Energetics of the AK13 Semi-Local Kohn-Sham Exchange Energy Functional

TL;DR

This paper investigates the energetics of the AK13 semi-local exchange functional, finding that non-self-consistent LDA applied to AK13 densities yields accurate energetics and structural properties, while preserving its improved orbital features.

Contribution

The study demonstrates that non-self-consistent LDA on AK13 densities provides a practical, accurate, and computationally efficient approach for predicting structural properties and band structures.

Findings

Non-self-consistent LDA on AK13 densities yields good energetics.

AK13 retains its orbital features after structural relaxation.

Non-self-consistent scheme is equivalent to a single external-potential dependent functional.

Abstract

The recent non-empirical semi-local exchange functional of Armiento and K\"ummel, the AK13 [PRL 111, 036402 (2013)] incorporates a number of features reproduced by higher-order theory. The AK13 potential behaves analogously with the discontinuous jump associated with the derivative discontinuity at integer particle numbers. Recent works have established that AK13 gives a qualitatively improved orbital description compared to other semi-local methods, and reproduces a band structure closer to higher-order theory. However, its energies and energetics are inaccurate. The present work further investigates the deficiency in energetics. In addition to AK13 results, we find that applying the local-density approximation (LDA) non-self-consistently on the converged AK13 density gives very reasonable energetics with equilibrium lattice constants and bulk moduli well described across 14 systems. We also confirm that the attractive orbital features of AK13 are retained even after full structural relaxation. Hence, the deficient energetics cannot be a result of the AK13 orbitals having adversely affected the quality of the electron density compared to that of usual semi-local functionals; an improved orbital description and good energetics are not in opposition. We also prove that the non-self-consistent scheme is equivalent to using a single external-potential dependent functional in an otherwise consistent KS-DFT scheme. Furthermore, our results also demonstrate that, while an internally consistent KS functional is presently missing, non-self-consistent LDA on AK13 orbitals works as a practical non-empirical computational scheme to predict geometries, bulk moduli, while retaining the band structure features of AK13 at the computational cost of semi-local DFT.