To separate the layer and its periodic images, we used a vacuum of 23.518 Å along the [100] direction. In the DMET calculations, we place a dummy oxygen atom at the vacancy to provide basis functions to span the electron density of the defect. For the mono-vacancy, the dummy oxygen and four nearest atoms Mg atoms are treated using the polarized triplezeta basis set (GTH-TZVP) whereas the rest of the atoms are treated with the polarized double-zeta basis set (GTH-DZVP). For the di-vacancy, the dummy oxygens and six nearest Mg atoms are treated using the polarized triple-zeta basis set (GTH-TZVP) whereas the rest of the atoms are treated with the polarized double-zeta basis set (GTH-DZVP). The two and three layered models are constructed by placing non-defective one and two layers of Mg 18 O 18 below the first layer respectively. For these models the GTH-TZVP is used for the dummy oxygen and nine nearest atoms (4 O and 5 Mg) while GTH-DZVP is used for all other atoms.