Analysis of torsional vibrations of an ethane molecule


Based on the solution for the Mathieu equation, we obtained wave functions for the internal rotation of an ethane molecule that satisfy the symmetry properties of the group G36. We calculated the frequency of the principal torsional transition (273 cm−1). The types of symmetry of the energy levels and transition probabilities in IR and Raman spectra are determined. We note drawbacks of divisible permutable-inverse nuclear groups and the groups of molecular symmetry associated with their construction, as well as difficulties that appear when equivalent rotations are used. The possibility of avoiding the application of an extended group is indicated.

This is a preview of subscription content, access via your institution.


  1. 1.

    H. C. Longuet-Higgins, Molecular Phys.,6, 445 (1963).

    Article  Google Scholar 

  2. 2.

    F. Bunker, Symmetry of Molecules and Molecular Spectroscopy [Russian translation], Vol. 2, Moscow (1981).

  3. 3.

    M. V. Vol’kenshtein, M. A. El’yashevich, and B. I. Stepanov, Vibrations of Molecules [in Russian], Moscow (1949).

  4. 4.

    W. J. Orville-Thomas (ed.), Internal Rotation of Molecules [Russian translation], Moscow (1977).

  5. 5.

    W. G. Fateley and F. A. Miller, Spectrochim. Acta,17, 857 (1961).

    Article  Google Scholar 

  6. 6.

    W. G. Fateley and F. A. Miller, Spectrochim. Acta,19, 611 (1963).

    Article  Google Scholar 

  7. 7.

    A. Charlsby, Proc. Phys. Soc.,54, 471 (1942).

    Article  Google Scholar 

  8. 8.

    J. K. G. Watson, Can. J. Phys.,43, 1996 (1965).

    MATH  ADS  Google Scholar 

  9. 9.

    N. V. McLachlan, Theory and Applications of Mathieu Functions [Russian translation], Moscow (1957).

  10. 10.

    J. Mathews and R. Walker, Mathematical Methods of Physics [Russian translation], Moscow (1972).

  11. 11.

    J. T. Hougen, Can. J. Phys.,42, 1920 (1964).

    Google Scholar 

  12. 12.

    D. Papousek and M. R. Aliev, Molecular Vibrational-Rotational Spectra, Prague (1982).

  13. 13.

    D. R. Lide, Jr., J. Chem. Phys.,29, 1426 (1958).

    Article  Google Scholar 

  14. 14.

    K. A. Strong and R. M. Brugger, J. Chem. Phys.,47, 421 (1967).

    Article  Google Scholar 

  15. 15.

    S. Weiss and G. E. Leroi, J. Chem. Phys.,48, 962 (1968).

    Article  Google Scholar 

  16. 16.

    M. R. Rasovskii, G. V. Khovrin, and N. P. Khomich, Izv. Timiryazev. Sel’sk.-Khoz. Akad.,2, 181 (1991).

    Google Scholar 

  17. 17.

    G. F. Lozenko, M. R. Rasovskii, I. V. Rybal’chenko, and G. V. Khovrin, Izv. Timiryazev. Sel’sk.-Khoz. Akad.,5, 182 (1991).

    Google Scholar 

Download references


Additional information

Belarusian State University, 4, F. Skorina Ave., Minsk, 220050, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 1, pp. 26–31, January–February, 1997.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Shundalov, M.B., Pitsevich, G.A., Bel’skii, A.M. et al. Analysis of torsional vibrations of an ethane molecule. J Appl Spectrosc 64, 22–28 (1997).

Download citation

Key words

  • symmetry group
  • torsional transition
  • Mathieu equation
  • IR spectrum
  • Raman spectrum
  • ethane