Bigeleisen-Mayer approximation

Comparison of the accuracies of the Chebyshev and Bernoulli approximations in Table XI shows the Chebyshev (L = 0) to be better than the Bernoulli by a factor of 5 to 10 at n = 1 the improvement increases to about 300 at n = 4. This was generally observed for all other isotopic substitutions tested the rate of convergence of the Chebyshev expansion is better than the Bernoulli expansion at any order, at any temperature. The Chebyshev expansion exists at any temperature, while the Bernoulli series diverges for most of the molecules at room temperature. Table XI also shows that the Bigeleisen-Mayer approximation. 

A useful approximation for the isotopes of heavy elements (Bigeleisen and Mayer, 1947) is... 

In the G(w)-approximation, introduced by Bigeleisen and Mayer (8) and later extended to higher orders by Bigeleisen (4), the reduced partition function ratio (Equation 1) is expanded in terms of the isotope frequency shifts, Au, = — Ui. The first three terms are... 

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