0d-15)
|
|
z=min((rhoa-rhob)/(rhoa+rhob),0.9999999999d0)
|
|
endif
|
|
|
|
z2=z*z
|
|
|
|
bd2=dexp(-0.547d0*rs)*(-0.388d0*rs+0.676*rs2)/rs2
|
|
bd3=dexp(-0.31d0*rs)*(-4.95d0*rs+rs2)/rs3
|
|
|
|
onepz=1.d0+z
|
|
onemz=1.d0-z
|
|
phi8=0.5d0*(onepz**f83+onemz**f83)
|
|
|
|
zp=onepz/2.d0
|
|
zm=onemz/2.d0
|
|
c45=(zp**2)*g0s(rs*zp**(-f13))+(zm**2)*g0s(rs*zm**(-f13))
|
|
c4=c45+(1.d0-z2)*bd2-phi8/(5.d0*alpha2*rs2)
|
|
c5=c45+(1.d0-z2)*bd3
|
|
|
|
bc2=-3.d0*(1-z2)*(g0f(rs)-0.5d0)/(8.d0*rs3)
|
|
bc4=-9.d0*c4/(64.d0*rs3)
|
|
bc3t=-(1-z2)*g0f(rs)*(2.d0*dsqrt(2.d0)-1)/(2.d0*dsqrt(pi)*rs3)
|
|
bc5t = -3.d0*c5*(3.d0-dsqrt(2.d0))/(20.d0*dsqrt(2.d0*pi)*rs3)
|
|
|
|
d0=(0.70605d0+0.12927d0*z2)*rs
|
|
delta2=0.073867d0*(rs**(1.5d0))
|
|
delta3=4*(d0**6)*bc3t+(d0**8)*bc5t;
|
|
delta4=4*(d0**6)*bc2+(d0**8)*bc4;
|
|
delta5=(d0**8)*bc3t;
|
|
delta6=(d0**8)*bc2;
|
|
delta=(delta2*(mu**2)+delta3*(mu**3)+delta4*(mu**4)+delta5*(mu**5)+delta6*(mu**6))/((1+(d0**2)*(mu**2))**4)
|
|
|
|
|
|
! multiply by rhot to get energy density
|
|
e=delta*rhot
|
|
|
|
end
|
|
|
|
!*****************************************************************************
|
|
double precision function g0s(rs)
|
|
!*****************************************************************************
|
|
! g"(0,rs,z=1) from Eq. 32 of
|
|
! Paziani, Moroni, Gori-Giorgi and Bachelet, PRB 73, 155111 (2006)
|
|
!
|
|
! Created: 26-08-11, J. Toulouse
|
|
!*****************************************************************************
|
|
implicit none
|
|
double precision rs
|
|
double precision rs2, f53, alpha2
|
|
parameter(f53 = 1.6666666666666667d0)
|
|
parameter(alpha2 = 0.2715053589826032d0)
|
|
rs2=rs*rs
|
|
g0s=(2.d0**f53)*(1.d0-0.02267d0*rs)/((5.d0*alpha2*rs2)*(1.d0+0.4319d0*rs+0.04d0*rs2))
|
|
end
|
|
|