Resolving the Marcus-Rehm-Weller Paradox in Electron Transfer

TL;DR

This paper resolves the apparent contradiction between Marcus and Rehm-Weller electron transfer kinetics by showing they are limits of a unified quantum model, explaining experimental data without additional assumptions.

Contribution

It introduces a quantum Hamiltonian framework that unifies Marcus and Rehm-Weller behaviors, clarifying their relationship and reproducing experimental results.

Findings

Rehm-Weller kinetics emerge as a limit of the same quantum model as Marcus theory.

The model predicts saturation in the adiabatic limit and decrease in the nonadiabatic limit.

Quantitative agreement with experimental data is achieved without diffusion assumptions.

Abstract

Marcus theory famously predicts that electron-transfer rates decrease once the thermodynamic driving force exceeds the reorganization energy. Yet many systems instead exhibit Rehm-Weller kinetics, in which the rate saturates rather than decreases. Here we show that these apparently contradictory phenomenologies emerge as opposite physical limits of the same two-level quantum Hamiltonian. In the normal region, the model recovers both Marcus and Rehm-Weller behavior. In the inverted region, however, it predicts Marcus's decreasing rate in the nonadiabatic limit but Rehm-Weller saturation in the adiabatic limit. Using physically realistic reorganization energies and electronic coupling values, we show that Rehm-Weller's data can be quantitatively reproduced within a microscopic quantum model without invoking diffusion limitations or phenomenological corrections.