Local density approximations from finite systems

TL;DR

This paper introduces new local density approximations derived from finite electron systems, aiming to improve density functional theory calculations by better capturing self-interaction effects.

Contribution

The authors develop LDAs from finite slab-like systems of electrons, offering an alternative to the traditional HEG-based LDA, and demonstrate their properties in one dimension.

Findings

LDAs effectively correct self-interaction errors

Less reliable under strong correlation or current flow

Comparison with exact solutions shows good agreement in certain regimes

Abstract

The local density approximation (LDA) constructed through quantum Monte Carlo calculations of the homogeneous electron gas (HEG) is the most common approximation to the exchange-correlation functional in density functional theory. We introduce an alternative set of LDAs constructed from slablike systems of one, two and three electrons that resemble the HEG within a finite region, and illustrate the concept in one dimension. Comparing with the exact densities and Kohn-Sham potentials for various test systems, we find that the LDAs give a good account of the self-interaction correction, but are less reliable when correlation is stronger or currents flow.