Locality of correlation in density functional theory.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• The Hohenberg-Kohn density functional theory (DFT) is foundational in quantum chemistry.
• The Thomas-Fermi (TF) approximation is a semiclassical model for electronic systems.
• Understanding approximations in DFT is crucial for accurate material property predictions.

Purpose of the Study:

• To analyze the behavior of density functionals in the large-Z (semiclassical) limit.
• To investigate the accuracy of local density approximations for atomic correlation energy.
• To establish benchmarks for developing non-empirical density functional approximations.

Main Methods:

• Analysis of atomic correlation energies in the large-Z limit.
• Comparison of theoretical limits with numerical data for atomic systems.
• Evaluation of local density approximations against derived asymptotic expansions.

Main Results:

• In the large-Z limit, kinetic and exchange energies in DFT become local, consistent with the TF approximation.
• Atomic correlation energy (EC) follows EC → -AC ZlnZ + BC Z as Z → ∞, with an estimated BC of 37 mhartree.
• Local density approximations accurately capture the AC term but yield incorrect BC values for correlation.

Conclusions:

• The large-Z limit provides a critical benchmark for DFT approximations, particularly for correlation energy.
• Local density approximations are less accurate for correlation energy alone compared to kinetic and exchange energies.
• A generalized form for the leading correction to local density approximations in the large-Z limit is proposed, dependent on the TF density.