Animated Solution for Chemistry - Coordination Compounds: Complete removal of both the axial ligands (along the z-axis) from an octahedral complex leads to which of the following splitting patterns? (relative orbital energies not on scale).

To understand the crystal field splitting in a square planar complex, we must first start with its parent geometry: the octahedral complex.

Imagine a central metal ion surrounded by six ligands positioned along the $+x,-x,+y,-y,+z,$ and $-z$ axes. In this spherically symmetric field, all five d-orbitals would have the same energy. However, the presence of the ligands creates an electrostatic field that breaks this degeneracy.

The d-orbitals split into two distinct sets based on their spatial orientation relative to the ligands. The $e_g$ set, consisting of the $d_{x^2-y^2}$ and $d_{z^2}$ orbitals, points directly at the ligands and experiences maximum repulsion, pushing its energy higher.

Conversely, the $t_{2g}$ set, comprising the $d_{xy},d_{yz},$ and $d_{zx}$ orbitals, points between the axes. These orbitals experience less direct repulsion, resulting in a lower energy state.

Now, let's perform a thought experiment. What happens if we take the two axial ligands along the z-axis and pull them completely away to infinity?

By removing these two ligands, our octahedral complex transforms into a square planar complex. This drastic change in geometry fundamentally alters the electrostatic repulsion pattern experienced by the d-orbitals.

The Z-Orbitals

Let's analyze the orbitals that have a z-component. Since the ligands on the z-axis are now gone, any orbital that lies along or contains the z-axis will experience significantly less repulsion.

The $d_{z^2}$ orbital, which previously pointed directly at the axial ligands, sees a massive drop in energy. Similarly, the $d_{xz}$ and $d_{yz}$ orbitals, which lie in planes containing the z-axis, also experience reduced repulsion and drop in energy.

In fact, the $d_{xz}$ and $d_{yz}$ orbitals become the lowest energy orbitals in the entire square planar splitting diagram.

The XY-Plane Orbitals

While the z-axis is now empty, the four ligands in the xy-plane remain perfectly intact.

The orbitals lying in this plane must now bear the brunt of the repulsion. The $d_{x^2-y^2}$ orbital, which points directly at the four remaining ligands along the x and y axes, experiences the absolute maximum repulsion. Its energy skyrockets to the very top of the diagram.

The $d_{xy}$ orbital, which lies between the ligands in the xy-plane, also experiences relatively higher repulsion compared to the z-orbitals. Consequently, its energy rises, often surpassing the energy of the $d_{z^2}$ orbital.

Putting all these shifts together, we arrive at the final crystal field splitting pattern for a square planar complex.

The energy order, from highest to lowest, is: $d_{x^2-y^2}>d_{xy}>d_{z^2}>d_{xz},d_{yz}$

This unique splitting pattern is incredibly important in coordination chemistry. The massive energy gap between the $d_{xy}$ and $d_{x^2-y^2}$ orbitals makes the square planar geometry highly favorable for metal ions with a $d^8$ electron configuration, such as $P{t}^{2+}$ and $P{d}^{2+}$.

The eight electrons pair up and completely fill the lower four orbitals, leaving the high-energy $d_{x^2-y^2}$ orbital completely empty. This results in a highly stable, diamagnetic complex!