Self-consistency iterations in electronic-structure calculations

The convergence of self-consistency iterations in electronic-structure calculations based on density-functional theory is examined by the linearization of the self-consistency equations around the exact solution. In particular, we study the convergence of the usual procedure employing a mixture of the input and output of the last iteration. We show that this procedure converges for a suitably chosen mixture. However, the convergence is necessarily slow in certain cases. These problems are connected either with large charge oscillations or with the onset of magnetism. We discuss physical situations where such problems occur. Moreover, we propose some improved iteration schemes which are illustrated in calculations for $3d$ impurities in Cu.