The quantum solvation, adiabatic versus nonadiabatic, and Markovian versus non-Markovian nature of electron transfer rate processes

TL;DR

This paper revisits electron transfer rate theory, emphasizing quantum solvation effects and the distinctions between adiabatic/nonadiabatic and Markovian/non-Markovian processes, revealing new mechanisms and characterizations in different regimes.

Contribution

It provides a comprehensive account of quantum solvation effects on electron transfer and introduces criteria for distinguishing Markovian and non-Markovian rate processes.

Findings

Quantum solvation induces transitions from barrier-crossing to tunneling.

Fast modulation favors nonadiabatic rate processes.

Non-Markovian behavior is prominent in symmetric systems with tunneling.

Abstract

In this work, we revisit the electron transfer rate theory, with particular interests in the distinct quantum solvation effect, and the characterizations of adiabatic/nonadiabatic and Markovian/non-Markovian rate processes. We first present a full account for the quantum solvation effect on the electron transfer in Debye solvents, addressed previously in J. Theore. & Comput. Chem. {\bf 5}, 685 (2006). Distinct reaction mechanisms, including the quantum solvation-induced transitions from barrier-crossing to tunneling, and from barrierless to quantum barrier-crossing rate processes, are shown in the fast modulation or low viscosity regime. This regime is also found in favor of nonadiabatic rate processes. We further propose to use Kubo's motional narrowing line shape function to describe the Markovian character of the reaction. It is found that a non-Markovian rate process is most likely to occur in a symmetric system in the fast modulation regime, where the electron transfer is dominant by tunneling due to the Fermi resonance.