Tightened Lieb-Oxford Bound for Systems of Fixed Particle Number

Area of Science:

• Quantum Chemistry
• Computational Materials Science

Background:

• The Lieb-Oxford bound provides a fundamental constraint for approximate exchange-correlation functionals in density-functional theory.
• Accurate functionals are crucial for predicting material properties and chemical reaction energetics.

Purpose of the Study:

• To investigate the impact of a nonempirically tightened Lieb-Oxford bound on the performance of the PBE exchange-correlation functional.
• To explore both universal and electron number-dependent forms of the tightened bound.

Main Methods:

• The Perdew-Burke-Ernzerhof (PBE) functional was tested using both the original and tightened Lieb-Oxford bounds.
• Performance was evaluated by examining atomization energies and bond lengths of various molecules.

Main Results:

• The PBE functional demonstrated remarkable insensitivity to changes in the Lieb-Oxford bound.
• Atomization energies showed a slight worsening, while bond lengths exhibited slight improvement with the tightened bound.

Conclusions:

• The PBE functional's robustness to the Lieb-Oxford bound justifies its original parameterization.
• Further research into enhancement factors sensitive to sharpened constraints may lead to improved functional development.