Point defects and impurities strongly affect the physical properties of materials and have a decisive impact on their performance in applications. First-principles calculations have emerged as a powerful approach that complements experiments and can serve as a predictive tool in the identification and characterization of defects. The theoretical modeling of point defects in crystalline materials by means of electronic-structure calculations, with an emphasis on approaches based on density functional theory (DFT), is reviewed. A general thermodynamic formalism is laid down to investigate the physical properties of point defects independent of the materials class (semiconductors, insulators, and metals), indicating how the relevant thermodynamic quantities, such as formation energy, entropy, and excess volume, can be obtained from electronic structure calculations. Practical aspects such as the supercell approach and efficient strategies to extrapolate to the isolated-defect or dilute limit are discussed. Recent advances in tractable approximations to the exchange-correlation functional ($\mathrm{DFT}+U$, hybrid functionals) and approaches beyond DFT are highlighted. These advances have largely removed the long-standing uncertainty of defect formation energies in semiconductors and insulators due to the failure of standard DFT to reproduce band gaps. Two case studies illustrate how such calculations provide new insight into the physics and role of point defects in real materials.

In ab initio theory, defects are routinely modeled by supercells with periodic boundary conditions. Unfortunately, the supercell approximation introduces artificial interactions between charged defects. Despite numerous attempts, a general scheme to correct for these is not yet available. We propose a new and computationally efficient method that overcomes limitations of previous schemes and is based on a rigorous analysis of electrostatics in dielectric media. Its reliability and rapid convergence with respect to cell size is demonstrated for charged vacancies in diamond and GaAs.

Discovery of elusive K₄O₆, an endothermic mixed peroxide–superoxide compound: In their Communication (DOI: 10.1002/anie.201809409), M. Jansen et al. report on the synthesis of K₄O₆ that owes its stability to the configurational entropy of polarons, and thus exists only above a distinct temperature threshold. The puzzling speed at which the all‐solid‐state reactions of formation and decomposition proceed, as a function of temperature, are illustratively documented by a real time video.