FURTHER-STUDIES OF ANISOTROPY IN THE T-1U-CIRCLE-TIMES-H(G) JAHN-TELLER SYSTEM

In the linear T(1u)xh(g) Jahn-Teller system, the adiabatic potential e nergy surface (APES) is a trough. However, in real systems, quadratic coupling will be present, which warps the APES to give wells of either D-3d or D-5d symmetry. The degeneracy of the vibrations within the we lls is also lifted. This anisotropy has recently been investigated in the T(1u)xh(g) system, and expressions for the frequencies in both typ es of wells obtained in the strong coupling limit using the method of Opik and Pryce. A scale transformation procedure was then used to inco rporate these results into expressions for the states in the wells and their associated energies. However, this calculation did not allow fo r second-order perturbation effects and is only valid in the strong co upling limit. In this paper, a revised scale transformation procedure is developed for the D-5d wells, which allows expressions for the anis otropic frequencies to be obtained without employing the Opik and Pryc e procedure. An expression is obtained for the phonon overlap that is correct to second-order and is not restricted to the strong coupling l imit. Results are then obtained for the ground-state energies and inve rsion splitting. For D-3d wells, the previous results are improved by application of a modified scale transformation procedure and overlaps correct to second order obtained. The results obtained in this paper a re of interest in studies of the C-60(-) anion state of the C-60 molec ule, which is known to occupy a T-1u orbital ground state.