Improved Self-consistent Field Iteration for Kohn–Sham Density Functional Theory

Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 142-154, March 2024.
Abstract. In this article, an improved self-consistent field iteration scheme is introduced. The proposed method has essential applications in Kohn–Sham density functional theory and relies on an extrapolation scheme and the least squares method. Moreover, the proposed solution is easy to implement and can accelerate the convergence of self-consistent field iteration. The main idea is to fit out a polynomial based on the errors of the derived approximate solutions and then extrapolate the errors into zero to obtain a new approximation. The developed scheme can be applied not only to the Kohn–Sham density functional theory but also to accelerate the self-consistent field iterations of other nonlinear equations. Some numerical results for the Kohn–Sham equation and general nonlinear equations are presented to validate the efficiency of the new method.