computed XC integrand at the full coupling strength (W λ=1 [ρ] of Eq. 4; physical electronic repulsion energy minus the Hartree energy). All MRF values have been obtained by using the MRF Gaussian basis solver described in Section 6 and the Hartee-Fock (HF) density. given by Eq. 41 with F given by Eq. 42; the orange curve in Fig. ]. We design 'MRF new' to ensure that its correlation energy densities are always negative as this is not the case with 'MRF original'. Unfortunately, we can see from for atoms, but still constrain the MRF correlation energy densities to always be negative, we consider the following optimization of MRF, with the following fluctuation function: