J-aggregates are a class of low-dimensional molecular crystals which display enhanced interaction with light. These systems show interesting optical properties as an intense and narrow red-shifted absorption peak (J-band) with respect to the spectrum of the corresponding monomer. The need to theoretically investigate optical excitations in J-aggregates is twofold: a thorough first-principles description is still missing and a renewed interest is rising recently in understanding the nature of the J-band, in particular regarding the collective mechanisms involved in its formation. In this work, we investigate the electronic and optical properties of a J-aggregate molecular crystal made of ordered arrangements of organic push-pull chromophores. By using a time dependent density functional theory approach, we assess the role of the molecular packing in the enhancement and red shift of the J-band along with the effects of confinement in the optical absorption, when moving from bulk to low-dimensional crystal structures. We simulate the optical absorption of different configurations (i.e., monomer, dimers, a polymer chain, and a monolayer sheet) extracted from the bulk crystal. By analyzing the induced charge density associated with the J-band, we conclude that it is a longitudinal excitation, delocalized along parallel linear chains and that its overall red shift results from competing coupling mechanisms, some giving red shift and others giving blue shift, which derive from both coupling between transition densities and renormalization of the single-particle energy levels.
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