On the evaluation and analysis of the Marcus–Hush–Chidsey integral

Chidsey’s implementation of the electron-exchange theories of Marcus and Hush leads to a prediction of the potential-dependence of electrochemical rate constants that is couched in terms of unfriendly integrals. Here we perform the integrations and recast the resulting series into formulas that are more easily enumerated and manipulated. Thereby, several observations are made concerning rate constants that follow the Marcus–Hush–Chidsey theory, and contrasted with the predictions of the Butler–Volmer model.

► The unfriendly Marcus–Hush–Chidsey integral has been solved.
► A simple and exact, though slow to execute, formula replaces the integral.
► Even simpler formulas are shown to apply in special circumstances.
► The Marcus–Hush theory is contrasted with the Butler–Volmer model.
► Behaviors for extreme values of the parameters are examined.