Understanding the Many-Body Basis Set Superposition Error: Beyond Boys and Bernardi.

Comput. 2015, 11, 5132-5143] as well as a related study by Mayer and Bakó [ J. Chem. Theory Comput. 2017, 13, 1883-1886] have proposed new frameworks for understanding BSSE in the many-body expansion. Although the two frameworks ultimately propose the same working set of equations to the BSSE problem, their interpretations are quite different, even disagreeing on whether or not the solution is an approximation. In this work we propose a more general BSSE framework. We then show that, somewhat paradoxically, the two interpretations are compatible and amount to two different "normalization" conditions. Finally, we consider applications of these BSSE frameworks to small water clusters, where we focus on replicating high-accuracy coupled cluster benchmarks. Ultimately, we show for water clusters, using the present framework, that one can obtain results that are within ±0.5 kcal mol-1 of the coupled cluster complete basis set limit without considering anymore than a correlated three-body computation in a quadruple-ζ basis set and a four-body triple-ζ Hartree-Fock computation.