Knowledge Bank

Partition functions of diatomic molecules at low temperature are normally calculated from spectroscopic data for the low lying bound states. At high temperature, however, questions arise concerning how to treat the unbound molecular states, i.e., the quasibound resonances and the continuum vibrational states. A quantum formulation of the diatomic partition function is developed which 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 tunnelling 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 evaluation of thermodynamic properties. However, it is inconsistent to merely include the metastable phase without considering the remaining contributions from the continuum. We will show the correspondence between the exact quantal results and the approximation classical expressions for high temperature. The classical theory gives a simple and accurate procedure for extending thermodynamic tables to elevated temperature. Explicit calculations are presented for $Li2$ and $Na2$ and compared to the usual spectroscopic analysis inherent in the JANAF tables. Significant discrepancies occur for temperatures above $3000\circ K$.