The Jahn-Teller Model

The JT theorem defines the relationship between symmetry and stability of non-linear molecules and the origin of three-dimensional molecular structure as a function of o-a-m. 

The way to understand the first step in the formation of a molecule is to consider a given atom as surrounded by a number of non-interacting secondary atoms, or ligands. The energy and o-a-m of the central atom is affected by the presence of the coordination shell of ligands, within the demands of the relevant conservation laws. Their effect can be simulated by recalculation of the electronic energy and o-a-m of the central atom in the modified symmetry environment, defined by the distribution and nature of the ligands. 

An important special case arises when a valence electron of the central atom is on a degenerate energy level. Breaking the symmetry by some displacement, not of the totally symmetrical type, may lift the degeneracy and lower the total energy. Although such displacement lowers the total en- 

The original JT analysis examined the modification of central-field energy eigenvalues as a function of the representations of the important molecular symmetry groups. The results agree [65] with the heuristic analysis of o-a-m conservation. 

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Appendix A The Jahn-Teller Model and the Herzberg-Longuet-Higgins Phase Appendix B The Bom-Oppenheimer Treatment Appendix C Formulation of the Vector Potential References... 

APPENDIX A THE JAHN-TELLER MODEL AND THE HERZBERG-LONGUET-HIGGINS PHASE... 

If the states are degenerate rather than of different symmetry, the model Hamiltonian becomes the Jahn-Teller model Hamiltonian. For example, in many point groups D and so a doubly degenerate electronic state can interact with a doubly degenerate vibrational mode. In this, the x e Jahn-Teller effect the first-order Hamiltonian is then [65]... 

Figure 15. The two interacting cones within the Jahn-Teller model.

Baer R, Charutz D M, Kosloff R and Baer M 1996 A study of conical intersection effects on scattering processes—the validity of adiabatic single-surface approximations within a quasi-Jahn-Teller model J. Chem. Phys. 105 9141... 

It is convenient to discuss the linear Jahn-Teller model in the scaled complex representation... 

Some final comments on the relevance of non-adiabatic coupling matrix elements to the nature of the vector potential a are in order. The above analysis of the implications of the Aharonov coupling scheme for the single-surface nuclear dynamics shows that the off-diagonal operator A provides nonzero contiibutions only via the term (n A n). There are therefore no necessary contributions to a from the non-adiabatic coupling. However, as discussed earlier, in Section IV [see Eqs. (34)-(36)] in the context of the x e Jahn-Teller model, the phase choice t / = —4>/2 coupled with the identity... 

Scattering Calculation with the Quasi-Jahn-Teller Model... 

Warren KD (1984) Calculations of the Jahn-Teller Coupling Constants for d Systems in Octahedral Symmetry via the Angular Overlap Model. 57 119-145 Warren KD (1977) Ligand Field Theory off-Orbital Sandwich Complexes. 33 97-137 Warren KD (1976) Ligand Field Theory of Metal Sandwich Complexes. 27 45-159 Watson RE, Perlman ML (1975) X-Ray Photoelectron Spectroscopy. Application to Metals and Alloys. 24 83-132... 

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. 

Warren, K. D. Calculations of the Jahn-Teller Coupling Constants for d Systems in Octahedral Symmetry via the Angular Overlap Model. Vol. 57, pp. 119-145. 

Kambara presented a ligand field theoretical model for SCO in transition metal compounds which is based on the Jahn-Teller coupling between the d-electrons and local distortion as the driving force for a spin transition [193]. The author applied this model also to interpret the effect of pressure on the ST behaviour in systems with gradual and abrupt transitions [194]. By considering the local molecular distortions dynamically this model turned out to be suited to account for cooperative interactions during the spin transition [195]. 

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