Advances in electronic structure methods for defects and impurities in solids

Defects and impurities are often decisive in determining the physical properties of most materials. The process of defect identification and characterization is typically difficult and indirect, usually requiring an ingenious combination of different experimental techniques. First‐principles calculations have emerged as a powerful microscopic tool that complements experiments or sometimes even serves as the sole source of atomistic information due to experimental limitations. Still, first‐principles calculations based on density functional theory in the local density or generalized gradient approximations suffer from serious limitations when describing defects in solids. Recent advances in electronic structure methods, rapid increases in computing power, and the development of efficient algorithms indicate a promising future for computational defect physics. We review recent advances in the theory of defects in solids from the perspective of first‐principles calculations. We focus in particular on methods that improve the description of band gaps, leading to results that can be directly compared to experiments on a quantitative level. We discuss the use of LDA+ U in wide‐band‐gap materials, screened hybrid functionals, the quasiparticle GW method, and the use of modified pseudopotentials. Advantages and limitations of these methods are illustrated with examples.