The DMET calculations were carried out using the pDMET code developed in our group, which utilizes electron integrals and quantum chemistry solvers from PySCF. Wannierization was performed with the wannier90 program through the pyWannier90 interface. Geometry optimizations were performed with periodic boundary conditions at the gamma point, at the PBE level, using Quantum Espresso. In order to allow the localization of electrons within the cavity, a set of Gaussian basis functions was placed at the vacancy site. We used four defective supercells in this work-three primitive supercells (2 × 2 × 2, 3 × 3 × 3, 4 × 4 × 4) with 15, 53 and 127 atoms, respectively, and one conventional 2 × 2 × 2 supercell with 63 atoms (Figure ). The pseudopotential of Goedecker, Teter and Hutter (GTH) was used along with a combination of double-and triple-zeta valence polarized Gaussian basis sets consistent with this pseudopotential for all calculations. The description of basis sets and other computational details are provided in the Supporting Information.