Assessing Many-Body Effects of Water Self-Ions. II: H3O+(H2O)n Clusters.

The importance of many-body effects in the hydration of the hydronium ion (H3O+) is investigated through a systematic analysis of the many-body expansion of the interaction energy carried out at the coupled-cluster level of theory for the low-lying isomers of H3O+(H2O)n clusters with n = 1-5. This is accomplished by partitioning individual fragments extracted from the whole clusters into "groups" that are classified by both the number of H3O+ and water molecules and the hydrogen-bonding connectivity within a given fragment. Effects due to the presence of the Zundel ion, (H5O2)+, are analyzed by further partitioning fragment groups by the "context" of their parent clusters. With the aid of the absolutely localized molecular orbital energy decomposition analysis (ALMO EDA), this structure-based partitioning is found to largely correlate with the character of different many-body interactions, such as cooperative and anticooperative hydrogen bonding, within each fragment. This analysis emphasizes the importance of a many-body representation of inductive electrostatics and charge transfer in modeling the hydration of an excess proton in water. The comparison between the reference coupled-cluster many-body interaction terms with the corresponding values obtained with various exchange-correlation functionals demonstrates that many of these functionals yield an unbalanced treatment of the H3O+(H2O)n configuration space.