Mixed quantum-classical Liouville approach for calculating proton-coupled electron-transfer rate constants

Farnaz Shakib, Gabriel Hanna

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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 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.

Original languageEnglish (US)
Pages (from-to)3020-3029
Number of pages10
JournalJournal of Chemical Theory and Computation
Issue number7
StatePublished - Jul 12 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Physical and Theoretical Chemistry


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