VIBRONIC COUPLING EFFECTS IN THE C-60 MOLECULE - STUDIES OF T-CIRCLE-TIMES-H AND H-CIRCLE-TIMES-H JAHN-TELLER SYSTEMS

The C-60 molecule is known to exhibit a strong electron-phonon interac tion. Hence studies of the Jahn-Teller (JT) effect are important in un derstanding the properties of C-60 and related molecules. Many Jahn-Te ller (JT) effects are possible in the icosahedral (I-h) symmetry which the C-60 molecule possesses. The high degeneracies that can occur in this symmetry generate problems which are not seen in other systems. I n particular, the h-mode is found to be non-simply reducible in the li near H X h and quadratic T X h JT systems. Consequently, the choice of Clebsch-Gordan matrices and associated coupling constants is not uniq ue. Minima in the potential energy surface of either D-3d or D-5d symm etry are found in both of these systems. It is possible to make a choi ce of matrices such that the minima of one symmetry depend on one of t he h-type coupling constants, and the minima of the other symmetry on the other coupling constant. Either type of minima can be absolute min ima, depending upon the values of the coupling constants. The position s of the minima and their associated states can be determined using th e transformation method developed previously by the current authors fo r cubic symmetry. Symmetry-adapted states, which allow for tunnelling of the system between equivalent minima, can be obtained in both cases , and their energies calculated analytically. For the case of D-3d min ima in the H X h JT problem, we find that above a certain coupling str ength, the A type 'inversion' level has a lower energy than the H-stat e. This is the first known example of a linear JT system in which the JT effect alters the symmetry of the ground state. This result has bee n verified using arguments concerning Berry's phase, and is not simply a result of the details of the calculation or the method used.