Theory of geminate recombination on a lattice. IV. Results using large Coulomb radii on the simple cubic and square lattices

We have expanded the molecular theory of geminate recombination of charge-carrier pairs to the consideration of arbitrary Coulomb cutoff lengths. The results on the simple cubic and square lattices exhibit behavior typical of that observed experimentally. This behavior is controlled by a set of molecular parameters as well as the initial distribution of the electron about the hole. It is shown also that the temperature dependence in the infinite-sink limit is qualitatively Onsager-like, but does not quantitatively match the predictions of the Onsager formulation, reflecting previously noted deficiencies in the continuum approximation. It is also shown that the two parameters φ₀ and r₀ of the Onsager model cannot, in general, be regarded as giving the actual, physical initial quantum efficiency and initial separation of the charge carriers, respectively. In the course of these calculations, methods are developed for calculating two- and three-dimensional lattice Green's functions in the presence of an external electric field. Analytical and numerical methods are established, as well as recursion relations useful in calculation. A relationship is exhibited and utilized between two- and three-dimensional field-dependent Green's functions.