Marcus rate for electron transfer and the Goldilocks principle

TL;DR

This paper derives Marcus electron transfer rates in a quantum environment, linking optimal transfer to a specific environment correlation time, illustrating a Goldilocks principle where the best transfer occurs at a precise parameter value.

Contribution

It provides an explicit expression for environment correlation time in Marcus rates and demonstrates the Goldilocks principle in quantum electron transfer.

Findings

Optimal transfer governed by inverse root square of two

Explicit environment correlation time expression derived

Goldilocks principle illustrated in quantum transfer

Abstract

We examine electron transfer between two quantum states in the presence of a dissipative environment represented as a set of independent harmonic oscillators. For this simple model, the Marcus transfer rates can be derived and we show that these rates are associated to an explicit expression for the environment correlation time. We demonstrate that as a manifestation of the Goldilocks principle, the optimal transfer is governed by a single parameter which is equal to just the inverse root square of two.