Magic Numbers and Stabilities of Photoionized Water Clusters: Computational and Experimental Characterization of the Nanosolvated Hydronium Ion

The stability and distributions of small water clustersgeneratedin a supersonic beam expansion are interrogated by tunable vacuumultraviolet (VUV) radiation generated at a synchrotron. Time-of-flightmass spectrometry reveals enhanced population of various protonatedwater clusters (H+(H2O)( n )) based upon ionization energy and photoionization distancefrom source, suggesting there are "magic" numbers belowthe traditional n = 21 that predominates in the literature.These intensity distributions suggest that VUV threshold photoionization(11.0-11.5 eV) of neutral water clusters close to the nozzleexit leads to a different nonequilibrium state compared to a skimmedmolecular beam. This results in the appearance of a new magic numberat 14. Metadynamics conformer searches coupled with modern densityfunctional calculations are used to identify the global minimum energystructures of protonated water clusters between n = 2 and 21, as well as the manifold of low-lying metastable minima.New lowest energy structures are reported for the cases of n = 5, 6, 11, 12, 16, and 18, and special stability is identifiedby several measures. These theoretical results are in agreement withthe experiments performed in this work in that n =14 is shown to exhibit additional stability, based on the computedsecond-order stabilization energy relative to most cluster sizes,though not to the extent of the well-known n = 21cluster. Other cluster sizes that show some additional energetic stabilityare n = 7, 9, 12, 17, and 19. To gain insight intothe balance between ion-water and water-water interactionsas a function of the cluster size, an analysis of the effective two-bodyinteractions (which sum exactly to the total interaction energy) wasperformed. This analysis reveals a crossover as a function of clustersize between a water-hydronium-dominated regime for small clustersand a water-water-dominated regime for larger clusters around n = 17.