Splitting In The d-Orbital

Jahn-Teller Distortions

Definition

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.

To explain this it's easier to draw a diagram:

As stated, when molecule is degenerate it is unstable, so the energy levels split again accordingly to try and remove the degeneracy. Imagine a d⁴ high spin complex (above). This is degenerate because there is an electron in the d_z² energy level, but there isn't one in the d_x²-y². This means there will be repulsion in the z axis between the electron and the ligand, but not in the x or y axis. This then results in each energy level containing a z reduce in energy, and the energy levels with only x and y in them move up an energy level. Again as in normal splitting they spit equally to balance out the split, i.e. the d_xz and the d_yz move down ¹/₃d and the d_xy move up ²/₃d. The d_x²-y² and d_z² both distort even amounts.

Elongation and Compression

In the above case the electron went into the d_z², this means that the ligands in the z axis will be pushed further away then the ligands in the other axis which get shorter, this is called Elongation (picture below).

However if the electron was to go into the d_x²-y²

There would be a compression where the ligands on the x and y axis get pushed out and the ligands on the z axis will shorten. This is called compression.

Yahn-teller also occurs in d¹ d² complexes, but these distortions aren't as large as distortion involving the E_g level, as the electrons in the t_2g the electrons don't point directly at the ligands, as the do in the E_g.

Elongation of Compression

• d¹ - Compression. This is compression because the one electron can only go into the d_xy. (see picture)

  

• d² - Elongation. This is due to the lectrons into the d_xz and the d_yz. (see picture)

  

• d³ - No Distortion. There is no degeneracy here, so no Yahn-Teller distortion
• d⁴ - Either because the electron can go in either the of the d_z² or the d_x²-y² level.
• d⁵ - No Distortion. There is no degeneracy here, so no Yahn-Teller distortion