Shell Structures in Molecular Orbital Energy Diagrams for 'Small' Fullerene Cages: Free-Electron Versus Generator Orbital Models

Byline: Gordon J. Miller (1), John G. Verkade (1) Keywords: Huckel MO theory; generator orbitals; spherical harmonics; fullerenes Abstract: The nearly spherical nature of small fullerene cages C.sub.N (N&lt 70) suggests that their [pi] 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 [pi]-MO energy diagrams for any fullerene cage C.sub.N, and demonstrates the validity of a shell structure in these diagrams. Results are compared to simple central force (spherical) models for the calculations of [pi]-MO energies in fullerene cages. The GO approach provides a ready assignment of the [pi]-MOs to individual spherical harmonics and allows valuable interpretations of various physical phenomena. Author Affiliation: (1) Department of Chemistry, Iowa State University, Ames, IA, 50011, USA Article History: Registration Date: 08/10/2004