Application of the Energy Minimization Method to a Search for the Transition State for the H2 + D2 Exchange Reaction

  • Michael J. Rothman
  • Lawrence L. LohrJr.
  • Carl S. Ewig
  • John R. Van Wazer


A major question in quantum chemistry is: How do hydrogen molecules exchange hydrogen atoms? Many have considered this query,1-18 but none have satisfactorily answered it. Bimolecular exchange has been studied with increasingly sophisticated methodology (large configuration interactions, double-zeta-plus-polarization basis sets).7 Geometries considered for the transition-state include: squares,1,2,3,7 kites,2,7 tetrahedra,2,3 chains,2,3,5,7,13 trapezoids,2,7 Y’s,7 T’s,6 and rhomboids.2,3,7 To date, the lowest calculated Ab initio bimolecular adiabatic activation energy is about 490 kJ/mol above 2H2.13 In contrast, the experimental Arrhenius activation energy corresponding to a second order bimolecular reaction is about 170 kJ/mol above 2H2.16,18


Transition State Potential Energy Surface Reaction Path Transition State Energy Energy Minimization Method 


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  1. 1.
    H. Conroy and G. Malli, Molecular Schrödinger equation. IX. Square and rectangular states of H4 and the molecular ions \(H_{4}^{3+}\) and \(H_{4}^{2+}\), J. Chem. Phys. 50: 5049 (1969).CrossRefGoogle Scholar
  2. 2.
    C. W. Wilson Jr. and W. A. Goddard III, Ab initio calculations on the H2 + D2 = 2HD four-center exchange reaction. I. Elements of the reaction surface, J. Chem. Phys. 51: 716 (1969).CrossRefGoogle Scholar
  3. 2.
    C. W. Wilson Jr. and W. A. Goddard III, Orbitals, contragradience, and the reaction surface, J. Chem. Phys. 56: 5913 (1972).CrossRefGoogle Scholar
  4. 3.
    M. Rubinstein and I. Shavitt, Theoretical study of the potential surface for the H4 system by double-zeta configuration-interaction calculations, J. Chem. Phys. 51: 2014 (1969).CrossRefGoogle Scholar
  5. 4.
    D. M. Silver, Reaction paths for bimolecular hydrogen exchange, Chem. Phys. Lett. 14: 105 (1972).CrossRefGoogle Scholar
  6. 5.
    C. F. Bender and H. F. Schaefer III, Linear symmetric H4, J. Chem. Phys. 57: 217 (1972).CrossRefGoogle Scholar
  7. 6.
    B. Freihaut and L. M. Raff, Valence-bond study of the (H2, D2) exchange reaction mechanism, J. Chem. Phys. 58: 1202 (1973).CrossRefGoogle Scholar
  8. 7.
    D. M. Silver and R. M. Stevens, Reaction paths on the H4 potential energy surface, J. Chem. Phys. 59: 3378 (1973).CrossRefGoogle Scholar
  9. 8.
    J. S. Wright, Allowed and forbidden reaction paths for the H2 + D2 exchange reaction, Can. J. Chem. 53: 549 (1975).CrossRefGoogle Scholar
  10. 9.
    N. J. Brown and D. M. Silver, Comparison of reactive and inelastic scattering of H2 + D2 using four semiempirical potential energy surfaces, J. Chem. Phys. 72: 3869 (1980).CrossRefGoogle Scholar
  11. 10.
    R. G. Pearson, “Symmetry Rules for Chemical Reactions”, Wiley, New York (1976), pp. 43–48.Google Scholar
  12. 11.
    D. A. Dixon, R. M. Stevens, and D. R. Herschbach, Potential energy surface for bond exchange among three hydrogen molecules, Faraday Disc. Chem. Soc. 62: 110 (1977).CrossRefGoogle Scholar
  13. 12.
    A. J. C. Varandas and J. N. Murrell, A many-body expansion of polyatomic potential energy surfaces: Application to Hn systems, Faraday Disc. Chem. Soc. 62: 92 (1977).CrossRefGoogle Scholar
  14. 13.
    H. H. Huang and A. H. Pakiari, Floating spherical Gaussian orbital open-shell calculations on the four-electron H4 system, Int. J. Quantum Chem. 12: 593 (1977).CrossRefGoogle Scholar
  15. 14.
    G. A. Gallup, Electron tunneling, charge transfer, and the inter-molecular forces between two H2 molecules, J. Chem. Phys. 66: 2252 (1977).CrossRefGoogle Scholar
  16. 15.
    F. H. Ree and C. F. Bender, Repulsive intermolecular potential between two H2 molecules, J. Chem. Phys. 71: 5362 (1979).CrossRefGoogle Scholar
  17. 16.
    R. D. Kern and G. G. Nika, The rate of exchange of hydrogen and deuterium behind reflected shock waves. Dynamic analysis of time-of-flight mass spectrometry, J. Phys. Chem. 75: 1615 (1971).CrossRefGoogle Scholar
  18. 17.
    S. H. Bauer, D. M. Lederman, E. L. Resler, Jr., and E. R. Fisher, The homogeneous gas phase H2-D2 metathesis at room temperature: Reaction induced by specific vibrational excitation, Int. J. Chem. Kinet. 5: 93 (1973).CrossRefGoogle Scholar
  19. 18.
    A. Lifshitz and M. Frenklach, The reaction between H2 and D2 in a shock tube: Study of the atomic vs. molecular mechanism by atomic resonance absorption spectrometry, J. Chem. Phys. 67: 2803 (1977).CrossRefGoogle Scholar
  20. 19.
    S. H. Bauer, Review of 4-center exchange reactions, Annu. Rev. Phys. Chem. 30: 271 (1979).CrossRefGoogle Scholar
  21. 20.
    M. J. Rothman and L. L. Lohr, Jr., Analysis of an energy minimization method for locating transition states on potential energy hypersurfaces, Chem. Phys. Lett. 70: 405 (1980).CrossRefGoogle Scholar
  22. 21.
    E. A. McCullough, Jr. and D. M. Silver, Reaction path properties at critical points on potential surfaces, J. Chem. Phys. 62: 4050 (1975).CrossRefGoogle Scholar
  23. 22.
    M. C. Zerner, Geometry optimization of large systems, in: “Computational Methods for Molecular Structure Determination: Theory and Technique”, Proceedings of the workshop held at Indiana University, August 13–24, 1979, NRCC Proc. No. 8, Lawrence Berkeley Laboratory, University of California, Berkeley, chapter 14.Google Scholar
  24. 23.
    G. Das and A. C. Wahl, BISON-MC: A FORTRAN computing system for multi-configuration self-consistent-field (MCSCF) calculations on atoms, diatoms, and polyatomics, Argonne National Laboratory REP. ANL-7955, July 1972.Google Scholar
  25. 24.
    L. L. Lohr, Jr., A possible transition state for the H2 + D2 exchange reaction, Chem. Phys. Lett. 56: 28 (1978).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1981

Authors and Affiliations

  • Michael J. Rothman
    • 1
  • Lawrence L. LohrJr.
    • 1
  • Carl S. Ewig
    • 2
  • John R. Van Wazer
    • 2
  1. 1.Department of ChemistryThe University of MichiganAnn ArborUSA
  2. 2.Department of ChemistryVanderbilt UniversityNashvilleUSA

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