Toward Negatively Curved Carbons

ConspectusNegatively curved carbons are theoretical carbon allotropes as proposed by embedding heptagons or octagons in a graphitic lattice. Unlike five-membered rings in fullerenes, which induce positive curvature, the seven- or eight-membered rings induce negative curvature, giving rise to a variety of esthetic carbon nanostructures known as Mackay crystals or carbon schwarzites. In addition, hypothetical toroidal carbon nanotubes consisting of five-, six-, and seven-membered rings present positive curvature on the outside and negative curvature on the inside of the torus. These carbon allotropes with negative curvature are predicted to have interesting properties and potential applications on the basis of computational studies but are yet to be synthesized. A promising bottom-up approach to these intriguing but still imaginary carbon structures is organic synthesis of negatively curved polycyclic arenes, which are also known as negatively curved nanographenes. They not only are segments of negatively c...