Abstract
A general method of applying the modified sum rule for the vibrational frequencies of symmetrical isotopic molecules has been derived. This rule states that the difference in the sum of the frequency parameters between two isotopic molecules A and A*Δσ=Σλ(A)−Σλ(A*)is the same for the appropriate sets I, II, ... of the symmetry species. The sets I, II, ... are selected in accordance with the interactions between the equivalent atoms involved in the isotopic change from A into A*. Various sum-rule relations are obtained for a given pair of isotopic molecules depending upon the interaction terms of the potential function. The proof of the rule is given by using the property of the transformation from the internal coordinates into the symmetry coordinates. The application of the rule is illustrated for ethylene, benzene, and their deuterated homologs.
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