Theory of Vibronic Coupling in the Polariton States of Molecular Crystals

Abstract

A theory of the vibronic coupling in molecular exciton states in the presence of a radiation field is developed. Electronic and nuclear motion in isolated molecules is assumed to be separable, crystal states with two or more molecular excitations on different sites are excluded, and exciton–lattice phonon interactions ignored. The coupling process is examined, without using perturbation theory, from three points of view. In the first method solutions of a classical oscillating dipole model are derived. The second method develops the equivalent quantum theory, without the restriction to dipole interactions, by a one‐step diagonalization of the crystal Hamiltonian. In the third method explicit solutions of Agranovitch's polariton theory are obtained. The latter is also extended to include photon Umklapp processes and a connection established with calculations which use retarded dipole sums. It is shown that the polariton branches, corresponding to a stack of vibronic levels belonging to the same electronic state of the molecule, are coupled by a cooperative (or collective) interaction. As a result for intense transitions $\text{(f≃3)}$ the lowest Coulombic exciton and the highest ${k}\text{\hspace{0.17em}=\hspace{0.17em}0}$ polariton can be pushed far away from the other states and transformed into cooperative states. The exciton carries with it practically all the intensity of the original transitions and the ${k}\text{\hspace{0.17em}=\hspace{0.17em}0}$ polariton leads to the phenomenon of metallic reflection. The connection with previous treatments of the transition from weak to strong vibronic coupoing is discussed and the concept of very strong coupling defined as an extreme Simpson–Peterson limit.