Understanding and Design of Bidirectional and Reversible Catalysts of Multielectron, Multistep Reactions.

Some enzymes, including those that are involved in the activation of small molecules such as H2 or CO2, can be wired to electrodes and function in either direction of the reaction depending on the electrochemical driving force and display a significant rate at very small deviations from the equilibrium potential. We call the former property "bidirectionality" and the latter "reversibility". This performance sets very high standards for chemists who aim at designing synthetic electrocatalysts. Only recently, in the particular case of the hydrogen production/evolution reaction, has it been possible to produce inorganic catalysts that function bidirectionally, with an even smaller number that also function reversibly. This raises the question of how to engineer such desirable properties in other synthetic catalysts. Here we introduce the kinetic modeling of bidirectional two-electron-redox reactions in the case of molecular catalysts and enzymes that are either attached to an electrode or diffusing in solution in the vicinity of an electrode. We emphasize that trying to discuss bidirectionality and reversibility in relation to a single redox potential leads to an impasse: the catalyst undergoes two redox transitions, and therefore two catalytic potentials must be defined, which may depart from the two potentials measured in the absence of catalysis. The difference between the two catalytic potentials defines the reversibility; the difference between their average value and the equilibrium potential defines the directionality (also called "preference", or "bias"). We describe how the sequence of events in the bidirectional catalytic cycle can be elucidated on the basis of the voltammetric responses. Further, we discuss the design principles of bidirectionality and reversibility in terms of thermodynamics and kinetics and conclude that neither bidirectionality nor reversibility requires that the catalytic energy landscape be flat. These theoretical findings are illustrated by previous results obtained with nickel diphosphine molecular catalysts and hydrogenases. In particular, analysis of the nickel catalysts highlights the fact that reversible catalysis can be achieved by catalysts that follow complex mechanisms with branched reaction pathways.