IMPROVED SELF-CONSISTENT FIELD ITERATION FOR KOHN--SHAM DENSITY FUNCTIONAL THEORY\ast

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.