Skip to main content

Determination of the Bottleneck Regions of Potential Energy Surfaces for Atom Transfer Reactions by Variational Transition State Theory

  • Chapter
Potential Energy Surfaces and Dynamics Calculations

Abstract

A major difficulty in the calculation of reliable equilibrium rate constants for gas-phase bimolecular reactions is the lack of accurate information about potential energy surfaces. The calculation of accurate, detailed dynamical quantities such as inelastic and reactive cross sections requires a knowledge of the potential energy surface over large regions of the configuration space. Thermal rate constants represent an average of such detailed dynamical quantities, and as a result they are less sensitive to fine features of the surface. Thus accurate thermal rate constants may be calculated using less information about the potential surfaces than is required to calculate more detailed quantities; one of the goals of the present chapter is to discuss which regions of the surfaces are most important in controlling the rates of chemical reactions.

Lando Research Fellow, 1979, 1980

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

Access this chapter

eBook
USD 16.99
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

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. S. Glasstone, K. J. Laidler, and H. Eyring, “Theory of Rate Processes”, McGraw-Hill, New York (1941).

    Google Scholar 

  2. H. S. Johnston, “Gas Phase Reaction Rate Theory”, Ronald Press, New York (1966).

    Google Scholar 

  3. D. L. Bunker, “Theory of Gas Phase Reaction Rates”, Pergamon Press, Oxford (1966).

    Google Scholar 

  4. K. J. Laidler, “Theories of Chemical Reaction Rates”, McGraw-Hill, New York (1969).

    Google Scholar 

  5. E. Wigner, Calculation of the rate of elementary association reactions, J. Chem. Phys. 5: 720 (1937).

    Article  CAS  Google Scholar 

  6. J. Horiuti, On the statistical mechanical treatment of the absolute rate of chemical reaction, Bull. Chem. Soc. Japan 13: 210 (1938).

    Article  Google Scholar 

  7. J. C. Keck, Variational theory of chemical reaction rates applied to three-body recombinations, J. Chem. Phys. 32: 1035 (1960).

    Article  CAS  Google Scholar 

  8. J. C. Keck, Variational theory of reaction rates, Advan. Chem. Phys. 13: 85 (1967).

    Article  Google Scholar 

  9. P. Pechukas, Statistical approximations in collision theory, in: “Dynamics of Molecular Collisions, Part B”, W. H. Miller, ed., Plenum, New York (1976), p. 269.

    Chapter  Google Scholar 

  10. E. Pollak and P. Pechukas, Transition states, trapped trajectories, and classical bound states embedded in the continuum, J. Chem. Phys. 69: 1218 (1978).

    Article  CAS  Google Scholar 

  11. B. C. Garrett and D. G. Truhlar, Criterion of minimum state density in the transition state theory of bimolecular reactions, J. Chem. Phys. 70: 1593 (1979).

    Article  CAS  Google Scholar 

  12. B. C. Garrett and D. G. Truhlar, Generalized transition state theory. Classical mechanical theory and applications to collinear reactions of hydrogen molecules, J. Phys. Chem. 83: 1052, 3058(E) (1979).

    Google Scholar 

  13. K. Morokuma and M. Karplus, Collision dynamics and the statistical theories of chemical reactions. II. Comparison of reaction probabilities, J. Chem. Phys. 55: 63 (1971).

    Article  CAS  Google Scholar 

  14. G. W. Koeppl and M. Karplus, Comparison of 3D classical trajectory and transition-state theory reaction cross sections, J. Chem. Phys. 55: 4667 (1971).

    Article  CAS  Google Scholar 

  15. P. Pechukas and F. J. McLafferty, On transition-state theory and the classical mechanics of collinear collisions, J. Chem. Phys. 58: 1622 (1973).

    Article  CAS  Google Scholar 

  16. 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. Amer. Chem. Soc. 97: 892 (1975).

    Article  CAS  Google Scholar 

  17. W. J. Chesnavich, On the threshold behavior of collinear bimolecular exchange reactions, Chem. Phys. Lett. 53: 300 (1978).

    Article  CAS  Google Scholar 

  18. B. C. Garrett and D. G. Truhlar, Improved canonical variational theory for chemical reaction rates. Classical mechanical theory and applications to collinear reactions, J. Phys. Chem. 84: 805 (1980).

    Article  CAS  Google Scholar 

  19. E. Wigner, The transition state method, Trans. Faraday Soc. 34: 29 (1938).

    Article  CAS  Google Scholar 

  20. W. H. Miller, Quantum mechanical transition state theory and a new semiclassical model for reaction rate constants, J. Chem. Phys. 61: 1823 (1974).

    Article  CAS  Google Scholar 

  21. W. H. Miller, Semiclassical limit of quantum mechanical transition state theory for nonseparable systems, J. Chem. Phys. 62: 1899 (1975).

    Article  CAS  Google Scholar 

  22. W. H. Miller, Path integral representation of the reaction rate constant in quantum mechanical transition state theory, J. Chem. Phys. 63: 1166 (1975).

    Article  CAS  Google Scholar 

  23. D. G. Truhlar, Accuracy of trajectory calculations and transition state theory for thermal rate constants of atom transfer reactions, J. Phys. Chem. 83: 188 (1979).

    Article  CAS  Google Scholar 

  24. B. C. Garrett and D. G. Truhlar, Accuracy of tunneling corrections to transition state theory for thermal rate constants of atom transfer reactions, J. Phys. Chem. 83: 200, 3058(E) (1979).

    Google Scholar 

  25. B. C. Garrett and D. G. Truhlar, Generalized transition state theory. Quantum effects for collinear reactions of hydrogen molecules and isotopically substituted hydrogen molecules, J. Phys. Chem. 83: 1079 (1979).

    Article  CAS  Google Scholar 

  26. B. C. Garrett and D. G. Truhlar, Generalized transition state theory. Quantum effects for collinear reactions of hydrogen molecules and isotopically substituted hydrogen molecules, J. Phys. Chem. 84: 682(E) (1980).

    Google Scholar 

  27. B. C. Garrett, D. G. Truhlar, R. S. Grev, and A. W. Magnuson, Improved treatment of threshold contributions in variational transition-state theory, J. Phys. Chem. 84: 1730 (1980).

    Article  CAS  Google Scholar 

  28. B. C. Garrett, D. G. Truhlar, and R. S. Grev, Applications of variational transition-state theory and the unified statistical model to H + Cl2 → HCl + Cl, J. Phys. Chem. 84: 1749 (1980).

    Article  CAS  Google Scholar 

  29. B. C. Garrett, D. G. Truhlar, R. S. Grev, and R. B. Walker, Comparison of variational transition state theory and the unified statistical model with vibrationally adiabatic transmission coefficients to accurate collinear rate constants for T + HD → TH + D, J. Chem. Phys. 73: 235 (1980).

    Article  CAS  Google Scholar 

  30. B. C. Garrett, D. G. Truhlar, R. S. Grev, A. W. Magnuson, and J. N. L. Connor, Variational transition state theory, vibrationally adiabatic transmission coefficients, and the unified statistical model tested against accurate quantum rate constants for collinear F + H2, H + F2, and isotopic analogs, J. Chem. Phys. 73: 1721 (1980).

    Article  CAS  Google Scholar 

  31. B. C. Garrett and D. G. Truhlar, Generalized transition state theory calculations for the reactions D + H2 and H + D2 using an accurate potential energy surface: Explanation of the kinetic isotope effect, J. Chem. Phys. 72: 3460 (1980).

    Article  CAS  Google Scholar 

  32. B. C. Garrett and D. G. Truhlar, Reliable Ab initio calculation of a chemical reaction rate and a kinetic isotope effect: H + H2 and 2H + 2H2, Proc. Natl. Acad. Sci. USA 76: 4755 (1979).

    Article  CAS  Google Scholar 

  33. B. Liu, Ab initio potential energy surface for linear H3, J. Chem. Phys. 58: 1925 (1973).

    Article  CAS  Google Scholar 

  34. P. Siegbahn and B. Liu, An accurate three-dimensional potential energy surface for H3, J. Chem. Phys. 68: 2457 (1978).

    Article  CAS  Google Scholar 

  35. D. G. Truhlar and C. J. Horowitz, Functional representation of Liu and Siegbahn’s accurate Ab initio potential energy calculations for H + H2, J. Chem. Phys. 68: 2466 (1978).

    Article  CAS  Google Scholar 

  36. D. G. Truhlar and C. J. Horowitz, Functional representation of Liu and Siegbahn’s accurate Ab initio potential energy calculations for H + H2, J. Chem. Phys. 71: 1514(E) (1979).

    Article  Google Scholar 

  37. D. G. Truhlar and B. C. Garrett, Variational transition state theory, Acc. Chem. Res. 13: 440 (1980).

    Article  CAS  Google Scholar 

  38. B. C. Garrett and D. G. Truhlar, Generalized transition state theory. Bond-energy-bond-order method for canonical variational calculations with applications to hydrogen atom transfer reactions, J. Amer. Chem. Soc. 101: 4534 (1979).

    Article  CAS  Google Scholar 

  39. B. C. Garrett and D. G. Truhlar, Generalized transition state theory. Canonical variational calculations using the bond-energy-bond-order method for bimolecular reactions of combustion products, J. Amer. Chem. Soc. 101: 5207 (1979).

    Article  CAS  Google Scholar 

  40. B. C. Garrett and D. G. Truhlar, Variational transition state theory. Primary kinetic isotope effects for atom transfer reactions, J. Amer. Chem. Soc. 102: 2559 (1980).

    Article  CAS  Google Scholar 

  41. B. C. Garrett, D. G. Truhlar, and A. W. Magnuson, Variational transition state theory and vibrationally adiabatic transmission coefficients for the kinetic isotope effects in the Cl-H-H reaction system, J. Chem. Phys. 74: 1029 (1981).

    Article  CAS  Google Scholar 

  42. S. Chapman, B. C. Garrett, and W. H. Miller, Semiclassical transition state theory for nonseparable systems: Application to the collinear H + H2 reaction, J. Chem. Phys. 63: 2710 (1975).

    Article  CAS  Google Scholar 

  43. See also H. S. Johnston and D. Rapp, Large tunneling corrections in chemical reaction rates. II, J. Amer. Chem. Soc. 83: 1 (1961) and reference 39.

    Article  CAS  Google Scholar 

  44. E. Wigner, Über das Überschreiten von Potentialschwellen bei chemischen Reaktionen, Z. Phys. Chem. B 19: 203 (1932).

    Google Scholar 

  45. D. G. Truhlar and A. Kuppermann, Exact tunneling calculations, J. Amer. Chem. Soc. 93: 1840 (1971).

    Article  Google Scholar 

  46. D. G. Truhlar, The adiabatic theory of chemical reactions, J. Chem. Phys. 53: 2041 (1970), and references therein.

    Article  CAS  Google Scholar 

  47. R. A. Marcus and M. E. Coltrin, A new tunneling path for reactions such as H + H2 → H + H, J. Chem. Phys. 67: 2609 (1977).

    Article  CAS  Google Scholar 

  48. For a review see P. Pulay, Direct use of the gradient for investigating molecular energy surfaces, in: “Applications of Electronic Structure Theory”, H. F. Schaefer, ed., Plenum, New York (1977), p. 153.

    Chapter  Google Scholar 

  49. J. A. Pople, R. Krishnan, H. B. Schlegel, and J. S. Binkeley, Derivative studies in Hartree-Fock and Møller-Plesset theories, Int. J. Quantum Chem. Symp. 13: 255 (1979).

    Google Scholar 

  50. B. C. Garrett and D. G. Truhlar, Importance of quartic anharmonicity for bending partition functions in transition state theory, J. Phys. Chem. 83: 1915 (1979).

    Article  CAS  Google Scholar 

  51. For further discussion see D. G. Truhlar, discussion remarks, J. Phys. Chem. 83: 199 (1979).

    Article  Google Scholar 

  52. R. L. Jaffe, J. M. Henry, and J. B. Anderson, Variational theory of reaction rates: Application to F + H2 ⇌ FH + H, J. Chem. Phys. 59: 1128 (1973).

    Article  CAS  Google Scholar 

  53. G. W. Koeppl, Alternative locations for the dividing surface of transition state theory. Implications for application of the theory, J. Amer. Chem. Soc. 96: 6539 (1974).

    Article  CAS  Google Scholar 

  54. W. H. Miller, Unified statistical model for “complex” and “direct” reaction mechanisms, J. Chem. Phys. 65: 2216 (1976).

    Article  CAS  Google Scholar 

  55. G. Koeppl, progress report for Alfred P. Sloan Fellowship for Basic Research, Nov. 9, 1977 (unpublished).

    Google Scholar 

  56. E. Pollak and P. Pechukas, Unified statistical model for “complex” and “direct” reaction mechanisms: A test of the collinear H + H2 exchange reaction, J. Chem. Phys. 70: 325 (1979).

    Article  CAS  Google Scholar 

  57. P. Pechukas and E. Pollak, Classical transition state theory is exact if the transition state is unique, J. Chem. Phys. 71: 2062 (1979).

    Article  CAS  Google Scholar 

  58. J. P. Davis, A combined dynamical-statistical approach to calculating rates of complex bimolecular exchange reactions, J. Chem. Phys. 71: 5206 (1979).

    Article  CAS  Google Scholar 

  59. J. P. Davis, A combined statistical-dynamical approach to calculating rates of complex bimolecular exchange reactions: Asymmetric systems, J. Chem. Phys. 73: 2010 (1980).

    Article  CAS  Google Scholar 

  60. W. J. Chesnavich, T. Su, and M. T. Bowers, Ion-dipole collisions: Recent theoretical advances, in: “Kinetics of Ion-Molecule Reactions”, P. Ausloos, ed., Plenum, New York (1979), p. 31.

    Chapter  Google Scholar 

  61. W. J. Chesnavich, T. Su, and M. T. Bowers, Collisions in a non-central field: A variational and trajectory investigation of ion-dipole capture, J. Chem. Phys. 72: 2641 (1980).

    Article  CAS  Google Scholar 

  62. B. C. Garrett and D. G. Truhlar, Improved canonical variational theory for chemical reaction rates. Classical mechanical theory and applications to collinear reactions, J. Phys. Chem. 84: 805 (1980).

    Article  CAS  Google Scholar 

  63. E. Pollak, M. S. Child, and P. Pechukas, Classical transition state theory: A lower bound to the reaction probability, J. Chem. Phys. 72: 1669 (1980).

    Article  CAS  Google Scholar 

  64. E. Pollak and R. D. Levine, Statistical theories for molecular collisions: A maximum entropy derivation, J. Chem. Phys. 72: 2990 (1980).

    Article  CAS  Google Scholar 

  65. J. B. Anderson, Statistical theories of chemical reactions. Distributions in the transition region, J. Chem. Phys. 58: 4684 (1973).

    Article  CAS  Google Scholar 

  66. B. C. Garrett and D. G. Truhlar, unpublished.

    Google Scholar 

  67. E. K. Grimmelman and L. L. Lohr, On the exactness of classical transition state theory for collinear reactions, Chem. Phys. Lett. 48: 487 (1977).

    Article  Google Scholar 

  68. D. I. Sverdlik and G. W. Koeppl, An energy limit of transition state theory, Chem. Phys. Lett. 59: 449 (1978).

    Article  CAS  Google Scholar 

  69. D. I. Sverdlik, G. P. Stein, and G. W. Koeppl, The accuracy of transition state theory in its absolute rate, theory and variational formulations, Chem. Phys. Lett. 67: 87 (1979).

    Article  CAS  Google Scholar 

  70. D. Martin and L. M. Raff, A general procedure for classical variational rate calculations for three-body exchange reactions, J. Chem. Phys., submitted for publication.

    Google Scholar 

  71. 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 (1972).

    Article  CAS  Google Scholar 

  72. J. Troe, Unimolecular reactions, Int. Rev. Sci., Phys. Chem. Ser. Two 9: 1 (1976).

    CAS  Google Scholar 

  73. M. Quack and J. Troe, Unimolecular reactions and energy transfer of highly excited molecules, Specialist Periodical Reports Chem. Soc. Gas Kinetics and Energy Transfer 2: 175 (1977), and references therein.

    Article  CAS  Google Scholar 

  74. W. J. Chesnavich, L. Bass, T. Su, and M. T. Bowers, Multiple transition states In unimolecular reactions: A transition state switching model. Application to the C4H8 + system, preprint.

    Google Scholar 

  75. C. A. Parr and D. G. Truhlar, Potential energy surfaces for atom transfer reactions involving hydrogens and halogens, J. Chem. Phys. 75: 1844 (1971).

    Article  Google Scholar 

  76. D. G. Truhlar and R. E. Wyatt, H + H2: Potential energy surfaces and elastic and inelastic scattering, Advan. Chem. Phys. 36: 141 (1977).

    Article  CAS  Google Scholar 

  77. F. T. Wall and R. N. Porter, General potential-energy function for exchange reactions, J. Chem. Phys. 36: 3256 (1962).

    Article  CAS  Google Scholar 

  78. J. W. Duff and D. G. Truhlar, Effect of curvature of the reaction path on dynamic effects in endothermic reactions and product energies in exothermic reactions, J. Chem. Phys. 62: 2477 (1975).

    Article  CAS  Google Scholar 

  79. R. N. Porter and M. Karplus, Potential energy surface for H3, J. Chem. Phys. 40: 1105 (1964).

    Article  CAS  Google Scholar 

  80. L. M. Raff, L. Stivers, R. N. Porter, D. L. Thompson, and L. B. Sims, Semiempirical VB calculation of the (H2I2) interaction potential, J. Chem. Phys. 52: 3449 (1970).

    Article  CAS  Google Scholar 

  81. L. M. Raff, L. Stivers, R. N. Porter, D. L. Thompson, and L. B. Sims, Semiempirical VB calculation of the (H2I2) interaction potential, J. Chem. Phys. 58: 1271(E) (1973).

    Article  Google Scholar 

  82. H. S. Johnston and C. A. Parr, Activation energies from bond energies. I. Hydrogen transfer reactions, J. Amer. Chem. Soc. 85: 2544 (1963).

    Article  CAS  Google Scholar 

  83. S. W. Mayer, L. Schieler, and H. S. Johnston, Computation of high-temperature rate constants for bimolecular reactions of combustion products, Eleventh Symp. (Int.) Combustion 837 (1967).

    Google Scholar 

  84. M. J. Stern, A. Persky, and F. S. Klein, Force field and tunneling effects in the H-H-Cl reaction system. Determination from kinetic isotope effect measurements, J. Chem. Phys. 58: 5697 (1973).

    Article  CAS  Google Scholar 

  85. C. A. Parr, Ph.D. thesis, California Institute of Technology, Pasadena, 1968; C. A. Parr and A. Kuppermann, unpublished.

    Google Scholar 

  86. J. T. Muckerman, Applications of classical trajectory techniques to reactive scattering, Theoret. Chem.: Advan. Perspectives 6A: 1 (1981).

    Google Scholar 

  87. N. Jonathan, S. Okuda, and D. Timlin, Initial vibrational energy distributions determined by infrared chemiluminescence. III. Experimental results and classical trajectory calculations for the H + F2 system, Mol. Phys. 24: 1143 (1972).

    Article  CAS  Google Scholar 

  88. P. J. Kuntz, E. M. Nemeth, J. C. Polanyi, S. D. Rosner, and C. E. Young, Energy distribution among products of exothermic reactions. II. Repulsive, mixed, and attractive energy release, J. Chem. Phys. 44: 1168 (1968).

    Article  Google Scholar 

  89. J. A. Kaye and A. Kuppermann, Chem. Phys. Lett. 77: 573 (1981).

    Article  CAS  Google Scholar 

  90. A. M. G. Ding, L. J. Kirsch, D. S. Perry, J. C. Polanyi, and J. L. Schreiber, Effect of changing reagent energy on reaction probability and product energy distribution, Faraday Disc. Chem. Soc. 55: 252 (1973).

    Article  CAS  Google Scholar 

  91. J. C. Polanyi and N. Sathyamurthy, Location of energy barriers. VII. Sudden and gradual late-energy barriers, Chem. Phys. 33: 287 (1978).

    Article  CAS  Google Scholar 

  92. D. J. Douglas, J. C. Polanyi, and J. J. Sloan, Effect of changing reagent energy on reaction dynamics. VI. Dependence of reaction rates on vibrational energy excitation in substantially endothermic reactions, XH(v′) + Y → X + HY, Chem. Phys. 13: 15 (1976) (1976).

    Article  CAS  Google Scholar 

  93. P. J. Kuntz, E. M. Nemeth, J. C. Polanyi, and W. H. Wong, Distribution of reaction products. VI. Hot-atom reactions, T + HR, J. Chem. Phys. 52: 4654 (1970).

    Article  CAS  Google Scholar 

  94. T. Valencich, J. Hsieh, J. Kwan, T. Stewart, and T. Lenhardt, Simulation of the effects of translational and vibrational energy on H and D atom reactions with HCl and DCl, Ber. Bunsenges. Phys. Chem. 81: 131 (1977).

    Article  CAS  Google Scholar 

  95. B. R. Johnson and N. W. Winter, Classical trajectory study of the effect of vibrational energy on the reaction of molecular hydrogen with atomic oxygen, J. Chem. Phys. 66: 4116 (1967).

    Article  Google Scholar 

  96. M. Baer, An exact quantum mechanical study of the isotopic collinear reactive systems H2 + Cl and D2 + Cl, Mol. Phys. 27: 1429 (1974).

    Article  CAS  Google Scholar 

  97. See, e.g., H. Eyring, S. H. Lin, and S. M. Lin, “Basic Chemical Kinetics”, John Wiley & Sons, New York (1980), p. 145.

    Google Scholar 

  98. G. S. Hammond, A correlation of reaction rates, J. Amer. Chem. Soc. 77: 334 (1955).

    Article  CAS  Google Scholar 

  99. R. A. Eades and D. A. Dixon, personal communication.

    Google Scholar 

  100. T. A. Halgren and W. N. Lipscomb, Self-consistent-field wave-functions for complex molecules. The approximation of partial retention of diatomic differential overlap, J. Chem. Phys. 58: 1569 (1973).

    Article  CAS  Google Scholar 

  101. See, e.g., L. Melander and W. H. Saunders, Jr., “Reaction Rates of Isotopic Molecules”, John Wiley & Sons, New York (1980).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1981 Springer Science+Business Media New York

About this chapter

Cite this chapter

Garrett, B.C., Truhlar, D.G., Grev, R.S. (1981). Determination of the Bottleneck Regions of Potential Energy Surfaces for Atom Transfer Reactions by Variational Transition State Theory. In: Truhlar, D.G. (eds) Potential Energy Surfaces and Dynamics Calculations. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-1735-8_24

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-1735-8_24

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-1737-2

  • Online ISBN: 978-1-4757-1735-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics