  The geometrical and electronic structures of the 4 {\AA} diameter perfect and
deformed (5, 3) single-walled gold nanotube (SWGT) have been studied based upon
the density-functional theory in the local-density approximation (LDA). The
calculated relaxed geometries show clearly significant deviations from those of
the ideally rolled triangular gold sheet. It is found that the different
strains have different effects on the electronic structures and density of
states of the SWGTs. And the small shear strain can reduce the binding energy
per gold atom of the deformed SWGT, which is consistent with the experimentally
observed result. Finally, we found the finite SWGT can show the
metal-semiconductor transition.
