Investigations of the exchange energy of neutral atoms in the large-Z limit

TL;DR

This paper analyzes the asymptotic behavior of the exchange energy in neutral atoms at large atomic number Z, highlighting the limitations of current density functional approximations and providing detailed data on their performance.

Contribution

It offers a comprehensive data analysis of the exchange energy's asymptotic trend, oscillations, and the LDA contribution, emphasizing challenges in modeling with existing functionals.

Findings

Detailed asymptotic trend analysis of exchange energy

Identification of oscillations across periodic table rows

Assessment of density functional approximations' accuracy

Abstract

The non-relativistic large-$Z$ expansion of the exchange energy of neutral atoms provides an important input to modern non-empirical density functional approximations. Recent works report results of fitting the terms beyond the dominant term, given by the local density approximation (LDA), leading to an anomalous ZlnZ term that can not be predicted from naive scaling arguments. Here, we provide much more detailed data analysis of the mostly smooth asymptotic trend describing the difference between exact and LDA exchange energy, the nature of oscillations across rows of the periodic table, and the behavior of the LDA contribution itself. Special emphasis is given to the successes and difficulties in reproducing the exchange energy and its asymptotics with existing density functional approximations.