Question

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

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

Hint:

In tetrahedral fields, the $t_2$ set is higher in energy (unlike octahedral where the $e_g$ set is higher). $\Delta_t = \frac{4}{9}\Delta_o$.

Answer 1

The Correct Option is D

Step 1: Concept
In a tetrahedral crystal field, the four ligands approach the metal ion from alternate corners of a cube rather than along the axes.

Step 2: Analysis
The $d_{xy}$, $d_{yz}$, and $d_{xz}$ orbitals (the $t_2$ set) have their lobes directed between the axes, which happens to point closer toward the tetrahedral ligand positions. The $d_{x^2-y^2}$ and $d_{z^2}$ orbitals (the $e$ set) point along the axes, further away from the ligands.

Step 3: Conclusion
Therefore, the $t_2$ set ($d_{xy}$, $d_{yz}$, $d_{xz}$) experiences greater electrostatic repulsion and is raised to a higher energy level in the tetrahedral crystal field. This is the opposite of the octahedral splitting pattern.

Final Answer: (D)