Conjugated‐carbon nanostructures: Emergences

Abstract

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. K E Y W O R D S carbon nanostructures, electronic structure for conjugated carbon nanostructures, graphene 1 | INTRODUCTION The human use of conjugated-carbon nanostructures predates recorded history, with coal, charcoal, and peat used as fuels or as feedstock for colorants. Within the last two centuries, different benzenoids (often derived from coal) played an important role in the industrial revolution, providing feedstocks, dyes, plastics, and drugs, and also played a central role in the development of organic chemistry and the general idea of molecular structure.

Antiaromatic Molecules as Magnetic Couplers: A Computational Quest

“…Recently, Zeng and co-workers 2 noted that pro-aromatic and antiaromatic molecules exhibit an irresistible tendency to become diradicals in their ground electronic state, thus, emphasizing that the diradical character emerges as an important concept in chemistry characterizing organic opto-magnetic molecular systems. Such observation is consistent with studies 97 − 99 explaining the emergence of unpaired π-electron densities on graphene edges when the competition between local pairing and delocalized resonance yields unpaired electrons at the graphene edges of sufficiently wide graphene strips, for example, unpaired electrons on so-called “zig-zag” edges within the network of alternate π-networks, where carbon sites can be divided into starred and unstarred sets, where no member of either set is found being adjacent to a member of the same set. Thus, translationally symmetric graphene strips are predicted 97 to exhibit unpaired π-electron densities on opposite edges when the width of the strip gets sufficiently large for certain types of edge shapes, like “zig-zag” edge or “Klein edge”.…”

“…Aromaticity, magnetism, and chemical reactivity are of fundamental significance when exploring the physical and chemical properties of π-conjugated diradical systems and have been the subject of numerous studies. − The concept of bond breaking, for example, in the ring of an organic molecule, would lead to the formation of a diradical, or possibly zwitterion, and has preoccupied chemists trying to understand the electronic structure of molecules from first principles with, for example, articles having intriguing titles like “Do diradicals behave like radicals? 1 ” It is quite common to explore the breaking of chemical bonds in terms of the formation of radical fragments that require highly accurate accounting of electron correlation (both static or nondynamic as well as dynamic kind) , when exploring potential energy surfaces in chemical systems.…”