Crystal Field Splitting

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In an octahedral complex, which d-orbitals have higher energy under crystal field theory?

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1. **Crystal Field Theory (CFT)**: Ligands are treated as point charges. In an octahedral complex, ligands approach the metal along the $x, y,$ and $z$ axes.
2. **Orbital Alignment**:
   - **$e_g$ set ($d_{z^2}, d_{x^2-y^2}$)**: These orbitals have lobes pointing directly along the axes. They experience maximum repulsion from ligand point charges.
   - **$t_{2g}$ set ($d_{xy}, d_{yz}, d_{zx}$)**: These orbitals have lobes pointing between the axes. They experience less repulsion.
3. **Energy Shift**: The repulsion raises the energy of the $e_g$ orbitals above the average level (barycenter).
4. **Conclusion**: **$d_{z^2}$ and $d_{x²-y^2}$** have higher energy.

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Crystal Field Splitting

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