A 'clusters-in-liquid' method for calculating infrared spectra identifies the proton-transfer mode in acidic aqueous solutions

In liquid water the transfer of an excess proton between two water molecules occurs through the Zundel cation, H 2 O···H + ···OH 2. The proton-transfer mode is the asymmetric stretch of the central O···H + ···O moiety, but there is no consensus on its identification in the infrared spectra of acidic aqueous solutions. Also, in experiments with protonated gas-phase water clusters, its position shifts with cluster size, which makes its relationship with solution spectra unclear. Here we introduce a 'clusters-in-liquid' approach for calculating the infrared spectrum from any set of charges, even single protons. We apply this procedure to multistate empirical valence-bond trajectories of protonated liquid water and to ab initio molecular dynamics of the protonated water dimer and hexamer in the gas phase. The calculated proton-transfer mode is manifested in both systems as a peak near 1,740% cm -1, in quantitative agreement with a band of similar frequency in the experimental infrared spectrum of protonated water clusters.