Abstract

Electronic structure calculations involve complicated nonlinear models that require iterative algorithms to obtain approximate solutions. However, for complex molecular systems, the classical self-consistent field iteration does not converge or converges slowly. In order to improve the efficiency of self-consistent field iteration, we proposes a new accelerating algorithm. The main idea is to fit out a polynomial based on the error of the derived approximate solution, and then extrapolate the error into zero to obtain a new approximation. In each iteration step, the efficiency can be further improved through transforming the eigenvalue problem into a linear boundary value problem and a small-scale correction equation. The developed scheme can not only be applied to electronic structure calculation but also to accelerate the nonlinear iterations of other nonlinear equations. Some numerical results for electronic structure calculation and general nonlinear equations are presented to validate the efficiency of the new method.