Beyond the Dielectric Continuum: The Effect of the Electrolyte on the Rate of Electron Transfer Reactions from a Quantum Rate Dynamics Perspective

The solvent environment shapes electron transfer (ET) reactions, which researchers predominantly model using the semi-classical Marcus theory. This theory relies on reorganization energy (λ0) and describes the solvent as a dielectric continuum (implicit solvation). However, this approach often overlooks how electrolyte cation/anion pairs and the electronic structure of reactants directly influence ET. To address these gaps, we present quantum-rate (QR) theorya more general framework that explicitly incorporates classical and quantum energy states, as well as the discrete effects of electrolyte composition and reactant structure. QR theory extends Marcus theory by offering a unified quantum-dynamic perspective that treats Marcus ET theory as a special case. Specifically, QR theory reinterprets λ0, directly linking it to the balance between internal quantum energy (E ∝ e2/Cq) and external electrostatic screening energy (Ee ∝ e2/Ce) determined by electrolyte propertiesthus connecting λ0 to measurable circuit parameters (Cq and Ce). To validate the applicability of QR theory, we experimentally analyze diffusionless ET rate dynamics in redox-tagged monolayers. The study distinguishes two solvation regimes: (i) we probe “Explicit Solvation Effects” by varying the water/acetonitrile ratio with a fixed electrolyte to reveal how solvent composition changes the rate via electronic coupling (κ) and (ii) explore “Implicit/Continuum Solvation Effects” by varying both solvent and cation/anion pairs, finding agreement with Marcus-like continuum analysis in specific regimes. This work advances quantum electrochemistry by clarifying the definition and measurement of λ0 and specifying when to use implicit or explicit solvent models in quantum-dynamic ET descriptions.