Electronic states high-symmetry configuration

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.

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 . 

In many applications the positions of the nuclei are fixed (clamped nuclei approximation, Chapter 6), often in a high-symmetry configuration (cf. Appendix C, p. 903). For example, the benzene molecule in its ground state (after minimizing the energy with respect to the positions of the nuclei) has the symmetry of a regular hexagon. In such cases the electronic Hamiltonian additionally exhibits invariance with respect to some symmetry operations and therefore the wave functions are... 

The JT theorem [40] states that if in the high-symmetry configuration of a nonlinear polyatomic system the electronic state F is degenerate, there is at least one low-symmetry coordinate in the linear terms of the vibronic coupling that... 

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