The reaction of C-2 with growing single-wall carbon nanotubes of different chiralities is investigated using density functional theory. It is found that the energy of the frontier orbitals for (5,5) and (6,6) armchair carbon nanotubes exhibits periodic behavior with an increasing number of carbon atoms in the nanotube. Such periodic behavior induces oscillations in the reaction energy released by adsorption of C-2 to the nanotube open edge. In contrast, the energy of the frontier orbitals of the (6,5) chiral tube remains constant as the number of C atoms increases, and the same stability is observed in the adsorption energy. It is suggested that this may be one of the reasons for the low percent of armchair single-wall carbon nanotubes found in the experimental synthesis.