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We compare localization properties of one-dimensional Frenkel excitons withGaussian and Lorentzian uncorrelated diagonal disorder. We focus on the statesof the Lifshits tail, which dominate the optical response and low-temperatureenergy transport in molecular J-aggregates. The absence of exchange narrowingin chains with Lorentzian disorder is shown to manifest itself in the disorderscaling of the localization length distribution. Also, we show that the localexciton level structure of the Lifshits tail differs substantially for thesetwo types of disorder: In addition to the singlets and doublets of localizedstates near the bare band edge, strongly resembling those found for Gaussiandisorder, for Lorentzian disorder two other types of states are found in thisenergy region as well, namely multiplets of three or four states localized onthe same chain segment and isolated states localized on short segments.Finally, below the Lifshits tail, Lorentzian disorder induces stronglylocalized exciton states, centered around low energy sites, with localizationproperties that strongly depend on energy. For Gaussian disorder with amagnitude that does not exceed the exciton bandwidth, the likelihood to findsuch very deep states is exponentially small.

Localization properties of one-dimensional Frenkel excitons: Gaussian versus Lorentzian diagonal disorder