Russian Journal of Physical Chemistry B

, Volume 3, Issue 1, pp 24–29 | Cite as

The sums and densities of vibrational states in a system with a finite number of levels

  • M. L. Strekalov
Elementary Physicochemical Processes


An exact solution for the sums and densities of vibrational states in a system of “truncated” harmonic oscillators was obtained. Simple equations describing these results analytically were derived. Changes in these results caused by the inclusion of anharmonicity of vibrations were studied. The ability of the model to predict numbers of states was demonstrated for the example of NO2 molecules.


Partition Function Harmonic Oscillator Dissociation Energy Vibrational State Vibrational Level 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    E. E. Nikitin, Theory of Elementary Atomic-Molecular Processes in Gases (Khimiya, Moscow, 1970) [in Russian].Google Scholar
  2. 2.
    P. J. Robinson and K. A. Holbrook, Unimolecular Reactions (Wiley, New York, 1972; Mir, Moscow, 1975).Google Scholar
  3. 3.
    N. M. Kuznetsov, Kinetics of Monomolecular Reactions (Nauka, Moscow, 1982) [in Russian].Google Scholar
  4. 4.
    H. Eyring, S. H. Lin, and S. M. Lin, Basic Chemical Kinetics (Wiley, New York, 1980; Mir, Moscow, 1983).Google Scholar
  5. 5.
    E. W. Schlag and R. A. Sandsmark, J. Chem. Phys. 37(1), 168 (1962).CrossRefGoogle Scholar
  6. 6.
    M. Vestal, A. L. Wahrhaftig, and W. H. Johnston, J. Chem. Phys. 37(6), 1276 (1962).CrossRefGoogle Scholar
  7. 7.
    G. Z. Whitten and B. S. Rabinovich, J. Chem. Phys. 38(10), 2466 (1963).CrossRefGoogle Scholar
  8. 8.
    J. Troe, J. Chem. Phys. 66(11), 4758 (1977).CrossRefGoogle Scholar
  9. 9.
    T. Beyer and D. F. Swinehart, Commun. ACM 16, 379 (1973).CrossRefGoogle Scholar
  10. 10.
    S. E. Stein and B. S. Rabinovich, J. Chem. Phys. 58(6), 2438 (1973).CrossRefGoogle Scholar
  11. 11.
    J. R. Barker, J. Phys. Chem. 91(14), 3849 (1987).CrossRefGoogle Scholar
  12. 12.
    L. E. B. Börjesson, S. Nordholm, and L. L. Andersson, Chem. Phys. Lett. 186(1), 65 (1991).CrossRefGoogle Scholar
  13. 13.
    J. Troe, Chem. Phys. 190(2), 381 (1995).CrossRefGoogle Scholar
  14. 14.
    L. Ming, S. Nordholm, and H. W. Schranz, Chem. Phys. Lett. 248(3), 228 (1996).CrossRefGoogle Scholar
  15. 15.
    W. Forst, Chem. Phys. Lett. 262(5), 539 (1996).CrossRefGoogle Scholar
  16. 16.
    P. Parneix, N. T. Oanh, and P. Bréchignac, Chem. Phys. Lett. 357(1), 78 (2002).CrossRefGoogle Scholar
  17. 17.
    J. Riordan, An Introduction to Combinatorial Analysis (Wiley, New York, 1958; Inostrannaya Literatura, Moscow, 1963].Google Scholar
  18. 18.
    J. Riordan, Combinatorial Identities (Wiley, New York, 1968; Nauka, Moscow, 1982).Google Scholar
  19. 19.
    A. Delon and R. Jost, J. Chem. Phys. 95(8), 5686 (1991).CrossRefGoogle Scholar
  20. 20.
    A. Delon, R. Jost, and M. Lombardi, J. Chem. Phys. 95(8), 5701 (1991).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  • M. L. Strekalov
    • 1
  1. 1.Institute of Chemical Kinetics and Combustion, Siberian BranchRussian Academy of SciencesNovosibirskRussia

Personalised recommendations