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      The Basics of Electronic Structure Theory for Periodic Systems

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          Abstract

          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. In this paper of the series, the concepts needed to model infinite systems are introduced. These comprise the unit cell in real space, as well as its counterpart in reciprocal space, the Brillouin zone. Grids for sampling the Brillouin zone and finite k-point sets are discussed. For metallic systems, these tools need to be complemented by methods to determine the Fermi energy and the Fermi surface. Various schemes for broadening the distribution function around the Fermi energy are presented and the approximations involved are discussed. 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. Aspects of convergence with the number of basis functions and the number of k-points need to be addressed specifically for each physical property. The importance of this issue will be exemplified for force constant calculations and simulations of finite-temperature properties of materials. The methods developed for periodic systems carry over, with some reservations, to less symmetric situations by working with a supercell. The chapter closes with an outlook to the use of supercell calculations for surfaces and interfaces of crystals.

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          Most cited references36

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          Thermal Properties of the Inhomogeneous Electron Gas

          N. Mermin (1965)
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            Theory and Application for the Scanning Tunneling Microscope

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              Special points in the two-dimensional Brillouin zone

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                Author and article information

                Contributors
                Journal
                Front Chem
                Front Chem
                Front. Chem.
                Frontiers in Chemistry
                Frontiers Media S.A.
                2296-2646
                13 March 2019
                2019
                : 7
                Affiliations
                [1] 1Faculty of Physics, University of Duisburg-Essen , Duisburg, Germany
                [2] 2Max-Planck-Institut für Eisenforschung , Düsseldorf, Germany
                Author notes

                Edited by: Carsten Baldauf, Fritz-Haber-Institut, Germany

                Reviewed by: Sergey V. Levchenko, Skolkovo Institute of Science and Technology, Russia; Juan I. Beltrán, Complutense University of Madrid, Spain; Agnieszka Beata Kuc, Helmholtz-Zentrum Dresden-Rossendorf, Germany

                *Correspondence: Peter Kratzer peter.kratzer@ 123456uni-due.de

                This article was submitted to Theoretical and Computational Chemistry, a section of the journal Frontiers in Chemistry

                Article
                10.3389/fchem.2019.00106
                6424870
                d78fd6a7-0a33-47fc-951c-9eb7d4e1858c
                Copyright © 2019 Kratzer and Neugebauer.

                This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

                Page count
                Figures: 10, Tables: 1, Equations: 30, References: 61, Pages: 18, Words: 13908
                Funding
                Funded by: Deutsche Forschungsgemeinschaft 10.13039/501100001659
                Award ID: SFB1242, B02
                Categories
                Chemistry
                Review

                density functional theory,high-throughput calculations,brillouin zone sampling,supercell approach,convergence tests,solid-state chemistry techniques

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