A Noncommuting-generator approach to molecular symmetry

  • O. Sonnich Mortensen
Conference paper
Part of the Structure and Bonding book series (STRUCTURE, volume 68)


A novel method of treating point group symmetry is presented. It is based on finding common eigenfunctions to sets of non-commuting operators, the operators being suitably chosen generators for the point groups. The character tables of the conventional method are replaced by eigenvalue tables, that are no more complex than character tables but allow straight forward calculation of matrixelements (Wigner-Eckart theorem). Half-integer spin is treated as simply as integer spin, without introducing the socalled double groups.


Commutation Relation Point Group Coupling Coefficient Symmetry Operation Character Table 
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.
    Tinkham, M.: Group Theory and Quantum Mechanics, McGraw-Hill, New York 1964Google Scholar
  2. 2.
    Wigner, E. P.: Göttingen Nachrichten, Math.-Physik. KI. 546 (1932)Google Scholar
  3. 3.
    Bethe, H.: Ann. der Physik 3, 133 (1929)Google Scholar
  4. 4.
    Opechowski, W.: Physica 7, 552 (1940)CrossRefGoogle Scholar
  5. 5.
    Mortensen, O. Sonnich, Hassing, S.: in Advances in Infrared and Raman spectroscopy (ed. Clark, R. J. H., Hester, R. E.) Heyden, London 1979, p.1Google Scholar
  6. 6.
    Henry, B R., Tarr, A. W., Mortensen, O. Sonnich, Murphy W. F., Compton, D. A. C.: J. Chem. Phys. 79, 2583 (1983)CrossRefGoogle Scholar
  7. 7.
    Golebiewski, A.: Acta Phys. Pol. A37, 871 (1970)Google Scholar
  8. 8.
    Golebiewski, A.: Mol. Phys. 20, 481 (1971)CrossRefGoogle Scholar
  9. 9.
    Altmann, S.: Phil. Trans. Roy. Soc. (London) A255, 216 (1963)Google Scholar
  10. 10.
    Altmann, S.: Rev. Mod. Phys. 35, 641 (1963)CrossRefGoogle Scholar
  11. 11.
    Altmann, S.: Induced Representations in Crystals and Molecules, Academic Press, London 1977Google Scholar
  12. 12.
    Hougen, J. T.: J. Chem. Phys. 37, 1433 (1962)CrossRefGoogle Scholar
  13. 13.
    Longuet-Higgins, H. C.: Mol. Phys. 6, 445 (1963)CrossRefGoogle Scholar
  14. 14.
    Bunker, P. R.: in Vibrational Spectra (ed. Durig, J. R.) Elsevier, Amsterdam 1975, p. 1Google Scholar
  15. 15.
    Seitz, F.: Z. Krist. 88, 433 (1934); 90, 289 (1935); 91, 336 (1935); 94, 100 (1936)Google Scholar
  16. 16.
    Kramers, H. A.: Proc. Amsterdam Acad. 33, 959 (1930)Google Scholar
  17. 17.
    Griffith, J. S.: The Irreducible Tensor Method for Molecular Symmetry Groups, Prentice-Hall, New York 1962Google Scholar
  18. 18.
    Harnung, S. E.: Mol. Phys. 26, 473 (1973)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • O. Sonnich Mortensen
    • 1
  1. 1.Fysisk InstitutOdense UniversitetOdense MDenmark

Personalised recommendations