Proton transfer in benzoic acid crystals: Another look using quantum operator theory

We present a calculation of the rate of synchronous double proton transfer in benzoic acid crystals. Experiments on these systems have been performed over a wide range of temperatures (roughly 10-400°K). Even though the energetic barrier for proton transfer is rather high, the observed activation energy is low, while kinetic isotope experiments seem to indicate classical transfer. The system exhibits significant quantum character even at high temperatures and we show that the observed low activation energies can be reproduced assuming that the reaction is "assisted" by a low-frequency intramolecular mode, as has been suggested in different contexts by Benderskii [V. A. Benderskii, S. Yu. Grebenshchikov, and G. V. Mil'nikov, Chem. Phys. 194, 1 (1995)], Hynes [D. Borgis and J. Hynes, J. Chem. Phys. 94, 3619 (1991)] and Silbey [A. Suarez and R. Silbey, J. Chem. Phys. 94, 4809 (1991)]. We use our previous work on the quantum Kramers problem to perform a fully quantum calculation that incorporates symmetric coupling to the intramolecular mode and coupling to the condensed environment to all orders. We calculate the activation energies for hydrogen and deuterium transfer and we show that our results are in quantitative agreement with the experiment.