Abstract
We conducted a large-scale density-functional theory study on the influence of the exchange-correlation functional in the calculation of electronic band gaps of solids. First, we use the large materials data set that we have recently proposed to benchmark 21 different functionals, with a particular focus on approximations of the meta-generalized-gradient family. Combining these data with the results for 12 functionals in our previous work, we can analyze in detail the characteristics of each approximation and identify its strong and/or weak points. Beside confirming that mBJ, HLE16 and HSE06 are the most accurate functionals for band gap calculations, we reveal several other interesting functionals, chief among which are the local Slater potential approximation, the GGA AK13LDA, and the meta-GGAs HLE17 and TASK. We also compare the computational efficiency of these different approximations. Relying on these data, we investigate the potential for improvement of a promising subset of functionals by varying their internal parameters. The identified optimal parameters yield a family of functionals fitted for the calculation of band gaps. Finally, we demonstrate how to train machine learning models for accurate band gap prediction, using as input structural and composition data, as well as approximate band gaps obtained from density-functional theory.
Highlights
IntroductionDensity-functional theory (DFT)[1,2] has become the workhorse theory in computational chemistry and solid-state physics
Over the past decades, density-functional theory (DFT)[1,2] has become the workhorse theory in computational chemistry and solid-state physics
A summary of the MAE and MAPE for all fitted functionals is presented in Fig. 11, where the original functionals are shown for comparison
Summary
Density-functional theory (DFT)[1,2] has become the workhorse theory in computational chemistry and solid-state physics. This powerful approach is an exact and elegant reformulation of the many-body quantum mechanics that governs the behavior of electrons in all kinds of systems (atom, molecule, solid, etc.). The Kohn–Sham equations that stem from the theory[2] can be solved efficiently with modern computers These equations rely on a single approximation, namely the one for the exchange-correlation (xc) energy, which is responsible for the accuracy of the calculations[3]. Only a handful of them, such as the PBE from Perdew, Burke, and Ernzerhof[6,7] or the hybrids B3LYP8,9 and HSE06 from Heyd, Scuseria, and Ernzerhof[10,11], have found widespread use
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