  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.
