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.