Jahn-Teller effect definition

The Jahn-Teller effect [7-9,25] originates from vibronic coupling [19], In this chapter, we discuss the definition of vibronic coupling with emphasis on its difference from non-adiabatic coupling. 

Abstract Keeping in mind the pedagogical goal of the presentation the first third of the review is devoted to the basic definitions and to the description of the cooperative Jahn-Teller effect. Among different approaches to the intersite electron correlation in crystals the preference is with the most fundamental and systematic Hamiltonian shift transformation method. Order parameter equations and their connection to the crystal elastic properties and to the orbital ordering are considered. An especial attention is paid to the dynamics of Jahn-Teller crystals based on the coupled electronic, vibrational, and magnetic excitations which are of big interest nowadays in orbital physics. 

There would appear to be a definite Jahn-Teller effect in Cu(bipyridine) (F3C. CO. CH. CO. Cp3)2/ in which there are unequal Cu-0 bond lengths and moreover distortion of the normally symmetrical ligand, (g). 

Evidence of similar character can be adduced for many of the other transition-metal ions. For all the di- and tri-positive ions of the first transition series, it is certain that the aquoions are octahedral [M(H20)6]2(or3)+ species, although in those of Cr11, Mn111 and Cu11 there are definite distortions of the octahedra because of the Jahn-Teller effect (see Section 20-11). Information on aquo ions of the second and third transition series, of which there are only a few, however, is not so certain. It is probable that the coordination is octahedral in many, but higher coordination numbers may occur. 

Various other interactions have been considered as the driving force for spin-state transitions such as the Jahn-Teller coupling between the d electrons and a local distortion [73], the coupling between the metal ion and an intramolecular distortion [74, 75, 76] or the coupling between the d electrons and the lattice strain [77, 78]. At present, based on the available experimental evidence, the contribution of these interactions cannot be definitely assessed. Moreover, all these models are mathematically rather ambitious and do not show the intuitively simple structure inherent in the effect of a variation of molecular volume considered here. Their discussion has to be deferred to a more specialized study. 

For the chemist, the Jahn-Telkr effect is, in a way, the obverse side of the Tanabe-Kamimura theorem . The abstract formulation of the Jahn-Teller theorem is that two or more electronic states having identical energy in a definite symmetry of a non-linear molecule or polyatomic ion (with exception of Kramers doublets in the case of an odd number of electrons) spontaneously separate in energy, such that (at least) the state of... 

The main scientific disciplines of quantum chemistry and solid-state physics were developed by way of a mathematical simplification or approximation of the Schrodinger equation, known as the Born-Oppenheimer (B-O) approximation [1]. It does not only give the basis of almost all quantum chemical calculations, but it also provides the very concept of molecular structure [2]. There are two main contemporary trends in quantum chemistry that put a question mark over the B-O approximation and its role in the definition of (molecular) structure theories based on the incorporation of the centre-of-mass (COM) problem and applications in connection with the Jahn-Teller (J-T) effect. 

The most important consequence of the breakdown of the B-O approximation is indisputably the Jahn-Teller (J-T) effect [7], where the structure defined on the basis of this approximation does not in fact hold. The important role of the J-T effect is emphasized in Bersuker s book [8] Moreover, since the J-T effect has been shown to be the only source of spontaneous distortion of high-symmetry configurations, we come to the conclusion that the J-T effect is a unique mechanism of all the symmetry breakings in condensed matter. It is of course well known that problems related to the definition of crystallic structure in solid-state physics are mostly ignored assuming only BO structures. Nevertheless it is often criticised by scientists dedicated to studies of the J-T effect. For instance the proper understanding of superconductors should be evidently based on a solution of the non-adiabatic problem but the impact on the crystallic structure is neither reflected in the Frohlich Hamiltonian [9,10] nor in the BCS theory [11]. 

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