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It is the goal of this paper to calculate beta from the average bond length between two carbon atoms.

New approximations to the partition function of diatomic molecules are given. The semiclassical Wigner-Kirkwood expansion truncated at the second or fourth order diverges as T. Various methods of scaling the Wigner-Kirkwood expansion are given which avoid this disadvantage and give sufficient accuracy in the low-temperature region. In addition, two modifications of the Pitzer-Gwinn method are discussed. Most molecular potentials can be considered almost harmonic near the minimum. For the scaling of the Wigner-Kirkwood expansion, therefore, a functional form is chosen, which would be exact for every temperature in the case of a purely harmonic potential. In the high-temperature limit the scaled and the conventional Wigner-Kirkwood expansion become identical.

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