ANHARMONIC STRETCHING VIBRATIONS EXPRESSED AS LOCAL MODES

Various models used to interpret X-H stretch (or X-D or other weakly c oupled bond modes) overtone spectra in terms of local modes are consid ered. For general systems of coupled X-H stretching modes we demonstra te systematically the origin of local mode anharmonic coupling terms ( in a block-diagonal effective Hamiltonian) via the application of pert urbation theory to vibrational Hamiltonians expressed in internal (loc al) coordinates and which include anharmonic effects as well as quadra tic interbond coupling. Two approaches are presented: extension of the approximate anharmonically coupled anharmonic (Morse) oscillator (AAC AO) model and a perturbation theory treatment of a generalized local m ode model Hamiltonian. These results are tested by application of the derived formulae to model potentials. X-H stretching vibrational energ y levels are calculated for ammonia and silane and in the latter case compared with experimental data. Local mode anharmonicity constants ar e calculated for water and methyl bromide and two of its deuterated is otopomers. Comparisons with the harmonically coupled anharmonic oscill ator (HCAO) model show that serious systematic errors in the latter ma y be corrected whilst retaining a relatively simple effective Hamilton ian. The anomalously low magnitude of the lambda(HD) harmonic interbon d (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 loc al mode anharmonic couplings to systems in which Fermi resonances (wit h non-stretching modes) are also important. Applications to CH3F and C H2D2 are also briefly discussed.