Jahn–Teller distortions considered as steady state bifurcations

Abstract

The steady state bifurcation model can be used to determine the Jahn–Teller distortion modes of a molecule having symmetry point group G to lower symmetry structures having symmetry point groups H _j  ⊂ G. In order to find such distortion modes, the trace formula arising from bifurcation theory is applied to all subgroups H _j of G to give a sum of irreducible representations Γ(G → H _j ) corresponding to the possible distortion modes of G to H _j . These subgroups H _j correspond to epikernel subgroups of G for any irreducible representation of G found in Γ(G → H _j ). This method has been applied to Jahn–Teller distortions of square (D _{4 h} ), octahedral (O _h ), and icosahedral (I _h ) molecules leading to lower symmetry structures.

Acknowledgement

The author thanks the US National Science Foundation for support of this work under grant CHE-0209857.