ABSTRACT:The stability of toroidal and spherical carbon cage structures, constructed from five-and seven-membered rings, was studied using tight binding, Tersoff and Brenner potential based methods. A special tiling is presented for the torus of minimal strain energy. In order to make comparison between the results of various calculations we defined the σ AB square root average bond distance difference between the methods A and B. By addition of six-membered rings to the C 40 torus we obtained a toroidal C 60 carbon cage molecule. Key words: toroidal carbon structures; toroidal azulenoid; fullerene-like molecules S ince the discovery of the C 60 buckminsterfullerene [1], several new carbon structures were found in experimental and theoretical works [2 -5].For a closed carbon network of N 5 pentagons, N 6 hexagons, and N 7 heptagons, when each carbon atom has three neighbors, Euler's theorem gives that where χ is the Euler characteristic and g is the genus. The genus is the number of holes or handles, thus g = 1 for the torus and g = 0 for the sphere. The question arises whether there are closed-cage carbonic networks that do not contain hexagons. In the present work we shall study such kinds of toroidal and spherical carbon structures. From Eq.(1) follows that N 5 = N 7 for the torus and N 5 = N 7 + 12 for the sphere. We calculated the equilibrium structures in the frame work of a molecular mechanics procedure. The carbon-carbon interaction was described with the help of a tight-binding (TB) method [6]. The parameters were adjusted to the results of density functional calculations for graphite, diamond, and other carbon structures. In order to make a com-