  The Kohn-Sham equation is a powerful, widely used approach for computation of
ground state electronic energies and densities in chemistry, materials science,
biology, and nanosciences. In this paper, we study the adaptive finite element
approximations for the Kohn-Sham model. Based on the residual type a posteriori
error estimators proposed in this paper, we introduce an adaptive finite
element algorithm with a quite general marking strategy and prove the
convergence of the adaptive finite element approximations. Using D{\" o}rfler's
marking strategy, we then get the convergence rate and quasi-optimal
complexity. We also carry out several typical numerical experiments that not
only support our theory,but also show the robustness and efficiency of the
adaptive finite element computations in electronic structure calculations.
