Convergent and orthogonality preserving schemes for approximating the Kohn-Sham orbitals

Xiaoying Dai; Liwei Zhang; Aihui Zhou

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arXiv · 2111.02779

Convergent and orthogonality preserving schemes for approximating the Kohn-Sham orbitals

Xiaoying Dai·Liwei Zhang·Aihui Zhou

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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 exponentially 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.

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BibTeX RIS

Xiaoying Dai, Liwei Zhang, Aihui Zhou. 2021-11-03. Convergent and orthogonality preserving schemes for approximating the Kohn-Sham orbitals. https://arxiv.org/abs/2111.02779

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