  On the optical absorption and the density of states of Frenkel exciton
systems on square, rectangular, and triangular lattices with nearest-neighbor
interactions and a Gaussian distribution of transition frequencies. The
analysis is based on an elliptic integral approach that gives results over the
entire spectrum. It is found that the absorption is weakly affected by the
anisotropy in contrast to the density of states where the effects can be much
stronger. The results for the square 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 two-dimensional systems with dominant nearest-neighbor
interactions and Gaussian diagonal disorder where the optically excited states
are Frenkel excitons.
