Vibronic Coupling in the Exciton States of the Rigid-Lattice Model of Molecular Crystals

Abstract

The vibrational structure of the Frenkel exciton states of a molecular crystal is investigated by a variational technique using a rigid-lattice-model Hamiltonian. The spirit of the weak coupling formalism is strictly adhered to by constructing crystal wavefunctions from products of isolated molecule wavefunctions so that the only parameters of the theory are Franck—Condon factors and vibrational frequency shifts. The basis set consists of all vibronic, i.e., single particle, states belonging to the same electronic state transforming according to a given wave vector, plus a set of two-particle states in which vibronic and ground vibrational excitation occupy different sites. Interactions between single-particle states are treated in detail, as are interactions between one- and two-particle states. However, part of the interaction between certain two-particle states is neglected and this makes the treatment progressively less accurate for higher vibrational states and stronger coupling. Electron exchange effects, coupling of excitons to photons, higher electronic states, and ion-pair states are not considered. It is shown how each element of the conventional weak coupling energy matrix is supplemented by terms which account for the interaction between one- and two-particle states as well as interactions among the two-particle states. For a given wave vector each single-particle state is accompanied by a family of two-particle bands which rapidly increases in size for higher vibrational states. In the weak coupling limit the families are widely separated, while intermediate coupling corresponds to two-particle bandwidths comparable with the vibrational spacing. The onset of strong coupling corresponds to overlapping of adjacent families.