Approximate Isotopic Frequency Rule and Its Application to the Spectra of Complex Molecules

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Abstract
An isotopic frequency rule is derived which is valid to a good approximation for individual modes of fully substituted hydrogen‐containing groups in a complex molecule. It is given by λi/λ = 1 — (ΣjΔTj/ρT), where λ = 4π2ν2, ρ = mi/m = ratio of the isotopic to the normal mass, T = total kinetic energy associated with the vibration, and ΣjΔTj = differential kinetic energy associated with the substituted atoms. When applied to H2O and NH3 this rule reproduces frequency ratios to better than 0.5%. The rule is used to predict the frequency ratios for the various modes of the CH2 group, and with illustrations from the infrared spectra of high polymers it is shown how this rule can be of assistance in making assignments and in providing information on the separability of group vibrations.

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