Rate processes with non-Markovian dynamical disorder

TL;DR

This paper develops an analytical framework for understanding rate processes with non-Markovian dynamical disorder, revealing how conformational diffusion influences electron transfer regimes and uncovering paradoxical effects in the transition from fast to slow modulation.

Contribution

It introduces a tractable analytical model for non-Markovian conformational fluctuations affecting electron transfer rates, including detailed analysis of the transition regimes and conditions for paradoxical effects.

Findings

Transition from fast to quasi-static disorder with increasing conformational diffusion time.

Analytical expressions for relaxation and mean transfer time in non-Markovian models.

Identification of conditions leading to paradoxical effects in electron transfer dynamics.

Abstract

Rate processes with dynamical disorder are investigated within a simple framework provided by unidirectional electron transfer (ET) with fluctuating transfer rate. The rate fluctuations are assumed to be described by a non-Markovian stochastic jump process which reflects conformational dynamics of an electron transferring donor-acceptor molecular complex. A tractable analytical expression is obtained for the relaxation of the donor population (in the Laplace-transformed time domain) averaged over the stationary conformational fluctuations. The corresponding mean transfer time is also obtained in an analytical form. The case of two-state fluctuations is studied in detail for a model incorporating substate diffusion within one of the conformations. It is shown that an increase of the conformational diffusion time results in a gradual transition from the regime of fast modulation characterized by the averaged ET rate to the regime of quasi-static disorder. This transition occurs at the conformational mean residence time intervals fixed much less than the inverse of the corresponding ET rates. An explanation of this paradoxical effect is provided. Moreover, its presence is also manifested for the simplest, exactly solvable non-Markovian model with a biexponential distribution of the residence times in one of the conformations. The nontrivial conditions for this phenomenon to occur are found.