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

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 (v(1), v(2)), 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 2v(2) and of the combination band v(1) + v(2) The relations are tested with theoretical calculations for difluoro- and chlorofluoro-substituted ethenes, propadiene, and butatrienes.