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First Order Perturbation Theory in the Study of Molecular Vibrations: Isotopic Rules and Properties of the Different Approximations

The first order perturbation expressions for various molecular constants such as isotopic shifts (⊿λi, ⊿λi/λi), inverse isotopic shifts (⊿σi, ⊿σi/σi), Coriolis coupling constants (Δξij)and mean amplitudes of vibration (Δ∑ij) obtained using different equations and approximations are given in detail. The mathematical and physical properties of the different approximations are discussed extensively. Incidentally some isotopic rules obtained using the first order perturbation theory are presented.