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.