Advanced Group Theoretical Techniques and Their Application to Magnetic Circular Dichroism

  • Susan B. Piepho
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 43)


High symmetry coupling coefficients and the equations derived from them using the powerful methods of Racah algebra greatly simplify quantum mechanical calculations in high symmetry systems. All possible information based on symmetry alone is quickly obtained and thus the essential physical problem to be solved is uncovered. While the equations at first glance may have a horrifying complexity, they are actually quite simple to use. Wave functions need not be constructed and results may frequently be obtained by looking up a few coefficients in the appropriate tables.


Matrix Element Magnetic Circular Dichroism Reduce Matrix Element Irreducible Tensor Repeated Representation 
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. Griffith, J.S., The Irreducible Tensor Method for Molecular Symmetry Groups (Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1962 ).Google Scholar
  2. Dobosh, P.A., Phys. Rev. A 5, 2376 (1972). Dobosh’s \(W\left( {\begin{array}{*{20}{c}} {{a_i}\;b\,{c_l}}\\ {{d_k}\;e\,{f_j}} \end{array}} \right)\) is identical to our \(W{\left( {\begin{array}{*{20}{c}} {a\;b\,c}\\ {\;d\,e\,f} \end{array}} \right)_{ijkl}} \) Google Scholar

Several corrections to Ref. 2 are given in Ref 3:

  1. Dobosh, P.A., Mol. Phys. 27, 689 (1974).ADSCrossRefGoogle Scholar
  2. Fano, U. and Racah, G., Irreducible Tensorial Sets (Academic Press, Inc., New York, 1959 ).Google Scholar
  3. Piepho, S.B. and Schatz, P.N., Group Theory in Spectroscopy with Applications to Magnetic Circular Dichroism (John Wiley & Sons, to be published). Notation and definitions differ somewhat from those contained in the present article. Standard definitions and notation agreed on at the NATO conference are used in the book.Google Scholar
  4. Griffith, J.S., The Theory of Transition Metal Ions (Cambridge University Press, 1961 ).Google Scholar
  5. Derome, J.-R. and Sharp, W.T., J. Math. Phys. 6, 1584 (1965).MathSciNetADSMATHCrossRefGoogle Scholar
  6. Stephens, P.J., Adv. Chem. Phys. 35, 197 (1976).CrossRefGoogle Scholar
  7. Stephens, P.J., Suetaka, W. and Schatz, P.N., J. Chem. Phys. 44, 4592 (1966).ADSCrossRefGoogle Scholar
  8. Piepho, S.B., Inskeep, W.H., Schatz, P.N., Preetz, W. and Homborg, H., Mol. Phys. 30, 1569 (1975).ADSCrossRefGoogle Scholar
  9. Schatz, P.N., McCaffery, A.J., Suetaka, W., Henning, G.N., Ritchie, A.B. and Stephens, P.J., J. Chem. Phys. 45, 722 (1966).ADSCrossRefGoogle Scholar
  10. Piepho, S.B., Lester, T.E., McCaffery, A.J., Dickinson, J.R. and Schatz, P.N., Mol. Phys. 19, 781 (1970). The C0/D0 values in this paper use an orbital reduction factor, k, which multiplies (87) by k = 0.85. In our calculation in the text we assume k = 1.Google Scholar
  11. [13]
    Denning, R.G. and Spencer, J.A., Symposium of the Faraday Society 3, 84 (1969).CrossRefGoogle Scholar
  12. [14]
    Edmonds, A.R., Angular Momentum in Quantum Mechanics (Princeton University Press, Princeton, New Jersey, 1960 ).Google Scholar
  13. [15]
    Butler, P.H., Phil. Trans. Royal Soc. A 277, 545 (1975).ADSMATHCrossRefGoogle Scholar
  14. [16]
    Ballhausen, C.J., Introduction to Ligand Field Theory ( McGraw-Hill Book Company, New York, 1962 ).MATHGoogle Scholar

Copyright information

© Plenum Press, New York 1979

Authors and Affiliations

  • Susan B. Piepho
    • 1
  1. 1.Department of ChemistryRandolph-Macon Woman’s CollegeLynchburgUSA

Personalised recommendations