We compile a large data set designed for the efficient benchmarking of exchange–correlation functionals for the calculation of electronic band gaps. The data set comprises information on the experimental structure and band gap of 472 nonmagnetic materials and includes a diverse group of covalent-, ionic-, and van der Waals-bonded solids. We used it to benchmark 12 functionals, ranging from standard local and semilocal functionals, passing through meta-generalized-gradient approximations, and several hybrids. We included both general purpose functionals, like the Perdew–Burke–Ernzerhof approximation, and functionals specifically crafted for the determination of band gaps. The comparison of experimental and theoretical band gaps shows that the modified Becke–Johnson is at the moment the best available density functional, closely followed by the Heyd–Scuseria–Ernzerhof screened hybrid from 2006 and the high-local-exchange generalized-gradient approximation.

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.

Kohn-Sham (KS) density functional theory (DFT) is a very efficient method for calculating various properties of solids as, for instance, the total energy, the electron density, or the electronic band structure. The KS-DFT method leads to rather fast calculations, however the accuracy depends crucially on the chosen approximation for the exchange and correlation (xc) functional E xc and/or potential v xc . Here, an overview of xc methods to calculate the electronic band structure is given, with the focus on the so-called semilocal methods that are the fastest in KS-DFT and allow to treat systems containing up to thousands of atoms. Among them, there is the modified Becke-Johnson potential that is widely used to calculate the fundamental band gap of semiconductors and insulators. The accuracy for other properties like the magnetic moment or the electron density, that are also determined directly by v xc , is also discussed.

Density-functional tight-binding methods stand out as a very good compromise between accuracy and computational efficiency. These methods rely on parameter sets that have to be determined and tabulated for every pair of chemical elements. We describe an efficient, and to a large extent automatic, procedure to build such parameter sets. This procedure includes the generation of unbiased training sets and subsequent optimization of the parameters using a pattern search method. As target for the optimization we ask that the formation energy and the forces on the atoms calculated within tight-binding reproduce the ones obtained using density-functional theory. We then use this approach to calculate parameter sets for group IV elements and their binaries. These turn out to yield substantially better results than previously available parameters, especially in what concerns energies and forces.

A theoretical study of the phase diagram of two-dimensional silicon–carbon binaries unveils a large variety of electronic properties.