Rationalizing defect formation energies in metals and semiconductors with semilocal density functionals

TL;DR

This paper evaluates various density functional approximations for defect formation energies in metals and silicon, revealing that local density performs best for metals and LAK meta-GGA excels for silicon, guiding future functional improvements.

Contribution

It provides a detailed analysis of the performance of different density functionals on defect energies and identifies key ingredients influencing their accuracy.

Findings

LDA outperforms others for metals.

LAK meta-GGA yields high accuracy for silicon.

Critical regions in structures explain functional performance trends.

Abstract

The study of defects in materials is of utmost importance for technological applications and the design of new materials. In this work, we analyze the performance of density functional approximations on two prototypical sets of defective systems: monovacancies in eight fcc metals, and interstitials in the semiconductor Si-diamond. Specifically, we compute defect formation energies using the local density approximation, the Perdew-Burke-Ernzerhof generalized gradient approximation, the meta-generalized gradient approximations (meta-GGAs) strongly constrained and appropriately normed (SCAN), its regularized version (r2SCAN), the Lebeda-Aschebrock-Kummel (LAK) meta-GGA, and the Heyd-Scuseria-Ernzerhof screened hybrid functional. For metals, the local density approximation shows better performance compared to the other approximations, whereas for silicon, the meta-generalized gradient approximation Lebeda-Aschebrock-Kummel yields outstand- ing accuracy, surpassing the hybrid functional and approaching the results of more computationally demanding Quantum Monte Carlo methods. To rationalize the different performances, we study the semilocal ingredients rs, s and {\alpha} in both the pristine and defective structures. We identify critical regions that indicate the observed trends of the defect formation energies and pave the way for improving density functional approximations.