In this thesis, the Born-Oppenheimer curves for diatomic molecules are investigated in the Hartree-Fock model excluding the exchange term. It is exhibited that the curves have a universal behaviour at small internuclear distances which can be understood from the simpler Thomas-Fermi theory. Notably, we show that the atomic screenings in these two theories are comparable up to a distance from the nuclei which is independent of the atomic number. This is proven iteratively, by relating to suitable Thomas-Fermi models at dierent length scales. We in particular study solutions to the Thomas-Fermi partial dierential equation with two singularities and demonstrate that their asymptotic behaviour is universal. This thesis also contains a numerical investigation of the homonuclear Born-Oppenheimer curve in Thomas-Fermi theory which supports the analytic result.