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<p>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 H-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. </p>
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