Local mode and normal mode stretching vibrations in xh₄ and xh₃systems: Beyond the x, k relations

Attention is focused on the relationship between the normal mode and the 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 interrelationships, the so called ‘x, K relations’. In this paper, a boson shift operator formalism is used, following J. E. Baggott (1988, Molec. Phys., 65, 739), to transform the unconstrained normal mode models for XH₄ (T_d) and XH₃ (C_3v) molecules to equivalent local mode effective Hamiltonians which include anharmonic as well as harmonic couplings between the bond modes. Relationships between the unconstrained normal mode and anharmonically coupled local mode models are established which allow for more reliable schemes for the relaxation of the x, K relations than those suggested hitherto for systems containing three or four equivalent stretching vibrations. The magnitudes of the anharmonic coupling terms in the local mode model are estimated by transformation of literature ab initio normal mode anharmonicity constants for the C-H strectching vibrations of the methyl halides.