regards PBE and LDA results, the stability order between S z = 0 and 1 is reversed, and S z = 2 is less stable than S z = 0 by only 8-10 mE h . The defect crystalline orbitals are classified by symmetry and identified in the band structure with respect to the valence and conducting electrons. The formation energy of the vacancy, evaluated with six different functionals, is close to 7 eV for three of them (7.00 HSE06, 7.05 LDA, 7.11 PBE0), slightly smaller in B3LYP (6.74) and PBE (6.56). Cluster calculations (C 35 H 36 and C 455 H 196 ) are also performed in comparison with the supercell results and for obtaining, with the smaller one, a coupled-cluster estimate of the energy differences between the three spin states that turn out to be close to the ones obtained with hybrids.