Summary
In this paper we use the Birkhoff-Gustavson perturbation theory to analyze the vibrational modes of two linearly coupled Morse oscillators in the transition region from normal modes to local modes. Our study is based on: truncation of the Hamiltonian written in normal mode coordinates at the 4th order, transformation to normal form and analytical study; construction and use of the approximate integrals of motion of the exact Hamiltonian according to Birkhoff and Gustavson theory. By comparison with a previous analytical study, we demonstrate that perturbation theory, based either on local or normal modes can be used to accurately describe transition modes.
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Abbate, S., Ghisletti, D., Giorgilli, A. et al. Characterization of vibrational transition modes by use of normal forms. Theoret. Chim. Acta 87, 215–232 (1993). https://doi.org/10.1007/BF01112934
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DOI: https://doi.org/10.1007/BF01112934