Anisotropy and the inversion splitting in the T-1u circle times h(g) Jahn-Teller system

We present an analysis of the T(lu)xh(g) Jahn-Teller (JT) system in which both possible h-type quadratic terms are considered. It is well known that this results in pentagonal (D-5d) or trigonal (D-3d) minima on the potential energy surface, depending on the magnitudes of the coupling constants. Although the positions of the minima with quadratic couplings are known, the anisotropic effects which occur due to the lifting of the degeneracy of the h-vibrations by the quadratic coupling have not been studied before. Such effects have previously been found to be important in cubic systems. We investigate the nature of the minima by evaluating the curvature of the potential energy surface, and hence we determine the frequencies of the local vibrational modes in the strong-coupling limit as a function of the quadratic coupling strengths for the first time. We find that, in the linear coupling limit, the frequency of one of the e-modes at the minima tends to zero. This is as expected because, in this limit, the minimum-energy surface is a trough joining the D-3d and D-5d points. A scale transformation method is then used, which allows the anisotropy effect to be incorporated into the states associated with the D-5d wells. States having the required icosahedral symmetry of the system as a whole are then written down in terms of the anisotropic states. Specific results will be given for the dependence of the inversion splitting on the anisotropy. The new states are of significance because they are necessary for the calculation of further properties of these systems, such as reduction factors. The system is also a possible model for the ground state of the C-60(-) anion.