Jahn-Teller Distortion (Tetragonal Distortion)

Distortion Condition / Electronic Criteria:

$$\text{Jahn-Teller Effect } \iff \text{Asymmetric Filling of Degenerate Orbitals } (e_g \text{ or } t_{2g})$$

$$\text{Strong Distortion Criteria: Asymmetric filling in } e_g \text{ orbitals } (d^9, \text{ High-spin } d^4, \text{ Low-spin } d^7)$$

Concept: Any non-linear molecular system with a degenerate electronic ground state will undergo structural distortion to lower its symmetry and remove the degeneracy. In octahedral complexes with unequally filled $$e_g$$ orbitals (e.g., $$[\text{Cu}(\text{H}_2\text{O})_6]^{2+}$$ - $$d^9$$ system $$t_{2g}^6 e_g^3$$), two axial metal-ligand bonds stretch significantly longer than the four equatorial bonds (Z-out tetragonal elongation).

Notation:

• Z-out elongation = Two axial axial bonds ($$\text{M--L}_z$$) are longer than four equatorial bonds ($$\text{M--L}_{xy}$$)
• $$[\text{Cu}(\text{H}_2\text{O})_6]^{2+}$$ = example exhibiting severe Jahn-Teller elongation