Anharmonic stretching vibrations expressed as local modes

Abstract

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 bromid...