Three-dimensional periodic solids were among the first systems for which the theory of electronic structure was worked out. The chapter closes with an outlook to the use of supercell calculations for surfaces and interfaces of crystals. The methods developed for periodic systems carry over, with some reservations, to less symmetric situations by working with a supercell. The importance of this issue will be exemplified for force constant calculations and simulations of finite-temperature properties of materials. Aspects of convergence with the number of basis functions and the number of k-points need to be addressed specifically for each physical property. In order to obtain an interpretation of electronic structure calculations in terms of physics, the concepts of bandstructures and atom-projected and/or orbital-projected density of states are useful. Various schemes for broadening the distribution function around the Fermi energy are presented and the approximations involved are discussed. For metallic systems, these tools need to be complemented by methods to determine the Fermi energy and the Fermi surface. Grids for sampling the Brillouin zone and finite k-point sets are discussed. These comprise the unit cell in real space, as well as its counterpart in reciprocal space, the Brillouin zone. In this paper of the series, the concepts needed to model infinite systems are introduced. When density functional theory is used to describe the electronic structure of periodic systems, the application of Bloch's theorem to the Kohn-Sham wavefunctions greatly facilitates the calculations. 2Max-Planck-Institut für Eisenforschung, Düsseldorf, Germany.1Faculty of Physics, University of Duisburg-Essen, Duisburg, Germany.
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