where both calculations are performed using the same density functional and basis set. As a control experi- ment, we demonstrate in Fig. that convergence is indeed achieved for a set of F -(H 2 O) 15 clusters, using calculations at the Hartree-Fock (HF)/aug-cc-pVDZ level of theory. Residual errors spanning ≈ 2.5 kcal/mol, observed at the five-body level in Fig. , have elsewhere been shown to be artifacts of basis-set superposition error (BSSE). For Cl -(H 2 O) 9 , five body terms computed at the level of second-order Møller-Plesset perturbation theory (MP2)/aug-cc-pV5Z are negligibly small. HF-based MBE(n) calculations, for which there is no grid and no SIE, will serve as a baseline in the remaining discussion. For example, the analogous PBE/augcc-pVDZ data for (H 2 O) 15 are shown in Fig. , superimposed on the span of the corresponding HF-MBE(n) errors. As demonstrated in previous work, the PBE-MBE(n) errors diverge as n increases, with errors approaching ∼ 150 kcal/mol at the five-body level.