Kratzer Peter, Neugebauer Jörg
Faculty of Physics, University of Duisburg-Essen, Duisburg, Germany.
Max-Planck-Institut für Eisenforschung, Düsseldorf, Germany.
Front Chem. 2019 Mar 13;7:106. doi: 10.3389/fchem.2019.00106. eCollection 2019.
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.
当使用密度泛函理论描述周期性体系的电子结构时，将布洛赫定理应用于科恩-沈（Kohn-Sham）波函数极大地简化了计算。在本系列论文中，引入了对无限体系进行建模所需的概念。这些概念包括实空间中的晶胞及其在倒易空间中的对应物——布里渊区。讨论了用于布里渊区采样的网格和有限k点集。对于金属体系，这些工具需要辅以确定费米能和费米面的方法。介绍了在费米能附近展宽分布函数的各种方案，并讨论了其中涉及的近似。为了从物理角度解释电子结构计算结果，能带结构以及原子投影和/或轨道投影态密度的概念很有用。对于每种物理性质，都需要专门讨论基函数数量和k点数目的收敛问题。将通过力常数计算和材料有限温度性质的模拟来举例说明这个问题的重要性。通过使用超胞，为周期性体系开发的方法在有一些保留的情况下可以推广到对称性较低的情形。本章最后展望了超胞计算在晶体表面和界面方面的应用。
