Can we outperform the DIIS approach for electronic structure calculations?

This article regroups various results on self-consistent field algorithms for computing electronic structures of molecular systems. The first part deals with the convergence properties of the `conventional' Roothaan algorithm and of the level-shifting algorithm. In the second part, a new class of algorithms is introduced, for which convergence is guaranteed by mathematical arguments. Computational performance on various test problems is reported; advantages of this knew approach are demonstrated.