Jahn-Teller effect is typically observed in non linear molecules with asymmetric crystal fields (i.e. non spherical ligand fields) such as, octahedral and tetrahedral complexes.
The rule states that "any non-linear molecular system in a degenerate electronic state will be unstable and will undergo distortion to form a system of lower symmetry and lower energy, thereby removing the degeneracy".
So, how a linear molecule keep its degeneracy and stability simultaneously ??
Well, from a mathematical point of view, basically when you consider a perturbation that is an atomic displacement in order to evaluate the energy change when you produce a break in symmetry, you'll find that all linear matrix elements from that perturbation will vanish for linear point groups. Any breaking symmetry displacement of atoms will just increase all level's energy. This is nicely explained in the original Jahn and Teller paper from 1937: Article Stability of Polyatomic Molecules in Degenerate Electronic S...
Dear Fernando Igoa
I appreciate your attention
I already read the main article, my main concern is on physical perspective of Jahn-Teller disorders not mathematical concepts. However, I need to know about the following theories to understand the physical phenomenons of Jahn-Teller:
Now, I understand the physical principle of Jahn-Teller distortion on complex nonlinear molecules , but the main question about the linear molecules is still unsolved for me.
Dear Joachim Breternitz
Many thanks for your complete answer
I understand the whole thing. So, as you explained, due to symmetrical ligand fields the degeneracy of t2g and eg orbitals remain unchanged and only the outermost d-orbital splits as the result of hybridization between central atom and ligands in the z-direction. I think the same explanation may true for nonlinear complexes if the ligand fields have a complete spherical symmetry.
Thank you once again,
Best regards.
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