Effect of friction on electron transfer: The two reaction coordinate case

Abstract

Electron transfer is a very important reaction in many biological processes such as photosynthesis and oxidative phosphorylation. In many of these reactions, most of the interesting dynamics can be included by using two reaction coordinates: one fast (local high frequency vibration modes) and one slow (outersphere modes such as solvent polarization). We report a model to describe this problem, which uses path integral techniques to calculate electron transfer rates, and also to obtain the Fokker–Planck equations associated with this model. Different limiting cases lead to qualitatively different results such as exponential or nonexponential time decay for the donor survival probability. Conditions for the validity of the adiabatic or the nonadiabatic limits will be discussed. Application of this model to real systems is proposed, in particular for a porphyrin rigidly linked to a quinone, which is a very interesting model compound for primary events of photosynthesis. This model can also be used for other multicoordinate biological reactions such as ligand binding to heme proteins. Also, in the concluding part of Sec. III, we discuss the important limit where the fast vibronic mode is much faster than all the other nuclear modes coupled to the problem. In this limit the fast mode ‘‘renormalizes’’ the electronic matrix element, and this considerably simplifies the treatment of the problem, reducing it to coupling only to the slow modes.