Superexchange coupling and electron transfers in large three-dimensional disordered media

The superexchange coupling (V-s) in large three-dimensional electron-transfer systems is an intricate function of a huge number of variables suggesting the possibility for a self-averaged and universal behavior. By studying a wide class of disordered model systems presenting through-space interactions, we find that self-averaging does occur in narrow-band systems. V-s is then characterized by a unique control parameter (E/Gamma), the ratio of the energy gap to the half-bandwidth of the medium. The sign of E/Gamma, distinguishing electron- from hole-transfer processes, is a major determining factor of the behavior of V-s.