Continuous group invariances of linear Jahn-Teller systems. II. Extension and application to icosahedral systems
- 29 February 1980
- journal article
- Published by IOP Publishing in Journal of Physics C: Solid State Physics
- Vol. 13 (6) , 1029-1042
- https://doi.org/10.1088/0022-3719/13/6/013
Abstract
For pt.I see J. Phys. A (GB), vol.11, no.6, p.1045 (1978). Using cubic systems as illustrative examples the author derives and extends previous results on the invariances of Jahn-Teller systems using a more direct method. The theory is more general in being applicable to all simple-phase real-character physical symmetry groups. It is shown how various continuous groups can be generated by electronic operators and that if some set of even operators (those taking part in the Jahn-Teller effect) is closed under commutation with the generators of such a group then an invariant model can be set up by coupling modes equally. If all the even modes are coupled equally then the resulting model is invariant under SO(n) or Sp(n) where n is the degeneracy of the electronic state. The results are used to study the invariances of icosahedral Jahn-Teller systems. For a fivefold degenerate electronic state, SO(5) and SO(3) invariant models can be produced. For a fourfold degenerate state, an SO(4) invariant model can be produced. The single mode, threefold degenerate state model is invariant under SO(3).Keywords
This publication has 11 references indexed in Scilit:
- Continuous group invariances of linear Jahn-Teller systemsJournal of Physics A: General Physics, 1978
- The Jahn-Teller effect in icosahedral molecules and complexesTheoretical Chemistry Accounts, 1978
- The Jahn-Teller effect in a 8quartet: equal coupling to and 2vibrationsJournal of Physics C: Solid State Physics, 1977
- Some fractional parentage coefficients for R5and their application to T⊗(ϵ + τ2) Jahn-Teller systems such as F and F+centresJournal of Physics C: Solid State Physics, 1976
- Coupling coefficients and tensor operators for chains of groupsPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1975
- Lie Groups and the Jahn–Teller EffectCanadian Journal of Physics, 1974
- Irreducible tensors in the octahedral spinor groupMolecular Physics, 1973
- The Jahn-Teller effect in a p state equally coupled to Egand T2gvibrationsJournal of Physics C: Solid State Physics, 1971
- Magneto-Optic Study of the Jahn-Teller Effect in the Excited Level of theF+Centers in CaOPhysical Review B, 1971
- Some simple R5 Wigner coefficients and their applicationNuclear Physics, 1965