![]() ![]() Moreover, the Kohn–Sham equations that stem from the theory 2 can be solved efficiently with modern computers. 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.). Over the past decades, density-functional theory (DFT) 1, 2 has become the workhorse theory in computational chemistry and solid-state physics. 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. The identified optimal parameters yield a family of functionals fitted for the calculation of band gaps. Relying on these data, we investigate the potential for improvement of a promising subset of functionals by varying their internal parameters. We also compare the computational efficiency of these different approximations. 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. 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. 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. 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.
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