The thermodynamic properties of diatomic molecules at elevated temperatures: Role of continuum and metastable states

Abstract

A complete quantum formulation of diatomic partition functions uses the energy variation of the elastic scattering phase shift to represent the phase space associated with the molecular continuum states. The resonance structure in the phase shift, due to tunneling through rotational barriers, gives a rigorous interpretation of the metastable states which lie behind the barrier, and we can justify the need to include such states in the evaluation of thermodynamic properties. However, we also find that it is inconsistent merely to include the metastable phase space without considering the remaining contributions from the continuum. If either component is ignored in treating the dimer, then, of necessity, their presence will appear as the virial coefficients which cause nonideal behavior for the atomic fragments of the molecule. Both approaches are consistent and yield a proper equation of state for the vapor. We will show quantitative agreement between the exact quantal results and the approximate classical expressions for the partition function at high temperatures. Since the classical theory automatically includes all the effects of the molecular continuum, we suggest that this is both the simplest and most unambiguous procedure for extending thermodynamic tables to elevated temperatures. Explicit calculations are presented for Li2 and Na2.