Small World Carbon Nanomaterials: Density Functional Theory Simulations

The possible existence of small, pure carbon molecules based on physical small-world networks is addressed using density functional theory calculations. A ring of atoms with one or more small-world connections between pairs of non-nearest-neighbor sites was chosen for the network topology. The small-world connections are made with and without additional carbon atoms placed along the link. The energy per atom of these small-world carbon systems is compared with benchmark carbon clusters such as the C$_{20}$ ring, bowl, and cage isomers, the C$_{60}$ Buckyball, monocyclic pure carbon rings ranging from C$_{4}$ to C$_{60}$, bare linear carbon chains ranging from C$_{2}$ to C$_{48}$, fullerenes ranging from C$_{20}$ to C$_{60}$, and various all-carbon graphitic fragments. The energy per atom results for these materials provides an indication that some of these pure-carbon small-world nanomaterials are reasonable for real world synthesis.