Geometry and orbital symmetry relationships of giant and hyperfullerenes: C 240, C 540, C 960 and C 1500

Abstract

From the truncation of the triangular faces of an icosahedron, a method is devised to perceive the geometrical relationship between the (giant) fullerene components of hyperfullerenes: C 60, C 240, C 540, C 960 and C 1500. This method also allows the calculation of the number of hexagonal faces (besides the 12 pentagonal faces), vertices and edges of any giant fullerene of such I h symmetry. From symmetry considerations, the irreducible representations of all of the σ and π molecular orbitals of such giant fullerenes are deduced. The cage diameters and the distance between two neighboring encapsulating cage fullerenes are estimated. the overlap integrals between nearest neighbor carbon atoms based on their orientational relationship are calculated. The relative sizes of the integrals may be used to estimate the relative bonding strength and interaction potentials of these fullerenes.