Effects of off-diagonal disorder on localization of electronic excitations in mixed molecular solids

In this paper we explore the effects of off-diagonal disorder on electronic energy transfer (EET) in an impurity band of an isotopically-mixed, organic solid at low temperatures. We have considered the localization of an elementary excitation in a system characterized by both diagonal disorder, originating from inhomogeneous broadening W of the site-excitation energies, and of off-diagonal disorder arising from the energetic spread σ of the transfer integrals. We have utilized an exact expression for the self-energy of a disordered system where both the site-excitation energies and the transfer integrals are characterized by a Lorentzian distribution, together with the localization function method of Liciardello and Economou to establish the localization condition in the center of the impurity band. Model calculations were performed for a Bethe lattice and for the Hubbard density of states, demonstrating the enhancement of delocalization due to off-diagonal disorder, whereupon the Anderson transition (AT) will be exhibited at higher values of W than in the original Anderson model (OAM), when σ = 0. For large values of the ratio W/σ ≳ 12 the effects of off-diagonal disorder are negligible. Numerical calculations of σ were performed for a random distribution of impurities, while W was roughly estimated for recent spectroscopic measurements. These data, together with the results of the model calculations for a Bethe lattice, established the existence of the critical impurity concentration C̄ for EET in the impurity band. Off-diagonal disorder results in the lowering of C̄ relative to the OAM; however, the effect of diagonal disorder is dominant in determining the termination of EET in the impurity band.