Advertisement

Theoretica chimica acta

, Volume 32, Issue 1, pp 27–40 | Cite as

Symmetry coupling coefficients for point groups and the importance of Racah's Lemma for the standardization of phase

  • Edgar König
  • Stefan Kremer
Commentationes

Abstract

Useful approaches to the calculation of symmetry coupling coefficients 〈Г1 γ1Г2/2|Гγb〉 are reviewed. Since a common phase factor always remains undetermined for each trio ofГ1,Г2, andГ, a unique standardization of phase is proposed by the requirement, in Racah's lemma, (j1Г1a1,j2Г2a2|j Г ab) ≧ 0and real. In conjunction with the basis relations and the phase convention for Wigner coefficients, a novel method is suggested for the calculation of symmetry coupling coefficients in the group G from those in the subgroupGSU(2) orR3. The results apply in full generality to any point groupG, single or double group.

Key words

Coupling coefficients Lemma of Racah Phase standardization 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Edmonds, A. R.: Angular momentum in quantum mechanics. Princeton University Press: 1960Google Scholar
  2. 2.
    Rose, M. E.: Elementary theory of angular momentum. John Wiley 1957Google Scholar
  3. 3.
    Wigner, E. P.: Group theory and its application to the quantum mechanics of atomic spectra. Academic Press 1959Google Scholar
  4. 4.
    Fano, U., Racah, G.: Irreducible tensorial sets. Academic Press 1959Google Scholar
  5. 5.
    Condon, E. U., Shortley, G. H.: The theory of atomic spectra. Cambridge University Press 1935Google Scholar
  6. 6.
    Tanabe, Y., Sugano, S.: J. Phys. Soc. Japan9, 753 (1954)Google Scholar
  7. 7.
    Griffith, J. S.: The theory of transition metal ions. Cambridge University Press 1961Google Scholar
  8. 8.
    Griffith, J. S.: The irreducible tensor method for molecular symmetry groups. Prentice-Hall 1962Google Scholar
  9. 9.
    Koster, G. F., Dimmock, J. 0., Wheeler, R. G., Statz, H.: Properties of the thirty-two point groups.Google Scholar
  10. 10.
    Sugano, S., Tanabe, Y., Kamimura, H.: Multiplets of transition-metal ions in crystals. Academic Press 1970Google Scholar
  11. 11.
    Golding, R. M.: Mol. Phys.21, 157 (1971)Google Scholar
  12. 12.
    Harnung, S. E., Schäfer, C. E.: Struct. Bonding12, 201 (1972)Google Scholar
  13. 13.
    Koster, G. F.: Phys. Rev.109, 227 (1958)Google Scholar
  14. 14.
    Hollebone, B. R., Lever, A. B. P., Donini, J. C.: Mol. Phys.22, 155 (1971)Google Scholar
  15. 15.
    Kibler, M.: Int. J. Quantum Chem.3, 795 (1969)Google Scholar
  16. 16.
    König, E., Kremer, S.: Int. J. Quantum Chem., submittedGoogle Scholar
  17. 17.
    Racah, G.: Phys. Rev.76, 1352 (1949)Google Scholar
  18. 18.
    Schäffer, C. E., Jørgensen, C. E.: Mol. Phys.9, 401 (1965)Google Scholar
  19. 19.
    Schäffer, C. E.: Pure Appl. Chem.24, 361 (1970)Google Scholar
  20. 20.
    König, E., Kremer, S.: Theoret. Chim. Acta (Berl.), submittedGoogle Scholar

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • Edgar König
    • 1
  • Stefan Kremer
    • 1
  1. 1.Institute of Physical Chemistry IIUniversity of Erlangen-NürnbergErlangenGermany

Personalised recommendations