Corpus ID: 236134271

Bifurcation of dividing surfaces constructed from a pitchfork bifurcation of periodic orbits in a symmetric potential energy surface with a post-transition-state bifurcation

@inproceedings{Katsanikas2021BifurcationOD,
  title={Bifurcation of dividing surfaces constructed from a pitchfork bifurcation of periodic orbits in a symmetric potential energy surface with a post-transition-state bifurcation},
  author={Matthaios Katsanikas and Makrina Agaoglou and Stephen Wiggins},
  year={2021}
}
In this work we analyze the bifurcation of dividing surfaces that occurs as a result of a pitchfork bifurcation of periodic orbits in a two degrees of freedom Hamiltonian System. The potential energy surface of the system that we consider has four critical points:two minima, a high energy saddle and a lower energy saddle separating two wells (minima). In this paper we study the structure, the range, and the minimum and maximum extent of the periodic orbit dividing surfaces of the family of… Expand

References

SHOWING 1-10 OF 29 REFERENCES
Bifurcations of dividing surfaces in chemical reactions.
TLDR
It is found that the occurrence of new periodic orbits emanated from these bifurcations prevents the existence of a unique non-return TS, so that for high energies, the transition state theory cannot be longer applied to calculate the reaction probability. Expand
BIFURCATION DIAGRAMS OF PERIODIC ORBITS FOR UNBOUND MOLECULAR SYSTEMS : FH2
Abstract We present bifurcation diagrams of periodic orbits for the collinear FH2 reactive system. The principal families which originate from the van der Waals minima and the saddle point areExpand
Bifurcations of transition states: Morse bifurcations
A transition state for a Hamiltonian system is a closed, invariant, oriented, codimension-2 submanifold of an energy level that can be spanned by two compact codimension-1 surfaces of unidirectionalExpand
Bifurcations of normally hyperbolic Invariant Manifolds in analytically Tractable Models and Consequences for reaction Dynamics
TLDR
The breakdown of normal hyperbolicity and its consequences for reaction dynamics are studied using simple, two degree-of-freedom Hamiltonian models where calculations for the different geometrical and dynamical quantities can be carried out exactly. Expand
The time evolution of the trajectories after the selectivity in a symmetric potential energy surface with a post-transition-state bifurcation
Selectivity is an important phenomenon in chemical reaction dynamics. This can be quantified by the branching ratio of the trajectories that visit one or the other wells to the total number ofExpand
Nonstatistical dynamics on potentials exhibiting reaction path bifurcations and valley-ridge inflection points.
TLDR
It is found that apparently minor variations in the potential lead to significant changes in the reaction dynamics, and when dissipative effects are incorporated, the product ratio depends in a complicated and non-monotonic fashion on the dissipation parameter. Expand
Chaotic dynamics in multidimensional transition states.
TLDR
It is found that the transition state first looses and then, surprisingly, regains its normal hyperbolicity, and the important phase space structures of transition state theory will, therefore, exist at most energies above the threshold. Expand
Transition states, trapped trajectories, and classical bound states embedded in the continuum
We show that the best choice of transition state, for the atom exchange reaction in a classical collinear collision of an atom with a diatomic, is a classical bound state embedded in the continuum: aExpand
Sampling Phase Space Dividing Surfaces Constructed from Normally Hyperbolic Invariant Manifolds (NHIMs).
TLDR
It is shown for both 2 and 3 DoF systems that a version of the general sampling procedure provides points on the analytically defined DS with the correct microcanonical density on the constant-energy DS. Expand
Bifurcation of no-return transition states in many-body chemical reactions.
TLDR
The method reveals a new aspect of bifurcation for systems of many dof, i.e., the action variables of the bath dof play a role of control parameters as long as they remain approximately conserved. Expand
...
1
2
3
...