diff --git a/src/eDFT/UVWN5_lda_correlation_individual_energy.f90 b/src/eDFT/UVWN5_lda_correlation_individual_energy.f90 index 80c6990..beb8031 100644 --- a/src/eDFT/UVWN5_lda_correlation_individual_energy.f90 +++ b/src/eDFT/UVWN5_lda_correlation_individual_energy.f90 @@ -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