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

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.