How tight is the Lieb-Oxford bound?

Area of Science:

• Quantum Chemistry
• Computational Materials Science
• Condensed Matter Physics

Background:

• Density-functional theory (DFT) relies on accurate exchange-correlation (xc) functionals for describing electronic structure.
• Universal constraints on xc energy are crucial for developing improved DFT functionals.
• The Lieb-Oxford bound is a fundamental constraint on the xc energy.

Purpose of the Study:

• To investigate the universal property of the Lieb-Oxford lower bound for xc functionals.
• To determine the optimal prefactor C in the Lieb-Oxford bound across various systems.
• To assess the impact of the bound's prefactor on the performance of modern xc functionals.

Main Methods:

• Surveyed exact or near-exact data for xc energies of atoms, ions, molecules, and solids.
• Included data from model Hamiltonians: electron liquid, Hooke's atom, and Hubbard model.
• Analyzed physically realistic density distributions to evaluate the Lieb-Oxford bound.

Main Results:

• All investigated physically realistic density distributions are consistent with a tighter Lieb-Oxford bound prefactor (C≤1).
• Class-specific, but not fully universal, bounds were derived for large system categories.
• The commonly used Lieb-Oxford bound prefactor of 1.68 may be too large for many systems.

Conclusions:

• A tighter universal Lieb-Oxford bound (C≤1) is supported by a wide range of physical systems.
• Revisiting the prefactor C in the Lieb-Oxford bound is essential for developing more accurate xc functionals.
• Changes to the prefactor C will significantly influence the predictive power of current DFT functionals.