Theory of the interaction of Frenkel excitons with local and extended perturbations in one-dimensional molecular crystals. Application of the Green’s function formalism to the energy funnel and cluster problem

Abstract

The Green’s function formalism is applied to calculate the perturbed Frenkel exciton states in the presence of local and extended perturbations in one-dimensional molecular crystals. Analytically exact criteria for the existence of bound and antibound exciton states are given for (1) a local perturbation, (2) for the energy funnel problem, and (3) for the cluster problem. A reduced Green’s function formalism (RGF) is presented and applied to the calculation of the effective energy funnel radii of primary guest molecules, surrounded by their own electronically induced dipolar, quadrupolar, or exponential energy funnels.