First, we investigate the performance of pDME-PDFT in calculating the S 0 → S 1 and S 0 → T 1 excitations of the F-center which is a neutral oxygen mono-vacancy (OV) on the (100) monolayer of MgO. Experimentally, detecting F centers on MgO surfaces presents a challenge due to its surface sensitivity, resulting in a range of S 0 → S 1 transitions observed between 1-5 eV as reported in Table . A quantum mechanics/molecular mechanics (QM/MM) approach, utilizing the multireference configuration interaction method, for a cluster model of the oxygen mono-vacancy predicted excitation energies of 3.24 eV for the S 0 → S 1 transition and 1.93 eV for the S 0 → T 1 transition. The MgO lattice is composed of Mg 2+ and O 2- ions, and when an oxygen atom is removed, it leaves behind two electrons in the defect site that occupy two defect-localized states between the valence band maximum (VBM) and the conduction band minimum (CBM). The computational model is illustrated in Figure . To examine how the excitation energies vary with the embedding space, we consider three impurity clusters of increasing size, as depicted in Figure . Figure shows the two active natural orbitals used for the minimal (2,2) active space in all calculations presented in Figures and. This active space has been used previously for the F-center. The two active orbitals have a 1g and a 2u symmetry in the D 4h point group. In Figures and, we show the vertical excitation energies of the S 0 → T 1 and S 0 → S 1 transitions in the OV system, respectively, as a function of the inverse of the number of embedding orbitals, using the minimal (2,2) active space. Specifically, the plot of excitation energies is shown as a function of N AO /N emb where N AO represents the total number of basis functions in the system considered (here Mg 18 O 18 ) and N emb is the number of embedding orbitals in the impurity clusters considered. We compare them to the corresponding nonembedded results represented by hollow markers. The values are reported in Table . The excitation energies computed using pDME-tPBE and pDME-tPBE0 agree to within 0.06 eV of the non-embedded reference values for all impurity clusters considered. NEVPT2-DMET, on the other hand, shows a higher sensitivity to the impurity cluster . This is expected since NEVPT2-DMET cannot describe electron correlation outside the embedding space. Considering the S 0 → T 1 gap, for example, the NEVPT2-DMET difference with respect to the non-embedding reference ranges from 0.17 eV to 0.05 eV. As previously done for NEVPT2-DMET, the linear dependence of the excitation energies with respect to the inverse of the number of embedding orbitals was utilized to extrapolate the non-embedding limit. Here, the non-embedding limit corresponds to the point where N AO /N emb =1, i.e.