Marcus' electron transfer rate revisited via a Rice-Ramsperger-Kassel-Marcus analogue: A unified formalism for linear and nonlinear solvation scenarios

TL;DR

This paper revisits Marcus' electron transfer rate formula by deriving a RRKM analogue that applies to both linear and nonlinear solvation scenarios, offering a unified theoretical framework.

Contribution

It introduces a RRKM-based formalism that extends Marcus' rate to nonlinear solvation cases, unifying different solvation scenarios within a single approach.

Findings

The RRKM analogue recovers Marcus' rate in linear cases.

The formalism applies to quadratic and nonlinear solvation scenarios.

Critical analysis of Fermi's golden rule results is provided.

Abstract

In the pioneering work by R. A. Marcus, the solvation effect on electron transfer (ET) processes was investigated, giving rise to the celebrated nonadiabatic ET rate formula. In this work, on the basis of the thermodynamic solvation potentials analysis, we reexamine Marcus' formula with respect to the Rice-Ramsperger-Kassel-Marcus (RRKM) theory. Interestingly, the obtained RRKM analogue, which recovers the original Marcus' rate that is in a linear solvation scenario, is also applicable to the nonlinear solvation scenarios, where the multiple curve{crossing of solvation potentials exists. Parallelly, we revisit the corresponding Fermi's golden rule results, with some critical comments against the RRKM analogue proposed in this work. For illustration, we consider the quadratic solvation scenarios, on the basis of physically well-supported descriptors.