First- and second-order vibronic reduction factors are calculated analytically for the H⊗(g⊕h) Jahn-Teller system in Ih symmetry. Results are given as a function of the strength of the coupling of the H orbital to the vibrations of h and g symmetries. As the product systems H⊗g and H⊗h contain repeated representations, the calculations of many of the reduction factors are more complicated than in other systems. These complications and their implications are analysed in detail. This system models the ground state of hole-doped C60 material, which has possible applications for high-temperature superconductivity.

Analytical expressions for the vibronic states and energy spectrum of the icosahedral G ⊗ (g ⊕ h) Jahn-Teller system are derived. From these states, expressions for first-and second-order vibronic reduction factors are determined as a function of the strengths of the coupling of the G orbital to the g and h modes of vibration. The possibility of the vibronic ground state being a singlet A state, rather than the G state that would be expected in the absence of vibronic coupling, is explored. The reduction factors obtained provide a convenient basis for the modelling of spectra involving some of the excited states of the fullerene molecule C 60 and related ions.

By comparison with other systems, vibronic coupling between an h-type vibration and an H-type electronic level in a H⊗h Jahn–Teller system would be expected to result in a vibronic H-type ground state. However, it is already known that an A state can cross over the H state at a given coupling strength and become the ground state if the ground adiabatic potential energy surface contains minima of D3d symmetry. This is an unusual property of the H⊗h Jahn–Teller system. In this article, the physics behind the crossover is analyzed in terms of competition between tunneling paths between D3d wells of C1 and C2 symmetries. The H⊗h Jahn–Teller system is relevant to some fullerenes and other icosahedral complexes.

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