text: Metallic doping of a (6,6) CNT has been modeled in a su- 
  percell containing six repeated minimal unit cells along the 
  CNT axis (dimensions: 15 ˚A×15 ˚A×14.622 ˚A). For this size 
  of supercell a Γ-point sampling of the Brillouin zone was 
  found to be sufﬁcient. The formation energy for creating a 
  vacancy (VC) occupied by a transition metal atom (M) was 
  calculated using the relation 
  
  Eform[M@VC] = E[M@VC] + nE[C] − E[M@NT]  (1) 
  
  where E[M@VC] is the total energy of a transition metal 
  atom occupying a vacancy in the nanotube, n is the number 
  of carbon atoms removed to form the vacancy, E[C] is the en- 
  ergy per carbon atom in a pristine nanotube, and E[M@NT] 