A procedure for rapid and highly accurate computation of Marcus–Hush–Chidsey rate constants

Theoretical modelling and digital simulation of electro-analytical experiments for electrochemical reactions subject to the Marcus–Hush–Chidsey kinetics have recently attracted considerable attention. Such simulations are difficult, due to the lack of fast and accurate algorithms for computing rate constants which are expressed by complicated integrals. By modifying series expansions for the integrals, reported by Oldham and Myland [K.B. Oldham, J.C. Myland, J. Electroanal. Chem. 655 (2011) 65], an approximate procedure of calculating the rate constants is obtained, which is not only inexpensive computationally, but also highly accurate. Further reduction of the computational cost is achieved by replacing one of the integrals by a piecewise polynomial approximation. Theoretical arguments and computational tests suggest that the relative error of the procedure is about 10−14−10−15. This is close to the error (of about 10−16) of computing exponential factors in the Butler–Volmer model, when standard double precision variables are used for simulation. Simultaneously, the computational time is only about 111 times longer compared to the time of computing the exponential factors. The procedure should therefore be of interest to those who simulate electro-analytical experiments.