Toroidal and spherical fullerene‐like molecules with only pentagonal and heptagonal faces

Abstract

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-

Two-dimensional matter: order, curvature and defects

“…After the discovery of carbon nanotubes in 1991 and the subsequent theoretical construction (later followed by the experimental observation) of graphitic tori, this class of polyhedra has drawn considerable attention and many possible tessellations of the circular torus have been proposed by the community [174,175,176,177,178,179,180,181,182,183,184]. Here we review the construction of a defect-free triangulated torus and we show how the most symmetric defective triangulations can be generally grouped into two fundamental classes corresponding to symmetry groups D nh and D nd respectively.…”

“…In the past few years, alternative constructions of triangulated tori have been proposed as well as novel geometrical and graph-theoretical methods to express the coordinates of their three-dimensional structures (see for example Kirby [180], László at al [181,182], Diudea et al [183,184]). Here we choose to focus on the defect structure associated with the two most important class TPn and TAn with groups D nh and D nd .…”

Analysis of the Relationship among the Graphs Isomorphic to Multilayered Cyclic Fence Graphs (MLCFG)

“…[14][15][16] Mathematical features of MLCFGs might have some crucial role in analyzing the reaction graphs which Balaban and others have proposed for discussing the complexity of chemical reactions and related phenomena. [17][18][19][20][21] 2. DEFINITIONS For recognizing the symmetry of these families of graphs, the "Hamilton wheel graph", H (n,{j k }), has been defined, whose vertices are lying on an n-membered cyclic graph, C n .…”

The Electronic Structure of Nonpolyhex Carbon Nanotubes

“…1,2 The case of the nonpolyhex nanotubes is much more complicated. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] There is not yet an available general formula for the geometric and electronic structures of the nonpolyhex nanotubes when they contain pentagons and heptagons as well. 18,19 In ref 20 we presented a method for describing the geometrical structures of nonhexagonal nanotubes, nanocoils, and nanotori.…”