T. Komatsuzaki et Rs. Berry, Regularity in chaotic reaction paths III: Ar-6 local invariances at the reaction bottleneck, J CHEM PHYS, 115(9), 2001, pp. 4105-4117
We recently developed a new method to extract a many-body phase-space divid
ing surface, across which the transmission coefficient for the classical re
action path is unity. The example of isomerization of a 6-atom Lennard-Jone
s cluster showed that the action associated with the reaction coordinate is
an approximate invariant of motion through the saddle regions, even at mod
erately high energies, at which most or all the other modes are chaotic [J.
Chem. Phys. 105, 10838 (1999); Phys. Chem. Chem. Phys. 1, 1387 (1999)]. In
the present article, we propose a new algorithm to analyze local invarianc
es about the transition state of N-particle Hamiltonian systems. The approx
imate invariants of motion associated with a reaction coordinate in phase s
pace densely distribute in the sea of chaotic modes in the region of the tr
ansition state. Using projections of distributions in only two principal co
ordinates, one can grasp and visualize the stable and unstable invariant ma
nifolds to and from a hyperbolic point of a many-body nonlinear system, lik
e those of the one-dimensional, integrable pendulum. This, in turn, reveals
a new type of phase space bottleneck in the region of a transition state t
hat emerges as the total energy increases, which may trap a reacting system
in that region. (C) 2001 American Institute of Physics.