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We present an efficient particle-particle random phase approximation (ppRPA)approach that predicts accurate excitation energies of point defects, includingthe nitrogen-vacancy (NV$^-$) and the silicon-vacancy (SiV$^0$) centers indiamond and the divacancy center (VV$^0$) in 4H silicon carbide, with errorswithin 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 calculatedas the differences between the two-electron removal energies of the($N+2$)-electron system. We demonstrate that the ppRPA excitation energiesconverge rapidly with a few hundred of canonical active-space orbitals. We alsoshow that active-space ppRPA has weak DFT starting-point dependence and issignificantly cheaper than the corresponding ground-state DFT calculation. Thiswork establishes ppRPA as an accurate and low-cost tool for investigatingexcited-state properties of point defects and opens up new opportunities forapplications of ppRPA to periodic bulk materials.

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