Understanding the structures of medium-sized protonated water clusters [H⁺(H₂O)_n] has made a significant advancement recently thanks to the development of new experimental techniques and high-level computational methods. A combination of vibrational predissociation spectroscopy and ab initio calculations was shown to be effective in elucidating the structures of the clusters as a function of their temperature and size. The combined study revealed several intriguing features (such as symmetric hydrogen bonds) that could not be found for neutral water clusters. However, similar to its neutral counterpart, the number of stable isomers increases exponentially with cluster size (n), making direct structural identification of medium-sized clusters difficult. Despite the difficulties, both experimental and computational results indicated a smooth change in hydrogen-bond topology from tree-like, single-ring, multiple-ring to polyhedron-like structures (and their mixtures) as n increases from 5 to 28. The excess proton can be symmetrically hydrated at n = 6-8. Five-membered ring isomers can form at n = 7 and 8 as the low-lying minima. Only a single feature (∼3695 cm^-1) in the free OH stretching region was observed for H⁺(H₂O)₂₁ and H⁺(H₂O)₂₈, suggesting that all surface water molecules are linked in a similar 3-coordinated (double-acceptor-single-donor, (AAD)) configuration in both “magic number” clusters. The clathrate-like structures open up at higher temperatures, as evidenced by the increased intensity of the free-OH stretching absorption band (∼3715 cm^-1) of 2-coordinated (single-acceptor-single-donor, (AD)) water molecules. Further understanding of the structures and thermal properties of these clusters is gained through the studies with Monte Carlo (MC) and molecular dynamics simulations, ion reactivity and thermal dissociation measurements, as well as Ar tagging experiments.

Contents	PAGE
1. Introduction	554
2. Experiments	555
2.1. Hydrogen-bond topologies	556
2.2. “Magic number” clusters	559
2.3. Symmetric proton hydration	562
2.4. Cluster temperatures	564
3. Theories	567
3.1. Global minimum structures	567
3.2. Thermal and dynamical effects	572
4. Conclusion	574
Acknowledgements	451
References	451