Theory of geminate recombination on a lattice

Abstract

Central to the photogeneration process in molecular systems is the competition between the relaxation of an excited state (to the ground state) and the separation into an ion pair via charge transfer steps. We have developed the first comprehensive model of this process which depends on molecular parameters and denumerates the competition between the various rates. The model is discrete diffusion on a lattice in a combined Coulomb and external field. The model is solved exactly and is computationally straightforward. The analytic method we have used is quite general and can easily be extended to include a broad class of problems involving large numbers of (correlated) ‘‘special sites.’’ The main feature of the computation, needed to solve these problems, is the evaluation of the lattice Green’s functions in the presence of the electric field. Our solution has a larger range of applicability than the (continuum limit) Onsager theory and is more versatile in terms of initial conditions and modeling of transient phenomena. We will elaborate this approach and discuss our results for the quantum efficiency as a function of external field, temperature, and molecular concentration, η(E,T,c). We show that η(E,T,c) exhibits a diversity of behavior dependent on the relative magnitudes of inter- and intramolecular transition rates. Onsager-like behavior for η is contained in the infinite sink limit and more generally, η can change appreciably as a function of the molecular parameters even for a fixed initial separation r0. In this theory the r0 is geometry controlled, and the initial yield φ0 can be determined by the same competition of rates as control the long time yield. The short time yield is controlled by a few discrete hops and therefore follows an exponential decay as indicated by recent picosecond experiments. In general, within this framework, one can study the influence on η of such factors as dimensionality, lattice structure, disorder, tunneling transition rates, intramolecular rates, and intrinsic energy level differences.