  We have evaluated the energies required to twist carbon nanotubes (NTs), and
investigated the effects of these distortions on their electronic structure and
electrical properties. The computed distortion energies are high, indicating
that it is unlikely that extensive twisting is the result of thermal
excitation. Twisting strongly affects the electronic structure of NTs. Normally
metallic armchair $(n,n)$ NTs develop a band-gap which initially scales
linearly with twisting angle and then reaches a constant value. This saturation
is associated with a structural transition to a flattened helical structure.
The values of the twisting energy and of the band-gap are strongly affected by
allowing structural relaxation in the twisted structures. Finally, we have used
the Landauer-B{\"u}ttiker formalism to calculate the electrical transport of
the metal-NT-metal system as a function of the NT distortion.
