If only the first term of Eq. 41 is used, the resulting reduces to the the exact w λ,0 (r) via rm-MRF (i.e. w MRF c,λ=1 (r) = 0). If only the second term of Eq. 41 is used, the original σ λ=1 i (r) is recovered (Eq. 11) and the resulting w MRF λ=1 (r) is labeled as 'MRF original'. This second term term of Eq. 41 is essentially zero for the neon atom as all S i (r) values are large. Nonetheless, σ = 0 gives accurate W MRF λ=1 for atoms as mentioned earlier. Now we consider two different cases when all three terms of Eq. 41 are used. The first one with F (r) = 1 ('MRF UEG'), and the other is with F (r) given by Eq. 42 ('MRF new').