Intercell elastic coupling

At relatively high temperature, the elastic intercell coupling is averaged out. Therefore, at different elementary cells, geometric shapes and amplitudes of the JT distortions are independently random. In other words, there is some distortion-magnitude disorder in the crystal lattice. At average, the respective X-ray crystal structure looks perfectly tetragonal. 

As distinguished from the orbital pseudo spin, for the vibronic pseudo spin, the mechanism of intercell coupling is different. It is dominated by the respective terms of elastic intercell interaction. 

Correspondingly, vibronic pseudo spin space has to be extended to include all tunneling splitting components. In the case of quadratic E e coupling with three wells, it is expressed by the vibronic pseudo spin x = 1 matrices 3x3. Similar to the intermediate coupling case, the intersite vibronic exchange is dominated by the elastic intercell interaction (36). 

The key feature distinguishing the OOA from the cooperative JT effect is the way the chemical bonding effects are included. This will be an important part of the present study. In Sect. 2, we present a simple qualitative description of the cooperative JT effect. First, in Sect. 2.1, we demonstrate the chemical nature of the JT instability. In Sect. 2.2, the cooperative JT effect is presented as interplay of short-range chemical bonding effects with the long-range intercell elastic coupling. To reveal the most important differences of the two approaches from one another, in Sect. 3 we present a simplified version of the OOA. In Sect. 4, we discuss some additional effects that are closely related to JT instability in crystals. 

Developed by Englman and Halperin [4], the above steps represent the traditional way in the cooperative JT problem. It s conceptual advantage and important part is solving the respective one-cell JT problem (9) including the low-symmetry mean field (10) of all other distorted cells. In this way, both effects, the dynamic strengthening chemical bonds with low-symmetry lattice distortions and the intercell elastic coupling, are included. 

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