# What kinds of electron configurations can we get with octahedral and tetrahedral "Co"^(2+) complexes?

Mar 24, 2017

WARNING! Long answer! The octahedral complexes are either ${t}_{\textrm{2 g}}^{6} \textcolor{w h i t e}{l} {e}_{\textrm{g}}$ (low-spin) or ${t}_{\textrm{2 g}}^{4} \textcolor{w h i t e}{l} {e}_{\textrm{g}}^{3}$ (high-spin).

#### Explanation:

Almost all the tetrahedral complexes are ${e}_{\textrm{g}}^{4} \textcolor{w h i t e}{l} {t}_{\textrm{2 g}}^{3}$ (high-spin).

Crystal Field Theory

In an octahedral field, the the five degenerate $\text{d}$ orbitals are split into two groups:

• two high-energy orbitals, designated as ${e}_{g}$
• three low energy orbitals, designated as ${t}_{2} g$.

The difference between the energy levels is Δ_text(o).

The value of Δ_text(o) depends on both the metal and the nature of the ligands.

In a tetrahedral field, the energy levels are reversed.

The $\text{d}$ orbitals split into:

• three ${t}_{2} g$ high-energy orbitals
• two ${e}_{g}$ low-energy orbitals

Octahedral $\text{Co"^"2+}$ complexes

The electron configuration of $\text{Co"^"2+}$ is ${\text{[Ar]3d}}^{7}$.

When we have a strong-field ligand like $\text{CN"^"-}$, Δ_text(o) is relatively large.

The extra electrons occupy the lower ${t}_{2 g}$ set of orbitals before they go into the upper ${e}_{g}$ levels.

When we have a weak-field ligand like $\text{H"_2"O}$, Δ_text(o) is relatively small.

The electrons fill the orbitals in a Hund's Rule type of order and pair up only when they have no other choice.

["Co"("H"_2"O")_6]^"2+" has the maximum number of half-filled orbitals and is called a high-spin state.

A high-field ligand like $\text{CN"^"-}$ causes Δ_text(o) to be so large that the lower orbitals are filled in before the higher orbitals.

Thus, ["Co"("CN")_6]^"4-" has a filled set of low-energy orbitals and is called a low-spin state.

Tetrahedral $\text{Co"^"2+}$ complexes

Δ_text(t) is about half the size of Δ_text(o), so almost all tetrahedral complexes are weak field/high spin.

Thus, tetrahedral $\text{Co"^"2+}$ complexes have an ${e}_{\textrm{g}}^{4} \textcolor{w h i t e}{l} {t}_{\textrm{2 g}}^{3}$ configuration.