The Butler-Volmer (BV) equation has become the standard model for electrochemical reaction kinetics, and yet a century later, it still lacks a clear microscopic basis. Butler (1936) first derived the BV equation from Gurney’s (1936) seminal “quantum theory of electrolysis”, which assumes electron transfer (ET) or “neutralization” is a fast step coupled to proton transfer. Marcus (1956) famously challenged this picture with his theory of ET coupled to solvent reorganization, rather than ion transfer. Here, we present a unified quantum theory of coupled ion-electron transfer (CIET), which leads to a simple rate formula that smoothly interpolates between Marcus-like and BV-like kinetics for rate-limiting electron- or ion-transfer, respectively.1 CIET theory provides a powerful link between quantum chemistry and electrochemical engineering, as illustrated by examples of reaction kinetics in Li-ion2 and Li-air3 batteries and electrocatalysis. The theory predicts the metal dependence of the hydrogen evolution reaction (HER) and provides a mathematical framework to predict electrochemical reaction rates from ab initio quantum simulations.4
1 M. Z. Bazant, Unified quantum theory of electrochemical kinetics by coupled ion-electron transfer, Faraday Discussions 246, 60-124 (2023).
2 Y. Zhang et al., Lithion-ion intercalation by coupled ion-electron transfer, to appear in Science (2025). (chemRxiv)
3 P. Zhang, S. Pathak, M. Z. Bazant and P. Bai, Current-Dependent Morphologies of Insulating Electrodeposits in Li-O2 Batteries Controlled by Coupled Ion-Electron Transfer Kinetics, ACS Appl. Mater. Interfaces (2025).
4 J. H. Stenlid et al., Computational insights into electrolyte-dependent Li-ion charge-transfer kinetics at the LixCoO2 interface, ACS Energy Letters 9, 3608-3617 (2024).
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