Chemical applications of topology and group theory 32. The sphericity of fullerenes

Abstract

The lowest lying molecular orbitals for the C60n 2 approximated by spherical harmonics. Thus the molecular orbitals for these fullerenes start from a single lowest lying molecular orbital and cluster in groups of 1, 3, 5, 7, 9,..., orbitals corresponding to the 2L + 1 orbitals expected for the quantum number L = 0, 1, 2, 3, 4,..., respectively. Furthermore, the cluster of 2L + 1 molecular orbitals for 6⩽ L ⩽ 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 spherical approximation for the C60n 2 fullernes of icosahedral symmetry breaks down for the more weakly bonding and all antibonding orbitals, presumably because the increased number of nodes with increasing L makes these high lying molecular orbitals more sensitive to derivations from sphericity.