The ground state of the 3 A 2 triplet, belonging to the C 3v point group, is characterized by a doubly occupied a 1 orbital and singly occupied e x and e y orbitals, leading to the configuration For the detailed theoretical foundation of pDMET we refer to the literature 52 and 53. The pDMET algorithm starts with a mean-field calculation on the full system, in this case we used the periodic ROHF method. Since the translational symmetry is lost in the defective solid and we use sufficiently large supercells to model the defect, the Brillouin zone is sampled only at the Γ-point.