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A Mixed Quantum-Classical Liouville Approach for Calculating Proton-Coupled Electron Transfer Rate Constants.


In this work, we derive a general mixed quantum-classical formula for calculating thermal proton-coupled electron transfer (PCET) rate constants, starting from the time integral of the quantum flux-flux correlation function. This formula allows for the direct simulation of PCET reaction dynamics via the Mixed Quantum-Classical Liouville (MQCL) approach. Owing to the general nature of the derivation, this formula does not rely on any prior mechanistic assumptions and can be applied across a wide range of electronic and protonic coupling regimes. To test the validity of this formula, we applied it to a reduced model of a condensed phase PCET reaction. Good agreement with the numerically exact rate constant is obtained, demonstrating the accuracy of our formalism. We believe that this approach constitutes a solid foundation for future investigations of the rates and mechanisms of a wide range of PCET reactions.