On the Application of Perturbation Theory for the Calculation of Molecular Constants due to Small Mass Changes and on the Determination of Force Constants from Very Heavy Isotope Substitution

The first order perturbation theory has been used to develop the expressions for studying the mass effect on Coriolis coupling constants in isotopically substituted molecules. The corresponding treatment reported by Wilson, Decius, and Cross for the calculation of isotopic frequency shifts has been applied to a large number of molecules with heavy and very heavy atom isotopic substitution, for which the experimental data have been published in recent years. The use of a simple method (L matrix approximation) for the calculation of isotope shifts in molecules with small mass coupling, from the knowledge of the geometrical parameters only, is suggested. The results obtained using the perturbation theory for the calculation of Δv and Δζ are found to be quite encouraging. An outline of the utility of data on very heavy isotopic substitution for the determination of force constants is given with illustrative examples.