Fig. 12.1. Molecular orbital levels for Cw from a Hiickel calculation. The filled states are labeled '+' and the empty states '—'. The shading on the icosahedron on the right-hand side of the figure pertains to whether the wave function is negative or positive, and the figure schematically shows three nodes and odd parity for the wave function for the (,„ (/lu) triply degenerate conduction band level [12.4].

symmetry-imposed splittings of the molecular levels, which are then classified according to the symmetry of the icosahedral (or lower) symmetry group. In §12.1.2 we use this approach to give a physical picture of the level filling for the molecular states for fullerenes, and in §12.2 we review symmetry-based models that can be applied to account for experimental observations related to the electronic structure.

12.1.2. Level Filling for Free Electron Model

The simplest model that captures the essence of the electronic structure of fullerenes considers each Qq molecule to contain 180 a electrons in

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