Strain in Jahn–Teller systems as a precursor to co-operative interactions

The effect of co-operative Jahn–Teller interactions on a Jahn–Teller system is modelled using a linear coupling Hamiltonian together with an applied strain. Two cases are treated: the relatively simple E ⊗ e system, and the more complicated p2 ⊗ h system, which may be used to model C 60 2 - fullerene ions. In the E ⊗ e case, the Hamiltonian can be separated into a part that represents vibrations across a trough in the lowest adiabatic potential energy surface, and a part that represents rotations around the trough. The rotational part results in a wave function that can be conveniently expressed in terms of Mathieu functions, or alternatively as a Frobenius series. For the p2 ⊗ h system, the Hamiltonian can again be separated into vibrational and rotational parts, and the rotational part can be solved in terms of Frobenius series. The energies of the solutions are presented graphically and interpreted by comparison with existing results in the literature that assume the strain is sufficiently strong to convert the rotation to a vibration.