Remarkable diversity of carbon-carbon bonds: structures and properties of fullerenes, carbon nanotubes, and graphene

Large scientific community has been passionate in understanding different carbon nanostructures for last two decades. In this review, we present the general description of low-dimensional carbon allotropes such as fullerenes (0D), carbon nanotubes (1D), and graphene (2D). These structures have unique diversity of carbon-carbon bonds. Structures and electronic properties of fullerenes, small closed carbon cages, and giant fullerenes are illustrated. We point out the complexity in the area of fullerene research because of a wide range of structures and number of possible isomers of fullerenes. The concept of isolated pentagon rule in fullerenes is highlighted. We delineate the usefulness of pyramidalization angle in evaluating the curvature of fullerenes. The role of computational chemistry in identifying different isomers of fullerenes and validating the experimental results in ambiguous situations is also briefly mentioned. Properties of different types of carbon nanotubes, particularly single-walled carbon nanotubes (SWCNTs) and their structural features are summarized. The use of pyramidalization angle (theta (P)) and pi-orbital misalignment angles in predicting the reactivity of different carbon atom sites of SWCNTs is discussed. Finally, we outline the structures and electronic properties of graphene, and discuss the status of experimental investigations of this species.