Accurate Excitation Energies of Point Defects from Fast Particle-Particle Random 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 the silicon-vacancy (SiV$^0$) centers in diamond and the divacancy center (VV$^0$) in 4H silicon carbide, with errors within 0.2 eV compared with experimental values. Starting from the ($N+2$)-electron ground state calculated with the 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 of 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.