Jahn-Teller distortions considered as steady state bifurcations

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 Hj subset of G. In order to find such distortion modes, the trace formula arising from bifurcation theory is applied to all subgroups Hj of G to give a sum of irreducible representations Gamma(G -> Hj) corresponding to the possible distortion modes of G to Hj. These subgroups Hj correspond to epikernel subgroups of G for any irreducible representation of G found in Gamma(G -> Hj). This method has been applied to Jahn-Teller distortions of square (D-4h), octahedral (O-h), and icosahedral (I-h) molecules leading to lower symmetry structures.