Molecular Vibrations in the Exciton Theory for Molecular Aggregates. IV. Excited States of Weakly-coupled Systems

Abstract

The theory of the vibronic states of an electronically excited molecular aggregate is developed for the case of weak intermolecular interaction. The resulting description is complementary to that derived for the case of strong intermolecular interaction in Parts I-III of this series.¹ The intermolecular interaction term in the Hamiltonian is treated as a small perturbation. A particular set of zeroth-order functions for the problem, here called m-m functions, is defined. The interaction integrals between m-m functions are studied and certain of the m-m functions are corrected to the first order of perturbation theory. A criterion for the validity of the perturbation treatment is given. The effect of molecular vibrations in exciton theory is to inhibit intermolecular interaction. Expressions are obtained for the vibrational inhibition factors, and their properties are related to the molecular distortion in the vicinity of the electronically excited molecule. All theoretical results are discussed in comparison with those of Parts I-III. The results of the two methods of treatment are combined to give a general description of the excited states of molecular aggregates. It is shown that an exciton together with the associated molecular distortion in polymeric aggregates may be regarded as a quasiparticle analogous to the polaron in a molecular crystal.