Electrochemical Proton-Coupled Electron Transfer of an Osmium Aquo Complex: Theoretical Analysis of Asymmetric Tafel Plots and Transfer Coefficients

Electrochemical proton-coupled electron transfer of an osmium aquo complex attached to a self-assembled monolayer on a gold electrode is studied with a recently developed theoretical formulation. The calculated hydrogen/deuterium kinetic isotope effect for the standard rate constant, the cathodic transfer coefficient at zero overpotential, and the Tafel plot are in excellent agreement with experimental data. The input quantities to the heterogeneous rate constant expressions were calculated with density functional theory in conjunction with dielectric continuum models, and no parameters were fit to experimental data. The theoretical calculations indicate that the asymmetry of the Tafel plot and the deviation of the transfer coefficient at zero overpotential from the standard value of one-half arise from the change in the equilibrium proton donor-acceptor distance upon electron transfer. The direction of the asymmetry and deviation from one-half is determined by the sign of this distance change, and the magnitude of these effects is determined by the magnitude oft his distance change, as well as the reorganization energy and the distance dependence of the overlap between the initial and Final proton vibrational wave functions. This theory provides experimentally testable predictions for the impact of specific system properties on the qualitative behavior of the Tafel plots.