Conjugated‐carbon nanostructures: Emergences

General emergent features of conjugated‐carbon nanostructures are sought. Here, “general” indicates applicability over a broad class of such structures, including graphene and buckytubes, possibly with boundaries or other sorts of defects or decorations, or rather general substructures of graphene or of buckytubes. In addition, “emergent” means that different characteristics and properties are novel and are evidenced from different models, for example, from resonance theory and Hückel theory, preferably with evidence that the features persist upon elaboration. One robust emergent feature is “Dirac cones” in the band structure of graphene and some related materials. Another interesting feature is novel “blended” boundary orbitals that are delocalized longitudinally along the boundary direction while being variably localized in the transverse direction. Furthermore, defects at the ends of polymer chains may be localized or delocalized depending on local features—although the ideas apply more widely to different conjugated‐carbon structures including molecules. Explicit formulas are derived to elucidate the asymptotic behavior of unpaired electron density at the ends of selected benzenoid polymers and its relation to the associated HOMO‐LUMO gap. Our approach offers a general framework to understand ab initio results, which may, at first sight, appear to be unconventional or counterintuitive to some common ideas of bonding patterns in conjugated carbon nanostructures.