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Volume 16, Issue 1
Convergent and Orthogonality Preserving Schemes for Approximating the Kohn-Sham Orbitals

Xiaoying Dai, Liwei Zhang & Aihui Zhou

DOI: 10.4208/nmtma.OA-2022-0026

Numer. Math. Theor. Meth. Appl., 16 (2023), pp. 1-25.

Published online: 2023-01

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  • Abstract

To obtain convergent numerical approximations without using any orthogonalization operations is of great importance in electronic structure calculations. In this paper, we propose and analyze a class of iteration schemes for the discretized Kohn-Sham Density Functional Theory model, with which the iterative approximations are guaranteed to converge to the Kohn-Sham orbitals without any orthogonalization as long as the initial orbitals are orthogonal and the time step sizes are given properly. In addition, we present a feasible and efficient approach to get suitable time step sizes and report some numerical experiments to validate our theory.

  • Keywords

Gradient flow based model, density functional theory, orthogonality preserving scheme, convergence, temporal discretization.

  • AMS Subject Headings

37M15, 37M21, 65M12, 65N25, 81Q05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-16-1, author = {Dai , XiaoyingZhang , Liwei and Zhou , Aihui}, title = {Convergent and Orthogonality Preserving Schemes for Approximating the Kohn-Sham Orbitals}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2023}, volume = {16}, number = {1}, pages = {1--25}, abstract = {

To obtain convergent numerical approximations without using any orthogonalization operations is of great importance in electronic structure calculations. In this paper, we propose and analyze a class of iteration schemes for the discretized Kohn-Sham Density Functional Theory model, with which the iterative approximations are guaranteed to converge to the Kohn-Sham orbitals without any orthogonalization as long as the initial orbitals are orthogonal and the time step sizes are given properly. In addition, we present a feasible and efficient approach to get suitable time step sizes and report some numerical experiments to validate our theory.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2022-0026 }, url = {http://global-sci.org/intro/article_detail/nmtma/21341.html} }
TY - JOUR T1 - Convergent and Orthogonality Preserving Schemes for Approximating the Kohn-Sham Orbitals AU - Dai , Xiaoying AU - Zhang , Liwei AU - Zhou , Aihui JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 1 EP - 25 PY - 2023 DA - 2023/01 SN - 16 DO - http://doi.org/10.4208/nmtma.OA-2022-0026 UR - https://global-sci.org/intro/article_detail/nmtma/21341.html KW - Gradient flow based model, density functional theory, orthogonality preserving scheme, convergence, temporal discretization. AB -

To obtain convergent numerical approximations without using any orthogonalization operations is of great importance in electronic structure calculations. In this paper, we propose and analyze a class of iteration schemes for the discretized Kohn-Sham Density Functional Theory model, with which the iterative approximations are guaranteed to converge to the Kohn-Sham orbitals without any orthogonalization as long as the initial orbitals are orthogonal and the time step sizes are given properly. In addition, we present a feasible and efficient approach to get suitable time step sizes and report some numerical experiments to validate our theory.

Dai , XiaoyingZhang , Liwei and Zhou , Aihui. (2023). Convergent and Orthogonality Preserving Schemes for Approximating the Kohn-Sham Orbitals. Numerical Mathematics: Theory, Methods and Applications. 16 (1). 1-25. doi:10.4208/nmtma.OA-2022-0026
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