No abstract

In C60 molecules, the lowest unoccupied molecular orbital has T1u symmetry. The orbital is easily occupied by an electron through molecular inner excitation or doping and becomes an active Jahn-Teller (JT) electronic state. The T1u-hg- JT system is formed by the coupling of such an electronic state to a five-fold degenerate hg mode. The linear vibronic coupling in the system forms a trough on the adiabatic potential surface of the system, but D5d and D3d minima will be warped while considering the quadratic vibronic coupling. Phonon states in minima will have anisotropic effects and the vibrational frequencies should be different in different directions. This phenomenon will further affect the energy distribution, phonon overlap and tunneling effect in the system. The anisotropic effect is carefully studied in detail for D3d-minima. The energies and vibrational frequencies are calculated using unitary shift transformation, pick-Pryce method, scale transformation and energy minimization procedure. The energy gap and the variation of perturbation energy in minima are obtained in this paper and the same physical quantities in trough are derived through changing the values of the quadratic coupling constants.

Jahn-Teller (JT) systems contain typically a set of mutually equivalent energy minima in the lowest adiabatic potential energy surface. When one electron occupies the three degenerate electronic states in C60 molecules, the electronic states with a symmetry of T1u and the five degenerate vibrational states with a symmetry of hg will be interacted and form the T1uhg JT system. When the non-linear vibronic interaction is considered, the JT system will contain the D5d minima and D3d maxima, and vice versa. In this paper, on the basis of unitary shift transformation, the modified scale transformation is introduced and the anisotropic phenomenon is studied in the D5d minima for the T1uhg JT system. The results are incorporated into the expressions for the states in the D5d wells and their associate energies. The symmetries and their corresponding energies in the D5d wells in the electronic space are obtained. For finite couplings, the phonon overlap between wells and inversion splitting are also studied. The results obtained in this paper not only show that the anisotropic effect has a significant influence on the above physical quantities, but also are of interest in the studies of anion states (C-60) of the C60 molecules and other C60 anion-related materials.

A general form of Hamiltonian for vibronic Jahn-Teller systems is derived on the basis of adiabatic approximation and group theory. The electronic operators and active Jahn-Teller modes appearing in a vibronic system are also discussed. Further calculations of excited states in minima are carried out using unitary transformation method and energy minimization procedure. The results of energy splitting for an electronic triplet Jahn-Teller system are analyzed and compared with particular reference to tetrahedral and its related crystal systems. It is shown that the lift of electronic degeneracy can be quantitatively described by the decomposition of irreducible representations of related group and subgroups.