Localized spin defects in semiconductors with wide band gap have emerged as excellent qubit candidates. Accurate prediction of the electronic structure and characters of these spin defects demand first principles simulations e.g., by Density Functional Theory (DFT). However, DFT is not a good choice for spin defects having strongly correlated excited states that cannot be approximated by single Slater determinants. Although multireference methods are crucial for such systems, they are computationally so demanding that they are impractical to apply directly for solid-state defects that are described by periodic supercells containing several atoms. Quantum embedding theories offer an appealing solution to this, providing a trade-off between the computational cost and accuracy. To this end, our group has previously implemented the CASSCF/NEVPT2 solvers within the periodic version of Density Matrix Embedding Theory (pDMET) that allows to perform accurate and affordable ab initio electronic structure calculations on point defects in solids based on a local impurity model. It uses a high-level multireference method for the strongly correlated defect region while describing the rest of the system (environment) with a bath constructed from a singular value decomposition of a mean-field wave function. Such a method describes the explicit quantum entanglement between one or more fragments with its environment. It is now well-established that pDMET offers an efficient balance between the cost and accuracy for neutral point defects. However, charged defects such as the negatively charged nitrogen-vacancy center (NV<sup>-</sup>) in diamond are quite challenging to handle when periodic boundary conditions are applied. The spurious long-range Coulomb interactions of the defect charge density in the central supercell with those in the image cells give rise to divergence and finite-size errors in the calculation of total electrostatic energy. Care must be taken to overcome the divergence and to achieve a faster convergence with respect to the supercell size. We present the extension of pDMET for such charged defects with particular focus on the NV<sup>-</sup> defect in diamond.

Extension of periodic density matrix embedding theory for charged crystalline point defects

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