Evaluation of the Electrostatically Embedded Many-Body Expansion and the Electrostatically Embedded Many-Body Expansion of the Correlation Energy by Application to Low-Lying Water Hexamers

We have applied a many-body (MB) expansion, the electrostatically embedded many-body (EE-MB) approximation, and the electrostatically embedded many-body expansion of the correlation energy (EE-MB-CE), each at the two-body (MB = PA, where PA denotes pairwise additive) and three-body (MB = 3B) levels, to calculate total energies for a series of low-lying water hexamers using eight correlated levels of theory including second-order and fourth-order Møller-Plesset perturbation theory (MP2 and MP4) and coupled cluster theory with single, double, and quasipertubative triple excitations (CCSD(T)). Comparison of the expansion methods to energies obtained from full (i.e., unexpanded) calculations shows that the EE-3B-CE method is able to reproduce the full cluster energies to within 0.03 kcal/mol, on average. We have also found that the deviations of the results predicted by the expansion methods from those obtained with full calculations are nearly independent of the correlated level of theory used; this observation will allow validation of the many-body methods on large clusters at less expensive levels of theory (such as MP2) to be extrapolated to the CCSD(T) level of theory. Furthermore, we have been able to rationalize the accuracies of the MB, EE-MB, and EE-MB-CE methods for the six hexamers in terms of the specific many-body effects present in each cluster.