We present results of numerical simulations on optical properties of linear molecular aggregates with diagonal and offhyphen;diagonal disorder. In contrast to previous studies, we introduce offhyphen;diagonal disorder indirectly through Gaussian randomness in the molecular positions; this results in a strongly asymmetric distribution for the interactions. Moreover, we do not restrict to nearesthyphen;neighbor interactions. We simultaneously focus on several optical observables (absorption linewidth and line shift and superradiant behavior) and on the density and the localization behavior of the eigenstates (Frenkel excitons). The dependence of these optical properties on the disorder is investigated and expressed in terms of simple power laws. For offhyphen;diagonal disorder, such a study has not been performed before. In the case of diagonal disorder, we show that, in particular, the superradiant decay rate of the aggregates may be strongly affected by the inclusion of nonhyphen;nearesthyphen;neighbor interactions. Recent results of absorption line shape, superradiant emission, and resonance lighthyphen;scattering measurements on pseudoisocyanine aggregates can be understood on the basis of these calculations.
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