Correlated Orbital Theory (COT) provides an exact one-particle framework by imposing rigorous physical constraints on Kohn-Sham eigenvalues and, as a consequence, directly incorporates essential electron correlation into molecular orbitals. This approach paves the way toward a new class of approximations within Kohn-Sham Density Functional Theory (KS-DFT). However, since all existing quantum theory project functionals are derived from CAM-B3LYP, we pose the question: Can COT improve the hybrid versions of different exchange-correlation functionals as well? To that end, we explore two optimization strategies for adjusting the existing parameters within PBE0, TPSS0, and LC-PBE0: (i) the ionization potential condition and (ii) the HOMO-LUMO condition. In this sense, we critically assess how these functionals address the "Devil's Triangle" of KS-DFT: self-interaction error, integer discontinuity, and one-particle spectra. We further examine how the COT influences the description of two challenging properties, charge transfer and reaction barrier heights. Overall, enforcing both COT conditions systematically enhances the performance of functionals within the PBE family, although the description of reaction barriers still leaves room for improvement.
Mendes et al. (Sat,) studied this question.