Collective mode formulation of the response algorithm for solving Kohn-Sham equations

We have developed a "collective mode" version of the response-iteration algorithm for solving the nonlinear Kohn-Sham equations. The algorithm utilizes approximation methods for the density-density response function that are known from microscopic many-body theories of strongly interacting Fermi systems. The major advantage over our previously proposed algorithm (J. Auer and E. Krotscheck, Comput. Phys. Comm. 118 (1999) 139-144) is that the new method needs the computation of occupied states only. Using spherical jellium clusters with up to 2000 electrons as an example, we show that the approximations implicit to our new algorithms do not deteriorate the convergence rate. An even simpler version approximates the density-density response function by that of a charged bose gas with the same density. This algorithm converges somewhat more slowly, but still provides a viable method for solving Kohn-Sham equations for small clusters.