Article (Scientific journals)
Crossing the dividing surface of transition state theory. IV. Dynamical regularity and dimensionality reduction as as key features of reactive trajectories
Lorquet, Jean-Claude
2017In Journal of Chemical Physics, 146, p. 134310
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Keywords :
Transition state theory; reaction dynamics; classical trajectories; saddle points; reactive phase space; regular dynamics; dimensionality reduction; effective Hamiltonian; adiabatic decoupling; reaction path Hamiltonian model
Abstract :
[en] The atom-diatom interaction is studied by classical mechanics using Jacobi coordinates (R, r, θ). Reactivity criteria that go beyond the simple requirement of transition state theory (i.e., PR* > 0) are derived in terms of specific initial conditions. Trajectories that exactly fulfill these conditions cross the conventional dividing surface used in transition state theory (i.e., the plane in configuration space passing through a saddle point of the potential energy surface and perpendicular to the reaction coordinate) only once. Furthermore, they are observed to be strikingly similar and to form a tightly-packed bundle of perfectly collimated trajectories in the two-dimensional (R, r) configuration space, although their angular motion is highly specific for each one. Particular attention is paid to symmetrical transition states (i.e., either collinear or T-shaped with C2v symmetry) for which decoupling between angular and radial coordinates is observed, as a result of selection rules that reduce to zero Coriolis couplings between modes that belong to different irreducible representations. Liapunov exponents are equal to zero and Hamilton's characteristic function is planar in that part of configuration space that is visited by reactive trajectories. Detailed consideration is given to the concept of average reactive trajectory, which starts right from the saddle point and which is shown to be free of curvature-induced Coriolis coupling. The reaction path Hamiltonian model, together with a symmetry-based separation of the angular degree of freedom, provide an appropriate framework that leads to the formulation of an effective two-dimensional Hamiltonian. The success of the adiabatic approximation in this model is due to the symmetry of the transition state, not to a separation of time scales. Adjacent trajectories, i.e., those that do not exactly fulfill the reactivity conditions have similar characteristics, but the quality of the approximation is lower. At higher energies, these characteristics persist, but to a lesser degree. Recrossings of the dividing surface then become much more frequent and the phase space volume of initial conditions that generate recrossing-free trajectories decreases. Altogether, one ends up with an additional illustration of the concept of reactive cylinder (or conduit) in phase space that reactive trajectories must follow. Reactivity is associated with dynamical regularity and dimensionality reduction, whatever the shape of the potential energy surface, no matter how strong its anharmonicity, and whatever the curvature of its reaction path. Both simplifying features persist during the entire reactive process, up to complete separation of fragments. The ergodicity assumption commonly assumed in statistical theories is inappropriate for reactive trajectories.
Disciplines :
Chemistry
Author, co-author :
Lorquet, Jean-Claude ;  Université de Liège > Relations académiques et scientifiques (Sciences)
Language :
English
Title :
Crossing the dividing surface of transition state theory. IV. Dynamical regularity and dimensionality reduction as as key features of reactive trajectories
Publication date :
2017
Journal title :
Journal of Chemical Physics
ISSN :
0021-9606
eISSN :
1089-7690
Publisher :
American Institute of Physics Inc., United States
Volume :
146
Pages :
134310
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
since 05 May 2017

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