That is why the other two w MRF c,λ=1 (r) in Fig. are negative everywhere since they are obtained from Eq. 41. While the magnitude of 'MRF UEG' is reasonable, it misses the shell structure of the exact w c,λ=1 (r). 'MRF new' is the most accurate here and highlights the the importance of using F (r) in Eq. 41 to improve MRF. Also, the s(r) quantity equips 'MRF new' to capture the shell structure in the underlying correlation energy densities. This is further highlighted in Figure , where we compare the underlying σc,λ=1 L (r) with 'exact' σc,λ=1 (r) obtained via rm-MRF from accurate w λ=1 (r) (further technical details are given in the caption of the figure).