Born-Oppenheimer potential energy surfaces for Kohn-Sham models in the local density approximation

We show that the Born-Oppenheimer potential energy surface in Kohn-Sham theory behaves like the corresponding one in Thomas-Fermi theory up to $o(R^{-7})$ for small nuclear separation $R$. We also prove that if a minimizing configuration exists, then the minimal distance of nuclei is larger than some constant which is independent of the nuclear charges.