Local Excitations of a Charged Nitrogen Vacancy in Diamond with Multireference Density Matrix Embedding Theory

We investigate the negatively charged nitrogen-vacancy center in diamond using periodic density matrix embedding theory (pDMET). To describe the strongly correlated excited states of this system, the complete active space self-consistent field (CASSCF) followed by n-electron valence state second-order perturbation theory (NEVPT2) was used as impurity solver. Since the NEVPT2-DMET energies show a linear dependence on the inverse of the size of the embedding subspace, we performed an extrapolation of the excitation energies to the non-embedding limit using linear regression. The extrapolated NEVPT2-DMET first triplet-triplet excitation energy is 2.31 eV and that for the optically inactive singlet-singlet transition is 1.02 eV, both in agreement with the experimentally observed vertical excitation energies of ~2.18 eV and ~1.26 eV, respectively. This is the first application of pDMET to a charged periodic system and the first investigation of the NV- defect using NEVPT2 for periodic supercell models.