Electronic Structure of (n,0) Zigzag Carbon Nanotubes: Cluster and Crystal Approach

We study the electronic structure of (n,0) zigzag carbon nanotubes by means of two complementary numerical methods. Using the semiempirical PM3 method, we carry out quantum-chemical calculations for tube fragments of different symmetry and size, which represent these tubes. Using the tight-binding method, we proceed in parallel to determine the band structure of these tubes. The effect of cluster size on the structure of frontier orbitals and on the cluster stability is investigated for the (6,0) tube. We show that the highest occupied molecular orbitals (HOMOs) and the lowest unoccupied molecular orbitals (LUMOs) of the (n,0) tube fragments are localized on the edge atoms. The comparison between the band structure of the (6,0) tube and the molecular orbitals of the (6,0) tube fragment with 13 carbon hexagons along the tube axis indicates that the spatial structure of the HOMO′s and the LUMO′s directly corresponds to that of the Bloch wave functions of occupied and unoccupied π bands near the Fermi level.