Near-locality of exchange and correlation density functionals for 1- and 2-electron systems

TL;DR

This paper introduces LSDA0, a new local spin density approximation that models exchange-correlation energies of 1- and 2-electron systems well, emphasizing near-locality and satisfying exact constraints.

Contribution

The paper presents LSDA0, a novel LSDA that accurately models exchange-correlation energies for simple systems and explores the concept of orbital locality.

Findings

LSDA0 models hydrogen and 1-2 electron systems effectively.

LSDA0 agrees well with exact results for finite, curved two-electron densities.

Orbital locality can be quantified by the ratio of exchange energy to its lower bound.

Abstract

The uniform electron gas and the hydrogen atom play fundamental roles in condensed matter physics and quantum chemistry. The former has an infinite number of electrons uniformly distributed over the neutralizing positively-charged background, and the latter only one electron bound to the proton. The uniform electron gas was used to derive the local spin density approximation (LSDA) to the exchange-correlation functional that undergirds the development of the Kohn-Sham density functional theory. We show here that the ground-state exchange-correlation energies of the hydrogen atom and many other 1- and 2-electron systems are modeled surprisingly well by a different local spin density approximation (LSDA0). Our LSDA0 is constructed to satisfy exact constraints, but agrees surprisingly well with the exact results for a uniform two-electron density in a finite, curved three-dimensional space. We also apply LSDA0 to excited or noded 1-electron densities. Furthermore, we show that the locality of an orbital can be measured by the ratio between the exact exchange energy and its optimal lower bound.