Kinetics of Proton Discharge on Metal Electrodes: Effects of Vibrational Nonadiabaticity and Solvent Dynamics

Abstract

Proton discharge on metal electrodes, also denoted the Volmer reaction, is a critical step in a wide range of electrochemical processes. This electrochemical proton-coupled electron transfer (PCET) reaction is predominantly electronically adiabatic in aqueous solution and is typically treated as fully adiabatic. Recently, a theoretical model for this PCET reaction was developed to generate the vibronic free energy surfaces as functions of a collective solvent coordinate and the distance of the proton-donating acid from the electrode. Herein a unified formulation is devised to describe such PCET reactions in terms of a curve crossing between two diabatic vibronic states corresponding to the lowest two proton vibrational states, employing an interpolation scheme that spans the adiabatic transition state theory, nonadiabatic Fermi golden rule, and solvent-controlled regimes. In contrast to previous treatments, application of this formulation to the aqueous Volmer reaction highlights the importance of vibrational nonadiabaticity and solvent dynamics. The calculated transfer coefficients and kinetic isotope effects are in reasonable agreement with experimental measurements. These fundamental insights have broad implications for understanding electrochemical processes.

Advances and challenges for experiment and theory for multi-electron multi-proton transfer at electrified solid–liquid interfaces

“…Recently, a vibronically nonadiabatic process was suggested to underlie the Volmer step at a Au electrode in acidic conditions. 94 The theoretical calculation of the Z-log j k plot using the vibronically nonadiabatic PCET theory agreed well with the experimental observations, and therefore this theoretical work suggested that a nonadiabatic process could have an important role for electrode processes. However, the experimental Z-log j k plot for a Au electrode in acidic conditions shows a linear Z-log j k feature with a potentialindependent K H/D of ca.…”

“…However, this phenomenon can also be explained within a theoretical framework in which the proton is fully quantized for all overpotentials. 93,94 Under the above simple picture, we can confirm the existence of a NQE in an electrode process. However, the important issue here is how to see a chemical or physical picture of a quantum electrode process that is solely dominated by quantum effects, especially ''deep'' tunneling (see Section 6 for details).…”

“…However, this type of potential-dependent kinetic isotope effect can also be described with a vibronically nonadiabatic PCET theory in which the transferring hydrogen nucleus is quantized over the entire range of overpotentials (see Section 5). 93 Moreover, a unified framework with a quantized proton can interpolate between adiabatic TST behavior and nonadiabatic behavior, 94 and in some cases a single reaction can span both regimes for different distances from the electrode surface. In addition, an increase of EC-KIE along with an increase of driving force is unusual from the point of the BEP principle, which is another indication of NQEs.…”

Revisiting the Volmer–Heyrovský mechanism of hydrogen evolution on a nitrogen doped carbon nanotube: constrained molecular dynamics versus the nudged elastic band method

“…Our findings indicating the significance of solvent dynamics when studying interfacial proton-coupled electron transfer corroborate recent theoretical results accounting for vibrational nonadiabaticity and solvent relaxation dynamics. 83 While a comprehensive computational treatise of electrochemical phenomena is still complicated by the lack of well applicable grand canonical methods, our work exemplifies the importance of incorporating solvent dynamics in the rigorous description of reactions at solid-liquid interfaces and presents an important step towards more accurate electrochemical simulations. The herein applied constrained molecular dynamics simulations employing the proposed reaction coordinates could e.g.…”

“…It is furthermore noteworthy that the herein observed significance of solvent dynamics in the proper description of the Volmer-Heyrovský mechanism has been inferred recently for the Volmer step also using a theoretical PCET formalism accounting for vibrational nonadiabaticity and solvent relaxation dynamics. 83 Due to the observed considerable influence of solvent reorganization, the Chan-Nørskov charge-extrapolation scheme 43,44 applied to the CI-NEB calculations to derive energy profiles at constant electrode potentials is deemed inapplicable for the dynamic results. Indeed, since it appears that solvent relaxation dynamics play an important role also in the case of simple proton transfer reactions, the whole underlying notion of describing the electrostatic contribution to the energy change along a reaction path as purely capacitive is placed in a questionable light.…”