Topology, connectivity, and electronic structure of C and B cages and the corresponding nanotubes

After a brief discussion of the structural trends which appear with an increasing number of atoms in B cages, a one-to one correspondence between the connectivity of B cages and C cage structures will be proposed. The electronic level spectra of both systems from Hartree-Fock calculations is given and discussed. The relation of curvature introduced into an originally planar graphitic fragment to pentagonal "defects" such as are present in buckminsterfullerene is also briefly treated. A study of the structure and electronic properties of B nanotubes will then be introduced. We start by presenting a solution of the free-electron network approach for a "model boron" planar lattice with local coordination number 6. In particular the dispersion relation E(k) for the pi-electron bands, together with the corresponding electronic Density Of States (DOS), will be exhibited. This is then used within the zone-folding scheme to obtain information about the electronic DOS of different nanotubes obtained by folding this model boron sheet. To obtain the self-consistent potential in which the valence electrons move in a nanotube, "the March model" in its original form was invoked, and the results are reported for a carbon nanotube. Finally, heterostructures, such as BN cages and fluorinated buckminsterfullerene, will be briefly treated, the new feature here being electronegativity difference.