The factorization of buckminsterfullerene into cyclocarbon components

Abstract

The algorithm CYCLO-60† has been used to compute the structures of all 158 different factorizations of buckminsterfullerene ( I h - C 60) into cyclocarbon components, where a cyclocarbon is defined as a monocyclic ring of carbon atoms. This algorithm identifies all solutions by systematically assigning each of the 32 faces of I h - C 60 cage to one of two domains. The algorithm is structured to maximize the speed of this computational process by minimizing the total number of permutations that need to be considered. Of the 158 factorizations, 42 are made up of combinations of cyclocarbons of a reasonable size ( C n ; n ⩾ 12). These solutions are of interest as they suggest suitable precursor molecules for the directed synthesis of I h - C 60 and its heterofullerene and endohedral derivatives under relatively mild experimental conditions.