STRUCTURAL MOTIFS AND THE STABILITY OF FULLERENES

Full geometry optimization has been performed within the semiempirical QCFF/PI model for the 1812 fullerene structural isomers of C-60 forme d by 12 pentagons and 20 hexagons. All are local minima on the potenti al energy hypersurface. Correlations of total enery with many structur al motifs yield highly scattered diagrams, but some exhibit linear tre nds. Penalty and merit functions can be assigned to certain motifs: in clusion of a fused pentagon pair entails an average penalty of 111 kJ mol(-1); a generic hexagon triple costs 23 kJ mol(-1); a triple (open or fused) comprising a pentagon between two hexagonal neighbors gives a stabilization of 19 kJ mol(-1). These results can be understood in t erms of the curved nature of fullerene molecules: pentagons should be isolated to avoid sharp local curvature, hexagon triples are costly be cause they enforce local planarity and hence imply high curvature in a nother part of the fullerene surface, but hexagon-pentagon-hexagon tri ples allow the surface to distribute steric strain by warping. The bes t linear fit is found for H, the second moment of the hexagon-neighbor -index signature, which fits the total energies with a standard deviat ion of only 53 kJ mol(-1) and must be minimized for stability; this in dex too can be interpreted in terms of curvature.