The importance of many-body effects in the hydration of the hydronium ion (HO) 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 HO(HO) clusters with = 1-5. This is accomplished by partitioning individual fragments extracted from the whole clusters into "groups" that are classified by both the number of HO and water molecules and the hydrogen-bonding connectivity within a given fragment. Effects due to the presence of the Zundel ion, (HO), 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 HO(HO) configuration space.
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