On the onset of strong mode coupling in small polyatomic molecules

Abstract

The number of vibrational states corresponding to separable, quasiperiodic motion of low dimensionality is estimated by a generalization of the analysis of the quantum‐mechanical Hénon–Heiles problem by Hose and Taylor. The number of nonseparable states with strongly coupled modes appears to overwhelm the number of separable ‘‘quasiperiodic’’ states whenever the molecule in question contains five or more vibrational quanta, and may dominate for states with four or even three vibrational quanta. Some comments are made to try to clarify the concepts of separability and quasiperiodicity.