Understanding the Structure of [Ni(CN)4]^2- using CFT

The question asks about the structure of the complex ion [Ni(CN)₄]^2- according to Crystal Field Theory (CFT).

To determine the structure, we need to consider the metal ion, its oxidation state, the number of ligands, and the nature of the ligand.

• Metal Ion: The metal ion is Nickel (Ni).
• Oxidation State of Ni: Let the oxidation state of Ni be 'x'. The complex has a charge of -2, and the cyanide ligand (CN^-) has a charge of -1.

  x + 4(-1) = -2

  x - 4 = -2

  x = +2

  So, Nickel is in the +2 oxidation state, i.e., Ni²⁺.
• Electronic Configuration of Ni²⁺:

  The atomic number of Ni is 28. The electronic configuration of Ni is [Ar] 3d⁸ 4s².

  The electronic configuration of Ni²⁺ is [Ar] 3d⁸.

• Number of Ligands: There are four CN^- ligands. This indicates a coordination number of 4.
• Nature of the Ligand: CN^- (cyanide) is a strong field ligand.

For a complex with coordination number 4, the common geometries are tetrahedral and square planar. According to CFT, the geometry adopted depends on the d-electron configuration of the metal ion and the strength of the ligands.

For a d⁸ metal ion (like Ni²⁺) with a coordination number of 4:

• Tetrahedral geometry: The d orbitals split into e and t₂ levels. The energy gap is relatively small. In this case, the 8 electrons would fill as $\text{e}^4 \text{t}_2^4$, resulting in two unpaired electrons. Tetrahedral complexes with d⁸ ions are usually paramagnetic.
• Square planar geometry: The d orbitals split into four different energy levels: d_xz, d_yz < d_z² < d_xy < d_x²-y². The energy gap between the highest filled orbital and the empty d_x²-y² orbital is large, especially with strong field ligands. With a strong field ligand like CN^-, the large splitting energy favors pairing of electrons.

Let's fill the 8 electrons in the square planar d-orbital splitting:

• (d_xz, d_yz): 4 electrons (paired)
• (d_z²): 2 electrons (paired)
• (d_xy): 2 electrons (paired)
• (d_x²-y²): 0 electrons

Total electrons filled = 4 + 2 + 2 + 0 = 8. All 8 electrons are paired in the square planar arrangement when the ligand is strong field.

A square planar d⁸ complex with strong field ligands is diamagnetic (zero unpaired electrons). Experimental evidence shows that [Ni(CN)₄]^2- is diamagnetic, which is consistent with the square planar structure.

Therefore, according to CFT, the complex ion [Ni(CN)₄]^2- has a square planar structure due to the d⁸ configuration of Ni²⁺ and the presence of the strong field ligand CN^-, which causes a large crystal field splitting and favors electron pairing.

Based on this analysis, the structure of [Ni(CN)₄]^2- is square planar.