Random Lattice Calculations on Frenkel Excitons in Disordered Molecular Crystals—1B2u Naphthalene

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Abstract
Using the recently acquired exciton dispersion relations for crystalline naphthalene, we have calculated the density‐of‐states functions for heavily doped isotopic binary mixed crystals of naphthalenes with arbitrary compositions and various energy separations (trap depths). This constitutes the first attempt to extend the negative factor counting (NFC) method, developed originally for lattice phonons, to a real physical system of three‐dimensional molecular excitons. In most calculations, a total of 1280 molecules were included. The exciton interactions, which included both the translationally equivalent and the interchange equivalent ones, involved all 16 neighbors. Calculations based on the coherent potential approximation (CPA) were also performed for comparison. It was concluded that these two sets of calculations compared very well except in the split‐band limit and at low concentrations. Under these conditions the cluster or conglomerate states become important and the computer‐simulated density‐of‐states functions revealed some fine structure, which was completely indiscernible in the density‐of‐states function based on CPA. This fine structure is experimentally significant. The relationship between the Green's function method and the moment trace method was investigated in the light of these new results. Particularly, some of the lower moments were calculated for the density‐of‐states functions and compared with those calculated from the exact expressions in our previous paper. It was shown numerically that the CPA results indeed agree with the exact moments up to the seventh order