Application of the Coherent Potential Approximation to the Excited Electronic States of Substitutionally Disordered Molecular Crystals

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Abstract
In this paper we apply the coherent potential approximation for the calculation of the density of excited electronic states and of the optical properties of a variety of isotopically mixed molecular crystals where the pure crystal exciton band structure and density of state is determined by one, two, and three dimensional interactions. The crystal Hamiltonian is characterized by a random diagonal part and by a translationally invariant off diagonal part. Numerical results are provided for the following systems: (a) a one dimensional chain in the amalgamation limit, in the persistence case and in the separated bands limit; (b) the lowest triplet state of naphthalene in the separated bands case; (c) the lowest singlet state of naphthalene in the amalgamation limit, in the persistence case and in the separated bands limit. (d) The lowest singlet state of benzene in the persistence case and in the separated bands limit. These calculations demonstrated the general features of the density of states in substitutionally disordered crystals, such as the erosion of the Van Hove singularities in the band(s), and the nature of the intensity distribution such as number of Davydov components, their relative intensities, location, and widths. The predictions of the CPA for the moments of the density of states and for the optical properties concur with the predictions of the general moment expansion method for a configurationally averaged crystal. A general CPA scheme is provided to handle tertiary mixed crystals, which are of some experimental interest. To account for the concentration dependence of the optical properties of isotopically mixed benzene, we provide a semiquantitative extension of the CPA scheme, where the isotope effect on the environmental shift term is incorporated into the virtual crystal Hamiltonian resulting in concentration dependent diagonal terms in the crystal Hamiltonian.