| Abstract
| - The vibronic couplings for the phenoxyl/phenol and the benzyl/toluene self-exchange reactionsare calculated with a semiclassical approach, in which all electrons and the transferring hydrogen nucleusare treated quantum mechanically. In this formulation, the vibronic coupling is the Hamiltonian matrix elementbetween the reactant and product mixed electronic−proton vibrational wavefunctions. The magnitude ofthe vibronic coupling and its dependence on the proton donor−acceptor distance can significantly impactthe rates and kinetic isotope effects, as well as the temperature dependences, of proton-coupled electrontransfer reactions. Both of these self-exchange reactions are vibronically nonadiabatic with respect to asolvent environment at room temperature, but the proton tunneling is electronically nonadiabatic for thephenoxyl/phenol reaction and electronically adiabatic for the benzyl/toluene reaction. For the phenoxyl/phenol system, the electrons are unable to rearrange fast enough to follow the proton motion on theelectronically adiabatic ground state, and the excited electronic state is involved in the reaction. For thebenzyl/toluene system, the electrons can respond virtually instantaneously to the proton motion, and theproton moves on the electronically adiabatic ground state. For both systems, the vibronic coupling decreasesexponentially with the proton donor−acceptor distance for the range of distances studied. When thetransferring hydrogen is replaced with deuterium, the magnitude of the vibronic coupling decreases andthe exponential decay with distance becomes faster. Previous studies designated the phenoxyl/phenolreaction as proton-coupled electron transfer and the benzyl/toluene reaction as hydrogen atom transfer. Inaddition to providing insights into the fundamental physical differences between these two types of reactions,the present analysis provides a new diagnostic for differentiating between the conventionally definedhydrogen atom transfer and proton-coupled electron transfer reactions.
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