Gradient Flow Based Discretized Kohn-Sham Density Functional Theory
Abstract
In this paper, we propose and analyze a gradient flow based Kohn-Sham density functional theory. First, we prove that the critical point of the gradient flow based model can be a local minimizer of the Kohn-Sham total energy. Then we apply a midpoint scheme to carry out the temporal discretization. It is shown that the critical point of the Kohn-Sham energy can be well-approximated by the scheme. In particular, based on the midpoint scheme, we design an orthogonality preserving iteration scheme to minimize the Kohn-Sham energy and show that the orthogonality preserving iteration scheme produces approximations that are orthogonal and convergent to a local minimizer under reasonable assumptions. Finally, we report numerical experiments that support our theory.
Keywords
Cite
@article{arxiv.1907.06321,
title = {Gradient Flow Based Discretized Kohn-Sham Density Functional Theory},
author = {Xiaoying Dai and Qiao Wang and Aihui Zhou},
journal= {arXiv preprint arXiv:1907.06321},
year = {2019}
}