A unified quantum rate theory of electron transfer: conceptual advances in quantum electrochemistry

Abstract

This viewpoint on recent advances in quantum electrochemistry demonstrates how quantum-rate (QR) theory unifies the Levich, Dogonadze, and Kuznetsov (LDK) and Marcus electron-transfer (ET) theories from the 1960s within a common framework. In particular, QR theory simplifies to these classical models when quantum coherence is a necessary condition for applying electrodynamics. Notably, quantum coherence emerges at the point where Marcus's ET theory predicts the maximum rate, when the driving force of the reaction equals the reorganization energy. Building on these connections, QR theory further links quantum conductance and the electron transfer rate constant through quantum capacitance. To clarify these relationships, we analyze ET reactions in molecular switches under transient and dynamic regimes using QR theory and compare them to key mesoscopic ‘dry’ (solid-state) experiments. Significantly, while quantum coherence is observed at lower temperatures in solid-state experiments, it is present at room temperature during ET reactions in ‘wet’ electrolyte environments. This underscores the crucial role of the ‘wet’ environment in maintaining quantum coherence during ET reactions.