Odashima and Capelle (OC) recently presented a nonempirical, nonlocal, approximate exchange-correlation density functional constructed from exact exchange and the Lieb-Oxford bound [M. M. Odashima and K. Capelle, Phys. Rev. A 79, 062515 (2009)] https://doi.org/10.1103/PhysRevA.79.062515. Our “Rung 3.5” exchange energy, built from the product of the Kohn-Sham one-particle density matrix and a semilocal model density matrix, provides an upper bound to exact exchange via the Cauchy-Schwarz inequality. The present work combines this bound with the OC construction to yield nonempirical Rung 3.5 functionals. Numerical tests indicate that these functionals provide reasonable treatments of many molecular properties, and suggest areas for improvement. The results illustrate the promise of the OC construction and the utility of Rung 3.5 exchange in constraint satisfaction.
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