  We present a first-principles study of Peierls distortions in
\emph{trans}-polyacetylene, polyacene, and armchair $(n,n)$ carbon nanotubes.
Our findings suggest that the ground-state geometries of armchair $(n,n)$
carbon nanotubes, with $n$ up to 6, exhibit a Peierls distortion as it is found
for \emph{trans}-polyactetylene. In contrast to previous studies in which no
Peierls distortion is found with conventional local and semi-local density
functionals, we use a hybrid functional whose exact-exchange admixture has been
specifically optimized for the problem at hand.
