Assessing the Extent of Potential Inversion by Cyclic Voltammetry: Theory, Pitfalls, and Application to a Nickel Complex with Redox-Active Iminosemiquinone Ligands

Potential inversion refers to the situation where a protein cofactor or a synthetic molecule can be oxidized or reduced twice in a cooperative manner; that is, the second electron transfer is easier than the first. This property is very important regarding the catalytic mechanism of enzymes that bifurcate electrons and the properties of bidirectional redox molecular catalysts that function in either direction of the reaction with no overpotential. Cyclic voltammetry is the most common technique for characterizing the thermodynamics and kinetics of electron transfer to or from these molecules. However, a gap in the literature is the absence of analytical predictions to help interpret the values of the voltammetric peak potentials when potential inversion occurs; the cyclic voltammograms are therefore often analyzed by simulating the data, with no discussion of the possibility of overfitting and often no estimation of the error on the determined parameters. Here we formulate the theory for the voltammetry of freely diffusing or surface-confined two-electron redox species in the experimentally relevant irreversible limit where the peak separation depends on the scan rate. We explain why the model is intrinsically underdetermined, and we illustrate this conclusion by analysis of the voltammetry of a nickel complex with redox-active iminosemiquinone ligands. Being able to characterize the thermodynamics of two-electron electron-transfer reactions will be crucial for designing more efficient catalysts.