Comparison of local density functionals based on electron gas and finite systems

TL;DR

This paper compares local density functionals derived from both the homogeneous electron gas and finite systems, revealing their similarities and differences in various density regimes, with implications for density functional theory accuracy.

Contribution

The study introduces a HEG-based LDA for 1D spinless electrons and compares it to finite LDAs, highlighting their similarities and differences in different density regimes.

Findings

Finite LDAs outperform in high-density systems.

All LDAs are inadequate in low-density, strongly correlated systems.

Finite LDAs better describe self-interaction corrections.

Abstract

A widely used approximation to the exchange-correlation functional in density functional theory is the local density approximation (LDA), typically derived from the properties of the homogeneous electron gas (HEG). We previously introduced a set of alternative LDAs constructed from one-dimensional systems of one, two, and three electrons that resemble the HEG within a finite region. We now construct a HEG-based LDA appropriate for spinless electrons in one dimension and find that it is remarkably similar to the finite LDAs. As expected, all LDAs are inadequate in low-density systems where correlation is strong. However, exploring the small but significant differences between the functionals, we find that the finite LDAs give better densities and energies in high-density exchange-dominated systems, arising partly from a better description of the self-interaction correction.