Lieb-Oxford bound and pair correlation functions for density-functional methods based on the adiabatic-connection...

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• The Lieb-Oxford bound provides a fundamental limit for exchange-correlation energy in density-functional theory.
• Accurate treatment of electron correlation is crucial for predicting molecular properties.
• The adiabatic-connection fluctuation-dissipation (ACFD) theorem offers a pathway to systematically improve correlation energy calculations.

Purpose of the Study:

• To investigate the compliance of various density-functional methods with the Lieb-Oxford bound.
• To assess the accuracy of correlation contributions to the pair density from ACFD methods.
• To compare the performance of different ACFD approaches for molecules and the homogeneous electron gas.

Main Methods:

• Evaluation of density-functional methods utilizing the ACFD theorem.
• Comparison of calculated correlation energies and pair densities against highly accurate reference data.
• Analysis of the Lieb-Oxford bound compliance for the helium atom, hydrogen molecule, and homogeneous electron gas.

Main Results:

• All tested ACFD methods obeyed the Lieb-Oxford bound for molecular systems.
• The Lieb-Oxford bound was violated by all methods for the homogeneous electron gas at low densities.
• The direct random phase approximation (dRPA) showed poorer performance compared to more advanced ACFD methods, especially for the pair density.

Conclusions:

• Advanced ACFD methods provide physically reasonable correlation contributions to the pair density, though improvements are needed for stretched molecules.
• The choice of ACFD method significantly impacts the adherence to fundamental bounds and the accuracy of correlation energy calculations.
• Further development of ACFD-based methods is necessary to achieve high accuracy across various electronic systems.