Dynamic Electrochemical Proton Discharge on Metal Electrodes: The Effects of Electronic Nonadiabaticity

Proton discharge on metal electrodes is a key step in many important electrochemical reactions. This proton-coupled electron transfer is typically a dynamic process, yet it is often treated adiabatically. Nonadiabatic effects arising from proton motion, however, can alter the electron transfer rate and lead to the excitation of coherent electron-hole (e-h) pairs within the metal electrode[1]. These e-h pairs, along with solvent mode excitations, act as additional channels for translational energy transfer, described in the framework of electronic friction.

In this study, we present a comprehensive theoretical investigation of the proton discharge dynamics on metal electrodes, explicitly accounting for energy dissipation into both electronic and phononic excitations. Utilizing the time-dependent Newns-Anderson-Schmickler model, we derive an effective electronic Hamiltonian that incorporates e-h excitations as a perturbation in the slow-motion limit. The proton's motion is coupled to both the solvent modes, modeled as a phonon bath, and the metal's electrons. Through the influence functional path-integral method[2], we derive a quasiclassical Langevin equation and provide a simplified expression for the electronic friction coefficient.

Our numerical simulations[3] reveal a significant shift in the onset of nonadiabatic electron occupation of the proton when electronic friction is considered, with substantial implications for the electron transfer rate.



[1] E. F. Arguelles and O. Sugino, J. Chem. Phys. 160, 144102 (2024).

[2] R. P. Feynman and F. L. Vernon, Ann. Phys. 24, 118 (1963).

[3] E. F. Arguelles and O. Sugino, in preparation.