Anisotropic effect on the vibronic reduction factors

The reduction factors p and q defined by Ham in the E ⊗ e JT system and their relation 2q − p = 1 have been well accepted and the concept of reduction factors is widely used in the studies of vibronic coupling. However, when the system is under the anisotropic conditions, the reduction factors and their relation will change accordingly. The first-order reduction factors p and q of E ⊗ e system were further studied using the method of unitary transformation here. The relation between p and q proposed by Ham was investigated under both conditions of the linear coupling and the anisotropic effects. The result demonstrated that the relation of 2q − p = 1 was only correct for the linear vibronic coupling, but not correct when the anisotropic effect was considered. This result suggested that the anisotropic effect influence considerably the reduction factors, and hence the physical properties of materials. Our method could be also applied to other JT systems, especially the highly symmetric JT systems involving C₆₀ molecules.