  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.
