Effect of sigma electrons on the pi-electron behavior in single-wall   carbon nanotubes
  The hybrid orbitals of single-wall carbon nanotubes are given according to the structure of the nanotube. Because the energy levels of these hybrid orbitals are close to each other, the sigma-orbitals will affect the behavior of the pi-electrons, which is called the scattering of pi- electrons. This scattering effect is taken into account in the nanotube and the local wave function of pi-electrons is constructed, which is called the extended Wannier function. In the Wannier representation, the electronic hopping energies and the energy gap of the tubes (9,0) and (9,9) are calculated. Our results show that the band gap of the tubes increases in direct ratio with the scattering coefficients of sigma-orbitals and this scattering is able to enhance the localization of pi-electrons. 
G.-P. Tong and Q.-P. Huang