  In this paper, we propose and analyze some practical Newton methods for
electronic structure calculations. We show the convergence and the local
quadratic convergence rate for the Newton method when the Newton search
directions are well-obtained. In particular, we investigate some basic
implementation issues in determining the search directions and step sizes which
ensures the convergence of the subproblem at each iteration and accelerates the
algorithm, respectively. It is shown by our numerical experiments that our
Newton methods perform better than the existing conjugate gradient method, and
the Newton method with the adaptive step size strategy is even more efficient.
