Understanding d $\rightarrow$ d Transitions and Ligand Strength

The energy of the lowest energy d $\rightarrow$ d transition in transition metal complexes is determined by the crystal field splitting energy, denoted as $\Delta_o$. A larger $\Delta_o$ corresponds to higher energy transitions.

The magnitude of $\Delta_o$ depends significantly on the nature of the ligands surrounding the metal ion. Ligands are ranked according to their ability to cause splitting in their strength, known as the spectrochemical series.

Spectrochemical Series and Ligand Comparison

The spectrochemical series orders ligands from weakest field to strongest field:

• $H_2O$ (Water) is a relatively weak field ligand.
• $NH_3$ (Ammonia) is a stronger field ligand than $H_2O$.
• $CN^-$ (Cyanide) is a very strong field ligand, significantly stronger than both $H_2O$ and $NH_3$.

Therefore, the order of ligand strength is: $H_2O < NH_3 < CN^-$

Order of Crystal Field Splitting ($\Delta_o$)

For the same metal ion ($Cr^{3+}$ in this case), the crystal field splitting energy ($\Delta_o$) follows the same order as the ligand strength:

$\Delta_o([Cr(H_2O)_6]^{3+}) < \Delta_o([Cr(NH_3)_6]^{3+}) < \Delta_o([Cr(CN)_6]^{3-})$

Determining the Transition Energy Order

The lowest energy d $\rightarrow$ d transition corresponds to the complex with the smallest $\Delta_o$. Based on the order of $\Delta_o$ derived above, the order of the lowest energy d $\rightarrow$ d transition is:

$[Cr(H_2O)_6]^{3+} < [Cr(NH_3)_6]^{3+} < [Cr(CN)_6]^{3-}$

This corresponds to the energy required for an electron to be promoted from a lower energy d-orbital to a higher energy d-orbital.