On the Vibrational Interlacing Rule in Deuterated Thiophene: I. Out-of-plane Vibrations

According to the interlacing rule, if A and Bτ are two molecules which differ by a single isotopic substitution at atomic site τ, vibrational frequencies of a molecule A are interlaced with the vibrational frequencies of molecule Bτ. This rule is valid within the harmonic approximation, and in the case of planar molecules one has two interlacing rules, one for in-plane and another for out-of-plane frequencies. The validity of this rule is verified for theoretical and experimental out-of-plane frequencies of thiophene and deuterated thiophene molecules. This rule can help to analyze vibrational spectra, especially in assignments of experimental frequencies to various vibrational types