Level and wave function statistics of a localized 1D Frenkel exciton at the bottom of the band

We focus on the statistics of the energy levels and wave functions of a one-dimensional weakly localized Frenkel exciton at the bottom of the band, i.e. those determining optical response. We show that the well-overlapped states undergo level repulsion. This repulsion results in a local discrete energy structure of a localized Frenkel exciton similar to the energy structure of an ideal linear chain. The disorder degree scaling of the overlap integrals of the squared exciton wave functions, important for the exciton transport, is studied as well.