, The project leading to this publication has received funding from Excellence Initiative of Aix-Marseille University -A*Midex, a French "Investissements d'Avenir" programme. The authors are members of the French Bioinorganic Chemistry group

M. C. Henstridge, E. Laborda, N. V. Rees, and R. G. Compton, Marcus-Hush-Chidsey theory of electron transfer applied to voltammetry: A review, Electrochim. Acta, vol.84, pp.12-20, 2012.

R. A. Marcus, Chemical and electrochemical electron-transfer theory, Annual Review of Physical Chemistry, vol.15, issue.1, pp.155-196, 1964.

J. M. Savéant and C. Costentin, Elements of molecular and biomolecular electrochemistry, 2019.

C. E. Chidsey, Free energy and temperature dependence of electron transfer at the metal-electrolyte interface, Science, vol.251, issue.4996, pp.919-922, 1991.

S. W. Feldberg, Implications of Marcus-Hush theory for steady-state heterogeneous electron transfer at an inlaid disk electrode, Anal. Chem, vol.82, issue.12, pp.5176-5183, 2010.

M. Honeychurch, Effect of electron-transfer rate and reorganization energy on the cyclic voltammetric response of redox adsorbates, Langmuir, vol.15, issue.15, pp.5158-5163, 1999.

J. Savéant, Effect of the electrode continuum of states in adiabatic and nonadiabatic outer-sphere and dissociative electron transfers. use of cyclic voltammetry for investigating nonlinear activation-driving force laws, J. Phys. Chem. B, vol.106, issue.36, pp.9387-9395, 2002.

T. M. Nahir, On the calculation of rate constants by approximating the Fermi-Dirac distribution with a step function, Journal of Electroanalytical Chemistry, vol.518, issue.1, pp.47-50, 2002.

, The exact series used by Oldham and Myland is slightly different because they are computing a slightly different integral, but this formula was derived using their approach, vol.10

K. B. Oldham and J. C. Myland, On the evaluation and analysis of the Marcus-Hush-Chidsey integral, Journal of Electroanalytical Chemistry, vol.655, issue.1, pp.65-72, 2011.

A. Migliore and A. Nitzan, Nonlinear charge transport in redox molecular junctions: a Marcus perspective, ACS Nano, vol.5, issue.8, pp.6669-6685, 2011.

A. Migliore and A. Nitzan, On the evaluation of the Marcus-Hush-Chidsey integral, Journal of Electroanalytical Chemistry, vol.671, pp.99-101, 2012.

L. K. Bieniasz, A procedure for rapid and highly accurate computation of Marcus-Hush-Chidsey rate constants, Journal of Electroanalytical Chemistry, vol.683, pp.112-118, 2012.

B. A. Mamedov, Analytical evaluation of the Marcus-Hush-Chidsey function using binomial expansion theorem and error functions, Journal of Mathematical Chemistry, vol.51, issue.10, pp.2699-2703, 2013.

H. O. Finklea, Consequences of a potential-dependent transfer coefficient in AC voltammetry and in coupled electron-proton transfer for attached redox couples, Journal of Electroanalytical Chemistry, vol.495, issue.2, pp.79-86, 2001.

J. Hale, The potential-dependence and the upper limits of electrochemical rate constants, J. Electroanal. Chem. Interfacial Electrochem, vol.19, pp.80131-80138, 1968.

Y. Zeng, R. B. Smith, P. Bai, and M. Z. Bazant, Simple formula for Marcus-Hush-Chidsey kinetics, J. Electroanal. Chem, vol.735, issue.0, pp.77-83, 2014.

, The times were measured using a single core of and Intel Xeon CPU E5620 running at 2.40GHz under Linux. The C program was compiled by gcc version 6.2.1, using the -O3 optimization option

R. Piessens, E. De-doncker-kapenga, C. W. Überhuber, D. K. Kahaner, and Q. , of Springer Series in Computational Mathematics, vol.1, p.304, 1983.

M. Galassi, J. Davies, J. T. Gough, G. Jungman, P. Alken et al., GNU Scientific Library Reference Manual, 2003.

, Note that, since the terms are very similar, they take the same time to compute

W. Fraser, A survey of methods of computing minimax and near-minimax polynomial approximations for functions of a single independent variable, Journal of the ACM (JACM), vol.12, issue.3, pp.295-314, 1965.

H. A. Heering, J. Hirst, and F. A. Armstrong, Interpreting the catalytic voltammetry of electroactive enzymes adsorbed on electrodes, J. Phys. Chem. B, vol.102, issue.35, pp.6889-6902, 1998.

J. Hirst and F. Armstrong, Fast-scan cyclic voltammetry of protein films on pyrolytic graphite edge electrodes: Characteristics of electron exchange, Anal. Chem, vol.70, issue.23, pp.5062-5071, 1998.

M. C. Henstridge, E. Laborda, and R. G. Compton, Asymmetric Marcus-Hush model of electron transfer kinetics: Application to the voltammetry of surface-bound redox systems, J. Electroanal. Chem, vol.674, pp.90-96, 2012.

K. Weber and S. E. Creager, Voltammetry of redox-active groups irreversibly adsorbed onto electrodes. treatment using the Marcus relation between rate and overpotential, Analytical Chemistry, vol.66, issue.19, pp.3164-3172, 1994.

L. N. Trefethen and J. A. Weideman, The exponentially convergent trapezoidal rule, SIAM Review, vol.56, issue.3, pp.385-458, 2014.

V. Fourmond, QSoas: a versatile software for data analysis, Anal. Chem, vol.88, issue.10, pp.5050-5052, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01414965

D. Suwatchara, N. V. Rees, M. C. Henstridge, E. Laborda, and R. G. , Compton, Experimental comparison of the Butler-Volmer and Marcus-Hush-Chidsey formalisms of electrode kinetics: The reduction of cyclooctatetraene at mercury hemispherical electrodes via cyclic and square wave voltammetries, Journal of Electroanalytical Chemistry, vol.665, pp.38-44, 2012.

E. Laborda, M. C. Henstridge, and R. G. Compton, Asymmetric Marcus theory: application to electrode kinetics, Journal of Electroanalytical Chemistry, vol.667, pp.48-53, 2012.

E. Laborda, M. C. Henstridge, C. Batchelor-mcauley, and R. G. , Compton, Asymmetric Marcus-Hush theory for voltammetry, Chem. Soc. Rev, vol.42, issue.12, pp.4894-4905, 2013.

Y. Zeng, P. Bai, R. B. Smith, and M. Z. Bazant, Simple formula for asymmetric Marcus-Hush kinetics, Journal of Electroanalytical Chemistry, vol.748, pp.52-57, 2015.