Abstract
Based on LCAO calculations, there are four atomic orbitals ( ) per atom. We thus have eight Bloch orbitals in the two atoms in a unit cell. We have constructed the Hamiltonian matrix., including 2s and 2p orbitals to take into account the mixing effect of σ and π orbitals due to the curvature of tubes with small radii, and we calculate the band structure of carbon nanotubes including up to third-nearest neighbors interactions numerically. We find tube curvature may significantly affect the electronic properties and the third-neighbor interactions reduce the energy gap. Our results show that the (4,0) and (6,0) tubes have no energy gap at the Fermi level and are in good agreement with first-principles calculations, and with decreasing radius, the effect of third-neighbor interactions on the gap becomes more important. We show the importance of calculations including up to third-nearest neighbors interactions.