Two-Exciton States of the Rigid-Lattice Model of a Molecular Crystal

A theory is developed which can treat Frenkel and Wannier excitons, weak vibronic coupling, and exciton–exciton reactions for the rigid-lattice model of a molecular crystal. The treatment assumes tight-binding wavefunctions but allows for electron exchange contributions to interaction matrix elements. States belonging to different two-particle channels are assumed to couple only through single-exciton states so that direct interaction between channels is ignored. By two-particle states we mean states containing an electron and hole, or a vibronic and vibrational exciton, or two vibronic excitons. The coupling of Frenkel and Wannier excitons to each other and to the conduction band is briefly discussed. A previously derived theory of weak vibronic coupling is extended to include phonon propagation and states of the isolated molecules which are not Born–Oppenheimer separable. Finally, for the two-exciton system a Green's function expression for the energy levels is given.