ANALYSIS OF THE T-1U-CIRCLE-TIMES-H(G) JAHN-TELLER SYSTEM AS A MODEL FOR C-60 MOLECULES

The T(1u)xh(g) Jahn-Teller system is studied analytically on an icosahedral cluster model. This system is a model for the effects of vibronic coupling in the C-60 molecule. Vibronic coupling is very important in this system because both the electronic and vibrational states are of high symmetry. The method employed is to apply a unitary transformation to the Hamiltonian for the system in order to obtain expressions for the states associated with minima in the potential-energy surface. Quadratic coupling terms are included in the Hamiltonian in order to obtain distinct minima located at either pentagonal (D-5h) or trigonal (D-3h) positions in Q space. These states are good eigenstates of the system as a whole in very strong coupling. For finite couplings, projection operator techniques are then used to obtain explicit expressions for the vibronic ground and inversion states from these basis states for both the pentagonal and trigonal cases. Expressions for the corresponding energies are then derived as a function of the coupling constants. These results are necessary in order to be able to calculate further properties of the system, such as Jahn-Teller reduction factors, which are in turn necessary to explain experimental data on these systems.