title: Regular dynamics in transition states with flat saddles.
abstract: In the vicinity of a transition state, the dynamics is constrained by approximate local invariants of the motion even if the potential energy surface is anharmonic. The concept of local regularity near a saddle point is investigated in the framework of classical mechanics. The dynamics along the reaction coordinate decouples locally into a reactive mode and several bounded degrees of freedom. The partial energy stored in the unbounded mode is adiabatically invariant. Starting from a purely harmonic situation at the saddle point, anharmonicity coefficients are observed to come into play in a sequential way in the laws of motion. In most cases, each kind of anharmonic coefficient can be related to a particular feature of the potential energy surface or of the reaction path. These regularities account for previous classical trajectory calculations by Berry and co-workers, who observed that for flat saddles (i.e., those characterized by a low value of the modulus of the imaginary frequency), trajectories become temporarily collimated and less chaotic during passage through the transition state.
authors.affiliation: Department of Chemistry, University of Liège, Sart-Tilman (Bâtiment B6), Liège, Belgium. jc.lorquet@ulg.ac.be
authors.forename: J C
authors.initials: JC
authors.lastname: Lorquet