The pristine cubic MgO crystal exhibits octahedral (O h ) symmetry. The nearest pair of magnesium (Mg) atoms are 4.26 Å apart in the PBE-optimized geometry. Upon removing an oxygen atom, the resulting vacancy retains the original symmetry, but the two electrons trapped in the vacancy cause a slight outward shift (0.04 Å) of the six closest magnesium (Mg) atoms surrounding the oxygen vacancy (OV). This defect generates an occupied totally symmetric (a 1g ) s-type single-electron state within the band gap as well as a set of three unoccupied p-type atomic orbital states (t 1u ) above the conduction band (Figure ). Both Once the DMET embedding space (consisting of fragment and bath orbitals) is generated through the ROHF trial wave function, we define the complete active space (CAS) with two active electrons in five active orbitals (2e,5o), shown in Figure below. This includes the defect localized a 1g and three degenerate t 1u orbitals, along with the CBM orbital. The CASSCF impurity ground state wave function is dominated by the a ↑↓ 1g determinant. The CAS selected here is larger than the minimal active space of (2e,2o), previously used in symmetry-constrained cluster calculations. The use of periodic boundary conditions facilitates the straightforward treatment of delocalized CBM-like orbitals because of the absence of spurious boundary effects. Scrutinizing the CAS-DMET active space, our optimized CBM orbital has no inversion center, meaning the photoionization process is dipole forbidden, since the ground state is closed-shell. In case delocalized orbitals with an inversion center were available at higher energies, we also checked a (2e,8o) CAS. No delocalized states with u-symmetry in the targeted energy range were obtained. Therefore, our initial goal is to compute the energy difference between 1 A 1g and 1 T 1u states. Figure shows the linear trend of CAS-DMET and NEVPT2-DMET excitation energies with embedding size, for each supercell, for the local singlet transition ( 1 A 1g → 1 T 1u ) and for the excitation to the delocalized state associated to the CBM ( 1 A 1g → 1 CBM ).