Polytope models for local icosahedral packing: An electronic structure analysis

The electronic properties of recently developed icosahedral packing schemes using polytope {3,3,5} (a packing of atoms on S3, the surface of the unit sphere in four dimensions, with perfect icosahedral symmetry) are analyzed within the framework of a d-band, tight-binding model. It is shown that there is a one-parameter family of prescriptions for defining the interatomic couplings, which preserves the icosahedral symmetry and generalizes earlier schemes. The bonding energies for several representative cases are calculated and compared to those in the fcc structure. The results are extremely sensitive to the prescription used to define the couplings.