Toroidal forms of graphitic carbon

A series of the toroidal cage forms of graphitic carbon is proposed. They have local topological structures of positive Gaussian curvature (for instance ${\mathrm{C}}_{60}$) and of negative Gaussian curvature. The toroidal forms consist of fivefold, sixfold, and sevenfold carbon rings. The cohesive energies of the tori (${\mathrm{C}}_{\mathit{n}}$, where n ranges from 120 to 1920), which are calculated by molecular dynamics, indicate that these structures are energetically more stable than ${\mathrm{C}}_{60}$. These structures are also found to be thermodynamically stable by means of a finite-temperature simulation.