Acta Numerica (2019), pp. 405{539 c Cambridge University Press, 2019 doi:10.1017/S0962492919000047 Printed in the United Kingdom Numerical methods for Kohn{Sham density functional theory Lin Lin∗ Department of Mathematics, University of California, Berkeley, and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA E-mail:
[email protected] Jianfeng Luy Department of Mathematics, Department of Physics, and Department of Chemistry, Duke University, Durham, NC 27708, USA E-mail:
[email protected] Lexing Yingz Department of Mathematics and Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA 94305, USA E-mail:
[email protected] Kohn{Sham density functional theory (DFT) is the most widely used elec- tronic structure theory. Despite significant progress in the past few decades, the numerical solution of Kohn{Sham DFT problems remains challenging, especially for large-scale systems. In this paper we review the basics as well as state-of-the-art numerical methods, and focus on the unique numerical challenges of DFT. ∗ Partially supported by the US National Science Foundation via grant DMS-1652330, and by the US Department of Energy via grants DE-SC0017867 and DE-AC02- 05CH11231. y Partially supported by the US National Science Foundation via grants DMS-1454939 and ACI-1450280 and by the US Department of Energy via grant DE-SC0019449. z Partially supported by the US Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, the `Scientific Discovery through Ad- vanced Computing (SciDAC)' programme and the US National Science Foundation via grant DMS-1818449. Downloaded from https://www.cambridge.org/core.