O–O hemi-bonding in cationic water clusters: Benchmarks from DFT, PNO-LCCSD(T), and FN-DMC

Water cluster cations serve as prototypical models for ionized aqueous environments and provide an ideal platform for examining the stability of O–O hemi-bonded motifs. Despite extensive studies, the relative energetics of hemi-bonded and proton-transferred structures, as well as their dissociation behavior, remain challenging to describe accurately. In this work, we present a systematic benchmark study of cationic water clusters (H₂O)_n⁺ (n = 2–8), with particular emphasis on O–O hemi-bonded systems. Relative energies between hemi-bonded and proton-transferred isomers, energy differences among hemi-bonded configurations, O–O bond dissociation energies of noncyclic hemi-bonded species, and complete dissociation energies are evaluated. High-level CCSD(T)-F12b/CBS calculations establish a clear energetic ordering, showing that proton-transferred isomers are consistently more stable than hemi-bonded structures, while alternative hemi-bonded configurations are separated by much smaller energy gaps. The O–O bond dissociation energies substantially exceed typical hydrogen-bond strengths, confirming the presence of strong three-electron hemi-bonding interactions. Benchmarking against these reference data reveals that hybrid meta-generalized gradient approximation (meta-GGA) functionals with high exact exchange and spin-component-scaled double hybrids provide the most reliable density functional theory performance for relative energies, whereas dissociation energies remain challenging for most density functional approximations. Explicitly correlated PNO-LCCSD(T)-F12 and fixed-node diffusion Monte Carlo with T-move treatment deliver uniformly high accuracy, highlighting their suitability as robust reference approaches for larger hemi-bonded systems beyond the reach of canonical coupled-cluster methods.