Original scientific paper

Vibrational Isotope Effect of Planar Molecules by the Low Rank Perturbation Method: Deuterated Ethylenes

Tomislav P. Živković ; Ruđer Bošković Institute, P.O.B. 1016, HR-10001 Zagreb, Croatia

Abstract

Planar molecules A and B, which are identical except for isotopic substitutions at various atomic sites τ, are considered. Out-of-plane frequencies ω_k and normal modes Ψ_k of the perturbed isotopic molecule B are expressed in terms of out-of-plane frequencies ν_i and out-of-plane normal modes Φ_i of unperturbed molecule A. Complete specification of unperturbed normal modes Φ_i is not required. All that is needed are amplitudes ⟨τ|Φ_i⟩ of normal modes Φ_i at sites τ of isotopic substitution. The interlacing rule that interlaces frequencies ω_k with frequencies ν_k is derived. The method is applied to all deuterated ethylenes. Out-of-plane frequencies of deuterated ethylenes are in excellent agreement with the interlacing rule. There is only one serious discrepancy, which might be due to an experimental error. In the ethylene case, out-of-plane amplitudes ⟨τ|Φ_i⟩ are determined by symmetry alone. Hence, out-of-plane frequencies and normal modes of all deuterated ethylenes depend only on the three experimental out-of-plane frequencies of ethylene. Standard error of the calculated out-of-plane frequencies (expressed in cm–1) is only 2.92 cm–1.

Keywords

vibrational isotope effect; low rank perturbation; deuterated ethylenes; out-of-plane vibrations

Hrčak ID:

132311

URI

https://hrcak.srce.hr/132311

Publication date:

1.12.1999.

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