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The treatment of atomic anions with Kohn-Sham density functional theory (DFT)has long been controversial since the highest occupied molecular orbital (HOMO)energy, $E_{HOMO}$, is often calculated to be positive with most approximatedensity functionals. We assess the accuracy of orbital energies and electronaffinities for all three rows of elements in the periodic table (H-Ar) using avariety of theoretical approaches and customized basis sets. Among all of thetheoretical methods studied here, we find that a non-empirically tunedrange-separated approach (constructed to satisfy DFT-Koopmans' theorem for theanionic electron system) provides the best accuracy for a variety of basis sets- even for small basis sets where most functionals typically fail. Previousapproaches to solve this conundrum of positive $E_{HOMO}$ values have utilizednon-self-consistent methods; however electronic properties, such as electroniccouplings/gradients (which require a self-consistent potential and energy),become ill-defined with these approaches. In contrast, the non-empiricallytuned range-separated procedure used here yields well-defined electroniccouplings/gradients and correct $E_{HOMO}$ values since both the potential andresulting electronic energy are computed self-consistently. Orbital energiesand electron affinities are further analyzed in the context of the electronicenergy as a function of electronic number (including fractional numbers ofelectrons) to provide a stringent assessment of self-interaction errors forthese complex anion systems.

Accurate Electron Affinities and Orbital Energies of Anions from a Non-Empirically Tuned Range-Separated Density Functional Theory Approach