An assessment of orbital energy corrections for the direct random phase approximation and explicit <i>σ</i>-functionals

The <i>σ</i>-functionals developed in the Görling group [J. Chem. Phys. <b>154</b>, 014104 (2021); <i>ibid.</i> <b>155</b>, 134111 (2021)] facilitate impressive improvements over the direct random phase approximation (dRPA) and provide chemical accuracy for a broad spectrum of benchmarks concerning reaction energies and barrier heights, but struggle considerably with problems related to self-interaction. We herein assess two possible corrections to the orbital energies in the construction of the non-interacting response function for the dRPA and <i>σ</i>-functionals: (i) The scaling corrections of Yang and co-workers, which have been successfully applied within DFT, and (ii) the admixture of exact exchange in a post-SCF fashion similar to some double-hybrid functionals. An analysis of static shifts to the virtual orbital energies reveals the choice of corrections to be a difficult balancing act, as the effect of the corrections vastly differs between benchmark sets. Scaling corrections are found to provide substantial improvements to self-interaction problems, but seem adversarial for thermochemistry in combination with RPA. The post-SCF inclusion of exact exchange in combination with a semicanonical projection is shown to retain the accuracy of <i>σ</i>-functionals over a wide range of exact exchange admixtures and reduces the computational cost of the SCF calculation compared to hybrid functionals, but provides smaller improvements to self-interaction problems than scaling corrections for the most challenging cases.