Periodic orbits and bifurcation diagrams of acetyleneÕvinylidene revisited

Transitions from normal-mode to local-mode states in the two bending oscillations of acetylene observed in spectroscopic studies, as well as the existence of localized vibrational states in vinylidene above the isomerization barrier to acetylene, are examined by constructing continuation/ bifurcation diagrams of periodic orbits on a global potential-energy surface. The principal families of periodic orbits, which provide a faithful representation of the overtone vibrational states, show pitchfork bifurcations for the asymmetric stretch and the two bending families of acetylene, the fingerprints of the normalto local-mode transitions, whereas for vinylidene most of the principal families of periodic orbits remain stable above the isomerization potential barrier, thus supporting the existence of localized vinylidene states. © 2003 American Institute of Physics. @DOI: 10.1063/1.1565991#