Robust mixing for ab initio quantum mechanical calculations

We study the general problem of mixing for ab initio quantum mechanical problems. Guided by general mathematical principles and the underlying physics, we propose a multisecant form of Broyden's second method for solving the self-consistent field equations of Kohn-Sham density-functional theory. The algorithm is robust, requires relatively little fine tuning, and appears to outperform the current state of the art, converging for cases that defeat many other methods. We compare our technique to the conventional methods for problems ranging from simple to nearly pathological.