Particle–Particle\nRandom Phase Approximation\nfor Predicting Correlated Excited States of Point Defects

The\nparticle–particle random phase approximation\n(ppRPA)\nwithin the hole–hole channel was recently proposed as an efficient\ntool for computing excitation energies of point defects in solids\n[<i>J. Phys. Chem. Lett.</i> 2024, 15, 2757–2764].\nIn this work, we investigate the application of ppRPA within the particle–particle\nchannel for predicting correlated excited states of point defects,\nincluding the carbon-vacancy (VC) in diamond, the oxygen-vacancy (VO)\nin magnesium oxide (MgO), and the carbon dimer defect (C<sub>B</sub>C<sub>N</sub>) in two-dimensional hexagonal boron nitride (h-BN).\nStarting from a density functional theory calculation of the (<i>N</i> – 2)-electron ground state, vertical excitation\nenergies of the <i>N</i>-electron system are obtained as\nthe differences between the two-electron addition energies. We show\nthat active-space ppRPA with the B3LYP functional yields accurate\nexcitation energies, with errors mostly smaller than 0.1 eV for tested\nsystems compared to available experimental values. We further develop\na natural transition orbital scheme within ppRPA, which provides insights\ninto the multireference character of defect states. This study, together\nwith our previous work, establishes ppRPA as a low-cost and accurate\nmethod for investigating excited-state properties of point defect\nsystems.