Skip to main content

Reaction Path Models for Polyatomic Reaction Dynamics-- from Transition State Theory to Path Integrals

  • Chapter
Book cover The Theory of Chemical Reaction Dynamics

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

Abstract

The reaction path Hamiltonian model for the dynamics of general polyatomic systems is reviewed. Various dynamical treatments based on it are discussed, from the simplest statistical approximations (e.g., transition state theory, RRKM, etc.) to rigorous path integral computational approaches that can be applied to chemical reactions in polyatomic systems. Examples are presented which illustrate this “menu” of dynamical possibilities.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
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. For early work on reaction paths and reaction coordinates, see (a) S. Glasstone, K. J. Laidler, and H. Eyring, The Theory of Rate Processes (McGraw-Hill, New York, 1941); (b) R. A. Marcus, J. Chem. Phys. 45, 4493, 4500 (1966); 49, (1968); (c) G. L. Hofacker, Z. Naturforsch. Teil A 18, 607 (1963); J. Chem. Phys. 43, 208 (1965); (d) S. F. Fischer, G. L. Hofacker, and R. Seiler, J. Chem. Phys. 51, 3941 (1969).

    Google Scholar 

  2. Some of the recent papers by other workers on reaction path models are (a) S. F. Fischer and M. A. Ratner, J. Chem. Phys 57, 2769 (1972); (b) P. Russegger and J. Brickman, ibid. 62, 1086 (1975); 60, 1 (1977); (c) M. V. Basilevsky, Chem. Phys. 24, 81 (1977); 67, 337 (1982); M. V. Bailevsky and A. G. Shamov, ibid. 60, 349 (1981); (d) K. Fukui, S. Kato, and H. Fujimoto, J. Am. Chem. Soc. 97, 1 (1975); K. Yamashita, T. Yamabe, and K. Fukui, Chem. Phys. Lett. 84, 123 (1981); A. K. Fukui, Acc. Chem. Res. 14, 363 (1981); (e) K. Ishida, K. Morokuma, and A. Komornicki, J. Chem. Phys. 66, 2153 (1977); (f) A. Nauts and X. Chapuisat, Chem. Phys. Lett. 85, 212 (1982); X. Chapuisat, A. Nauts, and G. Durrand, Chem. Phys. 56, 91 (1981); (g) J. Pancir, Collect. Czech. Commun. 40, 1112 (1975); 42, 16 (1977); (h) G. A. Natanson, Mol. Phys. 46, 481 (1982).

    Article  Google Scholar 

  3. P. Pulay, in Applications of Electronic Structure, edited by H. F. Schaefer (Plenum, New York, 1977), p. 153; (b) J. W. Mclver, Jr. and A. Komornicki, J. Am. Chem. Soc. 94, 2625 (1972); (c) B. R. Brooks, W. E. Laidig, P. Saxe, J. D. Goddard, Y. Yamaguchi, and H. F. Schaefer, J. Chem. Phys. 72, 4652 (1980); (d) J. A. Pople, R. Krishnan, H. B. Schlegel, J. S. Binkley, Int. J. Quant. Chem. Symp. 13, 225 (1970); (e) Y. Osamura, Y. Yamaguchi, P. Saxe, M. A. Vincent, J. F. Gaw, and H. F. Schaefer, Chem. Phys. 72, 131, (1982); Y. Yamaguchi, Y. Osamura, G. Fitzgerald, H. F. Schaefer, J. Chem. Phys. 78, 1607 (1983); (f) P. Pulay, ibid. 78, 5043 (1983).

    Google Scholar 

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

    Article  CAS  Google Scholar 

  5. W. H. Miller, in Potential Energy Surfaces and Dynamics Calculations, edited by D. G. Truhlar (Plenum, New York, 1981), p. 265.

    Google Scholar 

  6. C. J. Cerjan, S.-h. Shi, and W. H. Miller, J. Phys. Chem. 86, 2244 (1982).

    Article  CAS  Google Scholar 

  7. S. K. Gray, W. H. Miller, Y. Yamaguchi, and H. F. Schaefer, J. Chem. Phys. 73, 2733 (1980).

    Article  CAS  Google Scholar 

  8. S. K. Gray, W. H. Miller, Y. Yamaguchi, and H. F. Schaefer, J. Am. Chem. Soc. 103, 1900 (1981).

    Article  CAS  Google Scholar 

  9. Y. Osamura, H. F. Schaefer, S. K. Gray, and W. H. Miller, J. Am. Chem. Soc. 103, 1904 (1981).

    Article  CAS  Google Scholar 

  10. B. A. Waite, S. K. Gray, and W. H. Miller, J. Chem. Phys. 78, 259 (1983).

    Article  CAS  Google Scholar 

  11. W. H. Miller, J. Phys. Chem. 87, 3811 (1983).

    Article  CAS  Google Scholar 

  12. See also, (a) R. T. Skodje, D. G. Truhlar, and B. C. Garrett, J. Phys. Chem. 85, 3019 (1981); (b) J. Chem. Phys. 77, 5955 (1982); (c) A. D. Isaacson and D. G. Truhlar, ibid. 76, 1380 (1982); (d) D. G. Truhlar, N. J. Kilpatrick, and B. C. Garrett, ibid. 78, 2438 (1983); (e) R. T. Skodje and D. G. Truhlar, ibid. 79, 4882 (1983); (f) R. T. Skodje, D. W. Schwenke, D. G. Truhlar, and B. C. Garrett, J. Phys. Chem. 88, 628; (g) B. C. Garrett and D. G. Truhlar, J. Chem. Phys. 81, 309 (1984).

    Article  Google Scholar 

  13. For an excellent review and recent developments see (a) P. Pechukas, in ‘Dynamics of Molecular Collisions’ Part B, Vol. 2 of Modern Theoretical Chemistry, edited by W. H. Miller (Plenum, New York, 1970), p. 285 etseq.; Annu. Rev. Phys. Chem. 32, 159 (1981); (b) D. G. Truhlar, W. L. Hase, and J. T. Hynes, J. Phys. Chem. 87, 2664 (1983).

    Google Scholar 

  14. W. H. Miller, J. Chem. Phys. 65, 2216 (1976).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  16. E. Pollak and P. Pechukas, J. Chem. Phys. 70, 325 (1979).

    Article  CAS  Google Scholar 

  17. B. C. Garrett and D. G. Truhlar, J. Phys. Chem. 83, 1052 (1979); 83, 3058(E) (1979).

    Article  CAS  Google Scholar 

  18. W. H. Miller and S.-h. Shi, J. Chem. Phys. 75, 2258 (1981).

    Article  CAS  Google Scholar 

  19. (a) W. H. Miller and F. T. Smith, Phys. Rev. A 17 939 (1978); see also related works by: (b) R. J. Cross, Jr., J. Chem. Phys. 49, 1753 (1968); 58, 5178 (1973); (c) I. L. Beigman, L. A. Vainshtein, I. I. Sobel'man, Zh. Eksp. Teor. Fiz. 57, 1465 (1969) (Sov. Phys. JETP (Engl. Transl.) 30, 920 (1973); (d) R. D. Levine and B. R. Johnson, Chem. Phys. Lett. 7, 404 (1970); (e) I. C. Percival and D. Richards, J. Phys. B 3, 1035 (1970); (f) A. P. Clark, A. S. Dickinson, and D. Richards, Adv. Chem. Phys. 36, 63 (1977).

    Article  CAS  Google Scholar 

  20. G. L. Hofacker and R. D. Levine, Chem. Phys. Lett. 9, 617 (1971).

    Article  CAS  Google Scholar 

  21. B. A. Waite and W. H. Miller, J. Chem. Phys. 76, 2412 (1982).

    Article  CAS  Google Scholar 

  22. W. H. Miller, S. D. Schwartz, and J. W. Tromp, J. Chem. Phys. 79, 4889 (1983).

    Article  CAS  Google Scholar 

  23. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals, (McGraw-Hill, New York, 1965) p. 273 et seq.

    Google Scholar 

  24. D. Thirumalai and B. J. Berne, J. Chem. Phys. 79, 5029 (1983); (b) D. Thirumalai, E. J. Bruskin, and B. J. Berne, J. Chem. Phys. 79, 5063 (1983); (c) D. Thirumalai and B. J. Berne, J. Chem. Phys. 81, 2512 (1984).

    Article  CAS  Google Scholar 

  25. K. Yamashita and W. H. Miller, J. Chem. Phys. 82, 0000 (1985).

    Article  CAS  Google Scholar 

  26. G. C. Schatz and A. Kuppermann, J. Chem. Phys. 65, 4668 (1976).

    Article  CAS  Google Scholar 

  27. K. Morokuma, S. Kato, and K. Hirao, J. Chem. Phys. 72, 6800 (1980).

    Article  CAS  Google Scholar 

  28. S. Kato and T. Yamabe, Int. J. Quant. Chem. 17, 177 (1983).

    Google Scholar 

  29. A. Tachibana, I. Okazaki, M. Koizumi, K. Hori, and T. Yamabe, J. Am. Chem. Soc. 107, 1190 (1985).

    Article  CAS  Google Scholar 

  30. T. Yamabe, K. Yamashita, M. Kaminiyama, M. Koizumi, A. Tachibana, and K. Fukui, J. Phys. Chem. 88, 1459 (1984).

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1986 D. Reidel Publishing Company

About this chapter

Cite this chapter

Miller, W.H. (1986). Reaction Path Models for Polyatomic Reaction Dynamics-- from Transition State Theory to Path Integrals. 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_2

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-4618-7_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8552-6

  • Online ISBN: 978-94-009-4618-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics