Analysis of hydrogen bonding in the OH stretch region of protonated water clusters

There are two types of bands in the OH stretch region of the vibrational spectra of hydrogen-bonded complexes; narrow peaks due to isolated OH stretches and a broadened feature reflecting the OH stretches involved in strong hydrogen bonding. This second region can be as wide as several hundred wavenumbers and is shifted to the red of the narrow peaks. In this work we focus on H$^{+}$(H$_{2}$O)$_{n}$, where n = 3 or 4.footnote{Relph, R. A.; Guasco, T. L.; Elliot, B. M.; Kamrath, M. Z.; McCoy, A. B.; Steele, R. P.; Schofield, D. P.; Jordan, K. D.; Viggiano, A. A.; Ferguson, E. E.; Johnson, M. A. textit{Science}, textbf{2010}, textit{327(5963)}, 308-312.} Both of these systems exhibit a very intense, broad H-bonded band. This breadth arises from coupling between the OH stretches and the low frequency modes. To understand the broadening observed in the spectra, we have developed a computational scheme in which we sample displacement geometries from the equilibrium structure based on the ground state harmonic wavefunction.footnote{Johnson, C. J.; Dzugan, L. C.; Wolk, A. B.; Leavitt, C. M.; Fournier, J. A.; McCoy, A. B.; Johnson, M. A. textit{J. Phys. Chem. A}, textbf{2014}, textit{118}, 7590-7597.} Then we combine the harmonic spectra in the OH stretch region for each computed geometry to generate the spectrum for each protonated water structure. Based on the large anharmonicities at play in these modes, we extend the approach using second-order perturbation theory to solve the reduced-dimensional Hamiltonian that involves only the HOH bends and the OH stretches. This is done by expressing the normal modes used to expand the Hamiltonian as linear combinations of internal coordinates. In this talk we will describe the approach used for these anharmonic calculations and report preliminary results for these protonated water clusters