Combined topological and energy analysis of the annealing process in fullerene formation. Stone–Wales interconversion pathways among IPR isomers of higher fullerenes

Abstract

An algorithm for finding all the possible products from consecutive generalized Stone–Wales (GSW) rearrangements of any fullerene or closed cage precursor has been developed. Combined with energy-minimization, the program provides a versatile tool for the analysis of extremely complex interconversion pathways in the annealing process of fullerene formation. This paper presents results of the following preliminary applications of the program: (1) identification of the shortest pathway from Wang’s C₆₀ cage precursor to [60-I_h]fullerene, (2) availability of GSW cascades for a large number of sixty-carbon cage precursors leading to [60-I_h]fullerene, (3) generation of interconversion pathways among IPR isomers of higher [n]fullerenes (n = 78, 80, 82, 84, 90), and (4) enumeration of fullerene isomers. The pathways map of [84]fullerene solved the pending problem of why the high-energy isomer, [84-D_2d(I)]fullerene, has been detected using a helium-labelling technique in the product mixture and confirmed by IGOR calculation: this particular isomer is the dead-end product of a downhill bypath.