Chapter 12. Effects of An Intrinsic Metric of Molecular Internal Space on Chemical Reaction Dynamics

  1. M. Toda3,
  2. T. Komatsuzaki4,
  3. T. Konishi5,
  4. R. S. Berry6 and
  5. S. A. Rice7
  1. Tomohiro Yanao1 and
  2. Kazuo Takatsuka2

Published Online: 27 JAN 2005

DOI: 10.1002/0471712531.ch12

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

Yanao, T. and Takatsuka, K. (2005) Effects of An Intrinsic Metric of Molecular Internal Space on Chemical Reaction Dynamics, 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.ch12

Editor Information

  1. 3

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

  2. 4

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

  3. 5

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

  4. 6

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

  5. 7

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

Author Information

  1. 1

    Department of Complex Systems Science, Graduate School of Information Science, Nagoya University, 464-8601, Nagoya, Japan

  2. 2

    Department of Basic Science, Graduate School of Arts and Sciences, University of Tokyo, Komaba, 153-8902, Tokyo, Japan

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

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Keywords:

  • cluster;
  • structural isomerization;
  • principal-axis frame;
  • Eckart frame;
  • hyperspherical coordinates;
  • centrifugal force;
  • metric;
  • gauge field;
  • normal mode;
  • falling cat

Summary

Kinematic effects arising from a metric and a gauge field in molecular internal space are studied in structural isomerization dynamics of three- and four-atom cluster with zero total angular momentum. The principal-axis hyperspherical coordinates (PAHC) are first employed to clarify both the mechanism of the isomerization reaction and associated kinematic effects. A force called “democratic centrifugal force” is obtained as a significant kinematic factor to dominate the isomerization dynamics. This force has an effect of inducing an asymmetry in mass balance of a system, and thereby brings about trapped motions in the vicinity of the transition states of the clusters coupling with the force arising from potential. We quantify the kinematic effects of a gauge field associated with the choice of Eckart frame, which is often disregarded in the conventional picture for molecular vibrations. Numerical study has revealed that the gauge field has an effect of suppressing the rate of isomerization reaction to a considerable amount. We also show mechanism of this suppressing effect in terms of the PAHC.