The Electronic Structure of Icosahedral Boron Clusters

The one-electron energy levels of icosahedral boron clusters have been calculated as a function of intericosahedral spacing maintaining the intraicosahedral spacing of α-boron. For crystalline lattice constants greater than 1.25 times the equilibrium one, band overlap occurs with concomitant metallic behavior. At smaller lattice constants, orbitals(bands) associated with bonds to adjacent icosahedra are lowered and orbitals(bands) associated with “antibonds” are raised. Four bands which were three quarters full become empty, while three bands which were empty become filled. This leads to an energy gap between the filled states and the empty states which accounts for the experimentally observed insulating behavior of this elemental material with three valence electrons per atom.