Bounds on Diatomic Molecules in a Relativistic Model

We consider diatomic systems in which the kinetic energy of the electrons is treated in a simple relativistic model. The Born-Oppenheimer approximation is assumed. We investigate questions of stability, deducing bounds on the number $N$ of electrons, the binding energy $\mathrm{\Delta }{E}_b$ and the equilibrium bond distance $R_0$. We use a known localization argument adopted to the present relativistic setting, with particular consideration of the critical point of stability, as well as the recently proved relativistic Scott correction.