ENERGETICS AND STRUCTURE OF TOROIDAL FORMS OF CARBON

Total-energy calculations for 13 different fullerene clusters, including 8 toroidal fullerenes, are performed using a parametrized tight-binding functional, and in select cases, an all-electron first-principles local-density functional. The tori considered here are composed of graphitelike six-membered rings, with five-membered rings on the outer surface of the torus providing positive Gaussian curvature, and seven-membered rings on the inner toroidal surface providing negative Gaussian curvature. Comparisons are made with energies calculated from a Stillinger-Weber-type potential for graphite, which is found to be inadequate for addressing relative energetic stability among the tori. Two empirical strain relations are tested against our tight-binding energy calculations. A simple elastic theory is found to give reasonably good energy orderings. Charge-density calculations on the tori reveal that electron density is enhanced for atoms in five-membered rings, and depleted for atoms in seven-membered rings. First-principles total-energy calculations indicate that a single potassium atom is bound to the center of a C144 torus by 0.5 eV. It is proposed that atoms with higher orbital angular momentum (e.g., Zr, etc.) may bond more tightly to the torus, and thus facilitate formation of C120 or similar tori. © 1994 The American Physical Society.