# What is the significance of the 3d_(x^2-y^2) atomic orbital?

Jul 5, 2017

Significance? Well, it corresponds to one of the magnetic quantum numbers in the set ${m}_{l} = \left\{- 2 , - 1 , 0 , + 1 , + 2\right\}$, and has ${m}_{l} = - 2$ by convention.

The $3 {d}_{{x}^{2} - {y}^{2}}$ orbital is the one lying along the axes:

COMMON BONDING CASES

Because of that, it is often used to $\sigma$ (sigma) bond with surrounding ligands, particularly in a transition metal complex. You'll see a strong contribution from this orbital most often in...

square planar complexes:

and octahedral complexes:

ENERGIES

In an atom, it is degenerate with the other $\text{four}$ $3 d$ orbitals, the ${d}_{{z}^{2}}$, ${d}_{x y}$, ${d}_{x z}$, and ${d}_{y z}$.

In a complex, the $d$ orbitals split in accordance with their symmetry (horizontal correspondence) and energy (vertical separations) with respect to the other $d$ orbitals:

(For the octahedral complex, the symmetries from top to bottom were ${E}_{g}$ and ${T}_{2 g}$, and for the square planar complex, the symmetries from top to bottom are ${B}_{1 g}$, ${B}_{2 g}$, ${A}_{1 g}$, and ${E}_{g}$.)