Group-Theoretical Treatment of Pseudo-Jahn-Teller Systems

  • Martin BrezaEmail author
Part of the Progress in Theoretical Chemistry and Physics book series (PTCP, volume 23)


According to Jahn-Teller (JT) theorem any nonlinear arrangement of atomic nuclei in electron degenerate state (except an accidental and Kramers degeneracy) is unstable. Pseudo-JT systems are treated as an analogy of JT theorem for pseudo-degenerate electron states. Stable nuclear arrangements of lower energy of such systems correspond to the minima of their potential energy surfaces (PES). In large systems the analytical description of their PES is too complicated and a group-theoretical treatment must be used to describe their stable structures. This may be based either on JT active coordinates– as in the epikernel principle– or on the electron states– as in the method of step-by-step descent in symmetry. This review explains the basic terms of group theory (especially of point groups of symmetry) and potential energy surfaces (extremal points and their characteristics) as well as the principles of group-theoretical methods predicting the extremal points of JT systems– the method of epikernel principle (based on JT active coordinates) and the method of step-by-step descent in symmetry (based on a consecutive split of the degenerate electron states). Despite these methods have been elaborated for the case of electron degeneracy, they are applicable to pseudo-degenerate electron states as well. The applications of both methods to pseudo-JT systems are presented on several examples and compared with the published results.


Electron State Potential Energy Surface Ground Electron State Excited Electron State Symmetry Operation 
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.



Slovak Grant Agency VEGA (Project No. 1/0127/09) is acknowledged for financial support.


  1. 1.
    Jahn HA, Teller E (1937) Proc R Soc Lond A 161:220CrossRefGoogle Scholar
  2. 2.
    Jahn HA (1938) Proc R Soc Lond A 164:117CrossRefGoogle Scholar
  3. 3.
    The Kramers degeneracy theorem states that the energy levels of systems with an odd number of electrons remain at least doubly degenerate in the presence of purely electric fields (i.e. no magnetic fields). Kramers HA (1930) Kon Acad Wet Amsterdam 33:959Google Scholar
  4. 4.
    Bersuker IB (2006) The Jahn-Teller effect. Cambridge University Press, LondonCrossRefGoogle Scholar
  5. 5.
    Ceulemans A, Beyens D, Vanquickenborne LG (1984) J Am Chem Soc 106:5824CrossRefGoogle Scholar
  6. 6.
    Ceulemans A (1987) J Chem Phys 87:5374CrossRefGoogle Scholar
  7. 7.
    Ceulemans A, Vanquickenborne LG (1989) Struct Bond 71:125Google Scholar
  8. 8.
    Breza M (2009) In: Koeppel H, Yarkoni DR, Barentzen H (eds) The Jahn-Teller-Effect. Fundamentals and implications for physics and chemistry, Springer Series in Chemical Physics, vol 97. Springer, Berlin, p 51Google Scholar
  9. 9.
    Pelikán P, Breza M (1985) Chem Zvesti 39:255Google Scholar
  10. 10.
    Breza M (1990) Acta Crystallogr B 46:573CrossRefGoogle Scholar
  11. 11.
    Breza M (2002) J Mol Struct Theochem 618:165CrossRefGoogle Scholar
  12. 12.
    Breza M (2003) Chem Phys 291:207CrossRefGoogle Scholar
  13. 13.
    Breza (1991) Chem Pap 45:473Google Scholar
  14. 14.
    Salthouse JA, Ware MJ (1972) Point group character tables and related data. Cambridge University Press, LondonGoogle Scholar
  15. 15.
    Boča R, Breza M, Pelikán P (1989) Struct Bond 71:57Google Scholar
  16. 16.
    Zlatar M, Schläpfer C-W, Daul C (2009) In: Koeppel H, Yarkoni DR, Barentzen H (2009) The Jahn-Teller-effect. Fundamentals and implications for physics and chemistry, Springer Series in Chemical Physics, vol 97, Springer, Berlin/Heidelberg, pp 131–165Google Scholar
  17. 17.
    Bruyndockx R, Daul C, Manoharan PT, Deiss E (1997) Inorg Chem 36:4251CrossRefGoogle Scholar
  18. 18.
    Zlatar M, Schläpfer C-W, Fowe EP, Daul C (2009) Pure Appl Chem 81:1397CrossRefGoogle Scholar
  19. 19.
    Hatanaka M (2009) J Mol Struct (Theochem) 915:69CrossRefGoogle Scholar
  20. 20.
    Jiang Q, Rittby CML, Graham WRM (1993) J Chem Phys 99:3194CrossRefGoogle Scholar
  21. 21.
    Yamamoto S, Saito S (1994) J Chem Phys 101:5484CrossRefGoogle Scholar
  22. 22.
    Yamagishi H, Taiko H, Shimogawara S, Murakami A, Noro T, Tanaka K (1996) Chem Phys Lett 250:165CrossRefGoogle Scholar
  23. 23.
    Halvick P (2007) Chem Phys 340:79CrossRefGoogle Scholar
  24. 24.
    Wörner HJ, Merkt F (2007) J Chem Phys 127:034303Google Scholar
  25. 25.
    Atanasov M, Schönherr (2002) J Mol Struct (Theochem) 592:79CrossRefGoogle Scholar

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© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Physical ChemistrySlovak Technical UniversityBratislavaSlovakia

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