Shell structures in molecular orbital energy diagrams for small fullerene cages: Free-electron versus generator orbital models

Abstract

The nearly spherical nature of small fullerene cages CN (N<70) suggests that their π molecular orbital (MO) energy diagrams should show a shell structure. Although group theoretical analysis of the Huckel-type energies for icosahedral and other highly symmetric cages confirms this assumption, this has not been established for fullerene cages in general. This work presents a simple computational algorithm based upon the canonical orthogonalization of generator orbitals (GOs) to analyze the π-MO energy diagrams for any fullerene cage CN, and demonstrates the validity of a shell structure in these diagrams. Results are compared to simple central force (spherical) models for the calculations of π-MO energies in fullerene cages. The GO approach provides a ready assignment of the π-MOs to individual spherical harmonics and allows valuable interpretations of various physical phenomena.