Skip to main content
SpringerLink
Log in

Dynamical Reaction Theory for Vibrationally Highly Excited Molecules

  • Chapter
Progress in Ultrafast Intense Laser Science

Part of the book series: Springer Series in Chemical Physics ((PUILS,volume 91))

  • 778 Accesses

Abstract

We review the present status of the dynamical reaction theory, which is based on the concepts of the Arnold webs and normally hyperbolic invariant manifolds (NHIMs). First, we discuss reaction processes under laser fields where the Arnold web in the potential well is nonuniform. In particular, we present the possibility of controlling reaction processes utilizing cooperative effects of laser fields and the Arnold web. Second, we present existence of fractional behavior for processes in nonuniform Arnold webs. Based on the fractional behavior, we cast doubt on the very existence of the concept of the reaction rate constant. Third, we show that the concept of transition states (TSs) itself has limitations because of chaos on the NHIM. These limitations become manifest for those reaction processes when bath modes are highly excited above the saddle by strong laser fields. We further discuss the possibility of extending the dynamical reaction theory to processes of going over multiple saddles and to those in quantum systems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R.D. Levine, Molecular Reaction Dynamics. (Cambridge, Cambridge, 2005)

    Google Scholar 

  2. E.R. Lovejoy, S.K. Kim, C.B. Moore, Science 256, 1541, 1992

    Article  ADS  Google Scholar 

  3. E.R. Lovejoy, C.B. Moore, J. Chem. Phys. 98, 7846, 1993

    Article  ADS  Google Scholar 

  4. N. Fenichel, Indiana Univ. Math. J. 21, 193, 1971

    Article  MATH  MathSciNet  Google Scholar 

  5. N. Fenichel, Indiana Univ. Math. J. 23, 1109, 1974

    Article  Google Scholar 

  6. N. Fenichel, Indiana Univ. Math. J. 26, 81, 1977

    Article  MATH  MathSciNet  Google Scholar 

  7. A.M. Ozorio De Almeida, N. De Leon, M.A. Mehta, C.C. Marston, Physica D 46, 265, 1990

    Article  MATH  ADS  MathSciNet  Google Scholar 

  8. N. De Leon, M.A. Mehta, R.Q. Topper, J. Chem. Phys. 94,8310, 1991

    Article  ADS  MathSciNet  Google Scholar 

  9. T. Uzer, C. Jaffé, J. Palacián, P. Yanguas, S. Wiggins, Nonlinearity 15, 957, 2002

    Article  MATH  ADS  MathSciNet  Google Scholar 

  10. S. Wiggins, Physica D 44, 471, 1990

    Article  MATH  ADS  MathSciNet  Google Scholar 

  11. M. Zhao, J. Gong, S.A. Rice, Adv. Chem. Phys. 130A, 1 (2005)

    Article  Google Scholar 

  12. M. Toda, Adv. Chem. Phys. 130A, 337 (2005)

    Article  Google Scholar 

  13. C. Jaffe, S. Kawai, J. Palacian, P. Yanguas, T. Uzer, Adv. Chem. Phys. 130A, 171 (2005)

    Article  Google Scholar 

  14. T. Komatsuzaki, R.S. Berry, Adv. Chem. Phys. 130A, 143 (2005)

    Article  Google Scholar 

  15. M. Toda, T. Komatsuzaki, T. Konishi, R.S. Berry, S.A. Rice, eds, in Geometric Structures of Phase Space in Multidimensional Chaos: Applications to Chemical Reaction Dynamics in Complex Systems, Adv. Chem. Phys. 130A, 130B (2005) and references therein

    Google Scholar 

  16. C.B. Li, Y. Matsunaga, M. Toda, T. Komatsuzaki, J. Chem. Phys. 125, 184301, 2005

    Article  ADS  Google Scholar 

  17. A.J. Lichtenberg, M.A. Lieberman, Regular and Chaotic Dynamics, 2nd edn. (Springer, Berlin, 1992)

    MATH  Google Scholar 

  18. B.V. Chirikov, Phys. Rep. 52, 263, 1979

    Article  ADS  MathSciNet  Google Scholar 

  19. C.C. Martens, M.J. Davis, G.S. Ezra, Chem. Phys. Lett. 142, 519, 1987

    Article  ADS  Google Scholar 

  20. S.A. Schofield, P.G. Wolynes, Chem. Phys. Lett. 217, 497, 1994

    Article  ADS  Google Scholar 

  21. M. Herman, J. Lievin, J.V. Auwera, A. Campargue, Global and accurate vibration Hamiltonian from high-resolution molecular spectroscopy, Adv. Chem. Phys. 108 (1999)

    Google Scholar 

  22. K. Yamanouchi, N. Ikeda, S. Tsuchiya, D.M. Joans, J.K. Lundberg, G.W. Adamson, R.W. Field, J. Chem. Phys. 95, 6330, 1991

    Article  ADS  Google Scholar 

  23. M.P. Jacobson, R.W. Field, J. Phys. Chem. A104, 3037, 2000

    Google Scholar 

  24. M.A. Temsamani, M. Herman, J. Chem. Phys. 102, 6371, 1995

    Article  ADS  Google Scholar 

  25. M.P. Jacobson, J.P. O'Brien, R.J. Silbey, R.W. Field, J. Chem. Phys. 109, 121, 1998

    Article  ADS  Google Scholar 

  26. M.E. Kellman, J. Chem. Phys. 93, 6630, 1990

    Article  ADS  Google Scholar 

  27. M. Toda, Adv. Chem. Phys. 123, 153, 2002

    Article  Google Scholar 

  28. R. Metzler, J. Klafter, Phys. Rep. 339, 1, 2000

    Article  MATH  ADS  MathSciNet  Google Scholar 

  29. H. Scher, E.W. Montroll, Phys. Rev. B 12, 2455, 1975

    Article  ADS  Google Scholar 

  30. W. Young, A. Pumir, Y. Pomeau, Phys. Fluids A 1, 462, 1989

    Article  MATH  ADS  MathSciNet  Google Scholar 

  31. Y.Y. Yamaguchi, Int. J. Bifurcat. Chaos 7, 839, 1997

    Article  Google Scholar 

  32. G.M. Zaslavsky, Hamiltonian Chaos and Fractional Dynamics. (Oxford, Oxford, 2004)

    Google Scholar 

  33. M. Takano, T. Takahashi, K. Nagayama, Phys. Rev. Lett. 80, 5691, 1998

    Article  ADS  Google Scholar 

  34. X. Yu, D.M. Leitner, J. Chem. Phys. 119, 12673, 2003

    Article  ADS  Google Scholar 

  35. W. Min, G. Luo, B.J. Cherayil, S.C. Kou, X.S. Xie, Phys. Rev. Lett. 94, 198302, 2005

    Article  ADS  Google Scholar 

  36. R.N. Mantegna, H.E. Stanley, An Introduction to Econophysics. (Cambridge, Cambridge, 2000)

    Google Scholar 

  37. T. Komatsuzaki, R.S. Berry, J. Chem. Phys. 110, 9160, 1999

    Article  ADS  Google Scholar 

  38. A. Shojiguchi, C.B. Li, T. Komatsuzaki, M. Toda, Phys. Rev. E 75, 0352046 2007

    Article  Google Scholar 

  39. A. Shojiguchi, C.B. Li, T. Komatsuzaki, M. Toda, (to be published)

    Google Scholar 

  40. C. Chandre, S. Wiggins, and T. Uzer, Physica D 181, 171, 2003

    Article  MATH  ADS  MathSciNet  Google Scholar 

  41. A. Shojiguchi, C.B. Li, T. Komatsuzaki, M. Toda, Phys. Rev. E 76, 056205, 2007; Phys. Rev. E 77, 019902 (E), 2008

    Article  ADS  Google Scholar 

  42. M. Toda, S. Adachi, K. Ikeda, Prog. Theor. Phys. Suppl. 98, 323, 1989

    Article  ADS  MathSciNet  Google Scholar 

  43. G. Casati, I. Guarneri, G. Maspero, Phys. Rev. Lett. 84, 63, 2000

    Article  ADS  Google Scholar 

  44. G.M. Zaslavsky, M. Edelman, Phys. Rev. E 56, 5310, 1997

    Article  ADS  MathSciNet  Google Scholar 

  45. L. Brillouin. Science and Information Theory. (Academic Press, New York, 1956)

    MATH  Google Scholar 

  46. H.S. Leff, A.F. Rex, ed., Maxwell's Demon 2. (IoP, Bristol, 2003)

    Google Scholar 

  47. C.M. Caves, Phys. Rev. Lett. 64, 2111, 1990

    Article  MATH  ADS  MathSciNet  Google Scholar 

  48. M.M. Millonas, Phys. Rev. Lett. 74, 10 (1995). In this study, he discussed possibility of Maxwell's demon by assuming non-thermal fluctuations. However, he did not present the origin of such fluctuations in molecular levels

    Article  ADS  Google Scholar 

  49. C.B. Li, A. Shojiguchi, M. Toda, T. Komatsuzaki, Phys. Rev. Lett. 97, 028302, 2006; Phys. Rev. Lett. 97, 129901, 2006

    Article  ADS  Google Scholar 

  50. K.R. Meyer, SIAM Rev. 28, 41, 1986

    Article  MATH  MathSciNet  Google Scholar 

  51. S. Sternberg, Duke Math. J. 24, 97, 1957

    Article  MATH  MathSciNet  Google Scholar 

  52. S. Sternberg, Am. J. Math. 80, 623, 1958

    Article  MATH  MathSciNet  Google Scholar 

  53. S. Wiggins. Introduction to Applied Nonlinear Dynamical Systems and Chaos. (Springer, New York, 2000)

    Google Scholar 

  54. S. Sternberg, Am. J. Math. 79, 809, 1957

    Article  MATH  MathSciNet  Google Scholar 

  55. M. Toda, Adv. Chem. Phys. 130A, 337, 2005

    Article  Google Scholar 

  56. S.C. Creagh, Nonlinearity 17, 1261, 2004

    Article  MATH  ADS  MathSciNet  Google Scholar 

  57. S.C. Creagh, Nonlinearity 18, 2089, 2005

    Article  MATH  ADS  MathSciNet  Google Scholar 

  58. R. Schubert, H. Waalkens, S. Wiggins, Phys. Rev. Lett. 96, 218302, 2006

    Article  ADS  Google Scholar 

  59. H. Waalkens, R. Schubert, S. Wiggins, Nonlinearity 21, R1, 2008

    Article  MATH  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physics Department Faculty of Science, Nara Women's University, Nara, 630-8506, Japan

    Mikito Toda

Authors
  1. Mikito Toda
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. MPI für Physik komplexer Systeme, Nöthnitzer Str. 38, Dresden, 01187, Germany

    Andreas Becker

  2. Department of Physics and JILA, University of Colorado, 440 UCB, Boulder, CO, 80309-0440, USA

    Andreas Becker

  3. Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, P.O.Box 800-21, Shanghai, 201800, China

    Ruxin Li

  4. Department for Physics Engineering Physics and Optics & Center for Optics Photonics and Laser, Laval University, Quebec City, Quebec, G1V 0A6, Canada

    See Leang Chin

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Toda, M. (2009). Dynamical Reaction Theory for Vibrationally Highly Excited Molecules. In: Yamanouchi, K., Becker, A., Li, R., Chin, S.L. (eds) Progress in Ultrafast Intense Laser Science. Springer Series in Chemical Physics, vol 91. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69143-3_5

Download citation

Publish with us

Policies and ethics

Search

Navigation