Defects and impurities are often decisive in determining the physical properties of materials. They control the conductivity of the material, and point defects also mediate diffusion. Experi-mental defect identification and characterization is typically difficult and indirect, usually requir-ing an ingenious combination of different techniques. First-principles calculations have emerged as a powerful approach that complements experiments and can now serve as a predictive tool. I will describe the general methodology for performing defect calculations based on density func-tional theory (DFT) [1,2]. This approach has proven its value as an immensely powerful tech-nique for assessing the structural properties of defects. However, it falls short when information about the electronic structure is required, at least when traditional functionals such as the local density approximation or generalized gradient approximation are used?an issue often referred to as the “band-gap problem”. I will discuss methods that address this problem and produce results that can be directly compared to experiments on a quantitative level, focusing on the use of screened hybrid functionals. The approach will be illustrated with a number of examples. In op-toelectronics, nitride semiconductors form the basis of the burgeoning technology of solid state lighting. Our calculations elucidate why magnesium is the only dopant that can be used for p-type doping in GaN . The hybrid functional approach also allows the description of charge localization and polaron formation, which will be illustrated with examples for oxides . Final-ly, I will show examples where point defects are actually playing an active role at the core of an application, for instance as qubits in quantum information science .
Work performed in collaboration with A. Janotti, C. Franchini, G. Kresse, J. Lyons, J. Varley, and J. Weber.
 C. G. Van de Walle and J. Neugebauer, J. Appl. Phys. 95, 3851 (2004).
 Advanced Calculations for Defects in Materials: Electronic Structure Methods, edited by A. Alkauskas, P. Deák, J. Neugebauer, A. Pasquarello, and C. G.Van de Walle (Wiley-VCH, 2011).
 J. L. Lyons, A. Janotti, and C. G. Van de Walle, Phys. Rev. Lett. 108, 156403 (2012).
 J. Varley, A. Janotti, C. Franchini, and C. G. Van de Walle, Phys. Rev. B 85, 081109 (2012).
 J. R. Weber, W. F. Koehl, J. B. Varley, A. Janotti, B. B. Buckley, C. G. Van de Walle, and D. D. Awschalom, Proc. Nat. Acad. Sci. 107, 8513 (2010).
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