  An elongation method based on ab initio quantum chemistry approaches is
presented. It allows to study electronic structures and coherent electron
transportation properties of single-walled carbon nanotubes (SWCNTs) up to 22nm
in length using the hybrid density functional theory. The 22nm long SWCNT,
consisting of more than ten thousands electrons, is the largest carbon nanotube
that has ever been studied at such a sophisticated all-electron level.
Interesting oscillating behaviour of the energy gap with respect to the length
of the nanotube is revealed. The calculated current-voltage characteristics of
SWCNTs are in excellent agreement with recent experimental results. It confirms
the experimental observation that a 15nm long SWCNT is still largely a
ballistic transport device. The proposed elongation method opens up a new door
for the first principle study of nano- and bio-electronics.
