  In this work we present ab initio calculations of the formation energies and
stability of different types of multi-vacancies in carbon nanotubes. We
demonstrate that, as in the case of graphene, the reconstruction of the defects
has drastic effects on the energetics of the tubes. In particular, the
formation of pentagons eliminates the dangling bonds thus lowering the
formation energy. This competition leads to vacancies having an even number of
carbon atoms removed to be more stable. Finally the appearance of magic numbers
indicating more stable defects can be represented by a model for the formation
energies that is based on the number of dangling bonds of the unreconstructed
system, the pentagons and the relaxation of the final form of the defect formed
after the relaxation.
