Electronic excited state transport in solution

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Abstract
The transport of electronic excitations between randomly distributed sites is examined. The Green function solution to the master equation is expanded as a diagrammatic series. Topological reduction of the series results in an expression for the Green function which is equivalent in form to the Green function solution of a generalized diffusion equation. The diagrammatic technique used suggests an interesting class of self‐consistent approximations. This self‐consistent method of approximation is applied to the specific case of the Förster transfer rate. The solutions obtained are well‐behaved for all times and all site densities and indicate that transport is nondiffusive at short times and diffusive at long times. The mean squared displacement of the excitation and the time derivative of the mean squared displacement are calculated. These calculations illustrate that the time regime in which diffusive transport occurs is dependent on density. For low density systems transport becomes diffusive only at very long time, i.e., more than a few lifetimes. For high densities transport becomes diffusive within one lifetime. The application of the picosecond transient grating technique to the study of this problem is briefly discussed.