Advertisement

Statistical Approximations in Collision Theory

  • Philip Pechukas
Part of the Modern Theoretical Chemistry book series (MTC, volume 2)

Abstract

This chapter is an introduction to statistical approximation in the theory of reactive collisions. The theme of the chapter is the transition state,* and the statistics in statistical theory is in essence just the counting of the various ways a system can pass through a transition state.

Keywords

Transition State Partition Function Saddle Point Orbital Angular Momentum Transition State Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. L. Bunker, Theory of Elementary Gas Reaction Rates, Pergamon Press, Inc., Elmsford, N.Y. (1966).Google Scholar
  2. 2.
    H. S. Johnston, Gas Phase Reaction Rate Theory, The Ronald Press Company, New York (1966).Google Scholar
  3. 3.
    K. J. Laidler, Theories of Chemical Reaction Rates, McGraw-Hill Book Company, New York (1969).Google Scholar
  4. 4.
    R. D. Levine and R. B. Bernstein, Molecular Reaction Dynamics, Oxford University Press, Inc., New York (1974).Google Scholar
  5. 5.
    E. E. Nikitin, Theory of Elementary Atomic and Molecular Processes in Gases, trans. by M. J. Kearsley, Clarendon Press, Oxford (1974).Google Scholar
  6. 6.
    R. D. Levine, Quantum Mechanics of Molecular Rate Processes, Clarendon Press, Oxford (1969).Google Scholar
  7. 7.
    R. B. Bernstein, A. Dalgarno, H. Massey, and I. C. Percival, Thermal scattering of atoms by homonuclear diatomic molecules, Proc. R. Soc. London Ser. A 274, 427–442 (1963).CrossRefGoogle Scholar
  8. 8.
    R. D. Levine and B. R. Johnson, Rotational excitation in molecular collisions: Statistical features of the S-matrix, Chem. Phys. Lett. 4, 365–368 (1969).CrossRefGoogle Scholar
  9. 9.
    J. B. Anderson, Statistical theories of chemical reactions. Distributions in the transition region, J. Chem. Phys. 58, 4684–4692 (1973).CrossRefGoogle Scholar
  10. 10.
    B. Widom, Reaction kinetics in stochastic models. II, J. Chem. Phys. 61, 672–680 (1974).CrossRefGoogle Scholar
  11. 11.
    J. C. Keck, Variational theory of reaction rates, Adv. Chem. Phys. 13, 85–121 (1967).CrossRefGoogle Scholar
  12. 12.
    H. Goldstein, Classical Mechanics, Addison-Wesley Publishing Company, Inc. Reading, Mass. (1951).Google Scholar
  13. 13.
    S. Chapman, S. M. Hornstein, and W. H. Miller, Accuracy of transition state theory for the threshold of chemical reactions with activation energy: Collinear and three-dimensional H+H2, J. Am. Chem. Soc. 97, 892–894 (1975).CrossRefGoogle Scholar
  14. 14.
    R. N. Porter and M. Karplus, Potential surface for H3, J. Chem. Phys. 40, 1105–1115 (1964).CrossRefGoogle Scholar
  15. 15.
    P. Pechukas and F. J. McLafferty, On transition-state theory and the classical mechanics of collinear collisions, J. Chem. Phys. 58, 1622–1625 (1973).CrossRefGoogle Scholar
  16. 16.
    R. L. Jaffe, J. M. Henry, and J. B. Anderson, Variational theory of reaction rates: Application to F+H2=HF+H, J. Chem. Phys. 59, 1128–1141 (1973).CrossRefGoogle Scholar
  17. 17.
    R. G. Pearson, Symmetry rules for chemical reactions, Acc. Chem. Res. 4, 152–160 (1971).CrossRefGoogle Scholar
  18. 18.
    H. Metiu, J. Ross, R. Silbey, and T. F. George, On symmetry properties of reaction coordinates, J. Chem. Phys. 61, 3200–3209 (1974).CrossRefGoogle Scholar
  19. 19.
    D. L. Hill and J. A. Wheeler, Nuclear constitution and the interpretation of fission phenomena, Phys. Rev. 89, 1102–1145 (1953).CrossRefGoogle Scholar
  20. 20.
    H. S. Johnston, Large tunnelling corrections in chemical reaction rates, Adv. Chem. Phys. 3, 131–170 (1961).CrossRefGoogle Scholar
  21. 21.
    H. S. Johnston and D. Rapp, Large tunnelling corrections in chemical reaction rates. II, J. Am. Chem. Soc. 83, 1–9 (1961).CrossRefGoogle Scholar
  22. 22.
    C. Eckart, The penetration of a potential barrier by electrons, Phys. Rev. 35, 1303–1309 (1930).CrossRefGoogle Scholar
  23. 23.
    R. A. Marcus, Generalization of the activated complex theory of reaction rates. I. Quantum mechanical treatment, J. Chem. Phys. 41, 2614–2623 (1964).CrossRefGoogle Scholar
  24. 24.
    R. A. Marcus, On the analytical mechanics of chemical reactions. Quantum mechanics of linear collisions, J. Chem. Phys. 45, 4493–4499 (1966).CrossRefGoogle Scholar
  25. 25.
    L. D. Landau and E. M. Lifshitz, Quantum Mechanics, Addison-Wesley Publishing Company, Inc., Reading, Mass. (1958).Google Scholar
  26. 26.
    D. G. Truhlar and A. Kuppermann, Exact tunneling calculations, J. Am. Chem. Soc. 93, 1840–1851 (1971).CrossRefGoogle Scholar
  27. 27.
    D. G. Truhlar and A. Kuppermann, A test of transition state theory against exact quantum mechanical calculations, Chem. Phys. Leu. 9, 269–272 (1971).CrossRefGoogle Scholar
  28. 28.
    D. G. Truhlar and A. Kuppermann, Exact and approximate quantum mechanical reaction probabilities and rate constants for the collinear H+H2 reaction, J. Chem. Phys. 56, 2232–2252 (1972).CrossRefGoogle Scholar
  29. 29.
    D. G. Truhlar, A. Kuppermann, and J. T. Adams, Exact quantum mechanical reaction probabilities and rate constants for the isotopic collinear H+ H2 reactions, J. Chem. Phys. 59, 395–402 (1973).CrossRefGoogle Scholar
  30. 30.
    F. J. McLafferty and P. Pechukas, Quantum transition state theory, Chem. Phys. Lett. 27, 511–514 (1974).CrossRefGoogle Scholar
  31. 31.
    W. H. Miller, Quantum mechanical transition state theory and a new semiclassical model for reaction rate constants, J. Chem. Phys. 61, 1823–1834 (1974).CrossRefGoogle Scholar
  32. 32.
    E. Wigner, On the quantum correction for thermodynamic equilibrium, Phys. Rev. 40, 749–759 (1932).CrossRefGoogle Scholar
  33. 33.
    W. H. Miller, Classical limit quantum mechanics and the theory of molecular collisions, Adv. Chem. Phys. 25, 69–177 (1974).CrossRefGoogle Scholar
  34. 34.
    W. H. Miller, Semiclassical limit of quantum mechanical transition state theory for non-separable systems, J. Chem. Phys. 62, 1899–1906 (1975).CrossRefGoogle Scholar
  35. 35.
    J. C. Keck, Statistical theory of chemical reaction rates, J. Chem. Phys. 29, 410–415 (1958).CrossRefGoogle Scholar
  36. 36.
    E. E. Nikitin, Statistical theory of endothermic reactions. Part I. Bimolecular reactions, Theor. Exp. Chem. USSR 1, 83–89 (1965).CrossRefGoogle Scholar
  37. 37.
    E. E. Nikitin, Statistical theory of exothermic ion—molecule reactions, Theor. Exp. Chem. USSR 1, 275–280 (1965).CrossRefGoogle Scholar
  38. 38.
    P. Brumer and M. Karplus, Collision complex dynamics in alkali halide exchange reactions, Faraday Discuss. Chem. Soc. 55, 80–92 (1973).CrossRefGoogle Scholar
  39. 39.
    J. Ford, The transition from analytic dynamics to statistical mechanics, Adv. Chem. Phys. 24, 155–185 (1973).CrossRefGoogle Scholar
  40. 40.
    W. H. Miller, Study of the statistical model for molecular collisions, J. Chem. Phys. 52, 543–551 (1970).CrossRefGoogle Scholar
  41. 41.
    J. C. Light, Phase-space theory of chemical kinetics, J. Chem. Phys. 40, 3221–3229 (1964).CrossRefGoogle Scholar
  42. 42.
    P. Pechukas and J. C. Light, On detailed balancing and statistical theories of chemical kinetics, J. Chem. Phys. 42, 3281–3291 (1965).CrossRefGoogle Scholar
  43. 43.
    J. Lin and J. Light, Phase-space theory of chemical kinetics. III. Reactions with activation energy, J. Chem. Phys. 45, 2545–2559 (1966).CrossRefGoogle Scholar
  44. 44.
    J. C. Light, Statistical theory of bimolecular exchange reactions, Discuss. Faraday Soc. 44, 14–29 (1967).CrossRefGoogle Scholar
  45. 45.
    R. A. Marcus, On the theory of energy distributions of products of molecular beam reactions involving transient complexes, J. Chem. Phys. 62, 1372–1384 (1975).CrossRefGoogle Scholar
  46. 46.
    R. A. Marcus, Chemical-reaction cross sections, quasiequilibrium, and generalized activated complexes, J. Chem. Phys. 45, 2138–2144 (1966).CrossRefGoogle Scholar
  47. 47.
    R. A. Marcus, On the theory of chemical-reaction cross sections. I. A statistical-dynamical model, J. Chem. Phys. 45, 2630–2638 (1966).CrossRefGoogle Scholar
  48. 48.
    S. A. Safron, N. D. Weinstein, D. R. Herschbach, and J. C. Tully, Transition state theory for collision complexes: Product translational energy distributions, Chem. Phys. Lett. 12, 564–568 (1972).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1976

Authors and Affiliations

  • Philip Pechukas
    • 1
  1. 1.Department of ChemistryColumbia UniversityNew YorkUSA

Personalised recommendations