Chemistry
Why Strong Field Ligands Increase Crystal Field Splitting
Quick fact
Ligands like CO and CN⁻ are called strong field ligands because they create a large energy gap between the t₂g and eg orbitals, often forcing electrons to pair up and yielding low-spin complexes, unlike weak field ligands like I⁻ or Br⁻.
Why this is interesting
You know that some metal complexes are intensely colored while others are pale, and some are magnetic while others are not. Why does the simple change of a ligand from water to cyanide radically alter the complex's properties?
Read the full explanation
Understanding Why Strong Field Ligands Increase Crystal Field Splitting
Imagine a metal ion surrounded by six ligands, like a ball held in a cage of six springs. These ligands are negative or polar, and they push on the d-orbitals of the metal. But not all d-orbitals point equally at those ligands. Some, like the d(x²−y²) and d(z²) orbitals, point directly at the ligands, while others, like the d(xy), d(xz), and d(yz), point between them. So the electron in a pointing-at-the-ligand orbital feels more repulsion than one in a between-the-ligands orbital. That difference in repulsion creates the energy splitting we call Δoct. Now, different ligands create different amounts of repulsion. Strong field ligands, such as cyanide (CN⁻) and carbon monoxide (CO), are small, polarizable, and can form strong bonds with the metal. Crucially, they are able to not only donate electrons to the metal (σ-donation) but also accept electron density back from the metal into their empty orbitals (π-acceptance). This back-donation removes electron density from the metal's d-orbitals, reducing electron-electron repulsion within the t₂g set and stabilizing those orbitals. The result is that the t₂g orbitals drop in energy relative to the eg set, and the gap between the two sets becomes larger. This larger Δoct is exactly what we mean by a strong field ligand.
A deeper explanation
The root cause of the increased crystal field splitting with strong field ligands lies in the interaction between the ligand and the metal d-orbitals. In the crystal field model, we treat the ligand as point charges, and the splitting arises from electrostatic repulsion. However, this model fails to fully explain why CO and CN⁻, which are not very negatively charged, are so strong. We need to consider the covalent contribution: σ-donation from the ligand to the metal raises the energy of the eg orbitals, while π-acceptance (or π-backbonding) stabilizes the t₂g orbitals. Strong σ-donors increase Δoct by pushing the eg orbitals up. Even more effective are π-acceptor ligands: they have empty π or p orbitals of appropriate symmetry to overlap with the filled t₂g metal d-orbitals. The metal donates electron density into these empty ligand orbitals, which effectively removes electron density from the t₂g set. This stabilizes the t₂g orbitals (lowers their energy) and, together with the raising of eg by σ-donation, enlarges Δoct. In contrast, weak field ligands like halides are π-donors; they have filled p orbitals that can donate into the t₂g set, pushing those orbitals up and reducing Δoct. Thus, the spectrochemical series – I⁻ < Br⁻ < Cl⁻ < F⁻ < OH⁻ < H₂O < NH₃ < en < CN⁻ < CO – reflects an increasing ability to raise eg and destabilize t₂g, with the strongest field ligands being those that combine strong σ-donation with strong π-acceptance. This mechanism is fundamental to predicting the magnetic properties of complexes, the intensity of their colors, and their behavior in spin crossover phenomena.