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Title: Numerical investigation of chaotic dynamics in multidimensional transition states
Author: Allahem, Ali Ibraheem
ISNI:       0000 0004 5348 2103
Awarding Body: Loughborough University
Current Institution: Loughborough University
Date of Award: 2014
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Many chemical reactions can be described as the crossing of an energetic barrier. This process is mediated by an invariant object in phase space. One can construct a normally hyperbolic invariant manifold (NHIM) of the reactive dynamical system which is an invariant sphere that can be considered as the geometric representation of the transition state itself. The NHIM has invariant cylinders (reaction channels) attached to it. This invariant geometric structure survives as long as the invariant sphere is normally hyperbolic. We applied this theory to the hydrogen exchange reaction in three degrees of freedom in order to figure out the reason of the transition state theory (TST) failure. Energies high above the reaction threshold, the dynamics within the transition state becomes partially chaotic. We have found that the invariant sphere first ceases to be normally hyperbolic at fairly low energies. Surprisingly normal hyperbolicity is then restored and the invariant sphere remains normally hyperbolic even at very high energies. This observation shows two different energy values for the breakdown of the TST and the breakdown of the NHIM. This leads to seek another phase space object that is related to the breakdown of the TST. Using theory of the dividing surface including reactive islands (RIs), we can investigate such an object. We found out that the first nonreactive trajectory has been found at the same energy values for both collinear and full systems, and coincides with the first bifurcation of periodic orbit dividing surface (PODS) at the collinear configuration. The bifurcation creates the unstable periodic orbit (UPO). Indeed, the new PODS (UPO) is the reason for the TST failure. The manifolds (stable and centre-stable) of the UPO clarify these expectations by intersecting the dividing surface at the boundary of the reactive island (on the collinear and the three (full) systems, respectively).
Supervisor: Not available Sponsor: Royal Embassy of Saudi Arabia Cultural Bureau in London
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Transition state theory ; Hamiltonian ; Dividing surface ; NHIM ; Centre manifold ; Lyapunov exponents ; Reactive island ; Stable and unstable cylindrical manifolds.