Acceleration of self-consistent field iteration for Kohn–Sham density functional theory

Density functional theory calculations involve complex nonlinear models that require iterative algorithms to obtain approximate solutions. The number of iterations directly affects the computational efficiency of the iterative algorithms. However, for complex molecular systems, classical self-consistent field iterations either do not converge, or converge slowly. To improve the efficiency of self-consistent field iterations, this paper proposes a novel acceleration algorithm, which utilizes some approximate solutions to fit the convergence trend of errors and then obtains a more accurate approximate solution through extrapolation. This novel algorithm differs from previous acceleration schemes in terms of both its ideology and form. Besides using the combination of the derived approximations, we also predict a more accurate solution based on the decreasing trend of error. The significant acceleration effect of the proposed algorithm is demonstrated through numerical examples.