Degeneracy, orbital Degenerate

In 1937 Jahn and Teller applied group-theoretical methods to derive a remarkable theorem nonlinear molecules in orbitally degenerate states are intrinsically unstable with respect to distortions that lower the symmetry and remove the orbital degeneracy.37 Although Jahn-Teller theory can predict neither the degree of distortion nor the final symmetry, it is widely applied in transition-metal chemistry to rationalize observed distortions from an expected high-symmetry structure.38 In this section we briefly illustrate the application of Jahn-Teller theory and describe how a localized-bond viewpoint can provide a complementary alternative picture of transition-metal coordination geometries. 

Jahn-Teller Effect. With the exception of d3, d5, and d8 configurations, the ground state in an octahedral crystal field is still orbitally degenerate. Some of this degeneracy is removed by the spin-orbit interaction. 

The Jahn-Teller theorem is important in considering the electronic states of polyatomic molecules. Jahn and Teller proved in 1937 that a nonlinear polyatomic molecule cannot have an equilibrium (minimum-energy) nuclear configuration that corresponds to an orbitally degenerate electronic term. Orbital degeneracy arises from molecular symmetry (Section 1.19), and the Jahn-Teller theorem can lead to a lower symmetry than... 

The regular octahedron of a d9 system is an abstraction since the JT effect applies the electronic ground state cannot be orbitally degenerate so that the tetragonal (eg-mode) distortion leads to the degeneracy removal. 

How do these conclusions fit in with the Jahn-Teller (49) theorem telling us that molecules with orbitally degenerate electronic states distort to lose this degeneracy Some of the distortions we have seen and rationalized are allowed under the Jahn-Teller scheme, but very importantly others are not (50). For example,... 

Vibronic interactions are also responsible for the JT effect which may appear when the ground state is orbitally degenerate. If the ground state wavefunctions are simply designated by [To, (where the index /u. reflects the degeneracy) the... 

Except some special cases, this way of understanding crystal structures provides reasonable results under condition that each elementary cell is in an orbital singlet (nondegenerate) electron ground state. If the ground state is orbitally degenerate, elementary cells are unstable with respect to low-symmetry nuclear distortions. This degeneracy-driven instability in crystals is known as the JT effect [1-3]. 

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