where s(r) is the usual reduced density gradient s(r) = |∇ρ(r)| / 2(3π 2 ) 1/3 ρ(r) 4/3 . This choice of F (r) ensures that at s = 0, the high accuracy of the new fluctuation function for MRF is preserved for the UEG. In the rapidly varying limit ( s → ∞), correlation vanishes and so does our σc,λ=1 L (r) term with this choice for F (r). Nonnegativity of the sum of the correlation terms in Eq. 41 ensures that w MRF λ=1 never lies above the exact w λ=0 and this was not the case with the original MRF (Eq. 11). ] The MRF functional has been evaluated on the CCSD/augcc-pCVTZ densities and the reference w c,λ=1 (r) has been obtained by using the same level of theory and are taken from Refs. . Inset shows the errors in approximate w c,λ=1 (r)