  The Marcus-Hush-Chidsey (MHC) model is well known in electro-analytical
chemistry as a successful microscopic theory of outer-sphere electron transfer
at metal electrodes, but it is unfamiliar and rarely used in electrochemical
engineering. One reason may be the difficulty of evaluating the MHC reaction
rate, which is defined as an improper integral of the Marcus rate over the
Fermi distribution of electron energies. Here, we report a simple analytical
approximation of the MHC integral that interpolates between exact asymptotic
limits for large overpotentials, as well as for large or small reorganization
energies, and exhibits less than 5\% relative error for all reasonable
parameter values. This result enables the MHC model to be considered as a
practical alternative to the ubiquitous Butler-Volmer equation for improved
understanding and engineering of electrochemical systems.
