Local mode and normal mode models for molecules with two non-equivalent C–H bonds

Abstract

For molecules with C–H bonds, a local mode description of the bonds is often adopted to interpret the C–H stretching overtone spectra, although a representation in terms of normal modes is also possible. The equivalence between the two alternative representations demands simple numerical equations between the normal mode anharmonicity constants x _rs and the quartic anharmonic coupling constants K _rstu , the so-called ‘x–K relations’. The relations appropriate for low symmetry molecules with two non-equivalent C–H bonds (ν₁, ν₂), such as XHC = CHY, are derived in this paper. The consequences of these relations are illustrated with a detailed analysis of the C–H stretching overtone region, where the naive application of the relations obtained for more symmetric molecules could lead to a different interpretation of the overtones 2v ₁ and 2ν₂ and of the combination band ν₁ + ν₂. The relations are tested with theoretical calculations for difluoro- and chlorofluoro-substituted ethenes, propadiene, and butatrienes.

Keywords:

• Local mode
• Normal mode
• Morse oscillators
• Quartic anharmonic interactions
• Darling–Dennison interactions