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Anharmonicity as a possible explenation of the Eigen-Zundel dilema in the IR spectrum of H+(H2O)21

The acid-base reaction is one of the most fundamental processes in solution and the protonated water clusters play an important role in many chemical and biological aspects. There are mainly two theories about the location of the proton in the water clusters. In the Eigen form the proton is strongly bound to a single bond (H3O+), while in the Zundel form2 lies midway between two water molecules (H2OH+-H2O). The H+(H2O)21 cluster shows an exceptional stability and it is kwon as the “magic number” in the mass distribution of H+(H2O)n.3 Theoretical calculations predicts for the H+(H2O)21 cluster an Eigen model with H3O+ on the surface of the cage.Very recently, Miyazaki et al. and Shin et al. were capable to isolate the protonated water clusters H+(H2O)n with n=6 to 27 in gas phase and measure their IR spectra from 2000 to 4000 cm-1, allowing the experimental characterisation of their Zundel and Eigen nature. They confirmed that the structure of H+(H2O)21 consists a pentagonal dodecahedra cage with an internal water. However, these studies could not determine whether the hydronium ion sits in the interior or on the surface of the water cage. In addition, the experimental spectra don’t show the characteristic intense and shifted O-H stretching vibration for the isolated H3O+ in the their IR spectra of H+(H2O)21 from 2000 to 4000 cm-1. Then, they could not determine whether the Eigen or the Zundel is the correct model for the H+(H2O)21 system. In these studies, it was pointing out the effect of the temperature and the possible contributions from more than one structural isomer of a given cluster size to explain the discrepancy between theoretical and experimental results. In the present work we present a complete different picture of this problem. We calculate the infrared anharmonic spectra of the H+(H2O)21 with the hydronium ion sits in the interior and on the surface of the water cage. We observe that the O-H stretching vibration for the isolated H3O+ can have red-shifts larger than 500 cm-1. The anharmonic effects play a crucial role to characterize the IR spectra of the protonated water clusters and our calculations indicate that the analysis of the IR spectra in the region below 2000 cm-1 can become crucial for the Eigen Zundel dilemma of H+(H2O)21 ​
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