Unusual temperature dependence of proton transfer 3. Classical Kramers' theory versus the Landau-Zener curve-crossing formulation

Previously, we measured the proton-transfer rate constant from strong photoacids to several solvents such as alcohols and water as a function of temperature. We found an unusual temperature dependence: at high temperature the rate constant is almost temperature independent whereas at low temperature the rate constant exhibits a strong temperature dependence and follows the inverse of the dielectric relaxation time of the particular solvent. We used the Landau-Zener curve-crossing formulation to calculate the proton-transfer rate constant. We explained the temperature dependence as a continuous transition from nonadiabatic (high-temperature) to solvent-controlled (low-temperature) limits. In this study, we used the classical Kramers' theory in the medium and strong-damping limits to calculate the transmission coefficient and rate constant. We found good correspondence between the experimental and calculated proton-transfer rate constant at all temperatures using both models. In both models, the dynamical parameter used to calculate the temperature dependence of the proton-transfer rate constant is the dielectric relaxation time of the particular solvent.