High-Symmetry Carbon Cages: Structures and Energetics
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ABSTRACTS OF PAPERS OF THE AMERICAN CHEMICAL SOCIETY (Vol.246)
The icosahedral fullerenes form a subset of a larger set of carbon cages that might be called carbon Goldberg polyhedra. These are formed by tiling the triangular faces of an appropriate convex polyhedron with graphenic sheets, and are possible for the three platonic solids that have triangular faces, namely the tetrahedron, the octahedron, and the icosahedron. Euler's criterion is satisfied by the meeting of three, four, or five graphenic faces at a vertex of the embedding figure, yielding either four 3-rings, eight 4-rings, or twelve 5-rings, in addition to some number of 6-rings. The isosahedral case yields the high-symmetry fullerenes, but very little is known to date about the two other cage types. For each geometrical embedding there are two classes of cage, one with Fn2 faces, the other with 3Fn2 faces, where F is the number of faces in the embedding polyhedron, and n is a positive integer. We present explicit geometrical constructions of the first several orders of such cages, and explore their energies, spin states, and optimum geometries using semi-empirical methods and density functional theory.
Macrae, Roderick M. and Vates, Jeremy, "High-Symmetry Carbon Cages: Structures and Energetics" (2013). Department of Chemistry and Physical Sciences. 4.