Coherent potential approximation for the absorption spectra and the densities of states of cubic Frenkel exciton systems with Gaussian diagonal disorder

Using the coherent potential approximation, we investigate the optical absorption and the density of states of Frenkel exciton systems on simple, body centered, and face centered cubic lattices with nearest-neighbor interactions and a Gaussian distribution of transition frequencies (i.e. Gaussian diagonal disorder). The analysis is based on an elliptic integral approach with a variety of variances. The results for the simple cubic lattice are in good agreement with the finite array calculations of Schreiber and Toyozawa. Our findings suggest that the coherent potential approximation can be useful in interpreting the optical properties of cubic crystals where the optically excited states are Frenkel excitons with the dominant interactions limited to nearest-neighbors.