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On the optical absorption and the density of states of Frenkel excitonsystems on square, rectangular, and triangular lattices with nearest-neighborinteractions and a Gaussian distribution of transition frequencies. Theanalysis is based on an elliptic integral approach that gives results over theentire spectrum. It is found that the absorption is weakly affected by theanisotropy in contrast to the density of states where the effects can be muchstronger. The results for the square lattice are in good agreement with thefinite array calculations of Schreiber and Toyozawa. Our findings suggest thatthe coherent potential approximation can be useful in interpreting the opticalproperties of two-dimensional systems with dominant nearest-neighborinteractions and Gaussian diagonal disorder where the optically excited statesare Frenkel excitons.

The effect of anisotropy on the absorption spectrum and the density of  states of two-dimensional Frenkel exciton systems with Gaussian diagonal  disorder