Chapter 4. Geometry of Phase-Space Transition States: Many Dimensions, Angular Momentum

  1. M. Toda2,
  2. T. Komatsuzaki3,
  3. T. Konishi4,
  4. R. S. Berry5 and
  5. S. A. Rice6
  1. Laurent Wiesenfeld

Published Online: 27 JAN 2005

DOI: 10.1002/0471712531.ch4

Geometric Structures of Phase Space in Multidimensional Chaos: Applications to Chemical Reaction Dynamics in Complex Systems, Volume 130

Geometric Structures of Phase Space in Multidimensional Chaos: Applications to Chemical Reaction Dynamics in Complex Systems, Volume 130

How to Cite

Wiesenfeld, L. (2005) Geometry of Phase-Space Transition States: Many Dimensions, Angular Momentum, in Geometric Structures of Phase Space in Multidimensional Chaos: Applications to Chemical Reaction Dynamics in Complex Systems, Volume 130 (eds M. Toda, T. Komatsuzaki, T. Konishi, R. S. Berry and S. A. Rice), John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471712531.ch4

Editor Information

  1. 2

    Physics Department, Nara Women's University, Nara, 630-8506, Japan

  2. 3

    Nonlinear Science Laboratory, Department of Earth and Planetary Sciences, Faculty of Science, Kobe University, Nada, Kobe, 657-8501, Japan

  3. 4

    Department of Physics, Nagoya University, Nagoya, 464-8602, Japan

  4. 5

    Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, USA

  5. 6

    Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 USA

Author Information

  1. Laboratoire d'Astrophysique, Observatoire de Grenoble, Université Joseph-Fourier, BP 53, F-38041 Grenoble Cédex 9, France

Publication History

  1. Published Online: 27 JAN 2005
  2. Published Print: 21 JAN 2005

Book Series:

  1. Advances in Chemical Physics

Book Series Editors:

  1. Stuart A. Rice

Series Editor Information

  1. Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 USA

ISBN Information

Print ISBN: 9780471711582

Online ISBN: 9780471712534

SEARCH

Keywords:

  • classical transition state theory;
  • Hamiltonian dynamics;
  • phase space geometry;
  • non-linear dynamics;
  • gas-phase chemistry;
  • isomerization;
  • molecular astrophysics

Summary

The geometrical structure of a classical transition state is described in details, with a careful introduction of all necessary tools: Hamiltonian dynamics, stability analysis, invariant manifolds, Poincar'e surface of section. Thanks to recent progresses in the understanding of dynamics with many degrees of freedom, possibly including angular momentum, a description of the structure of phase space in the neighborhood of saddle equilibrium points is possible. A transition state that connects different regions of space is built and described, with a progression from 1 degree of freedom to n≥3 degrees of freedom. Applications are found in the isomerization and reaction dynamics of simple molecular systems. The importance of angular momentum is described. Its prominent role is underlined in low energy collisions that prevail is the chemistry of astrophysical gases.