On the hybridization in some archimedean carbon clusters

Abstract

Hybridization, bond, and deviation angles as well as strain energies in Archimedean carbon clusters C,,, C,*, C,,, and CI2, are calculated within the iterated maximum overlap approximation.Recent laser irradiation experiments on graphite performed by Kroto et al.[ 11 have given rise to speculations on the existence of the stable cluster of 60 carbon atoms. It has been suggested that this cluster has the form of one of the Archimedean solids, namely that of a truncated icosahedron. The chemical name buckminsterfullerene was suggested for this cluster [ 1,2]. All atoms in buckminsterfullerene have a valency of three. In the present note we have studied hybridization, bond, and deviation angles in buckminsterfullerene and some other carbon clusters having in common the Archimedean lattice with the same valency condition [3]. The clusters studied are CZ4, C,,, C, , and Ciz0, which have the shape of the truncated octahedron, truncated cuboctahedron, truncated icosahedron, and truncated icosidodecahedron, respectively. The shapes of these clusters together with the enumeration of their atoms are depicted in Figure 1.The method used is the iterative maximum overlap approximation (IMOA) [4]. It considers the orthogonal local hybrid orbitalswhere the hybridization parameters, nAi = (1 -u~J / u~~, are varied until the maximum of the sum Eb of the weighted overlap integrals is attained Since the clusters studied here are constructed from carbon atoms only, the sum Eb simplifies to