A pairwise and two many-body models for water: Influence of nonpairwise effects upon the stability and geometry of (H2O)n cyclic (n=3–6) and cagelike (n=6–20) clusters

Three flexible models (PW, CMP and TCPE) are presented to study interactions occurring in water clusters. The total interaction energy is decomposed into five terms; repulsive, charge–charge, intramolecular relaxation, polarization, and hydrogen bonding. The parameters of the first three terms are the same for all of the three models. The polarization term is taken as a classical molecular many-body polarization potential for the CMP and TCPE models, while nonpairwise effects are omitted in the PW model. As nonpairwise effects occurring in water clusters greater than the dimer have a topological origin, such effects are introduced in the hydrogen bonding term of the TCPE model. Parameters of the three models are derived from ab initio calculations at the $\mathrm{MP2/6-311+G}\text{(2df,2p)}$ level on three water dimer structures and the cyclic water trimer. Application of the three models to water clusters $({\mathrm{H}}_{\mathrm{2}}\mathrm{O}{)}_n$ from $\text{n=3}$ to 20 exhibits that the nonpairwise effects in such clusters represent about 20% of their total binding energy and that the two nonpairwise effects considered suffice to describe most of the many-body effects. In particular, the many-body polarization term is mostly responsible for interoxygen distance contractions (relative to the dimer) in clusters greater than $\text{n=3.}$ In cyclic clusters, this term is responsible for 40%–70% of the total nonpairwise effect energy, while in cagelike clusters, for about 50%.