Accurate and convergent energetics of color centers by wavefunction theory

Ab initio description of point defects in semiconductors, characterized by in-gap states of significant multideterminant character, presents a longstanding theoretical challenge for density functional theory (DFT) methods. In this study, we devise a wavefunction theory (WFT) based ab initio methodology as a competing alternative approach. Specifically, we apply perturbation theory (NEVPT2 level) on top of a defect-localized many-body wavefunction (CASSCF level), which provides a balanced description of dynamic and static correlation effects, respectively. This quantum chemical methodology, exemplified for the NV$^-$ center in diamond in this study, is not only used for the calculation of energies and properties, but also for geometry optimization, performed for each electronic state individually. By relaxing cluster models of increasing size and investigating convergence behavior, we quantitatively reproduce (i) the full energy spectrum of NV$^-$ including the recently characterized high-energy states, (ii) the effect of Jahn-Teller distortion on measurable properties, (iii) the fine structure of ground and excited states, (iv) the pressure dependence of zero-phonon lines. Our findings showcase that applying conventional wave-function-based quantum chemistry on carefully crafted clusters can be a robust routine tool for discussing defect-state energetics.