We perform a large scale benchmark of machine learning methods for the prediction of the thermodynamic stability of solids. We start by constructing a data set that comprises density functional theory calculations of around 250000 cubic perovskite systems. This includes all possible perovskite and antiperovskite crystals that can be generated with elements from hydrogen to bismuth, excluding rare gases and lanthanides. Incidentally, these calculations already reveal a large number of systems (around 500) that are thermodynamically stable but that are not present in crystal structure databases. Moreover, some of these phases have unconventional compositions and define completely new families of perovskites. This data set is then used to train and test a series of machine learning algorithms to predict the energy distance to the convex hull of stability. In particular, we study the performance of ridge regression, random forests, extremely randomized trees (including adaptive boosting), and neural networks. We find that extremely randomized trees give the smallest mean absolute error of the distance to the convex hull (121 meV/atom) in the test set of 230000 perovskites, after being trained in 20000 samples. Surprisingly, the machine already works if we give it as sole input features the group and row in the periodic table of the three elements composing the perovskite. Moreover, we find that the prediction accuracy is not uniform across the periodic table, being worse for first-row elements and elements forming magnetic compounds. Our results suggest that machine learning can be used to speed up considerably (by at least a factor of 5) high-throughput DFT calculations, by restricting the space of relevant chemical compositions without degradation of the accuracy.

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.

Hybrid functionals are by now the state-of-the-art for the calculation of electronic properties of solids within density functional theory. The key to their performance is how a part of Fock exchange is mixed with a semilocal exchange-correlation functional. The choice of the mixing parameter is particularly critical in nonhomogeneous systems, such as an interface between two solid phases. In this work we propose a (non) local mixing function that is a functional of the electron density through an estimator of the local dielectric function. Using this mixing function to modify the PBE0 and the HSE06 hybrid functionals, we obtain band gaps and band-edge alignments at interfaces with an accuracy that is comparable to the one of the GW approximation. However, and in contrast to GW and other recent self-consistent schemes for the mixing parameter, our approach does not require the evaluation of the dielectric function and leads to a negligible increase of the computation time with respect to standard PBE0 or HSE06 hybrid calculations.

The density-functional theory (DFT) approximations that are the most accurate for the calculation of bandgap of bulk materials are hybrid functionals, such as HSE06, the modified Becke–Johnson (MBJ) potential, and the GLLB-SC potential. More recently, generalized gradient approximations (GGAs), such as HLE16, or meta-GGAs, such as (m)TASK, have also proven to be quite accurate for the bandgap. Here, the focus is on two-dimensional (2D) materials and the goal is to provide a broad overview of the performance of DFT functionals by considering a large test set of 298 2D systems. The present work is an extension of our recent studies [T. Rauch, M. A. L. Marques, and S. Botti, Phys. Rev. B 101, 245163 (2020); Patra et al., J. Phys. Chem. C 125, 11206 (2021)]. Due to the lack of experimental results for the bandgap of 2D systems, G0W0 results were taken as reference. It is shown that the GLLB-SC potential and mTASK functional provide the bandgaps that are the closest to G0W0. Following closely, the local MBJ potential has a pretty good accuracy that is similar to the accuracy of the more expensive hybrid functional HSE06.