Molecule Formation in the Inert Gases

Abstract

The Schrödinger energy eigenvalue equation for the relative motion of two inert gas atoms is solved approximately by fitting a Morse interatomic potential to the generally accepted Lennard-Jones 12–6 interatomic potential. A condition for binding is derived involving the phenomenological parameters present in the 12–6 potential; from the empirical values of these parameters one can then conclude that all the inert gases, except helium, do form stable diatomic molecules. A qualitative argument is presented showing that an hexatomic helium molecule may be stable. The vibration-rotation energy spectrum of the stable inert gas diatomic molecule is discussed. Finally, the partition function for the diatomic molecule is evaluated in an approximate way, whence, using the standard form for the equilibrium constant in terms of partition functions, it follows that at reasonable values of temperature and pressure several percent of the atoms are associated in the form of diatomic molecules.