CHEMICAL APPLICATIONS OF TOPOLOGY AND GROUP-THEORY .32. THE SPHERICITY OF FULLERENES

The lowest lying molecular orbitals for the C(60n)2 fullerenes of icos ahedral symmetry can be approximated by spherical harmonics. Thus the molecular orbitals for these fullerenes start from a single lowest lyi ng molecular orbital and cluster in groups of 1, 3, 5, 7, 9,..., orbit als corresponding to the 2L + 1 orbitals expected for the quantum numb er L = 0, 1, 2, 3, 4,..., respectively. Furthermore, the cluster of 2L + 1 molecular orbitals for 6 less than or equal to L less than or equ al to 11 in these fullerenes breaks up into a high lying subcluster of 12 orbitals and a low lying subcluster of 2L - 11 orbitals resembling the molecular orbital pattern for a cluster with L' = L - 6. This sph erical approximation for the C-60n(2) fullernes of icosahedral symmetr y breaks down for the more weakly bonding and all antibonding orbitals , presumably because the increased number of nodes with increasing L m akes these high lying molecular orbitals more sensitive to derivations from sphericity.