Theoretical analysis of the influence of stochastic gating on the transient effect in fluorescence quenching by electron transfer

Abstract

For electron transfer (ET) reactions in liquid media, it is not uncommon to find that the stereoselectivity, mutual orientations, conformational fluctuations, spin multiplicity restrictions of the reacting system may kinetically limit its reactivity. We assume that the system in question can stochastically interconvert between reactive (open gate) and nonreactive (closed gate) states at rates competitive with diffusion-influenced ET, and refer to this kind of reaction as stochastically gated diffusion-influenced ET reactions. We utilize the Zhou and Szabo model of stochastically gated diffusion-influenced reactions in order to study the effect of such stochastic fluctuations of reactivity on the transient kinetics of fluorescence quenching in through-solvent photoinduced ET reaction. Different types of transient kinetics, fluorophore gated vis-a-vis quencher gated, are demonstrated in terms of survival probability of the fluorophore, which shows that the analysis of experimental results ignoring such phenomena can be dramatically in error. Approximate analytical solutions of the theory based on projection operator formalism are presented. The exact numerical results including the role of liquid structure and the hydrodynamic hindrance of fluorophore-quencher diffusion rates are found to compare extremely well with the results obtained from a molecular dynamics simulation of the same reaction system. The simulations are based on the rate equations obtained from the first principle. Illustrative calculations and comparisons are presented to demonstrate the competitive interplay between the reaction sink strength, diffusion, and gating rates on the reaction kinetics. A simple method, based on the distribution of ET distance and quantum yield of ET of gateless reactions, is proposed to help delineate the features of such competitive interplay on the asymmetry of the reaction kinetics.