Which of the following are true about the energy of the given d-orbitals of a tetrahedral complex?

A. $$d_{xy} = d_{xz} > d_{x^2-y^2}$$
B. $$d_{xy} = d_{yz} > d_{z^2}$$
C. $$d_{x^2-y^2} > d_{z^2} > d_{xz}$$
D. $$d_{x^2-y^2} = d_{z^2} < d_{xz}$$

Choose the correct answer from the given below:

For a tetrahedral complex, the five degenerate $$d$$-orbitals split into two distinct energy levels due to electrostatic repulsion from the ligands:

1. Lower Energy Set ($$e$$ orbitals): Consists of $$d_{x^2-y^2}$$ and $$d_{z^2}$$. These point between the axes where ligand approach causes less repulsion.
2. Higher Energy Set ($$t_2$$ orbitals): Consists of $$d_{xy}$$, $$d_{yz}$$, and $$d_{xz}$$. These point directly toward the directions from which the ligands approach, experiencing more repulsion.

Therefore, the relative energies are:

$$d_{xy} = d_{yz} = d_{xz} > d_{x^2-y^2} = d_{z^2}$$

Evaluating the Statements:

• A. $$d_{xy} = d_{xz} > d_{x^2-y^2}$$  
  True (Both $$d_{xy}$$ and $$d_{xz}$$ belong to the higher-energy $$t_2$$ set, while $$d_{x^2-y^2}$$ belongs to the lower-energy $$e$$ set).
• B. $$d_{xy} = d_{yz} > d_{z^2}$$  
  True (Both $$d_{xy}$$ and $$d_{yz}$$ are in the higher $$t_2$$ set, and $$d_{z^2}$$ is in the lower $$e$$ set).
• C. $$d_{x^2-y^2} > d_{z^2} > d_{xz}$$
  False ($$d_{x^2-y^2}$$ and $$d_{z^2}$$ have equal energy).
• D. $$d_{x^2-y^2} = d_{z^2} < d_{xz}$$ True ($$d_{x^2-y^2}$$ and $$d_{z^2}$$ are equal and lower in energy than the $$t_2$$ orbital $$d_{xz}$$).

Correct Answer:

A, B and D only