The electronic structure of carbon nanotube bundles (CNTBs) can be a tough task for the routine first-principle calculation. The difficulty comes from several issues including the atomic structure, the boundary condition, and above all the very large number of atoms that makes the calculation quite cumbersome. In this work, we estimated the band gap of the CNTBs based on the results from single-walled carbon nanotubes (SWCNTs) under different deformations. The effects of squeezing, stretching, and torsion on the bands of SWCNTs were investigated through first-principle calculations, from which the band gaps of bundles were analyzed because the effects of these deformations were qualitatively independent when the distortions were small. Specifically, the gaps of (4,4) and (8,0) CNTBs under a reasonable torsional strength were predicted, wherein we were able to see metal–semiconductor and semiconductor–metal transitions, respectively. Such reversible mechanical modification of the conductivity may be helpful to the future band-gap engineering in nanoscale circuits. [ABSTRACT FROM AUTHOR]

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