Energetics and fullerene fractionation

The local-density-functional binding energies per carbon atom ${\mathrm{C}}_{50}$, ${\mathrm{C}}_{60}$, ${\mathrm{C}}_{70}$, ${\mathrm{C}}_{72}$, ${\mathrm{C}}_{76}$, ${\mathrm{C}}_{78}$, ${\mathrm{C}}_{84}$, ${\mathrm{C}}_{180}$, and ${\mathrm{C}}_{240}$ fullerenes and various isomers of these are computed at geometries that have been optimized using an empirical potential. Little is found to distinguish fullerenes that have been obtained experimentally and those that have not. It is unlikely that energetics plays a dominant role in determining which fullerenes are made in the Kra¨tschmer-Huffman process.