The high aspect ratio of carbon nanotubes makes them prone to bending. To
know how bending affects the tubes is therefore crucial for tube identification
and for electrical component design. Very few studies, however, have
investigated tubes under small bending well below the buckling limit, because
of technical problems due to broken translational symmetry. In this Letter a
cost-effective and exact modeling of singe-walled nanotubes under such small
bending is enabled by revised periodic boundary conditions, combined with
density-functional tight-binding. The resulting, bending-induced changes in
electronic and optical properties fall in clear chirality-dependent trend
families. While the correct trends require full structural relaxation, they can
be understood by one general argument. To know these trends fills a fundamental
gap in our understanding of the properties of carbon nanotubes.Comment: 4 pages, 3 figure