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

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Abstract
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.

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