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

Crystal field splitting describes the division of five degenerate d orbitals into two energy levels due to the influence of ligand interactions in a complex ion. The pattern of splitting is determined by the geometry of the complex, with octahedral complexes featuring stronger interactions along the axes. This results in higher energy for the d orbitals oriented on the axes (d_x²-y² and d_z²), known as the E set, and lower energy for those between the axes, known as the T set. The energy difference between these sets is represented by:

$\Delta$

the crystal field splitting energy. Understanding this concept is crucial as it explains the electronic structure and properties of transition metal complexes.

The crystal field splitting pattern for octahedral complexes has the d orbitals on or along the axes as having the higher energy.

Now crystal field splitting is the separation of degenerate D orbitals into non-degenerate sets. So remember the word degenerate means same energy. So we're taking the 5D orbitals that are on the same level, same energy, and we're basically separating them, creating one tier that's lower in energy and one that's higher in energy.

Now, the splitting pattern from complex depends upon its geometry, so we'll see based on the geometry of our complex ion. These 5D orbitals can orient themselves in different ways. Now here with octahedral crystal field splitting, we're going to say. Recall that in octahedral complexes, the ligand orbital interactions are on the axes or along the axes are the strongest ones. We're going to say this increases the energies of the orbitals that are oriented on the axes.

So if we take a look here, we have our six ligands that are the green dots. And remember, the two orbitals that lie on the axes or along the axes are dx2-y2 or dz2. They have the greatest energy, so we would orient them up here. And then these other three are the ones that lie in between the axes. They have less interaction and therefore would have lower energy. So we're placing them down here.

Now we're going to say that the difference in energy between these three bottom ones and then these two top ones, it is designated as Δ, represents our crystal field splitting energy. And we're going to say that this is the energy difference between the two sets, which are E and T₂ of orbitals. All right. So which one is E, which one is T₂? Well, in terms of this octahedral complex, we're going to say that our E equals doublet, which means it's the pair of orbitals, the two orbitals. So these two would be our E set.

And then T here stands for triplet, which is our three orbitals. So this would be our T set here. So just remember when we talk about crystal field splitting, we're looking at our five original D orbitals and we're separating them. One on the bottom is lower in energy and then up here higher in energy. For octahedral species, it's the ones that lie on the axis or along the axis that have greater energy because of greater interaction. That's why dx2-y2 and dz2 are up here. The other ones lie in between the axes. Less interaction, less energy. That's why they're lower down here. And again, their difference in levels is our delta, our crystal field splitting energy.

Example

For which of the following complexes, the energy of the T2 set is lower than the E set. So this question is actually easier than it appears. What they're really asking is to determine is which one of these complex ions represents an octahedral complex.

So remember to be octahedral you need your metal cation to be connected to six ligands. And if we look, the only option that has our metal cation connected to six ligands is option D.

Here we have cobalt 3 plus ion connected to six water molecules. This would give us an octahedral orientation, which in turn would mean that our T2 set of three orbitals is lower in energy than our E set of our pair of orbitals.

The following diagram shows crystal field splitting pattern for a complex. Which one of the complexes given below should best match the given diagram?

• A. [Ag(NH₃)₂]⁺
• B. [Cu(ox)₂]^2–
• C. [Cr(en)₃]³⁺
• D. [Fe(CO)₅]

Here’s what students ask on this topic:

According to crystal field theory, which orbitals in an octahedral complex would be higher in energy due to interaction with the ligands? Which ones should I check?

In crystal field theory, when considering an octahedral complex, the d-orbitals split into two different energy levels due to the interaction with the ligands. The five d-orbitals are divided into a set of three orbitals known as t_2g (d_xy, d_xz, d_yz) and a set of two orbitals called e_g (d_x²-y², d_z²).

In an octahedral field, the ligands approach the metal ion along the axes. This causes the d-orbitals that lie directly on these axes to experience a greater repulsion and thus, they are higher in energy. These are the e_g orbitals (d_x²-y² and d_z²). The t_2g orbitals (d_xy, d_xz, d_yz), which lie between the axes, experience less repulsion from the ligands and are therefore lower in energy.

So, when examining an octahedral complex in the context of crystal field theory, you should check the e_g orbitals (d_x²-y², d_z²) as they will be the ones higher in energy due to direct interaction with the ligands.

Which of the following orbitals belong to the higher energy group in crystal field theory, where octahedral metal orbitals are split into 2 groups of degenerate orbitals, one at lower energy, and one at higher energy? [Select all that apply]

In crystal field theory, when considering an octahedral metal complex, the five d orbitals split into two groups due to the electrostatic interactions between the metal ion and the ligands. The lower energy group consists of the d_xy, d_xz, and d_yz orbitals, which form the t_2g set. The higher energy group comprises the d_z² and d_x²-y² orbitals, which form the e_g set.

So, the orbitals that belong to the higher energy group in an octahedral crystal field are:

• d_z²
• d_x²-y²

These e_g orbitals experience a greater repulsion from the ligands that are positioned along the axes in an octahedral geometry, which results in their higher energy relative to the t_2g orbitals.