The vibrational energy states of two coupled modes in formaldehyde

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Abstract
This paper reports a comparative classical, semiclassical and quantum mechanical study of a model of two coupled modes in formaldehyde. The classical mechanics shows coexisting regular trajectories of three types: normal mode, local mode and precessional normal mode, and this behaviour is found to be well described by a generalization of Chirikov nonlinear resonance theory. A simple semiclassical theory based on the resonance hamiltonian predicts local mode and precessional near degeneracies and an approximately uniform spacing of normal mode eigenvalues, the predictions being confirmed by a full quantum mechanical calculation. Crude semiclassical estimates of the decay rates due to tunnelling from different states are in order of magnitude agreement with more accurate literature values. No evidence of significant classical (or quantum) chaotic behaviour was detected at energies below the dissociation limit.