Superexchange coupling and electron transfer in homogeneous three-dimensional systems: Site and bond disorders

The superexchange coupling (V-s) between two distant redox centers in large three-dimensional disordered media is studied by considering an electron-transfer model system made up of an aperiodic array of sites (s-type orbitals) interacting through an exponentially decaying function of distance. The associated one-particle, tight-binding Hamiltonian accounts for the simultaneous presence of both diagonal and off-diagonal disorders, leading to a stochastic variation of V-s. Exploring the statistical properties of V-s under variations of the orbital energies and couplings, we determine the conditions for self-averaged behavior of V-s and the amplitude of its fluctuations. For systems with wide electronic bands, V-s is found to exhibit large fluctuations, while these latter are small for narrow-band systems. Moreover, for a given bandwidth of the intermediate medium, systems with a higher density of sites behave in a more self-averaged way. An analytical description of the average behavior of V-s and of its fluctuations is provided in the narrow-band regime.