Which one of the following will yield the highest splitting of d orbitals?

\(CN^–\)

The correct answer is option 3. \(CN^–\).

In coordination chemistry, the splitting of d orbitals is a phenomenon known as crystal field splitting. It occurs when a central metal ion in a coordination complex is surrounded by ligands. The nature of the ligands determines the extent of splitting of the metal ion's d orbitals.

Ligands can be classified into two categories based on their ability to cause d orbital splitting:

1. Strong-field ligands:  These ligands cause a large energy difference (splitting) between the lower-energy set of d orbitals (\(t_{2g}\)) and the higher-energy set (\(e_g\)). Strong-field ligands typically have lone pair electrons or π-acceptor groups that interact strongly with the metal d orbitals.

2. Weak-field ligands: These ligands cause a smaller energy difference between the lower and higher-energy sets of d orbitals.

Now, let's examine the ligands provided in the options:

(1) \(S^{2-}\) (sulfide): Sulfide is generally a weak-field ligand. It does not cause significant splitting of d orbitals.

(2) \(OH^-\) (hydroxide): Hydroxide is also a weak-field ligand, and it does not lead to large d orbital splitting.

(3) \(CN^-\) (cyanide):  Cyanide is a strong-field ligand. The carbon and nitrogen atoms in the cyanide ion form a strong π bond with the metal, leading to significant d orbital splitting.

(4) \(EDTA^{4-}\) (ethylenediaminetetraacetate): EDTA is a weak-field ligand. It has multiple oxygen atoms in its structure, but its overall interaction with metal d orbitals is weaker compared to strong-field ligands like cyanide.

Therefore, among the given options, \(CN^-\) will yield the highest splitting of d orbitals due to its strong-field nature. The correct answer is option (3).