The dx² – y² and dz² orbitals in an octahedral complex experience more repulsion due to their orientation towards ligands, resulting in higher energy. The t₂g orbitals decrease in energy, while the eg orbitals increase by (3/5) ∆₀ and (2/5) ∆₀, respectively.
Why do the dx² – y² and dz² orbitals experience higher energy in an octahedral complex, and what is the resulting energy change for the t₂g and eg orbitals?
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In an octahedral complex, the dx² – y² and dz² orbitals experience higher energy due to increased repulsion between the metal and ligand electrons when these orbitals are directed towards the ligands. The ligands create an asymmetrical field, lifting the degeneracy of the d orbitals. As a result, the dx² – y² and dz² orbitals form the higher-energy eg set. The other d orbitals (dxy, dyz, and dxz), which experience less repulsion as they are directed between the axes, form the lower-energy t₂g set. The energy change for the eg orbitals is an increase by (3/5) ∆₀, while the t₂g orbitals decrease by (2/5) ∆₀.