In practice, small i max values are needed to achieve convergence. The second term in Eq. 33 is a resummation, whereas the first term requires an explicit summation and is thus Right panel: i-averaged σλ=1 (r s ) obtained from Eq. 34 and exact w λ=1 (r s ) [Eq. 16; PW92 parametrization] at different r s values. The insets zoom in on the plots at small and large r s values. more expensive. Physically this can be seen as if the reference electron interacts only with a set of i max -1 neighbors, and the remaining ones are only implicitly treated. We can check the convergence of MRF for the UEG w.r.t. i max by using the fluctuation function of Eq. 11 for λ = 1 . The convergence of w MRF λ=1 (r s ) w.r.t. i max at zero spin polarization is shown in the left panel of Fig. . We can see that for small r s only few electrons are needed to reach the convergence (for r s = 10, i max = 5 is more than enough, and for r s = 25, i max = 10 is more than enough). But, for r s = 100 the convergence is achieved at i max ∼ 100. Mathematically, this is because at small r s values i max quicker becomes much larger than σ i≥2 , since when r s → 0, σ i tends to 0 [Eqs. 11 and Eq. 31]. Physically, this is also an appealing feature of MRF, as larger i max values are needed to achieve the convergence as correlation becomes stronger with the increase of r s . In other words, a reference electron needs to "communicate" with more and more neighbors to describe the physics of the UEG as long-range fluctuations become more and more important as r s → ∞.