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Resonances in Reactions: A Semiclassical View

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The Theory of Chemical Reaction Dynamics

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

Abstract

Recent work on quantum coupled oscillators and the collinear dynamics of three bodies, as models for unimolecular and bimolecular reactions, is reviewed with special reference to the role of resonances. The approach, semiclassical in spirit, exploits the approximate separability of the radius of hyperspherical formulations and allows to localize the breakdown of adiabaticity at “ridges in the potential”, where transitions between modes occur.

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References

  1. As an introduction to a very extensive literature, see the recent books Resonances-Models and Phenomena, Eds. S. Albeverio, L. S. Ferreira and L. Streit (Lecture Notes in Physics 211, Springer-Verlag, Berlin 1984); Resonances in Electron-Molecule Scattering, van der Waals Complexes and Reactive Chemical Dynamics, Ed. D. G. Truhlar, ACS Symposium Series, 263 (1984).

    Google Scholar 

  2. See the books: M. S. Child, Molecular Collision Theory (Academic, New York, 1974) and Semiclassical Methods in Molecular Scattering and Spectroscopy, Ed. M. S. Child (Reidel, Dordrecht, 1980).

    Google Scholar 

  3. U. Fano, Phys.Rev., A22, 2660 (1980); Rep.Progr.Phys., 46, 97 (1983); in Atomic Physics, Vol. 8, Eds. I. Lindgren, A. Rosen and S. Svendberg (Plenum Press, New York, 1983); in Electronic and Atomic Collisions, Eds. J. Eichler, I. W. Hertel and N. Stolterfoht (North Holland, Amsterdam, 1984) p. 629.

    Google Scholar 

  4. See the proceedings of the 1983 Como Conference, Chaotic Behavior in Quantum Systems, Ed. G. Casati (Plenum Press, New York, 1985), especially papers by W. P. Reinhardt, by E. J. Heller and R. L. Sundberg, and by R. A. Marcus.

    Google Scholar 

  5. V. Aquilanti, S. Cavalli and G. Grossi, in Chaotic Behaviour in Quantum Systems, Ed. G. Casati (Plenum Press, New York, 1985) p. 299.

    Google Scholar 

  6. V. Aquilanti, G. Grossi and F. Pirani, in Electronic and Atomic Collisions, Invited Papers, Eds. J. Eichler, I. W. Hertel and N. Stolterfoht (North Holland, Amsterdam, 1984) p. 441.

    Google Scholar 

  7. See the contribution by J. Romelt in this book, and Section 3.

    Google Scholar 

  8. Ch. Schlier, in Energy Storage and Redistribution in Molecules, Ed. J. Hinze (Plenum Press, New York, 1983).

    Google Scholar 

  9. H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, 1950); V. I. Arnold, Mathematical Methods of Classical Mechanics (Springer, Berlin, 1978); B. V. Chirikov, Phys.Rept., 52, 263 (1979).

    Google Scholar 

  10. E. U. Condon, Phys.Rev., 31, 891 (1928); S. Fluegge, Practical Quantum Mechanics (Springer, Berlin, 1984).

    Google Scholar 

  11. A. H. Nayfeh, Perturbation Methods (Wiley, New York, 1973); W. Barrett, Phil.Trans.Roy.Soc.London, A301, 75,81,99,115,137 (1981).

    Google Scholar 

  12. V. Aquilanti, S. Cavalli and G. Grossi, Chem.Phys.Lett., 110, 43 (1984); also in Fundamental Processes in Atomic Collision Physics, Ed. H. Kleinpoppen (Plenum Press, New York, in press).

    Google Scholar 

  13. N. W. McLachlan, Theory and Application of Mathieu Functions (Clarendon, Oxford, 1947); J. Meixner and F. W. Schaefke, Mathieusche Funktionen und Sphaeroidfunktionen (Springer, Berlin, 1954); F. M. Arscott, Periodic Differential Equations (Pergamon Press, Oxford, 1964).

    Google Scholar 

  14. C. C. Lin and J. D. Swalen, Rev.Mod.Phys., 31, 841 (1959).

    CAS  Google Scholar 

  15. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).

    Google Scholar 

  16. W. H. Miller, J.Chem.Phys., 48, 1651 (1968); M. S. Child, Discussion Faraday Soc, 44, 68 (1967); J.Mol.Spectry., 53, 280 (1974); J. N. L. Connor, T. Uzer, R. A. Marcus and A. D. Smith, J.Chem.Phys., 80, 5095 (1984).

    Article  Google Scholar 

  17. J. C. Slater, Quantum Theory of Molecules and Solids, Vol. 2 (McGraw-Hill, New York, 1965).

    Google Scholar 

  18. E. Thiele and D. J. Wilson, J.Chem.Phys., 35, 1256 (1961); see also Section 2.2.

    Article  CAS  Google Scholar 

  19. W. Paul and H. Steinwedel, Z. Naturforsch, 8a, 448 (1953); W. Paul and M. Raether, Z. Physik, 140, 262 (1955); W. Paul, H. P. Reinhard and U. von Zahn, Z. Physik, 152, 143 (1958).

    Google Scholar 

  20. V. M. Frolov, Differential Equations, 18, 959 (1983).

    Google Scholar 

  21. V. Aquilanti, G. Grossi and A. Lagana’, Chem.Phys.Lett., 93, 174 (1982).

    Article  CAS  Google Scholar 

  22. V. Aquilanti, S. Cavalli and A. Lagana’, Chem.Phys.Lett., 93, 179 (1982).

    Article  CAS  Google Scholar 

  23. V. Aquilanti, S. Cavalli, G. Grossi and A. Lagana1, J.Mol.Struct., 93, 319 (1983).

    Article  Google Scholar 

  24. V. Aquilanti, S. Cavalli, G. Grossi and A. Lagana’, J.Mol.Struct., 107, 95 (1984).

    Google Scholar 

  25. F. T. Smith, Phys.Rev., 179, 111 (1969).

    Article  Google Scholar 

  26. J. Meixner, F. W. Schaefke and G. Wolf, Mathieu Functions and Spheroidal Functions and Their Mathematical Foundations, Lecture Notes in Mathematics, Vol. 837 (Springer, Berlin, 1980).

    Google Scholar 

  27. K. S. Lam and T. F. George, in Semiclassical Methods in Molecular Scattering and Spectroscopy, Ed. M. S. Child (Reidel, Dordrecht, 1980) Ch. 6.

    Google Scholar 

  28. Analytical continuation of eigenvalues is central also for recent developments in the numerical computation of scattering resonances. See 1, and also C. W. McCurdy and J. F. McNutt, Chem.Phys.Lett., 94, 306 (1983); A. D. Isaacson and D. G. Truhlar, Chem.Phys.Lett., 110, 130 (1984).

    Article  Google Scholar 

  29. For the role of reactive scattering resonances in photodissociation, see R. T Pack, J.Chem.Phys., 65, 4765 (1976); D. C. Clary, J.Phys. Chem. 86, 2569 (1982).

    Article  CAS  Google Scholar 

  30. D. W. Noid, M. L. Koszykowski and R. A. Marcus, Ann.Rev.Phys.Chem., 32, 267 (1981).

    Article  CAS  Google Scholar 

  31. G. Hose and H. S. Taylor, J.Chem.Phys., 76, 5356 (1982); Chem.Phys., 84, 375 (1984); G. Hose, H. S. Taylor and Y. Y. Bai, J.Chem.Phys., 80, 4363 (1984).

    Article  CAS  Google Scholar 

  32. M. S. Child, J.Mol.Spectry., 53, 280 (1974), and in Semiclassical Methods in Molecular Scattering and Spectroscopy, Ed. M. S. Child (Reidel, Dordrecht, 1980).

    Google Scholar 

  33. D. W. Noid, M. L. Koszykowski, M. Tabor and R. A. Marcus, J.Chem. Phys., 72, 6169 (1980); see also T. Uzer, D. W. Noid and R. A. Marcus, J.Chem.Phys., 79, 4412 (1983), and references therein.

    Article  CAS  Google Scholar 

  34. I. C. Percival, Advan.Chem.Phys., 36, 1 (1977), and references therein.

    Article  CAS  Google Scholar 

  35. B. A. Waite and W. H. Miller, J. Chem. Phys., 74, 3910 (1981); see also B. A. Waite, S. K. Gray and W. H. Miller, J.Chem.Phys., 78, 259 (1983), and references therein.

    Article  CAS  Google Scholar 

  36. Y. Y. Bai, G. Hose, C. W. McCurdy and H. S. Taylor, Chem.Phys.Lett., 99, 342 (1983).

    Article  CAS  Google Scholar 

  37. See papers by Marcus and co-workers, e.g. references [4] and [30], and references therein.

    Google Scholar 

  38. V. Aquilanti, S. Cavalii and G. Grossi, to be published.

    Google Scholar 

  39. J. N. L. Connor, in Semiclassical Methods in Molecular Scattering and Spectroscopy, Ed. M. S. Child (Reidel, Dordrecht, 1980) pp. 45–107; J. N. L. Connor and A. D. Smith, J.Chem.Phys., 78, 6161 (1983).

    Google Scholar 

  40. W. H. Miller, J.Am.Chem.Soc., 105, 216 (1983).

    Article  CAS  Google Scholar 

  41. See also V. Aquilanti and A. Lagana’, in Nonequilibrium Vibrational Kinetics, Ed. M. Capitelli (Springer, Berlin, in press).

    Google Scholar 

  42. See also J. O. Hirschfelder, Ann.Rev.Phys.Chem., 34, 1 (1983).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  44. See the contribution by W. H. Miller in this book.

    Google Scholar 

  45. F. T. Smith, J.Chem.Phys., 31, 1352 (1959).

    Article  CAS  Google Scholar 

  46. F. T. Smith, Phys.Rev., 120, 1058 (1960).

    Article  Google Scholar 

  47. F. T. Smith, J.Math.Phys., 3, 735 (1962); B. R. Johnson, J.Chem. Phys., 73, 5051 (1980); 79, 1906 (1983); 79, 1916 (1983); R. T Pack, Chem.Phys.Lett., 108, 333 (1984).

    Article  Google Scholar 

  48. See e.g. V. Aquilanti, G. Grossi and A. Lagana’, J.Chem.Phys., 76, 1587 (1982); G. Grossi, J.Chem.Phys., 81, 3355 (1984).

    Article  CAS  Google Scholar 

  49. See the contributions by A. Kuppermann and J. Romelt in this book.

    Google Scholar 

  50. J. M. Launay and M. LeDourneuf, J.Phys., B15, L455 (1982) and in Electronic and Atomic Collisions, Invited Papers, Eds. J. Eichler, I. W. Hertel and N. Stolterfoht (North Holland, Amsterdam, 1984) p. 635, introduced the hyperspherical adiabatic location of resonances and the role of the ridge for F+H2; for hyperspherical semiclassical models, see: V. K. Babamov, V. Lopez and R. A. Marcus, J.Chem.Phys., 78, 5621 (1983); 80, 1812 (1984); Chem.Phys.Lett., 101, 507 (1983); N. Abusalbi, D. J. Kouri, V. Lopez, V. K. Babamov and R. A. Marcus, Chem.Phys.Lett., 103, 458 (1984); H. Nakamura, J.Phys.Chem., 88, 4812 (1984).

    Google Scholar 

  51. S. Cavalli, Tesi di Laurea, Universita’ di Perugia, 1982.

    Google Scholar 

  52. C. H. Hiller, J. Manz, W. H. Miller and J. Römelt, J.Chem.Phys., 78, 3850 (1983).

    Article  CAS  Google Scholar 

  53. V. K. Babamov and R. A. Marcus, J.Chem.Phys., 74, 1790 (1981).

    Article  CAS  Google Scholar 

  54. See e.g. J. Manz, R. Meyer, E. Pollak and J. Römelt, Chem.Phys.Lett. 93, 184 (1982); D. C. Clary and J. N. L. Connor, J.Phys.Chem., 88, 2758 (1984); V. Aquilanti, S. Cavalii, G. Grossi and A. Lagana’, Hyperfine Interactions, 17, 739 (1984).

    Article  CAS  Google Scholar 

  55. B. C. Garrett, D. G. Truhlar, R. S. Grev, G. C. Schatz and R. B. Walker, J.Chem.Phys., 85, 3806 (1981).

    Article  CAS  Google Scholar 

  56. For sample calculations for 3-D at zero angular momentum, see: M. Mishra and J. Linderberg, Mol.Phys., 50, 91 (1983); Chem.Phys.Lett., 111, 439 (1984).

    Article  CAS  Google Scholar 

  57. D. M. Neumark, A. M. Wodtke, G. N. Robinson, C. C. Hayden and Y. T. Lee, J.Chem.Phys., 82, 3045 (1985); D. M. Neumark, A. M. Wodtke, G. N. Robinson, C. C. Hayden, K. Shobatake, R. K. Sparks, T. P. Schafer and Y. T. Lee, J.Chem.Phys., 82, 3067 (1985).

    Article  CAS  Google Scholar 

  58. H. Klar, Phys.Rev., A15, 1542 (1977).

    Google Scholar 

  59. V. Aquilanti, G. Grossi, A. Lagana’, E. Pelikan and H. Klar, Lettere Nuovo Cim., 41, 541 (1984).

    Article  CAS  Google Scholar 

  60. V. Aquilanti and G. Grossi, Letter Nuovo Cim., 42, 157 (1985).

    Article  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Chimica dell‘Universita’, 06100, Perugia, Italy

    Vincenzo Aquilanti

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  1. Vincenzo Aquilanti
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  1. University Chemical Laboratory, University of Cambridge, UK

    D. C. Clary

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© 1986 D. Reidel Publishing Company

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Aquilanti, V. (1986). Resonances in Reactions: A Semiclassical View. 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_15

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  • DOI: https://doi.org/10.1007/978-94-009-4618-7_15

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8552-6

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