  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.
