Inversion splittings and reduction factors for the H x (h x g) Jahn-Teller system

The H x (h x g) Jahn-Teller (JT) problem in icosahedral symmetry is analysed up to linear terms in the hamiltonian using an analytical unitary-transformation method. This unitary transformation results in states which are automatically vibronic, removing the need to multiply electronic states by displaced simple harmonic-oscillator functions. Minima on the energy surface of D5d and D3d symmetry are found, and the dynamic JT problem is solved for the case of D3d minima by introducing tunneling between different minima. Projection-operator techniques are used to find the required symmetrized tunneling states, allowing the corresponding inversion splitting and reduction factors to be calculated. The highest occupied molecular orbital (HOMO) in the fullerene C60 is of H symmetry, so that the work presented here represents a possible model for the ground state of the cation C601. (orig.)