Ligand trajectories for a degenerate Jahn–Teller system

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Abstract
The trajectories of the six ligands of the octahedral Jahn–Teller (JT) system T1⊗ (ε+τ2), in which the two modes ε and τ2 possess equal frequencies and are equally coupled to the electronic T1 state, are determined in the limit when the JT interaction is large compared to the kinetic energies of the ligands. They are found to correspond to a fast elliptical motion, characteristic of a classical harmonic oscillator, superposed on a slow circular rotational motion. The eccentricities, magnitudes of the major and minor axes, and directions of the normals to the planes of the ellipses change as the circular paths are followed. Elementary derivations are given for the energies of the rotational bands.