Knowledge Bank

Using the recently acquired exction dispersion $relations1$ 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 techniques developed originally for lattice phonons (associated with the negative eigenvalue theorem) to a real physical system of 3-dimensional molecuar excitins. In most calculations, a total of 1280 molecules were included. The exciton interactions which included both the translationally equivalent and the interchange equivalent ones invlved all sixteen neighbors. Calculations based on the coherent potential approximation (CPA), similar to those of previous $work2$, 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 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 the exact expressions. It was also shown that the CPA results always agree with the exact moments at least up to the 7th order.