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

1 Answer
Jul 5, 2017

Significance? Well, it corresponds to one of the magnetic quantum numbers in the set m_l = {-2, -1, 0, +1, +2}, and has m_l = -2 by convention.

The 3d_(x^2 - y^2) orbital is the one lying along the axes:

http://www.dlt.ncssm.edu/http://www.dlt.ncssm.edu/

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:

http://slideplayer.com/http://slideplayer.com/

and octahedral complexes:

https://www.andrew.cmu.edu/https://www.andrew.cmu.edu/

ENERGIES

In an atom, it is degenerate with the other "four" 3d orbitals, the d_(z^2), d_(xy), d_(xz), and d_(yz).

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:

https://chem.libretexts.org/https://chem.libretexts.org/

(For the octahedral complex, the symmetries from top to bottom were E_g and T_(2g), and for the square planar complex, the symmetries from top to bottom are B_(1g), B_(2g), A_(1g), and E_g.)