Accurate Excitation Energies of Point Defects from Fast Particle–Particle Random Phase Approximation Calculations

We present an efficient particle–particle random phase approximation (ppRPA) approach that predicts accurate excitation energies of point defects, including the nitrogen-vacancy (NV^–) and silicon-vacancy (SiV⁰) centers in diamond and the divacancy center (VV⁰) in 4H silicon carbide, with errors of ±0.2 eV compared with experimental values. Starting from the (N + 2)-electron ground state calculated with density functional theory (DFT), the ppRPA excitation energies of the N-electron system are calculated as the differences between the two-electron removal energies of the (N + 2)-electron system. We demonstrate that the ppRPA excitation energies converge rapidly with a few hundred canonical active-space orbitals. We also show that active-space ppRPA has weak DFT starting-point dependence and is significantly cheaper than the corresponding ground-state DFT calculation. This work establishes ppRPA as an accurate and low-cost tool for investigating excited-state properties of point defects and opens up new opportunities for applications of ppRPA to periodic bulk materials.