Basis of analysis beyond Dunhams theory, by van Vleck and others

BASIS OF ANALYSIS BEYOND DUNHAM S THEORY, BY VAN VLECK AND OTHERS 

For molecules containing light atoms, we accordingly neglect this effect of finite nuclear volume or field shift, but other effects prevent exact application of isotopic ratios that one might expect on the basis of a proportionality with in formula 13 instead of total F. For this reason we supplement term coefficients in formula 8 for a particular isotopic species i with auxiliary coefficients [54], 

Theoretical calculation of any atomic or molecular property through application of computational methods based on quantum mechanics or other sophisticated approach is typically practicable through approximate methods. The internuclear potential energy V(i ) independent of mass is conventionally derived from the results of computations of molecular electronic structure according to a scheme of wave mechanics, 

For a particular isotopic variant of a diatomic molecule with like charges on atomic centres, i.e. Za=Zb, and for which we assume no net molecular electric dipolar moment at any internuclear distance, i.e. p(i ) = 0 for all R, we hence express the coefficient of (v + I ) [ /( /+1)] in formula 27 as a sum. 

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