Improved Lieb-Oxford bound on the indirect and exchange energies

Abstract

The Lieb-Oxford inequality provides a lower bound on the Coulomb energy of a classical system of $N$ identical charges only in terms of their one-particle density. We prove here a new estimate on the best constant in this inequality. Numerical evaluation provides the value 1.58, which is a significant improvement to the previously known value 1.64. The best constant has recently been shown to be larger than 1.44. In a second part, we prove that the constant can be reduced to 1.25 when the inequality is restricted to Hartree-Fock states. This is the first proof that the exchange term is always much lower than the full indirect Coulomb energy.

Final version to appear in Lett. Math. Phys. This article belongs to the themed collection: "Mathematical Physics and Numerical Simulation of Many-Particle Systems"; V. Bach and L. Delle Site (eds.)

References in corpus (6)

• Gedanken Densities and Exact Constraints in Density Functional Theory
• Coulomb and Riesz gases: The known and the unknown
• How tight is the Lieb-Oxford bound?
• Improved Lieb-Oxford exchange-correlation inequality with gradient correction
• Lower Bounds on the Exchange-Correlation Energy in Reduced Dimensions
• Strictly correlated uniform electron droplets

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