Science in China Series B: Chemistry

, Volume 41, Issue 5, pp 460–470 | Cite as

A dynamical Lie algebraic mehtod for quantum reactive scattering

  • Daren Guan
  • Xizhang Yi
  • Shiliang Ding
  • Benhui Yang
  • Dongming Hua


The dynamical Lie algebraic method is used to describe the quantum reactive scattering. For the collinear exchange reaction A+BC→AB+C, an analytical expression for the reactive transition probability, which involves the main dynamic parameters of the system, is explicitly given. Numerical test calculations are carried out for the collinear reaction scattering H+H2 (n = 0)→H2 (n’ = 0)+H. The results show that the dynamical Lie algebraic method is very efficient for computing reaction probabilities.


dynamics of chemical reactions dynamical Lie algebraic method quantum reactive scattering 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Miller, W. H., Recent advances in quantum mechanical reactive scattering theory, including comparison of recent experiments with rigorous calculations of state-to-state cross sections for the H/D+H2+H2/HD+H reactions,Annu. Rev. Phys. Chem., 1990, 41: 245.Google Scholar
  2. 2.
    Lippmann, B. A., Schwinger, J., Variational principles for scattering processes (I),Phys. Rev., 1950, 79: 469.CrossRefGoogle Scholar
  3. 3.
    Gell-Mann, M., Goldberger, M. L., The fonnal theory of scattering,Phys. Rev., 1953, 91: 398.CrossRefGoogle Scholar
  4. 4.
    Ahassid, Y., Levine, R. D., Connection between the maximal entropy and the scattering theoretic analysis of collision processes,Phys. Rev. A, 1978, 18: 89.CrossRefGoogle Scholar
  5. 5.
    Guan, D., Yi, X., Ding, S. et al., Application of the Lie algebraic approach to diffractionally and rotationally inelastic molecule-surface scattering,Int. J. Quantum Chem. 1997, 63: 981.CrossRefGoogle Scholar
  6. 6.
    Guan, D., Yi, X., Ding, S. et al., Lie algebraic method for vibrational and rotational transitions in inelastic collisions of a molecule with a solid surface,Chem. Phys., 1997, 218: 1.CrossRefGoogle Scholar
  7. 7.
    Guan, D., Ding, S., Yang, B. et al., A Lie algebraic approach to the collinear collisions between two diatomic molecules,Int. J. Quantum Chem., 1997, 69: 168.Google Scholar
  8. 8.
    Guan, D., Yi, X., Ding, S. et al., Dynamical Lie algebraic description of reactive collisions,J. Mol. Sci. (in Chinese), 1997, 13: 135.Google Scholar
  9. 9.
    Duff, J. W., Truhlar, D. G., Exact quantum mechanical reaction probabilities for the collinear H+H2 reaction on a Porter-Karplus potential energy surface,Chem. Phys. Lett., 1973, 23: 327.CrossRefGoogle Scholar
  10. 10.
    Johnston, H. S., Pam, C., Activation energies from bond energies (I)—Hydrogen transfer reactions,J. Am. Chem. Soc., 1963, 85: 2544.CrossRefGoogle Scholar
  11. 11.
    Kuppermann, A., A useful mapping of triatomic potential energy surfaces,Chem. Phys. Lett., 1975, 32: 374.CrossRefGoogle Scholar
  12. 12.
    Yi, X., Ma, L.,Methods of Mathematical Physics in Chemistry and Biology (in Chinese)., Ji’nan: Shandong University Press, 1991.Google Scholar
  13. 13.
    Porter, R. N., Karplus, M., Potential energy surface for H3,J. Chem. Phys., 1964, 40: 1105.CrossRefGoogle Scholar
  14. 14.
    Johnson, R. E.,Introduction to Atomic and Molecular Collisions, New York: Plenum Press, 1982.Google Scholar

Copyright information

© Science in China Press 1998

Authors and Affiliations

  • Daren Guan
    • 1
  • Xizhang Yi
    • 1
  • Shiliang Ding
    • 2
  • Benhui Yang
    • 1
  • Dongming Hua
    • 2
  1. 1.Institute of Theoretical ChemistryShandong UniversityJi’nanChina
  2. 2.Department of PhysicsShandong Normal UniversityJi’nanChina

Personalised recommendations