A theoretical analysis of nuclear magnetic resonance experiments on proton transfer in benzoic acid crystals

Abstract

A theory of proton transfer reactions oriented toward transfer in solids is presented. This theory is used to interpret the experimental data of Nagaoka et al. [S. Nagaoka, T. Terao, F. Imashiro, A. Saika, and N. Hirota, J. Chem. Phys. 79, 4694 (1983)], who measured proton transfer rates in dicarboxylic acids by the use of NMR T1 measurements. The experiments, carried out over a large range of temperature, imply that the proton transfer rate is activated at high temperature and falls to a temperature-independent rate at low temperature. It is assumed that the proton motion occurs by tunneling between equivalent sites and is modulated by coupling to the acoustic phonons of the solid. The rate of transition is evaluated by the ‘‘golden rule,’’ the perturbation being the splitting between the localized states. It is shown that for the potential surfaces of interest here, another pair of localized states exist in the potential well and, for the higher temperatures of the experiment, excitation to this higher tunneling pair dominates the observed activation energy. Since the acoustic coupling model leads to a very small reorganization energy for the transfer, the medium’s nuclear degrees of freedom are tunneling even at high temperature. Therefore, the rate of tunneling between either pair of levels is found to be only very weakly temperature dependent.