Soviet Physics Journal

, Volume 30, Issue 8, pp 643–649 | Cite as

Calculation of the intensities of the vibrational-rotational lines of polyatomic molecules using the formalism of irreducible tensor systems

  • V. N. Savel'ev
  • O. N. Ylenikov
Optics and Spectroscopy


The theory of irreducible tensor systems is used to obtain general formulas for the dependence of the matrix elements of the transformed vibrational—rotational dipole moment on the rotational quantum numbers. The relations obtained are valid for molecules of arbitrary symmetry and can take into account all possible intramolecular effects and interactions (resonances, vibration—rotation interactions, splitting, etc.). As illustrations we consider molecules of the type XY4 (symmetry Td) and XY2 (symmetry C2v).


Matrix Element Dipole Moment Quantum Number General Formula Polyatomic Molecule 
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.

Literature cited

  1. 1.
    H. H. Nielsen, Rev. Mod. Phys.,23, 90 (1951).Google Scholar
  2. 2.
    G. Amat, H. H. Nielsen, and G. Tarrago, Rotation-Vibration of Polyatomic Molecules, Dekker, New York (1971).Google Scholar
  3. 3.
    U. Fano and G. Racah, Irreducible Tensorial Sets, Academic Press, New York (1959).Google Scholar
  4. 4.
    M. Hamermesh, Group Theory and Its Application to Physical Problems, Addison-Wesley, Reading, Mass.; Pergamon Press, Oxford (1962).Google Scholar
  5. 5.
    R. M. Good, Atmospheric Radiation. I. Theoretical Foundations [Russian translation], Mir, Moscow (1966).Google Scholar
  6. 6.
    A. E. Cheglokov and O. N. Ulenikov, J. Mol. Spectrosc.,110, 64 (1985).Google Scholar
  7. 7.
    O. N. Ulenikov, Avtoref. Dokt. Diss., Tomsk (1985).Google Scholar
  8. 8.
    D. T. Sviridov, R. K. Sviridova, and Yu. F. Smirnov, Optical Spectra of Transition Metal Ions in Crystals [in Russian], Nauka, Moscow (1976).Google Scholar
  9. 9.
    V. N. Savel'ev, O. N. Ulenikov, and A. E. Cheglokov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 4, 77 (1987).Google Scholar
  10. 10.
    J. M. Flaud and C. Camy-Peyret, J. Mol. Spectrosc.,55, 278 (1975).Google Scholar
  11. 11.
    A. D. Bykov, Yu. S. Makushkin, V. I. Serdukov, and O. N. Ulenikov, J. Mol. Spectrosc.,105, 397 (1984).Google Scholar
  12. 12.
    A. D. Bykov, V. P. Lopasov, Yu. S. Makushkin, L. N. Sinitsa, O. N. Ulenikov, and V. E. Zuev, J. Mol. Spectrosc.,94, 1 (1982).Google Scholar
  13. 13.
    Yu. S. Makushkin, V. N. Savel'ev, et al., Zh. Prikl. Spektrosk.,38, 671 (1983).Google Scholar
  14. 14.
    G. Guelachvili, O. N. Ulenikov, and G. A. Ushakova, J. Mol. Spectrosc.,108, 1 (1984).Google Scholar
  15. 15.
    G. Guelachvili, O. V. Naumenko, and O. N. Ulenikov, Appl. Opt.,23, 2962 (1984).Google Scholar
  16. 16.
    A. E. Cheglokov, Yu. A. Kuritsn, E. P. Snegirev, O. N. Ulenikov, and G. V. Vedeneeva, Mol. Phys.53, 287 (1984).Google Scholar
  17. 17.
    L. R. Brown, J. Mol. Spectrosc.,96, 94 (1982).Google Scholar

Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • V. N. Savel'ev
    • 1
  • O. N. Ylenikov
    • 1
  1. 1.Institute of Atmospheric OpticsSiberian Branch of the Academy of Sciences of the USSRUSSR

Personalised recommendations