Theoretica chimica acta

, Volume 35, Issue 1, pp 1–15 | Cite as

Consequences of resonance tunnelling in chemical kinetics

  • Mohamed W. Morsy
  • Ali Rabie
  • Abdelazim Hilal
  • Hermann Hartmann


The kinetic consequences of resonance tunnelling processes that may occur in chemical reactions are investigated in terms of a multi-centered unsymmetrical Eckart potential barrier. This potential function does not only simulate the possible existence of intermediate wells in the effective potential energy cut along the reaction path, but also is amenable to analytic solutions. The reaction rate as well as its dependence on temperature, reduced mass,Q-value, activation energy and barrier diffuseness are evaluated for successively increasing the number of barrier stages. Comparisons between results due to single and multi-humped potential energy barriers are made and discussed.

Key words

Resonance tunnelling in chemical kinetics Eckart function Multi-humped potential barrier 


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  1. 1.
    Roach,A.C.,Child,M.S.: Mol. Phys.14, 1 (1965)Google Scholar
  2. 2.
    Csizmadia,I.G.,Polanyi,I.C.,Roach,A.C.,Wong,W.H.: Can. J. Chem.47, 4079 (1969)Google Scholar
  3. 3.
    Polanyi,J.C.: Accounts Chem. Res.5, 161 (1972)Google Scholar
  4. 4.
    Levine,R.D.,Wu,S.-F.: Chem. Phys. Letters15, 557 (1971)Google Scholar
  5. 5.
    Wu,S.-F., Levine,R.D.: Mol. Phys.22, 881 (1971)Google Scholar
  6. 6.
    Wu,S.-F., Johnson,B.R., Levine,R.D.: Mol. Phys.25, 609 (1973)Google Scholar
  7. 7.
    Child,M.S.: Mol. Phys.12, 401 (1968)Google Scholar
  8. 8.
    Conner, J.N.L.: Mol. Phys.15, 37 (1968)Google Scholar
  9. 9.
    Fröman,N., Fröman,P.O.: JWKB Approximation, Amsterdam: North Holland 1955Google Scholar
  10. 10.
    Leboeuf,J.N., Sharma,R.C.: Can. J. Phys.51, 446 (1973)Google Scholar
  11. 11.
    Morsy,M.W.: Theoret. Chim. Acta (Berl.), To be publishedGoogle Scholar
  12. 12.
    Morsy,M.W., Hilal,A., Rabie,A., Hartmann,H.: Mol. Phys., to be publishedGoogle Scholar
  13. 13.
    Smith,F.T.: J. Chem. Phys.36, 248 (1962)Google Scholar
  14. 14.
    Eckart,C.: Phys. Rev.35, 1303 (1930)Google Scholar
  15. 15.
    Flügge,S.: Practical quantum mechanics I, p. 86. Berlin-Heidelberg-New York: Springer 1971Google Scholar
  16. 16.
    Erdelyi,A.: Higher Transendental Functions I, p. 56. New York: McGraw Hill 1953Google Scholar
  17. 17.
    Abramowitz,M., Stegun,I.A.: Handbook of mathematical functions. New York: Dover Publications 1965Google Scholar
  18. 18.
    Porter,R.N., Karplus,M.: J. Chem. Phys.40, 1105 (1964)Google Scholar

Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • Mohamed W. Morsy
    • 1
  • Ali Rabie
    • 1
  • Abdelazim Hilal
    • 1
  • Hermann Hartmann
    • 1
  1. 1.Institut für theoretische Chemie der Universität Frankfurt am MainFederal Republic of Germany

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