Based on CFT, in octahedral crystal field, $d$ orbitals split into orbitals of $t_{2g}$ and $e_g$ sets. Which d orbitals forms the $t_{2g}$ set?

$d_{xy}, d_{yz}, d_{xz}$

The correct answer is Option (1) → $d_{xy}, d_{yz}, d_{xz}$

Core Concept

In an octahedral crystal field, d orbitals split into two sets:

$t_2g$ (lower energy) → $dxy, dyz, dxz$

$e_g$ (higher energy) → $dx^2-y^2, dz^2$

Detailed Explanation

Option 1: $dxy, dyz, dxz$

These orbitals lie between the coordinate axes and experience less repulsion from ligands approaching along axes. Hence they form the lower energy tag set in an octahedral field.

Option 2: $dxy, dyz, dz^2$

dz2 points along the z-axis where ligands approach in an octahedral geometry. Due to direct interaction, it belongs to the $e_g$ set, not $t_2g$.

Option 3: $dx^2-y^2, dz^2$

Both these orbitals point directly along the axes toward ligands. This results in greater repulsion and higher energy, so they form the $e_g$ set.

Option 4: $dxy, dyz, dx^2-y^2$

$dx^2-y^2$ points along the $x$ and $y$ axes toward ligands, so it belongs to the $e_g$ set. Inclusion of this orbital makes the set incorrect.