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Periodic Orbits and Reactive Scattering: Past, Present and Future

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The Theory of Chemical Reaction Dynamics

Part of the book series: NATO ASI Series ((ASIC,volume 170))

Abstract

The study of periodic orbits embedded in the continuum has provided a new tool for understanding the dynamics of molecular collisions. The application of periodic orbit theory to classical variational transition state theory, quantal threshold and resonance effects is presented. Special emphasis is given to the stability analysis of periodic orbits in collinear and three dimensional systems. Future applications of periodic orbit theory are outlined.

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References

  1. J.T. Muckerman in Theoretical Chemistry: Theory of Scattering.D. Henderson, ed., Academic Press, New York, 1981, 6A, Chap. 1.

    Google Scholar 

  2. H. Eyring, J.Chem.Phys.3, 107 (1935).

    Article  CAS  Google Scholar 

  3. E. Wigner, Trans.Faraday Soc.34, 29 (1938).

    Article  CAS  Google Scholar 

  4. J. Horiuti, Bull.Chem.Soc.Japan 13, 210 (1938).

    Article  Google Scholar 

  5. J.C. Keck, Adv.Chem.Phys.13, 85 (1967).

    Article  Google Scholar 

  6. G.W. Koeppl, J.Amer.Chem.Soc.96, 6539 (1974).

    Article  CAS  Google Scholar 

  7. P. Pechukas in Dynamics of Molecular Collisions,Part B, W.H. Miller, ed., Plenum Press, New York, 1976, Chap. 6.

    Google Scholar 

  8. N. Minorsky, Nonlinear Oscillations,van Nostrand, Princeton, 1962, Chap. 5.

    Google Scholar 

  9. E. Pollak, M.S. Child and P. Pechukas, J.Chem.Phys. 72, 1669 (1980).

    Article  Google Scholar 

  10. J.C. Light and R.B. Walker, J.Chem.Phys.65, 4272 (1976).

    Article  CAS  Google Scholar 

  11. G. Hauke, J. Manz and J. Römelt, J.Chem.Phys.73, 5040 (1980).

    Article  CAS  Google Scholar 

  12. A. Kuppermann in Potential Energy Surfaces and Dynamics Calculations,D.G. Truhlar, ed., Plenum Press, New York, 1981, Chap. 16.

    Google Scholar 

  13. E. Pollak, J.Chem.Phys.75, 4435 (1981).

    Article  CAS  Google Scholar 

  14. E. Pollak and R.E. Wyatt, J.Chem.Phys.78, 4464 (1983).

    Article  CAS  Google Scholar 

  15. E. Pollak and R.E. Wyatt, J.Chem.Phys.81, 1801 (1984).

    Article  CAS  Google Scholar 

  16. M.S. Child and E. Pollak, J.Chem.Phys.73, 4365 (1980).

    Article  CAS  Google Scholar 

  17. E. Pollak and P. Pechukas, J.Chem.Phys.69, 1218 (1978).

    Article  CAS  Google Scholar 

  18. R.N. Porter and M. Karplus, J.Chem.Phys. 40,1105 (1964).

    Article  CAS  Google Scholar 

  19. E. Pollak and M.S. Child, Chem.Phys.60, 23 (1981).

    Article  CAS  Google Scholar 

  20. P. Pechukas and E. Pollak, J.Chen.Phusl 71, 2062 (1979).

    CAS  Google Scholar 

  21. D.I. Sverdlik and G.W. Koeppl, Chem.Phys. Lett.59, 449 (1978).

    Article  CAS  Google Scholar 

  22. J. Costley and P. Pechukas, J.Chem.Phys.77, 4957 (1982).

    Article  CAS  Google Scholar 

  23. E. Pollak in Theory of Chemical Reaction Dynamics,M. Baer, ed., CRC Press, Boca Raton, FL. in press.

    Google Scholar 

  24. E. Pollak, J.Chem.Phys.78, 1228 (1983).

    Article  CAS  Google Scholar 

  25. E. Pollak and M.S. Child, J.Chem.Phys.73, 4373 (1980).

    Article  CAS  Google Scholar 

  26. E. Pollak and P. Pechukas, J.Chem.Phys.79, 2814 (1973).

    Article  Google Scholar 

  27. A. Kuppermann, J.Phys.Chem.83, 171 (1979).

    Article  CAS  Google Scholar 

  28. R.A. Marcus, J.Chem.Phys.45, 4493, 4500 (1966).

    Article  CAS  Google Scholar 

  29. D.G. Truhlar, J.Chem.Phys.53, 2041 (1970).

    Article  CAS  Google Scholar 

  30. B.C. Garrett and D.G. Truhlar, J.Phys.Chem.83, 1079 (1979).

    Article  CAS  Google Scholar 

  31. S.L. Latham, J.F. McNutt, R.E. Wyatt and M.J. Redmon, J.Chem.Phys.69, 3746 (1978).

    Article  CAS  Google Scholar 

  32. E. Pollak, Chem.Phys.61, 305 (1981).

    Article  CAS  Google Scholar 

  33. E. Pollak and J. Römelt, J.Chem.Phys. 80, 3613 (1984).

    Article  CAS  Google Scholar 

  34. P. Siegbahn and B. Liu, J.Chem.Phys.68, 2457 (1978); D.G. Truhlar and C.J. Horowitz, J.Chem.Phys.68, 2466 (1978); 71, 1514(E) (1979).

    Article  CAS  Google Scholar 

  35. N. Abu Salbi and D.J. Kouri, private communication.

    Google Scholar 

  36. H.S. Johnston and D. Rapp, J.Amer.Chem.Soc.83, 1 (1961).

    Article  CAS  Google Scholar 

  37. D.K. Bondi, D.C. Clary, J.N.L. Connor, B.C. Garrett and D.G. Truhlar, J.Chem.Phys.76, 4986 (1982).

    Article  CAS  Google Scholar 

  38. B.C. Garrett and DIC. Truhlar, J.Chem.Phys.81, 309 (1984).

    Article  CAS  Google Scholar 

  39. For a recent review of resonances see ACS Symposium 263 (1984), edited by D.G. Truhlar.

    Google Scholar 

  40. R.D. Levine and S.F. Wu, Chem.Phys.Lett.11, 557 (1971).

    Article  Google Scholar 

  41. J.M. Launay and M. LeDorneuf, J.Phys.B 15, L455 (1982).

    Article  CAS  Google Scholar 

  42. J. Römelt, Chem.Phys.79, 197 (1983).

    Article  Google Scholar 

  43. J.N.L. Connor, Chem.Phys.Lett.4, 419 (1969).

    Article  CAS  Google Scholar 

  44. V. Aquilanti, S. Cavalli, G. Grossi and A. Lagana, J.Mol.Struct.93, 319 (1983

    Article  Google Scholar 

  45. E. Pollak and R.E. Wyatt, J.Chem.Phys.81, 1801 (1984).

    Article  CAS  Google Scholar 

  46. J.N.L. Connor, private communication.

    Google Scholar 

  47. E. Pollak, to be published.

    Google Scholar 

  48. E. Pollak, J.Chem.Phys.76, 5843 (1982).

    Article  CAS  Google Scholar 

  49. E. Pollak, Com.At.Mol.Phys.15, 73 (1984).

    CAS  Google Scholar 

  50. R.E. Wyatt and A.B. Elkowitz, J.Chem.Phys.63, 702 (1975).

    Article  Google Scholar 

  51. D.G. Truhlar, A.D. Isaacson and B.C. Garrett in Theory of Chemical Reaction Dynamics,M. Baer, ed., CRC Press, Boca Raton, FL. in press.

    Google Scholar 

  52. W.H. Miller, N.C. Handy and J.E. Adams, J.Chem.Phys.72, 99 (1980).

    Article  CAS  Google Scholar 

  53. F.T. Smith, Phys.Rev.Lett.45, 1157 (1980).

    Article  CAS  Google Scholar 

  54. M. Baer, D.J. Kouri and V. Khare, J.Chem.Phys.71, 1188 (1979).

    Article  Google Scholar 

  55. J.M. Bowman and K.T. Lee, J.Chem.Phys.72, 5071 (1980).

    Article  CAS  Google Scholar 

  56. D.C. Clary and J.N.L. Connor, J.Phys.Chem.88, 2758 (1984).

    Article  CAS  Google Scholar 

  57. E. Pollak, Chem.Phys.Lett.91, 27 (1982).

    Article  CAS  Google Scholar 

  58. C.C. Marston and R.E. Wyatt~in Resonances,D.G. Truhlar, ed., ACS Symposium Ser. 263, 441 (1984).

    Google Scholar 

  59. J.M. Bowman, Adv.Chem.Phys., in press.

    Google Scholar 

  60. L.D. Landau and E.M. Lifshitz, Quantum Mechanics,Pergamon Press, New York, 1977, pp. 410–420.

    Google Scholar 

  61. E. Pollak, J.Chem.Phys. 82, 106 (1985).

    Article  CAS  Google Scholar 

  62. G.C. Schatz, Chem.Phys.Lett.94, 183 (1983).

    Article  CAS  Google Scholar 

  63. D.J. Kouri, V. Khare and M. Baer, J.Chem.Phys.75, 1179 (1981).

    Article  Google Scholar 

  64. R.B. Walker and E. Pollak, J.Chem.Phys.,in press.

    Google Scholar 

  65. W.H. Miller, J.Chem.Phys.62, 1899 (1975).

    Article  CAS  Google Scholar 

  66. G.C. Schatz, J.Chem.Phys.74, 1133 (1981).

    Article  CAS  Google Scholar 

  67. D.G. Truhlar and A.D. Isaacson, J.Chem.Phys.77, 3516 (1982).

    Article  CAS  Google Scholar 

  68. W.J. Chesnavich, T. Su and M.T. Bowers, J.Chem.Phys.72, 2641(1980).

    Google Scholar 

  69. D.G. Truhlar, J.Chem.Phys.82, 2166 (1985).

    Article  CAS  Google Scholar 

  70. W.J. Chesnavich and M.T. Bowers, J.Chem.Phys.82, 2168 (1985).

    Article  CAS  Google Scholar 

  71. J.A. Dodd, D.M. Golden and J.I. Brauman, J.Chem.Phys.82, 2169 (1985).

    Article  CAS  Google Scholar 

  72. K. Rynefors and N. Markovic, Chem.Phys.92, 327 (1985).

    Article  CAS  Google Scholar 

  73. D.C. Clary, Molec.Phys.53, 3 (1984).

    Article  CAS  Google Scholar 

  74. Y. Zeiri and M. Shapiro, Chem.Phys. 31, 217 (1978).

    Article  CAS  Google Scholar 

  75. I. Noorbatcha and N. Sathyamurthy, Chem.Phys.77, 67 (1983).

    Article  CAS  Google Scholar 

  76. A. Carrington and R.A. Kennedy, J.Chem.Phys. 81,91 (1984).

    Article  CAS  Google Scholar 

  77. T. Carrington, Jr. and W.H. Miller, J.Chem.Phys.81, 3942 (1984).

    Article  CAS  Google Scholar 

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Author information

Authors and Affiliations

  1. Chemical Physics Department, Weizmann Institute of Science, Rehovot, 76100, Israel

    Eli Pollak

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  1. Eli Pollak
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Editor information

Editors and Affiliations

  1. University Chemical Laboratory, University of Cambridge, UK

    D. C. Clary

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© 1986 D. Reidel Publishing Company

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Pollak, E. (1986). Periodic Orbits and Reactive Scattering: Past, Present and Future. In: Clary, D.C. (eds) The Theory of Chemical Reaction Dynamics. NATO ASI Series, vol 170. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4618-7_6

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  • DOI: https://doi.org/10.1007/978-94-009-4618-7_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8552-6

  • Online ISBN: 978-94-009-4618-7

  • eBook Packages: Springer Book Archive

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