Angular electronic ‘band structure’ of molecules

First principles calculations of the electronic structure of spherical molecules reveals that the valence band dispersion and bands filling are almost completely determined by the properties of angular momentum operator. With a very high accuracy we find the single particle states to disperse with the averaged angular momentum ℓ as E ℓ = E 0 + ℓ ( ℓ + 1 ) / 2 R 2 . Deviation of the angular bands from a parabolic dispersion at large ℓ and all peculiarities in the band fillings of large fullerenes and their high symmetry derivatives can be explained within a unified picture as bands avoided crossing.