Characterization of vibrational transition modes by use of normal forms

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