Estimating the barrier to proton or deuteron tunnelling in hydrogen-bonded crystals

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Abstract
We represent a symmetric double minimum proton potential by two Morse functions placed back-to-back. The wave-functions and energy eigenvalues are determined by asymptotic analysis. Using as input the crystallographic atom positions and the frequencies of two infrared transitions we can deduce the well parameters for CrOOD. Using the same well parameters (but somewhat different atom positions) for CrOOH, we derive an energy structure in good agreement with the observed mid infrared, far infrared and neutron inelastic scattering spectra. The model should be useful for estimating the tunnelling integral in KDP-type ferroelectrics, and its dependence on the oxygen-oxygen separation.

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