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.