Resolving sequential electron–proton transfer kinetics for electrochemical CO2 reduction at the Cu(100)/H2O interface via a quantum-classical framework

Abstract

Electron-transfer (ET) and proton-transfer (PT) events occurring at electrochemical interfaces ultimately dictate the efficiency of electrocatalytic energy conversion and chemical synthesis. Despite their significance, a unified theoretical description of ET/PT dynamics has been challenging due to the entangled electronic, nuclear, and solvent degrees of freedom. Herein, we present a quantum-classical multiscale framework integrating constrained density functional theory (CDFT) with machine learning accelerated molecular dynamics (MLMD) to investigate ET and PT during electrochemical CO₂ reduction on Cu(100) in explicit water. Distinct ML potentials are trained for the adiabatic ground state and for two charge-localized diabatic states, enabling efficient configurational sampling while preserving quantum-mechanical fidelity in electronic energies and forces. The derived diabatic free-energy surfaces reveal that CO₂ first undergoes inner-sphere ET to yield chemisorbed *CO₂⁻, followed by PT to form *COOH. Solvent reorganization imposes kinetic constraints on the ET step yet counterintuitively stabilizes the *CO₂⁻ 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.