The exact classical vibrational-rotational partition function for the Woolley potential: calculations of the equilibrium constants for the formation of Ar-Ar and Mg-Mg

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Abstract
Exact analytical expressions are derived for the classical vibrational-rotational partition function and for the number of vibrational-rotational energy levels of the one-constant Woolley potential, which can be viewed as a deformed Lennard-Jones (12, 6) potential. These expressions are then used first to fit the Woolley potential to accurate analytic potentials of Ar2 and Mg2 by matching the total number of vibrational-rotational energy levels and, secondly, to calculate the corresponding classical equilibrium constants for the formation of these two molecules. The results are in excellent agreement with the exact classical and quantum-mechanical equilibrium constants calculated from the accurate analytic potentials by Dardi and Dahler (1990) with a maximum error of 4% for Ar2 and 2% for Mg2. In particular, they are in much better agreement than those calculated from various Lennard-Jones (12, 6) potentials.