Jahn–Teller distortions

Octahedral complexes of d⁹ and high-spin d⁴ ions are often distorted, e.g. CuF₂ (the solid state structure of which contains octahedrally sited Cu²⁺‏ centres ) and [Cr(H₂O)₆]²⁺‏, so that two metal–ligand bonds (axial) are different lengths from the remaining four (equatorial).

    This is shown in structures 1.1 (elongated octahedron) and 1.2 (compressed octahedron). For a high-spin d⁴ ion, one of the eg orbitals contains one electron while the other is vacant. If the singly occupied orbital is in the d_z2 , most of the electron density in this orbital will be concentrated between the cation and the two ligands on the z axis. Thus, there will be greater electrostatic repulsion associated with these ligands than with the other four and the complex suffers elongation (1.1). Conversely, occupation of the d_x2__y2 orbital would lead to elongation along the x and y axes as in structure 1.2.

    A similar argument can be put forward for the d⁹ configuration in which the two orbitals in the eg set are occupied by one and two electrons respectively. Electron-density measurements confirm that the electronic configuration of the Cr²⁺‏ ion in [Cr)H₂O(₆]²⁺‏ is approximately d_xy¹ d_yz¹ d_xz¹ d_z2¹. confirm that the electronic configuration of the Cr^2‏+ ion in [Cr(H₂O)₆]²⁺‏ is approximately d_xy¹ d_yz¹ d_xz¹ d_z²¹. The corresponding effect when the t_2g set is unequally occupied is expected to be very much smaller since the orbitals are not pointing directly at the ligands; this expectation is usually, but not invariably, confirmed experimentally.  Distortions of this kind are called Jahn–Teller distortions.

(1.1)                                                   (1.2)

   The Jahn–Teller theorem 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.