Polyatomic system instability

The necessary and sufficient condition of instability (lack of minimum of the AP) of high-symmetry configurations of any polyatomic system is the presence of two or more electronic states, degenerate (except 2-fold spin degeneracy) or pseudodegenerate, which interact sufficiently strong under the nuclear displacements in the direction of instability . 

Not so obvious is the JT origin of structural phase transitions in crystals without JT centers. For them it was shown that local PJT distortions may serve, in principle the same role as the JT distortions in JT crystals [2,4,9,10], Since it was proved that the PJT is the only possible source of instability of polyatomic systems, the PJT local distortions come out to be the only source of structural phase transitions in such crystals. It was also shown that just the long-range interactions without local distortions cannot produce structural phase transitions [12]. 

Somewhat paradoxically, symmetry is seen to play an important role in the understanding of the Jahn-Teller effect, the very nature of which is symmetry destruction [52], In a recent review the original paper published by Jahn and Teller [53] was called one of the most seminal papers in chemical physics [54], Only a brief discussion of this effect will be given here for more detail we refer the reader to References [55-59], Bersuker says that all structural instabilities and distortions of high-symmetry configurations of polyatomic systems are of Jahn-Teller origin (here he also refers to other related effects, such as the Renner-Teller effect and the pseudo-Jahn-Teller effect—they will be mentioned later). Bersuker likes to call this the... 

Thus, with these proofs two important additions to the previous traditional understanding of the JTE emerged (1) Any polyatomic system may be subject to the JTE, and (2) if there are instabilities and distortions of high-symmetry configurations, they are due to, and only to the JTE. Together with the previously achieved understanding of the role of quadratic terms of the vibronic coupling, the extended formulation of the JTE that includes the latest achievements in this field is as follows [1,8] ... 

An outline of the generalized JTE implications in electronic structure calculations is given showing the importance of this effect in both choosing the method and basis set of ab initio computation and rationalization of the results. The latter aspect is of special importance in transforming computer experiments in theoretical explanation and prediction of molecular properties. As the only source of instability and distortions of any polyatomic system the JTE serves as a general tool of (approach to) problem solving which in electronic structure calculations allow one to make conclusions based on first principles. 

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