Beyond the RPA on the cheap: improved correlation energies with the efficient "Radial Exchange Hole" kernel

TL;DR

This paper introduces the RXH kernel, a parameter-free exchange-correlation functional that significantly improves the accuracy of absolute correlation energy predictions in density functional theory while retaining computational efficiency.

Contribution

The authors develop a new radial exchange hole (RXH) kernel that enhances correlation energy calculations without additional parameters, outperforming previous kernels like RPA and PGG.

Findings

Thirteenfold reduction in atom correlation energy errors compared to RPA.

Threefold improvement over PGG kernel in correlation energy accuracy.

Moderate improvements in van der Waals $C_6$ coefficients, especially for highly polarizable atoms.

Abstract

The "ACFD-RPA" correlation energy functional has been widely applied to a variety of systems to successfully predict energy differences, and less successfully predict absolute correlation energies. Here we present a parameter-free exchange-correlation kernel that systematically improves absolute correlation energies, while maintaining most of the good numerical properties that make the ACFD-RPA numerically tractable. The "RXH" kernel is constructed to approximate the true exchange kernel via a carefully weighted, easily computable radial averaging. Correlation energy errors of atoms with two to eighteen electrons show a thirteenfold improvement over the RPA and a threefold improvement over the related "PGG" kernel, for a mean absolute error of 13mHa or 5%. The average error is small compared to all but the most difficult to evaluate kernels. van der Waals $C_6$ coefficients are less well predicted, but still show improvements on the RPA, especially for highly polarisable Li and Na.