Exciton-photon coupling in molecular crystals

The theory of Frenkel molecular excitons is extended to include the effect of retardation , in the dipole approximation, on the mixing of exciton bands arising from different electronic states. The Hamiltonian does not contain any instantaneous intermolecular interactions and treats exciton-photon and intermolecular interactions on an equal footing. The exciton energy levels are calculated to the fourth order in electronic charge using graphs of the time-ordered type and it is shown that retardation results in a replacement of instantaneous dipole potentials by retarded resonance potentials. A number of results for a system of three identical molecules with one in an excited state are calculated simultaneously.