Building of fullerenes and the K(4 n+ 2) rule

Abstract

Recently with the discovery of fullerene-60 and the advent of new synthetic techniques, great interest has arisen in investigating such carbon clusters in the fields of chemistry and physics [l], In order to show the surprising stability of these clusters, many theoretical calculations, ranging from simple Hiickel type ones to ab initio ones, have been done and the so called “spheroidal aromaticity” has been proposed /2] in analogy to the special stability of planar benzene. Accordingly, Tang and Li [3] have recently proposed a geometrical structure rule for both carbon and boron clusters, which is based on the consideration of their geometrical symmetry, and was obtained by repeatedly decapping and capping the framework with Ih or Oh symmetry to obtain a series of stable clusters. However, the rule fails to explain the existence of no Ih or Oh shaped carbon clusters, such as CSO, C,,,, Ce4, etc. Fowler and Steer [4,53 have proposed a leapfrog operation to generate stable carbon clusters, which led to the derivation of 6n $60 rule. It can be seen that this rule is unable to predict the stable existence of Cm, C,, Cg8, etc. In contrast to the strong emphasis placed on the static structure of fullerenes, less attention has been paid to their kinetics [l]. In this paper, a possible clustering mechanism of carbon and a corresponding structure rule, that is the K(4n + 2) rule, based on chemical kinetics are proposed. The clustering mechanism and structure role can be employed to