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An efficient procedure is introduced to obtain the basis-set limit in electronic structure calculations of large molecular and ionic clusters. This approach is based on a Boys–Bernardi-style counterpoise correction for clusters containing arbitrarily many monomer units, which is rendered computationally feasible by means of a truncated many-body expansion. This affords a tractable way to apply the sequence of correlation-consistent basis sets (aug-cc-pVXZ) to large systems and thereby obtain energies extrapolated to the complete basis set (CBS) limit. A three-body expansion with three-body counterpoise corrections is shown to afford errors of ≲0.1–0.2 kcal/mol with respect to traditional MP2/CBS results, even for challenging systems such as fluoride–water clusters. A triples correction, δ_CCSD(T) = E_CCSD(T) – E_MP2, can be estimated accurately and efficiently as well. Because the procedure is embarrassingly …