Isotopic mass dependence of the dissociation equilibrium of diatomic molecules

Abstract

From calculations on the harmonic oscillator–rigid rotator approximation Byers-Brown conjectured that d In K/d In m(K= equilibrium constant; m= mass of an atom) for the dissociation of diatomic molecules changes sign at a certain temperature. Using three different methods: Mayer–Mayer series expansion of the parton function from spectroscopic energy levels, thermodynamic perturbation theory in operator form, and lower bounds with variation, it can be shown that the conjecture is qualitatively correct for the rotating Morse oscillator. Anharmonicity is taken into account in the last method correctly, but the vibration–rotation interaction presents difficulties.