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Topological Resonance Energy of Fullerenes

A new algorithm for computation of a matching polynomial is outlined. It has been successfully applied for evaluation of the topological resonance energy (TRE) of all fullerene isomers with up to, and including, 70 carbon atoms. The obtained results indicate a high correlation between TRE values and π-electronic energies (Eπ), which was found to be a consequence of the invariance of the reference energy values for a given size of isomers. A similar high correlation was established between TRE and Eπ values normalized to a number of carbon atoms, thus extending over different sizes of fullerene isomers. These results show that the resonance energy does not bring any new insight into stabilities of different fullerene isomers which is not already achieved by consideration of Eπ.