IntroductionFirst-principles electronic-structure methods allow studying a wide range of physical and chemical properties of materials by means of numerical calculations. Ideally, these computational techniques are not based on any empirical parameters, which makes them suitable for predicting novel materials and their properties. Recent developments in theoretical formalisms, numerical algorithms, and computer hardware have led to some spectacular successes and broad application of first-principles techniques in condensed matter physics, materials science, and chemistry. Among the existing first-principles approaches, density functional theory (DFT) [1, 2] has become especially popular as it provides a good compromise between accuracy and computational cost. This method has been instrumental in developing the emerging field of topological insulators (TIs). In particular, already the first works on bismuth chalcogenide TIs have been strongly supported by DFT calculations [3,4]. Several DFT-based predictions of novel topological materials have been successfully confirmed in experiments (e.g., Refs [5,6] followed by Refs [7,8]), and a large number of predicted materials keep motivating experimental research.DFT [1,2] is an approach to overcome the intractability of interacting quantum mechanical many-body problems [9-15]: DFT recasts an interacting many-body equation into a set of self-consistent noninteracting single-particle equations, the so-called Kohn-Sham (KS) equations [2]. In KS equations, all complex manybody effects of the Hamiltonian are lumped into the exchange-correlation term, which is a universal functional of the electron density depending only on three spatial coordinates. In this way, one can avoid working directly with the manybody wavefunction with a very large number of degrees of freedom for realistic systems.DFT is, in principle, an exact theory, and would describe exactly the many-body properties if the exact form of the exchange-correlation functional is known. However, this functional is so far unknown, and thus in practical applications of DFT it is unavoidable to employ its approximate forms among which the Topological Insulators: Fundamentals and Perspectives, First Edition. Edited