Anharmonic stretching vibrations expressed as local modes

Various models used to interpret X-H stretch (or X-D or other weakly coupled bond modes) overtone spectra in terms of local modes are considered. For general systems of coupled X-H stretching modes we demonstrate systematically the origin of local mode anharmonic coupling terms (in a block-diagonal effective Hamiltonian) via the application of perturbation theory to vibrational Hamiltonians expressed in internal (local) coordinates and which include anharmonic effects as well as quadratic interbond coupling. Two approaches are presented: extension of the approximate anharmonically coupled anharmonic (Morse) oscillator (AACAO) model and a perturbation theory treatment of a generalized local mode model Hamiltonian. These results are tested by application of the derived formulae to model potentials. X-H stretching vibrational energy levels are calculated for ammonia and silane and in the latter case compared with experimental data. Local mode anharmonicity constants are calculated for water and methyl bromide and two of its deuterated isotopomers. Comparisons with the harmonically coupled anharmonic oscillator (HCAO) model show that serious systematic errors in the latter may be corrected whilst retaining a relatively simple effective Hamiltonian. The anomalously low magnitude of the HD harmonic interbond (near-resonant) coupling constant determined in an earlier study of CHD₂Cl is rationalized by analysis of previously neglected anharmonic effects. This last application demonstrates the relevance of these local mode anharmonic couplings to systems in which Fermi resonances (with non-stretching modes) are also important. Applications to CH₃F and CH₂D₂ are also briefly discussed.