Stability Prediction in C40 Fullerenes

The well-known “isolated pentagon rule” IPR is described in quantitative terms provided by the layer matrix of valences, constructed on the dual of the associate molecular graph of fullerenes. The derived pentagon valence pv parameter correlates well (it describes more than 90% of variance) with the PM3 heat of formation of small fullerenes C40. The equivalence classes of their vertices, edges and faces are also deducible from some layer matrix invariants. They are important in simulating the 13C NMR spectrum and/or in predicting the products of addition reactions of fullerenes.1