Phase space geometry and reaction dynamics near index two saddles

Details Phase space geometry and reaction dynamics near index two saddles Phase space geometry and reaction dynamics near index two saddles

2009-02-23

arxiv.org/abs/0902.4014v1

Nonlinear Sciences

Chaotic Dynamics

43 pages, 4 figures

Scientific paper

We study the phase space geometry associated with index 2 saddles of a potential energy surface and its influence on reaction dynamics for $n$ degree-of-freedom (DoF) Hamiltonian systems. For index 1 saddles of potential energy surfaces (the case of classical transition state theory), the existence of a normally hyperbolic invariant manifold (NHIM) of saddle stability type has been shown, where the NHIM serves as the "anchor" for the construction of dividing surfaces having the no-recrossing property and minimal flux. For the index 1 saddle case the stable and unstable manifolds of the NHIM are co-dimension one in the energy surface, and act as conduits for reacting trajectories in phase space. The situation for index 2 saddles is quite different. We show that NHIMs with their stable and unstable manifolds still exist, but that these manifolds by themselves lack sufficient dimension to act as barriers in the energy surface. Rather, there are different types of invariant manifolds, containing the NHIM and its stable and unstable manifolds, that act as co-dimension one barriers in the energy surface. These barriers divide the energy surface in the vicinity of the index 2 saddle into regions of qualitatively different trajectories exhibiting a wider variety of dynamical behavior than for the case of index 1 saddles. In particular, we can identify a class of trajectories, which we refer to as "roaming trajectories", which are not associated with reaction along the classical minimum energy path (MEP). We illustrate the significance of our analysis of the index 2 saddle for reaction dynamics with two examples.

Affiliated with

Also associated with

No associations

Rating

Phase space geometry and reaction dynamics near index two saddles does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Phase space geometry and reaction dynamics near index two saddles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Phase space geometry and reaction dynamics near index two saddles will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-171524