Density-functional study of Peierls instability in carbon nanotubes using hybrid functionals

We present a first-principles study of Peierls distortions in \emph{trans}-polyacetylene, polyacene and armchair $(n,n)$ carbon nanotubes. All calculations were done within density- functional theory using a gaussian basis set. We show that while density only functionals (LDA, GGA) cannot reproduce the experimentally mesured dimerization in \emph{trans}- polyactetylene, hybrid functionals including Hartree-Fock exchange can give the correct geometry. These findings suggest that armchair $(n,n)$ carbon nanotubes could have a nonsymmetric ground state; in contradiction with what is commonly accepted. Indeed, the B3LYP functional (which includes 20\% of exact exchange) opens a gap of 0.26 eV and 0.12 eV for the $(3,3)$ and $(6,6)$ carbon nanotubes respectively. Accordingly, dimerization amplitudes of 0.005 \AA~and 0.002 \AA~are obtained. It is found that the dimerization and the band gap are proportional to the the amount of exact exchange included in the functional.