Effects of structural disorder on the optical properties of molecular crystals

In this paper we advance a model for absorption line shapes of Frenkel excitons in molecular crystals, considering the effects of static disorder and of weak exciton-phonon coupling. Our treatment is limited to single-particle excitations located at the bottom of the exciton band. The effects of disorder scattering at zero temperature are handled by applying the average t matrix, single-site approximation to a system characterized by a Gaussian distribution of site excitation energies. The simultaneous effects of disorder scattering and of phonon scattering were treated by the introduction of an effective exciton-phonon Hamiltonian, which was subsequently utilized within the framework of the single-site approximation for disorder scattering at finite temperatures. Model calculations of the optical absorption line shapes were performed for a quasi-one-dimensional system. The zero-temperature line shapes are asymmetrically broadened, the high energy edge being close to a Lorentzian, while the low energy edge decreases fast with decreasing energy. This asymmetry disappears at higher temperatures where phonon scattering effects dominate. We propose that the asymmetric low-temperature absorption band in 1, 4-dibromonaphthalene originates from the effects of structural disorder. The asymmetric optical line broadening experimental data for this quasi-one-dimensional system are well accounted for in terms of our theory.