Weighted HOMO-LUMO energy separations of properly closed-shell fullerene isomers

The HOMO-LUMO energy separation has been used as an index of kinetic stability for fullerenes. However, its utility is rather limited, in that a larger fullerene molecule in general has a smaller HOMO-LUMO energy separation even if it is kinetically stable. The T value, i.e., the HOMO-LUMO energy separation weighted with the number of carbon atoms, is free from this kind of difficulty. Properly closed-shell isomers of fullerenes with antibonding LUMOs were found to have an exceptionally large T value irrespective of the number of constituent carbon atoms and are hence predicted to be kinetically very stable. Thus, the antibonding character of the LUMOs is one of the determinants for kinetically stabilizing fullerene molecules.