Vibronic coupling higher order

Fig. 1 The adiabatic potential surface of an electronic Eg state due to the linear vibronic interaction with a vibrational mode top) the mexican hat-shaped curve on the left is modified by higher order coupling terms, yielding a three minima-refinement, which is shown in a cross section perpendicular to the energy axes on the right. The potential surface, resulting from Tg Eg coupling (amidst), leads to an analogous three-well-structure already in first order - each of these corresponding to a tetragonal polyhedron distortion along one of the three molecular axes. The vibrational ai and e modes are shown on the bottom (adopted from [2])...

In the case of E e coupling, under some special conditions, including higher orders of JT coupling can result in six wells [1,2]. Correspondingly, in this case, the extended vibronic pseudo spin is expressed by spin-5/2 matrices 6 x 6. In the linear T t2 case, there are four symmetry equivalent wells [2]. Correspondingly, the matrices of extended vibronic pseudo spin are 4x4, and the respective pseudo spin value is r = 3/2. 

The benzene preresonance Raman spectra show also fairly strong activity of the first overtone of mode Vi4(b2 ). This mode is dipole forbidden and thus cannot directly obtain its intensity through coupling of B2 with the ground state as discussed in Section IX,D. However, it is possible to formulate several higher-order vibronic coupling schemes that yield such overtone activity, depending on which state is the resonant state. The Raman intensity probably derives from the dipole allowed 2 transition... 

Another problem originates in the fact that a multimode vibronic coupling should be considered in higher orders of the theory at least the mode is to be included beginning with the second order. Therefore the analytic forms of the adiabatic potential surfaces need a rederivation. Finally, some structural transitions should be either included or deleted from the Jahn-Teller mechanism, and the symmetry descent concept is useful along these lines. 

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