Question

Which of the following d-orbitals experience more repulsion in the crystal field splitting of octahedral complex ?

• A. \( d_{xy}, d_{yz}, d_{xz} \)
• B. \( d_{x^2-y^2}, d_{z^2} \)
• C. \( d_{xy}, d_{x^2-y^2} \)
• D. \( d_{xz}, d_{z^2} \)

Hint:

In Octahedral splitting: \( e_{g} \) (axial) is high energy, \( t_{2g} \) (non-axial) is low energy.
In Tetrahedral splitting, the order is reversed because ligands approach between the axes.

Answer 1

The Correct Option is B

Step 1: Picture where the six ligands sit.
In an octahedral complex the six ligands approach the metal ion straight along the $+x, -x, +y, -y, +z, -z$ directions, that is, directly along the three Cartesian axes.
Step 2: Picture where each set of d-orbitals points.
The orbitals $d_{xy}, d_{yz}, d_{xz}$ have their lobes sitting between the axes, at $45^\circ$ to them, so ligands approaching along the axes largely miss these lobes. The orbitals $d_{x^2-y^2}$ and $d_{z^2}$, on the other hand, have their lobes pointing exactly along the axes.
Step 3: Compare the electrostatic repulsion felt by each set.
Since like charges repel more strongly the closer they get, orbitals lying right in the path of the ligands feel much stronger repulsion than orbitals lying off to the side. This is exactly why the axial set is pushed up in energy to become the $e_g$ level while the other three settle down as the $t_{2g}$ level.
Step 4: Identify the answer.
The orbitals facing the greatest repulsion are the axial ones. \[ \boxed{d_{x^2-y^2}, d_{z^2}} \]