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.