How the Zundel (H₅O₂⁺) Potential Can Be Used to Predict the Proton Stretch and Bend Frequencies of Larger Protonated Water Clusters

From a series of seminal experiments on the IR spectra of protonated water clusters and associated theoretical analyses, it is clear that the energies and spectral features of the proton stretch and bend modes are very sensitive functions of the cluster size. Here we show that this dynamic range can be understood by examining the sensitivity of these modes in the potential of the Zundel cation, H₅O₂⁺, as the separation of the two water monomers is varied. As this distance increases, the proton increasingly localizes on a monomer, and this is encoded in the IR spectrum of the proton vibrational modes. The quantitative predictions from this simple correlation are verified for the H₇O₃⁺ and H₉O₄⁺ clusters, for which new benchmark harmonic frequencies are reported. The predictions are also in good accord with trends seen experimentally and previous calculations for these and five other clusters, including H⁺(H₂O)₂₁.