Effective Two-Body Interactions.

Cooperative or nonadditive effects contribute to the pairwise noncovalent interaction of two molecules in a cluster or the condensed phase in ways that depend on the specific arrangements and interactions of the other surrounding molecules that constitute their environment. General expressions for an effective two-body interaction are presented, which are correct to increasing orders in the many-body expansion. The simplest result, correct through third order, requires only seven individual calculations, in contrast to a linear number of three-body contributions. Two applications are presented. First, an error analysis is performed on a model (H2O)8 cluster which completes the first solvation shell of a central water-water hydrogen bond. Energy decomposition analysis is performed to show that the largest effects of cooperativity on the central hydrogen bond arise from electrical polarization. Second, the nature of cooperative effects on proton transfer in an HCl + (H2O)4 cluster is characterized.