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Numerical methods for Kohn–Sham density functional theory

Published online by Cambridge University Press:  14 June 2019

Lin Lin ,
Jianfeng Lu  and
Lexing Ying
Lin Lin
Affiliation:
Department of Mathematics, University of California, Berkeley, and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA E-mail: linlin@math.berkeley.edu
Jianfeng Lu
Affiliation:
Department of Mathematics, Department of Physics, and Department of Chemistry, Duke University, Durham, NC 27708, USA E-mail: jianfeng@math.duke.edu
Lexing Ying
Affiliation:
Department of Mathematics and Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA 94305, USA E-mail: lexing@stanford.edu
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Abstract

Kohn–Sham density functional theory (DFT) is the most widely used electronic 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.

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Type
Research Article
Information
Acta Numerica , Volume 28 , 01 May 2019 , pp. 405 - 539
Copyright
© Cambridge University Press, 2019 

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Footnotes

†

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.

‡

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.

§

Partially supported by the US Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, the ‘Scientific Discovery through Advanced Computing (SciDAC)’ programme and the US National Science Foundation via grant DMS-1818449.

References

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