On the Electronic States of Substitutionally Disordered Molecular Crystals

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Abstract
In this paper we consider the optical properties of heavily doped molecular crystals where the constituents differ by isotopic substitution. Four different situations were considered determined by the perturbation strength relative to the second moment and to the width of the density of states in the pure crystal: (a) separated bands; (b) persistence case; (c) incipient band gap; (d) amalgamation limit. The properties of the effective Hamiltonian for a configurationally averaged mixed molecular crystal containing an arbitrary number of molecules per unit cell were explored. Information on the intensity distribution in optical absorption by a binary crystal can be obtained from the moments of the spatially averaged mixed crystal Hamiltonian. In the amalgamation limit the crystal exhibits the gross features of a virtual crystal and the number of the polarized intensity distributions is equal to that of the pure crystal, while in the separated band case and in the persistence case the number of polarized intensity distributions is double that in the pure crystal. The coherent potential approximation based on a local approximation for the self‐energy and on neglecting multiple scattering effects was extended to handle the general case of a multiply branched exciton band. Concerning the general question of the persistence of the Davydov splitting in a mixed crystal, general arguments are provided that symmetry restrictions can be relaxed and that the Davydov splitting is exhibited by a substitutionally disordered system described by a Hamiltonian which is characterized by a random diagonal part and by a translationally invariant off‐diagonal part. The number of these Davydov components is determined by the perturbation strength.

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