Accurate electron affinities from anion HOMO energies within the self-consistent random phase approximation

Density functional calculations of small anions using the self-consistent random phase approximation (scRPA) optimized effective potential method are presented. scRPA calculations provide bound anions with the negative of the highest occupied molecular orbital (HOMO) energy closely matching the electron affinity of the corresponding neutral systems. For a benchmark of small atomic and molecular anions, electron affinities calculated as the negatives of HOMO energies from scRPA calculations are substantially more accurate than those from calculations with local, semilocal, global hybrid, and even range-separated hybrid exchange-correlation functionals, such as the well-established LC-ωPBE functional considered as an example. The superior performance of the scRPA method compared to conventional Kohn-Sham (KS) approaches lies in its ability to provide a closer approximation to the exact KS potential. Specifically, scRPA exchange-correlation potentials exhibit the correct -1/r asymptotic behavior and closely resemble the exact exchange-correlation potential in the molecular region. In addition to the standard scRPA method, we also explored the hybrid scRPA (hscRPA) approach, which incorporates a fraction of nonlocal Hartree-Fock exchange. The hscRPA method addresses convergence challenges that may arise in standard scRPA calculations associated with a vanishing HOMO-LUMO gap. At the same time, hscRPA also provides bound anions with accurate HOMO energies.