Vibrational Structure of Electronic States of Molecular Aggregates. I. A Variation Approach to Dimeric Systems

Abstract

The vibrational structure of electronic states of molecular aggregates is studied, using a simplified model. In this model the intermolecular electronic coupling is treated by tight‐binding theory, and the electron (exciton)‐vibration interaction is described in terms of a potential well in which the electron (exciton) is trapped. Both interactions are approximated by constant parameters, which, in typical molecular crystals, are of the order of an internal vibrational energy quantum. These parameters govern the motion of a quasiparticle, consisting of the electron (exciton) together with its well, which is called a polaron (excitaron). Earlier treatments, based on comparable models, are confined to cases in which either the coupling or the well is a small perturbation. In this paper a variation method is developed and applied to molecular dimers. The wavefunctions corresponding to these limiting cases are combined to form a trial function. Eigenfunctions and eigenvalues are derived which behave properly in the limits and join smoothly in the intermediate region. The method provides a suitable basis for quantitative computations. An interesting qualitative feature of the model is the ``thermal dissociation'' of the polaron (excitaron).