Can a quadrupole form in a purely organic crystalline material? I'm a chemist so bear with me here. This is a question about small molecules, such as biphenyls. In the solid-state biaromatic systems without steric hinderance forms planar conjugated structures. By choosing specific substituents it is possible to polarize such systems. In extreme cases, DFT calculations show, that there is almost no electron density at the one end of the molecule and all of it located at the other. As such, there is a linear polarization of this molecule having a δ(+) at one end and a δ(-) at the other end.
First of all, can such species be considered a dipole? If so what kind of a dipole is it?
Secondly, in the solid-state, there is a specific crystal lattice packing for most of such molecules where the δ(+)-δ(-) plane is located above a  δ(-)-δ(+) plane. Such packing is energetically favorable because of the through-space electrostatic interactions between δ(+) and δ(-) in adjacent molecules which minimizes local positive and negative charges. Simply put a polarized vector --> is put below another equal and opposite vector <--. To me it looks like a quadrupole, is this true?
Finally, such packing as discussed above produces unorthodox behavior of these molecules with respect to electronic transitions and light emission of excited states.
 A: First, your first question ("what kind of dipole is it?") is not clear for me.
Then, please correct me if I misunderstand you: we consider solid-state system which consists of biphenyl fragments with substituents?
In my view, the answer is simple. $\pi$-system has a quadrupole moment (at least in a certain approximation because multipole expansion consists all terms).This moment is briefly discussed in this article and here. Also, it seems useful to read about $\pi$-$\pi$ stacking, ref. Therefore, in my opinion (I considered quadrupole interactions in aromatic systems long time ago and my opinion may be not so authoritative) that your statement about quadrupoles is correct. Aromatic systems have quadrupole moment and it is possible to vary it by appropriate substituents. These molecules can form a crystal (for instance, liquid crystal) but it seems to be not so stable due to non-covalent nature of interaction. Also, different polymers wtih biphenyl base can form liquid crystals.
Finally, could you please provide more details about your last statement (about electronic transitions & light emissions)?
