Analysis of the transition from Normal Modes to Local Modes in a system of two harmonically coupled Morse oscillators

The system consisting of two Morse oscillators coupled via either a potential or a kinetic quadratic term is considered. The corresponding classical equations of motion have been numerically integrated and the initial conditions have been systematically analyzed in the regime of low total excitation energy of the system. Particular attention was paid to the full characterization of an intermediate type of motion, herein called transition mode, which appears at total energy values in between those typical of normal modes and those where local and normal modes coexist. A previously proposed perturbative approach (Jaffé C, Brumer P (1980) J Chem Phys 73:5646) is reanalyzed and compared with the results of numerical experiments, with the purpose of lending further support to the existence of transition modes.