The Exact Icosahedral Symmetry Relations for Atomic Overlaps, Molecular Orbitals and Vibrational Species of C₆₀ Buckyballs

Abstract

A computer adapted vector method and Euler angle transformation procedures are used to generate the relationship between the atomic orbitals of icosahedral C60 Buckminsterfullerene cluster and to produce symmetry adapted molecular orbitals and vibrational species. The atomic overlaps based on the orientational relationship of the orbitals are used to compute the approximate molecular orbital energies and normalization constants. One of the vibrations of Au, symmetry is used to interpret the isomeric (dyotropic) rearrangement that breaks and forms two bonds to change two pentagons to two hexagons and vice versa.