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This paper benchmarks the performance of various density functional approximations (DFAs) – LDA, PBE, SCAN, r2SCAN, LAK meta-GGA, and HSE hybrid functional – in predicting defect formation energies in metals (monovacancies in eight fcc metals) and semiconductors (interstitials in Si-diamond). The study finds that LDA performs best for metals, while the LAK meta-GGA excels for silicon, even outperforming the HSE hybrid functional. By analyzing the semilocal ingredients (rs, s, and α) in pristine and defective structures, the authors identify critical regions that explain the observed performance trends of different DFAs.
Surprisingly, a meta-GGA functional (LAK) rivals computationally expensive hybrid functionals and approaches Quantum Monte Carlo accuracy for predicting defect formation energies in silicon.
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.