if we assume that ∆E n and ∆E n-1 have opposite signs. Here, N F (n) is the number of n-body subsystems and ∆E n is the mean n-body correction term. Because the number of fragments increases combinatorially, the magnitude of ∆E n can decrease order-by-order (as in Fig. ) yet the product N F (n) ∆E n may still be large enough to cause divergence. If divergence of MBE(n) calculations is indeed driven by combinatorial error accumulation, then smaller clusters with fewer fragments should exhibit improved convergence properties. To examine this hypothesis, we extracted clusters F -(H 2 O) N with N = 5-25 from a molecular dynamics simulation of F -(H 2 O) 128 . The absolute error per monomer in ∆E int , computed at the PBE/aDZ level, is plotted in Fig. up to N = 15 and plots up to N = 25 can be found in Figs. S5-S7, for both PBE/ aDZ and HF/aDZ calculations. Normalizing the errors by the number of monomers accounts for overall errors that are expected to be size-extensive (i.e., a roughly constant error per hydrogen bond), and indeed the normalized HF errors in Figs. S5-S7 are independent of cluster size. In contrast, PBE errors diverge as N increases, for MBE(3), MBE(4), and MBE (5). We posit that SIEinduced error accumulation explains divergent behavior in DFT-MBE(n) calculations that has been documented previously by our group. Examining the PBE-MBE(n) results in Fig. and moving up the ladder from n = 2 to n = 5, we observe an order-by-order reduction in the error for small clusters, up to F -(H 2 O) 8 . For larger clusters, however, MBE(4) affords a larger error than MBE(3) and by F -(H 2 O) 16 , the two-body expansion affords the smallest error per monomer. For larger clusters, higher-order n-body terms are actually detrimental to the accuracy! Considering the product N F (n) ∆E n in eqn. (2) suggests two strategies for improving convergence of MBE(n): either reduce the per-fragment error via strategies to mitigate SIE, or else reduce the number of fragments via screening. Both strategies are pursued in Section 3.