Evidence for a continuous transition from nonadiabatic to adiabatic proton transfer dynamics in protic liquids

The reversible proton dissociation and geminate recombination of photoacids is studied as a function of temperature in monols, diols, and glycerol. For this purpose, we use a strong photoacid 5,8-dicyano-2-naphthol (DCN2) (pK*(a)approximate to -4.5 in water), capable of transferring a proton to alcohols. The experimental data are analyzed by the Debye-Smoluchowski equation, which is solved numerically with boundary conditions to account for the reversibility of the reaction. At high temperature, the proton-transfer rate is almost temperature independent, wheras at low temperature, the rate constant has strong temperature dependence. The unusual temperature dependence is explained using Borgis-Hynes proton transfer theory, based on the Landau-Zener curve crossing formulation. The high-temperature behavior of the rate constant denotes the nonadiabatic limit, whereas the low-temperature behavior denotes the adiabatic limit. We have used an approximate expression for the proton-transfer rate, which bridges the nonadiabatic and the solvent controlled adiabatic limit to fit the temperature dependence curve of the experimental proton-transfer rate constant.