  Results of the bond lengths for various chiralities of single-wall carbon
carbon nanotubes (SWNTs) (armchair, zigzag and chiral) are obtained. We use
modified helical and rotational symmetries to describe the structure of SWNTs
and Tersoff potential to minimize the energy of these tubes. It emerges that in
general, two bond lengths are required for obtaining minimum energy structure,
in contrast to one bond length commonly used. The difference in bond lengths
depends on chirality and radius of achiral tubes. Significantly, even a small
deviation from zigzag or armchair character leads to interesting behavior of
bond lengths. A reduction in diameter is responsible for difference in the bond
lengths of achiral nanotubes. We also calculate the bond lengths under
hydrostatic pressure. The behavior of bond lengths for armchair single-wall
nanotubes when calculated under pressure shows that the larger bond length
decreases faster with pressure in comparison to the shorter bond length. At
some critical pressure (depending upon the radius of the tube), the two bond
lengths become equal to each other, reversing their difference above this
critical pressure. We suggest that this behavior can be exploited to
experimentally determine the chirality and radius of the carbon nanotubes, for
example by observing the presence and disappearance of modes typical of two
different bond lengths. This change occurs only within a few GPa of pressure.
