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 - <p style="text-align: justify;">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.</p>