Acceleration of self-consistent electronic-structure calculations: Storage-saving and multiple-secant implementation of the Broyden method

On the basis of the Broyden method to solve simultaneous nonlinear equations, we present efficient computational schemes for acceleration of self-consistent electronic-structure calculations. The schemes, designed to achieve smoother and faster convergence on limited-storage conditions, involve a storage-saving representation of an approximate quasi-Newton matrix mathematically: valid even when iteration history data are partially discarded. Moreover, to avoid numerical instability, a vector space where the? multiple-secant condition is satisfied is determined dynamically. The efficiency and stability of the schemes is confirmed by the self-consistent electronic-structure calculations of a Si (011) surface model.