Dependence of the Thomas-Fermi energy on the nuclear coordinates

Let E(R), respectively e(R), denote the total energy, respectively the electronic contribution to the energy, in the Thomas-Fermi theory for a system of two fixed nuclei a distance R apart. We prove that e(R) and -E(R) increase as R does. For the case of N fixed nuclei, we prove the monotonicity of e and E under certain displacements of the coordinates of the nuclei. The analogous result for the electronic contribution of the Born-Oppenheimer energy is proved. (orig.)