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fix correlation individual energies

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This commit is contained in:
Pierre-Francois Loos 2020-07-08 11:57:04 +02:00
parent 467fa5d08c
commit 253058056b
1 changed files with 45 additions and 47 deletions
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92
src/eDFT/UVWN5_lda_correlation_individual_energy.f90
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@ -61,6 +61,39 @@ subroutine UVWN5_lda_correlation_individual_energy(nGrid,weight,rhow,rho,Ec)
! spin-up contribution
if(ra > threshold .or. raI > threshold) then
r = ra
rI = raI
rs = (4d0*pi*r/3d0)**(-1d0/3d0)
x = sqrt(rs)
x_f = x*x + b_f*x + c_f
xx0_f = x0_f*x0_f + b_f*x0_f + c_f
q_f = sqrt(4d0*c_f - b_f*b_f)
ec_f = a_f*( log(x**2/x_f) + 2d0*b_f/q_f*atan(q_f/(2d0*x + b_f)) &
- b_f*x0_f/xx0_f*( log((x - x0_f)**2/x_f) + 2d0*(b_f + 2d0*x0_f)/q_f*atan(q_f/(2d0*x + b_f)) ) )
drsdra = - (36d0*pi)**(-1d0/3d0)*r**(-4d0/3d0)
dxdrs = 0.5d0/sqrt(rs)
dxdx_f = 2d0*x + b_f
decdx_f = a_f*( 2d0/x - 4d0*b_f/( (b_f+2d0*x)**2 + q_f**2) - dxdx_f/x_f &
- b_f*x0_f/xx0_f*( 2/(x-x0_f) - 4d0*(b_f+2d0*x0_f)/( (b_f+2d0*x)**2 + q_f**2) - dxdx_f/x_f ) )
decdra_f = drsdra*dxdrs*decdx_f
Ec(1) = Ec(1) + weight(iG)*(ec_z + decdra_f*r)*rI
end if
! up-down contribution
if(ra > threshold .or. raI > threshold) then
r = ra + rb
@ -132,73 +165,38 @@ subroutine UVWN5_lda_correlation_individual_energy(nGrid,weight,rhow,rho,Ec)
! spin-down contribution
if(rb > threshold .or. rbI > threshold) then
r = ra + rb
rI = raI + rbI
r = rb
rI = rbI
rs = (4d0*pi*r/3d0)**(-1d0/3d0)
z = (ra - rb)/r
x = sqrt(rs)
fz = (1d0 + z)**(4d0/3d0) + (1d0 - z)**(4d0/3d0) - 2d0
fz = fz/(2d0*(2d0**(1d0/3d0) - 1d0))
d2fz = 4d0/(9d0*(2**(1d0/3d0) - 1d0))
x_p = x*x + b_p*x + c_p
x_f = x*x + b_f*x + c_f
x_a = x*x + b_a*x + c_a
xx0_p = x0_p*x0_p + b_p*x0_p + c_p
xx0_f = x0_f*x0_f + b_f*x0_f + c_f
xx0_a = x0_a*x0_a + b_a*x0_a + c_a
q_p = sqrt(4d0*c_p - b_p*b_p)
q_f = sqrt(4d0*c_f - b_f*b_f)
q_a = sqrt(4d0*c_a - b_a*b_a)
ec_p = a_p*( log(x**2/x_p) + 2d0*b_p/q_p*atan(q_p/(2d0*x + b_p)) &
- b_p*x0_p/xx0_p*( log((x - x0_p)**2/x_p) + 2d0*(b_p + 2d0*x0_p)/q_p*atan(q_p/(2d0*x + b_p)) ) )
ec_f = a_f*( log(x**2/x_f) + 2d0*b_f/q_f*atan(q_f/(2d0*x + b_f)) &
ec_f = a_f*( log(x**2/x_f) + 2d0*b_f/q_f*atan(q_f/(2d0*x + b_f)) &
- b_f*x0_f/xx0_f*( log((x - x0_f)**2/x_f) + 2d0*(b_f + 2d0*x0_f)/q_f*atan(q_f/(2d0*x + b_f)) ) )
ec_a = a_a*( log(x**2/x_a) + 2d0*b_a/q_a*atan(q_a/(2d0*x + b_a)) &
- b_a*x0_a/xx0_a*( log((x - x0_a)**2/x_a) + 2d0*(b_a + 2d0*x0_a)/q_a*atan(q_a/(2d0*x + b_a)) ) )
ec_z = ec_p + ec_a*fz/d2fz*(1d0-z**4) + (ec_f - ec_p)*fz*z**4
dzdrb = -(1d0 + z)/r
dfzdz = (4d0/3d0)*((1d0 + z)**(1d0/3d0) - (1d0 - z)**(1d0/3d0))/(2d0*(2d0**(1d0/3d0) - 1d0))
dfzdrb = dzdrb*dfzdz
drsdrb = - (36d0*pi)**(-1d0/3d0)*r**(-4d0/3d0)
drsdra = - (36d0*pi)**(-1d0/3d0)*r**(-4d0/3d0)
dxdrs = 0.5d0/sqrt(rs)
dxdx_p = 2d0*x + b_p
dxdx_f = 2d0*x + b_f
dxdx_a = 2d0*x + b_a
decdx_p = a_p*( 2d0/x - 4d0*b_p/( (b_p+2d0*x)**2 + q_p**2) - dxdx_p/x_p &
- b_p*x0_p/xx0_p*( 2/(x-x0_p) - 4d0*(b_p+2d0*x0_p)/( (b_p+2d0*x)**2 + q_p**2) - dxdx_p/x_p ) )
decdx_f = a_f*( 2d0/x - 4d0*b_f/( (b_f+2d0*x)**2 + q_f**2) - dxdx_f/x_f &
- b_f*x0_f/xx0_f*( 2/(x-x0_f) - 4d0*(b_f+2d0*x0_f)/( (b_f+2d0*x)**2 + q_f**2) - dxdx_f/x_f ) )
decdx_a = a_a*( 2d0/x - 4d0*b_a/( (b_a+2d0*x)**2 + q_a**2) - dxdx_a/x_a &
- b_a*x0_a/xx0_a*( 2/(x-x0_a) - 4d0*(b_a+2d0*x0_a)/( (b_a+2d0*x)**2 + q_a**2) - dxdx_a/x_a ) )
decdra_f = drsdra*dxdrs*decdx_f
decdrb_p = drsdrb*dxdrs*decdx_p
decdrb_f = drsdrb*dxdrs*decdx_f
decdrb_a = drsdrb*dxdrs*decdx_a
Ec(3) = Ec(3) + weight(iG)*(ec_z + decdra_f*r)*rI
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 &
+ (decdrb_f - decdrb_p)*fz*z**4 + (ec_f - ec_p)*dfzdrb*z**4 + 4d0*(ec_f - ec_p)*fz*dzdrb*z**3
Ec(2) = Ec(2) + weight(iG)*(ec_z + decdrb*r)*rI
end if
end do
Ec(2) = Ec(2) - Ec(1) - Ec(3)
end subroutine UVWN5_lda_correlation_individual_energy