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qp2/src/dft_utils_func/ecmd_lda.irp.f

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2020-04-07 11:03:19 +02:00
!****************************************************************************
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