Crystal Field Theory: Tetrahedral Complexes - Online Tutor, Practice Problems & Exam Prep

• In tetrahedral complexes, the ligand orbital interactions are strongest between the axes, affecting the dxy, dyz, and dxz orbitals.
• The dxy, dyz, and dxz orbitals have the highest energy due to strong interactions and are grouped at the top of the crystal field diagram as a triplet (t2g).
• The dx^2-y^2 and dz^2 orbitals, which lie along the axes, have less interaction and therefore lower energy, represented as a pair (e).
• The energy difference between these sets of orbitals is denoted as delta (Δ), the crystal field splitting energy.
• Tetrahedral complexes exhibit the smallest crystal field splitting energy (Δ) compared to octahedral and square planar complexes.

The crystal field splitting pattern for tetrahedral complexes has the d orbitals in between the axes as having the higher energy.

Now recall in tetrahedral complexes that the ligand orbital interactions be in between, the axes are the strongest. And if we're talking about our 5D orbitals, the ones that lie in between the axes are dxy, dyz and dxz. Remember, the interaction there is the highest, therefore they should have the highest energy.

So when we segregate these different types of orbitals from one another to create our crystal field diagram here, we place the three of them up top here. So here we'd have dxy, dyz and dxz. There are three of them. And remember 3 here would stand for triplet so that's why it's T2 set for these three d2-y2 and d2.

These are the orbitals that lie along or on the axes. They have less interaction and therefore they would have less energy. That's where they're down here. And there's a pair of them, two of them, and we use a notation of Eo. They would represent our E set.

The difference in energy between these orbitals is Δ. Our crystal field splitting energy, and in fact tetrahedral complexes have the smallest Δ. So keep that in mind as we talk about different complexes in relation to tetrahedral, octahedral and square planar complexes. Out of those 3, tetrahedral complexes have the smallest Δ.

Example

Which one of the following complexes will have the smallest energy gap between the E_SET and the T₂ set of orbitals? So our energy gap Here they're just talking about Δ which is our crystal field energy, here splitting energy, and they want the smallest one that happens with tetrahedral complexes.

To be a tetrahedral complex you need to have a metal cation connected to four ligands or have a metal connected to four ligands. If we take a look here, the only one that has a metal connected to four ligands is option D. In it we have copper 2 plus connected to four bromide ions.

The other ones don't work because in the first one we have 6 ligands, so that would be octahedral. We have OX 3 is not. We don't even need to worry about if it's monodentate, bidentate, polydentate 3. Here we need 4 ligands. EDTA. Here we're only showing one. But EDTA, remember is a polydentate ligand, so it has six donor atoms.

The only one that fits the great description of having four ligands or 4 donor atoms is option D. This will result in the smallest energy gap.

For which of the following complexes, the energies of the dx2−y2 and dz2 orbitals will be lower than the other three d orbitals?

• A. [Co(en)₃]³⁺
• B. [Ni(CN)₄]^2–
• C. [Zn(H₂O)₄]²⁺
• D. [AuCl₂]^–