Proton Discharge on a Gold Electrode from Triethylammonium in Acetonitrile: Theoretical Modeling of Potential-Dependent Kinetic Isotope Effects.

The discharge of protons on electrode surfaces, known as the Volmer reaction, is a ubiquitous reaction in heterogeneous electrocatalysis and plays an important role in renewable energy technologies. Recent experiments with triethylammonium (TEAH) donating the proton to a gold electrode in acetonitrile demonstrate significantly different Tafel slopes for TEAH and its deuterated counterpart, TEAD. As a result, the kinetic isotope effect (KIE) for the hydrogen evolution reaction changes considerably as a function of applied potential. Herein a vibronically nonadiabatic approach for proton-coupled electron transfer (PCET) at an electrode interface is extended to heterogeneous electrochemical processes and is applied to this system. This approach accounts for the key effects of the electrical double layer and spans the electronically adiabatic and nonadiabatic regimes, as found to be necessary for this reaction. The experimental Tafel plots for TEAH and TEAD are reproduced using physically reasonable parameters within this model. The potential-dependent KIE or, equivalently, isotope-dependent Tafel slope is found to be a consequence of contributions from excited electron-proton vibronic states that depend on both isotope and applied potential. Specifically, the contributions from excited reactant vibronic states are greater for TEAD than for TEAH. Thus, the two reactions proceed by the same fundamental mechanism yet exhibit significantly different Tafel slopes. This theoretical approach may be applicable to a wide range of other heterogeneous electrochemical PCET reactions.