Calculation of Vibronic Couplings for Phenoxyl/Phenol and Benzyl/Toluene Self-Exchange Reactions: Implications for Proton-Coupled Electron Transfer Mechanisms

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Abstract
The vibronic couplings for the phenoxyl/phenol and the benzyl/toluene self-exchange reactions are calculated with a semiclassical approach, in which all electrons and the transferring hydrogen nucleus are treated quantum mechanically. In this formulation, the vibronic coupling is the Hamiltonian matrix element between the reactant and product mixed electronic−proton vibrational wavefunctions. The magnitude of the vibronic coupling and its dependence on the proton donor−acceptor distance can significantly impact the 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 a solvent environment at room temperature, but the proton tunneling is electronically nonadiabatic for the phenoxyl/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 the electronically adiabatic ground state, and the excited electronic state is involved in the reaction. For the benzyl/toluene system, the electrons can respond virtually instantaneously to the proton motion, and the proton moves on the electronically adiabatic ground state. For both systems, the vibronic coupling decreases exponentially with the proton donor−acceptor distance for the range of distances studied. When the transferring hydrogen is replaced with deuterium, the magnitude of the vibronic coupling decreases and the exponential decay with distance becomes faster. Previous studies designated the phenoxyl/phenol reaction as proton-coupled electron transfer and the benzyl/toluene reaction as hydrogen atom transfer. In addition 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 defined hydrogen atom transfer and proton-coupled electron transfer reactions.

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