Weak-Coupling Theory of the Vibrational Structure of Molecular Exciton States

Abstract

The weak-coupling theory of molecular exciton states is extended to include the interaction of a vibronic (vibrational—electronic) exciton with its dissociated states in which vibrational and vibronic excitations occur on different sites. Only nondegenerate electronic states of the free molecule are considered. The spirit of the weak-coupling limit is rigorously adhered to in that no approximations are made concerning the nature of the molecular potential-energy surfaces. Analogy with exciton trapping by impurities leads to the notion of vibrational capture by vibronic excitons. There are also correlated or secondary capture states in which the vibrational exciton follows the vibronic exciton at a fixed distance as it moves through the crystal. Expressions containing the frequency shifts and Franck—Condon factors of the isolated molecule as parameters are derived for the energy and intensity of the capture state. In two special models the effects of large frequency shift and equal Franck—Condon factors are treated. For a linear chain with nearest-neighbor interactions, explicit formulas are derived for the transition probability and compression of the exciton band due to coupling with dissociated states.