Complexes

Is there a way to determine how many high and low energy levels the degenerate d orbitals will split into, or is it just a case of having to learn it?

Octahedral complexes split into 3 low (t2g) and 2 high (eg) orbitals

Tetrahedral complexes split into 3 high and two low (although not exactly the same energy)

Just learn it!

You can determine the splittings of the orbitals from the symmetry of the complex. This is beyond A level I'm afraid, but you can think of it simply like this:

The easiest example is an octahedral complex. Let the z-axis run vertically (through two of the ligands). The $d_{z^2}$ orbital will point towards these ligands. This creates a favourable overlap, lowering the energy of this orbital. Similarly, the $d_{xy}$ and $d_{x^2-y^2}$ orbitals will point towards the 4 ligands in the x-y plane, lowering the energy of these orbitals. This gives us three orbitals with low energy. The $d_{xz}$ and $d_{yz}$ orbitals do not point towards the ligands and are thus higher in energy.

You can determine the splittings of the orbitals from the symmetry of the complex. This is beyond A level I'm afraid, but you can think of it simply like this:

The easiest example is an octahedral complex. Let the z-axis run vertically (through two of the ligands). The $d_{z^2}$ orbital will point towards these ligands. This creates a favourable overlap, lowering the energy of this orbital. Similarly, the $d_{xy}$ and $d_{x^2-y^2}$ orbitals will point towards the 4 ligands in the x-y plane, lowering the energy of these orbitals. This gives us three orbitals with low energy. The $d_{xz}$ and $d_{yz}$ orbitals do not point towards the ligands and are thus higher in energy.

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Haven't you got that a little bit wrong?

The d orbitals are all raised in energy as the interaction between the ligand orbitals and the d orbitals is a destabilising one.

In an octahedral complex, the z^2 and x^2-y^2 (e_g set) are both raised in energy more than the others (xy, xz and yz - the t_2g set). This is because if you consider the ligands to lie on each of the 3 axes, the e_g set point straight at the ligands and are hence raised in energy, and the t_2g set point between the ligands and are not raised in energy as much. You can also tell that the orbitals are split in this fashion by looking at the symmetry tables for the O_h point group. The way you described it doesn't give you the orbital degeneracies in the right way.


You're right... As far as I understand things.