LOCAL MODE AND NORMAL-MODE STRETCHING VIBRATIONS IN XH(4) AND XH(3) SYSTEMS - BEYOND THE X, K RELATIONS

Attention is focused on the relationship between the normal mode and t he local mode descriptions of the stretching vibrations of polyatomic molecules. The harmonically coupled local mode model requires that the equivalent normal mode model parameter set obeys certain fixed interr elationships, the so called 'x,K relations'. In this paper, a boson sh ift operator formalism is used, following J. E. Baggott (1988, Molec. Phys., 65, 739), to transform the unconstrained normal mode models for XH(4) (T-d) and XH(3) (C-3v) molecules to equivalent local mode effec tive Hamiltonians which include anharmonic as well as harmonic couplin gs between the bond modes. Relationships between the unconstrained nor mal mode and anharmonically coupled local mode models are established which allow for more reliable schemes for the relaxation of the x,K re lations than those suggested hitherto for systems containing three or four equivalent stretching vibrations. The magnitudes of the anharmoni c coupling terms in the local mode model are estimated by transformati on of literature ab initio normal mode anharmonicity constants for the C-K strectching vibrations of the methyl halides.