Resolving sequential electron–proton transfer kinetics for electrochemical CO ₂ reduction at the Cu(100)/H ₂ O interface <i>via</i> a quantum-classical framework

intermediate through ion-dipole interactions, modulating the vibronic couplings. For PT, solvent relaxation dynamically adjusts the equilibrium donor-acceptor distance, thereby augmenting the Franck-Condon overlap between reactant and product vibronic wavefunctions in excited proton vibrational states, which facilitates nonadiabatic transitions across diabatic surfaces. Rate constants extracted by combining diabatic vibronic PCET theory with generalized Langevin equation-derived Grote-Hynes theory show that the sequential ET-PT pathway outpaces concerted PCET by about 5 orders of magnitude at the potential of zero charge (PZC). This methodology establishes a robust paradigm for dissecting ET and PT kinetics at electrochemical interfaces, emphasizing the interplay of quantum nuclear effects, vibronic couplings, and solvent fluctuations.