The WIEN2k program is based on the augmented plane wave plus local orbitals (APW+lo) method to solve the Kohn–Sham equations of density functional theory. The APW+lo method, which considers all electrons (core and valence) self-consistently in a full-potential treatment, is implemented very efficiently in WIEN2k, since various types of parallelization are available and many optimized numerical libraries can be used. Many properties can be calculated, ranging from the basic ones, such as the electronic band structure or the optimized atomic structure, to more specialized ones such as the nuclear magnetic resonance shielding tensor or the electric polarization. After a brief presentation of the APW+lo method, we review the usage, capabilities, and features of WIEN2k (version 19) in detail. The various options, properties, and available approximations for the exchange-correlation functional, as well as the external libraries or programs that can be used with WIEN2k, are mentioned. References to relevant applications and some examples are also given.

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.

Recently, exchange-correlation potentials in density functional theory were developed with the goal of providing improved band gaps in solids. Among them, the semilocal potentials are particularly interesting for large systems since they lead to calculations that are much faster than with hybrid functionals or methods like GW. We present an exhaustive comparison of semilocal exchange-correlation potentials for band gap calculations on a large test set of solids, and particular attention is paid to the potential HLE16 proposed by Verma and Truhlar. It is shown that the most accurate potential is the modified Becke–Johnson potential, which, most noticeably, is much more accurate than all other semilocal potentials for strongly correlated systems. This can be attributed to its additional dependence on the kinetic energy density. It is also shown that the modified Becke–Johnson potential is at least as accurate as the hybrid functionals and more reliable for solids with large band gaps.

Nowadays pseudopotential density-functional theory calculations constitute the standard approach to tackle solid-state electronic problems. These rely on distributed pseudopotential tables that were built from all-electron atomic calculations using few popular semi-local exchange-correlation functionals, while pseudopotentials based on more modern functionals, like meta-GGA and hybrid functionals, or for many-body methods, such as $GW$, are often not available. Because of this, employing pseudopotentials created with inconsistent exchange-correlation functionals has become a common practice. Our aim is to quantify systematically the error in the determination of the electronic band gap when cross-functional pseudopotential calculations are performed. To this end we compare band gaps obtained with norm-conserving pseudopotentials or the projector-augmented wave method with all-electron calculations for a large dataset of 473 solids. We focus in particular on density functionals that were designed specifically for band-gap calculations. On average, the absolute error is about 0.1~eV, yielding absolute relative errors in the 5-10\% range. Considering that typical errors stemming from the choice of the functional are usually larger, we conclude that the effect of choosing an inconsistent pseudopotential is rather harmless for most applications. However, we find specific cases where absolute errors can be larger than 1~eV, or others where relative errors can amount to a large fraction of the band gap.

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 $E_{\mathrm{xc}}$ and/or potential $v_{\mathrm{xc}}$ . 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 bandgap of semiconductors and insulators. The accuracy for other properties like magnetic moment or electron density, that are also determined directly by $v_{\mathrm{xc}}$ , is also discussed.

Several recent studies have shown that SCAN, a functional belonging to the meta-generalized gradient approximation (MGGA) family, leads to significantly overestimated magnetic moments in itinerant ferromagnetic metals. However, this behavior is not inherent to the MGGA level of approximation since TPSS, for instance, does not lead to such severe overestimations. In order to provide a broader view of the accuracy of MGGA functionals for magnetism, we extend the assessment to more functionals but also to antiferromagnetic solids. The results show that to describe magnetism there is overall no real advantage in using a MGGA functional compared to GGAs. For both types of approximation, an improvement in ferromagnetic metals is necessarily accompanied by a deterioration (underestimation) in antiferromagnetic insulators, and vice versa. We also provide some analysis in order to understand in more detail the relation between the mathematical form of the functionals and the results.