We have performed systematic calculations for single vacancies and their related point defects in achiral carbon nanotubes using a tight-binding model. Our calculations clarify that the local structures around single vacancies in such tubes do reconstruct with no constraint. We find that the structural configuration and formation energy of the resulting point defect are dependent on the radius and chirality, as well as the electric properties of a tube. The electronic structures of the single vacancies also depend strongly upon the chirality of the carbon nanotubes.

The chemical hardness of a cluster is defined as ͑IP− AE͒ / 2, where IP is the value of the ionization potential and AE is the value of the electron affinity of the cluster. The code used for calculation of the chemical hardness had a bug so that the calculated chemical hardness shown in Fig. 4 is not correct. Figure 4͑c͒ should be replaced by the new figure provided here.This revision of Fig. 4͑c͒ does not change the conclusions mentioned in the paper. FIG. 4. ͑a͒ IP's of diamondoids vs polymantane order. ͑b͒ AE's of diamondoids vs polymantane order. ͑c͒ The hardness of diamondoids vs the polymantane order.

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