Energetics of large carbon clusters:  Crossover from fullerenes to nanotubes

The energetics of large-sized fullerenes and carbon nanotubes is investigated through first-principles pseudopotential calculations for the carbon cluster of ${\mathrm{C}}_N$ $(60\mathrm{}<~N<~540).$ The strain energy due to the presence of pentagons, in addition to the curvature effect, makes an important contribution to the energetics of the fullerenes and nanotubes and accurately describes the N dependence of the energy of the spherical fullerenes. Our model predicts that a nanotube of $\sim 13\hspace{0.5em}\AA$ in diameter [for example, a (9,9) or (10,10) tube] is energetically most stable among various single-walled nanotubes and fullerenes, consistent with many experimental observations.