Exciton–lattice interaction and the line shape of exciton absorption in molecular crystals

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Abstract
The exciton–lattice interaction cannot be treated adiabatically in many molecular crystals where the exciton bandwidth is at most comparable to lattice‐vibration energies. It cannot also be treated perturbationally at about room temperatures where the absorption line width of excitons is comparable to the larger of the exciton bandwidth and lattice‐vibration energies in most molecular crystals. A simple model which describes excitons in molecular crystals from a unified viewpoint is proposed. The model has three characteristic energies: the half‐width B of the exciton band, the average amplitude of the scattering potential for excitons produced by lattice vibrations D, and the inverse of the correlation time of the potential fluctuation γ on the order of lattice‐vibration energies in units of C=1. It describes singlet excitons when B≳γ and triplet excitons when B≪γ. The dynamical‐coherent‐potential approximation applied to this model bridges reasonably the following two limits: the strong‐scattering limit for D≫B and D≫γ in which the exciton absorption has a Gaussian line shape, and the weak‐scattering limit for D≪B or D≪γ in which the exciton absorption has a motionally narrowed Lorentzian line shape. The exponentially decreasing low‐energy absorption tail, obeying the Urbach–Martienssen rule, grows up as B/γ increases towards the adiabatic limit of B/γ ≫1. The model is consistently applied to observed exciton spectra in various molecular crystals.