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.

Path-integral calculation of the second virial coefficient including intramolecular flexibility effects

“…Since the dissociation energy of a hydrogen molecule corresponds to a temperature ∼5 × 10 4 K and we will be concerned with temperatures less than or equal to 2000 K, only the bound states of H 2 contribute significantly to the value of q rel 1 , and the dissociation can be neglected in the calculation of B(T). 23,24 …”

“…(24) in Ref. 2 after the misprints in the latter expression are corrected (the trace should apply only to the exponential term and "−1" should be replaced by "−V ").…”

Thermodynamic properties of oxygen molecules at high temperatures

“…At high temperatures, several molecular electronic states may be occupied and the second virial coefficient is given by [6,10] …”

Effective-range approximations for resonant scattering of cold atoms

“…Effective-range expansions have been invoked to include the role of collisions at finite energy in few-body phenomena [21][22][23][24][25] and to correct for the zero-point energy in optical lattice physics [26]. The energy-variation of the phase shift is needed to obtain the contribution of two-body collisions to low-energy partition functions and thermodynamic properties of cold gases [27]. The effective range is known to vary around Feshbach resonances [14,25,[28][29][30][31], but there has been no in-depth numerical study of the behavior of η(E), a(E), and r eff as B is tuned across Feshbach resonances of different types.…”