Vibrational Structure of Electronic States of Molecular Aggregates. II. Extended Weak-Coupling Theory of One-Dimensional Lattices

The model developed in the preceding paper is applied to one-dimensional lattices. The treatment is restricted to weak intermolecular coupling. A perturbation method is developed, in which the exchange term is expanded in powers of the phonon concentration. The expansion is carried through to second order, whereas previous treatments involve only first order terms. This method justifies earlier conclusions that, in the weak-coupling region, the average polaron (excitaron) bandwidth is a decreasing function of temperature. The calculations are extended to higher coupling values by a variation approach, which is a simplified version of the variation method of Paper I. This approach, which amounts to mixing limiting wavefunctions corresponding to equal quantum numbers, accounts for the electron (exciton)—phonon interaction. The more elaborate methods of Paper I become unwieldy here. Preliminary calculations suggest, however, that its conclusion with respect to ``thermal dissociation'' of polarons may be carried over to lattices.