  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 Broydens second method for solving the
self-consistent field equations of Kohn-Sham density functional theory. The
algorithm is robust, requires relatively little finetuning 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.
