AN ANALYTICAL MODEL FOR THE H-CIRCLE-TIMES(H-CIRCLE-PLUS-G) JAHN-TELLER SYSTEM

The H x (h + g) Jahn-Teller (JT) problem is investigated analytically using a unitary transformation method. Minimization of the adiabatic e nergy surface for this problem results in wells of either D-5d or D-3d symmetry, depending on the coupling strengths. The dynamic JT problem is then solved in the tunnelling regime using projection operators to find symmetrized combinations of the states associated with the wells . By analogy to other IT systems, the ground state would be expected t o have the same degeneracy as the original: orbital state, and thus to be an I I-type quintet. However, it is found that there are a range o f couplings strengths for the g and h modes for which the tunnelling g round state for the D-3d wells can be an A-type singlet. A similar res ult was recently found for the pure H x h JT system. It is also found that for D-3d wells, the limiting value of the tunnelling splitting be tween the H and A states for a pure H x g system tends to 2 (h) over b ar omega in weak coupling, whilst for a pure H x h system it tends to (h) over bar omega. For systems coupled to both modes, the value of th e tunnelling splitting strongly depends upon which of the two modes is dominant. Both the level ordering in strong coupling and the anomalou s behaviour in weak coupling can be shown to be fundamental symmetry p roperties of these IT systems, and not consequences of the details of our model. The JT systems studied here are possible models for the gro und state of the cation C-60(+) and for an excited state of the anion C-60(-).