High-symmetry configuration

As an effect of the linear and quadratic vibronic integrals the adiabatic potential surface stays no longer paraboloid-shaped. It exhibits an additional warping with several local minima and saddle points out of the reference high-symmetry configuration Q0. 

There are several obvious mechanisms that lower both the internal energy and symmetry. These are first of all electron-nuclear bonding and interatomic and intermolecular interactions. They underlie the formation of condensed matter (atoms, molecules, and solids) by cooling which takes place in a series of typical SB. Beside these cases there are many SB that are at first sight not associated with bonding, but with spontaneous distortions of high-symmetry configurations (which... 

Fig. 1. The adiabatic potentials (AP) in the Jahn-Teller (a), Renner-Teller (b), and pseudo-Jahn-Teller (c) effects for systems with a double degenerate electronic term interacting with one coordinate Q (E bi problem in the JT case). In all three cases the ground state is unstable in the high-symmetry configuration <2 = 0, while the stable configurations at Q0 are at lower symmetry. The differences between these cases are in the behavior of the AP at Q = 0.

An important question is whether the JT vibronic coupling (JT, RT, and PJT) mechanism of SB is unique, or it is applicable to a limited number of special cases and hence there may be other mechanisms of SB that are in principle different from the JT one. The answer is that the JT mechanism of spontaneous distortions of high-symmetry configurations (chemically stable systems and transition states of chemical reactions) that leads to SB is unique, and there is no other in principle different mechanism that produces such distortions [1,2,5,11], It was also shown that in ensembles of systems (e.g. local centers in crystals), just the interaction between them (e.g. mutual polarization) cannot produce SB without local (JT) distortions of each system [12]. The JT effects provide thus the necessary and sufficient condition of SB in the systems under consideration. 

However, so far all the applications of the JT effect theory were realized only for chemically bonded systems in their high-symmetry configuration and transition states of chemical reactions. We show here that this is an unnecessary restriction the JT type instability is inherent to all the cases of degeneracy or pseudodegeneracy in molecular systems and condensed matter including nonbonded states in molecule formation from atoms, intermolecular interaction, and chemical reactions. 

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 . 

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] ... 

Consider the example of the Na4 cluster [16], In its high-symmetry configuration the four sodium atoms are arranged in a tetrahedron. The four 3s valence orbitals in this conformation form a and t2 symmetrised orbitals. In the Na4 system the valence electronic configuration is producing electronic terms... 

In any of these cases the charge distribution is nontotally symmetric and distorts the high-symmetry configuration. In other words, if the PJTE conditions are met, it is more energetically convenient for the system to pair its electrons in the same orbital and distort the nuclear framework than to remain symmetrical and high-spin under Hund s rule. 

As shown in the Sect. 2, the JT theorem predicts a spontaneous distortion of the high symmetry configuration. Group theory allows finding the irreducible representation of the non-totally symmetric vibrations in the HS conformation, which are JT active and remove the degeneracy and lead to a stabilization of the system by lowering the... 

Fig. 19 A graphical depiction of the variation in the energies of the upper (excited) and lower (ground) potential energy surfaces in normal-mode or g-space for the quadratic F (8) e JT problem. The origin corresponds to the system in its degenerate, high-symmetry configuration shown in Fig. 18...

The representation of the full eigenfunction of the system in the form (26) is based on the assumption that the interatomic distances at the minima points of the adiabatic potential do not differ very much from that of the high-symmetry configuration, and the deviations of the rotational functions from the spherical-top ones may be neglected. If these small deviations are taken into account, a small splitting of the degenerate vibronic-... 

The generalized Jahn-Teller effect (JTE) [including proper JTE, pseudo-JTE (PJTE), and Renner-Teller effects (RTE)] in its present understanding is a local feature of any polyatomic system that describes its properties in high-symmetry configurations... 

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