Jahn-Teller theorem levels

Appendix D Degenerate and Near-Degenerate Vibrational Levels Appendix E Adiabatic States in the Vicinity of a Conical Intersection 1, Jahn-Teller Theorem... 

This last reference is for those who would like to see the Jahn-Teller theorem at a technical level. 

Geometric phase effect (GPE) (Continued) adiabatic states, conical intersections invariant operators, 735-737 Jahn-Teller theorem, 733-735 antilinear operator properties, 721-723 degenerate/near-degenerate vibration levels, 728-733... 

Fig. 4.20 Cyclic systems with degenerate energy levels tend to undergo a geometric distortion to remove the degeneracy, a consequence of the Jahn-Teller theorem...

The Jahn-Teller theorem per se does not predict which type of distortion will take place other than that the center of symmetry will remain. The z ligands can move oul as in the example discussed above or they can move in. For a "z-in distortion, the splitting pattern is similar to that observed for a z-out, but the energy ordering within the and levels is inverted (see Fig. I I.47b). 

Let us now examine the octahedral trans MY4Y2 molecule and ask using the angular overlap model which distortion out of 30 and 31 will be most favored without any preconceptions induced via the Jahn-Teller theorems. 33 shows the energy levels for... 

A Copper(II) is a Jahn-Teller ion and normally sits in a distorted lattice site. The configuration of copper is which leads to an unpaired electron in the e level in an octahedral crystal field. The Cg level consists of the degenerate and d, orbitals. According to the Jahn-Teller theorem, the system distorts to remove the degeneracy and lower the overall energy of the system. Hence one set of bonds (four in plane, or two axial) become longer than the others and the copper ion has a distorted geometry. 

In an octahedral crystal field, the ground state is T2- Spin-orbit coupling splits this state, with lowest, hence allowing the Jahn-Teller theorem to be applicable. This splits the state into and jB. Spin-orbit coupling splits these levels and the m, = 0 level lies lowest in zero field. Since the lowest level is not a Kramer s doublet, no ESR spectrum is expected. The levels split as for the ion. g j varies from 4 to 10. 

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