Electron transfer in the nonadiabatic regime: Crossover from quantum-mechanical to classical behaviour

TL;DR

This paper analyzes nonadiabatic electron transfer using the spin-boson model, providing analytic rate formulas across all temperatures and highlighting quantum effects at low temperatures and their gradual disappearance as temperature rises.

Contribution

It offers the first comprehensive analytic expressions for electron transfer rates across all temperature regimes in the biased spin-boson model, including low-temperature quantum corrections.

Findings

Quantum features like rate maximum shift and asymmetry are prominent at low temperatures.

The rate formula covers the entire temperature range from quantum to classical regimes.

Low temperature corrections are explicitly derived for the Ohmic case.

Abstract

We study nonadiabatic electron transfer within the biased spin-boson model. We calculate the incoherent transfer rate in analytic form at all temperatures for a power law form of the spectral density of the solvent coupling. In the Ohmic case, we present the exact low temperature corrections to the zero temperature rate for arbitrarily large bias energies between the two redox sites. Both for Ohmic and non-Ohmic coupling, we give the rate in the entire regime extending from zero temperature, where the rate depends significantly on the detailed spectral behaviour, via the crossover region, up to the classical regime. For low temperatures, the rate shows characteristic quantum features, in particular the shift of the rate maximum to a bias value below the reorganization energy, and the asymmetry of the rate around the maximum. We study in detail the gradual extinction of the quantum features as temperature is increased.