Curve crossing formulation for proton transfer reactions in solution

A Landau-Zener curve crossing formulation is developed for proton transfer rate constants over the range of proton coupling. This approach spans the weak coupling regime, where the transfer is a nonadiabatic proton tunneling, to the strong coupling regime, where at the reaction transition state the proton motion is a quantized vibration lying above the barrier in the proton coordinate. The theory requires that there is strong coupling of the proton transfer solute to the surrounding polar solvent and includes the influence of the vibrational motion of the heavy particles between which the proton transfers, Analytic formulas are given for the rate constants in various limits of the proton coupling strength and the vibrational frequency of the heavy particle motion.