Snapshots of Proton Accommodation at a Microscopic Water Surface: Understanding the Vibrational Spectral Signatures of the Charge Defect in Cryogenically Cooled H+(H2O)n=2-28 Clusters

We review the role that gas-phase, size-selected protonated water clusters, H+(H2O)(n), have played in unraveling the microscopic mechanics responsible for the spectroscopic behavior of the excess proton in bulk water. Because the larger (n >= 10) assemblies are formed with three-dimensional cage morphologies that more closely mimic the bulk environment, we report the spectra of cryogenically cooled (10 K) clusters over the size range 2 <= n <= 28, over which the structures evolve from two-dimensional arrangements to cages at around n = 10. The clusters that feature a complete second solvation shell around a surface-embedded hydronium ion yield spectral signatures of the proton defect similar to those observed in dilute acids. The origins of the large observed shifts in the proton vibrational signature upon cluster growth were explored with two types of theoretical analyses. First, we calculate the cubic and semidiagonal quartic force constants and use these in vibrational perturbation theory calculations to establish the couplings responsible for the large anharmonic red shifts. We then investigate how the extended electronic wave functions that are responsible for the shapes of the potential surfaces depend on the nature of the H-bonded networks surrounding the charge defect. These considerations indicate that, in addition to the sizable anharmonic couplings, the position of the OH stretch most associated with the excess proton can be traced to large increases in the electric fields exerted on the embedded hydronium ion upon formation of the first and second solvation shells. The correlation between the underlying local structure and the observed spectral features is quantified using a model based on Badger's rule as well as via the examination of the electric fields obtained from electronic structure calculations.