It has long been a challenge to calculate electronic structures and properties of molecular systems containing more than 10000 electrons using first-principles approaches. We have developed an elongation method that allows to treat 59 nm long single-walled carbon nanotubes (SWCNTs) containing 4770 carbon atoms at the hybrid density functional theory level. An unexpected oscillating behaviour of the energy gap with respect to the length of the nanotube is observed. The calculated current voltage characteristics of sub-20 nm SWCNTs are in excellent agreement with the experimental results, revealing the underlying mechanism of electron transport in nanosized SWCNTs for the first time. (c) 2005 Elsevier B.V. All rights reserved.