A rapidly converging algorithm for solving the Kohn-Sham and related   equations in electronic structure theory
  We describe a rapidly converging algorithm for solving the Kohn--Sham equations and equations of similar structure that appear frequently in calculations of the structure of inhomogeneous electronic many--body systems. The algorithm has its roots the Hohenberg-Kohn theorem and solves directly for the electron density; single--particle wave functions are only used as auxiliary quantities. The method has been implemented for symmetric ``slabs'' of jellium as well as for spherical jellium clusters. Starting from very rough guesses for the initial electron density, convergence is reached within a few iterations. The iterations are driven by the static electric susceptibility. 
J. Auer and E. Krotscheck