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