In panel (b) of Figs. and, we shift from global E λ c to its spatially-and λ-resolved counterpart, e λ c (r), plotted versus the distance from the nucleus r, and scaled by the spherical volume element 4πr 2 . The λ-averaged (Eq. 22) correlation energies, e c (r), are also shown. For Ne 8+ , the e λ c (r) curve for larger λ lies entirely below that for smaller λ (no crossings). By contrast, for H -, the e λ=1 c (r) curve has a region where it dips below those at lower λ. In Fig. In panel (c) of Figs. and, we show the operatorresolved components of e λ c (r): e ee c (r), e J c (r), and e K c (r) (see Eq. 34). The term e ee c (r) dominates, while e J c (r) and e K c (r) are smaller, with opposite signs, and nearly canceling each other. The magnitudes of e J c (r) and e K c (r) decrease significantly from H -to Ne 8+ . This trend is expected for the He isoelectronic series, where e J c (r) and e K c (r) are predicted to vanish as Z → ∞. This occurs because the small-λ (MP2) limit-which is more dominant at larger Z for the helium isoelectronic series-yields vanishing contributions for these terms (Sec. IV B). For more representative systems belonging to the He isoelectronic series, see Sec. S4 in the SI. Figs. and show the same MPAC quantities as Figs. and, but for the Be isoelectronic series ions, Li -(Z = 3) and Ne 6+ (Z = 10). Although the Be series densities also become more compact with increasing Z 4 , near-degeneracy effects-absent in the He series-lead to notably different behavior in correlation effects. This is already reflected in the global E λ c , which does not become more linear as we go from Li -to Ne 6+ (panel (a) of Figs. and), in stark contrast to the trend from H - to Ne 8+ (panel (a) of Figs. and). Moving to panel (b) of Figs. and, we can see that for Li -, e λ c (r) becomes increasingly negative as λ increases, with no crossings observed. By contrast, for Ne 6+ , crossings are observed, and the λ = 1 curve has a region that is less negative than some lower-λ curves. The contrasting behavior between the Be and He isoelectronic series is also evident in the operator-resolved components of e λ c (r) shown in panel (c) of Figs. and. For Li -, e J c (r) is notably large [see Fig. ] and is particularly dominant in the valence region. A large magnitude of e λ c,J (r) = -∆ρ λ (r)v HF H (r) (follows from Eqs. 22, 23 and 29) reflects that ρ λ (r) densities change substantially when λ goes from 0 to 1. Moving to Fig. , for Ne 6+ the magnitude of e J c (r) becomes comparable to that of e ee c (r) and significantly exceeds the other two contributions in the inter-shell region. Furthermore, unlike in the He isoelectronic series, e J c (r) and e K c (r) do not vanish at larger Z for the Be isoelectronic series (compare Fig. ) for Ne 8+ with Fig. (c) for Ne 6+ ). This again underscores the general trend of this section that local correlation effects are very different between the He and Be isoelectronic series. For more representative systems belonging to the Be isoelectronic series, see Sec. S5 in the SI. FIG. : Correlation energies with respect to isoelectronic series of Helium and Beryllium obtained from the λ-averaged reference, the modified-Padé [Eq. 43 and e 1 c (r)] and MP2 [Eq. 36]. For H - an uncontracted aug-cc-pVQZ basis was used, whereas for the rest of the systems an uncontracted cc-pVQZ basis was used.