While Ti³⁺, V³⁺, Fe³⁺ and Co²⁺ can afford a large number of tetrahedral complexes, Cr³⁺ never does this, the reason being

Crystal field stabilization energy in octahedral vis-a-vis tetrahedral Cr³⁺ system plays the deciding role

The correct answer is option 1. Crystal field stabilization energy in octahedral vis-a-vis tetrahedral Cr³⁺ system plays the deciding role.

Let us delve deeper into why \(Cr^{3+}\) prefers octahedral complexes over tetrahedral complexes, especially compared to other transition metal ions like \(Ti^{3+}\), \(V^{3+}\), \(Fe^{3+}\), and \(Co^{2+}\).

Factors Influencing Complex Formation:

Electron Configuration: Chromium \((Cr)\) in its \(+3\) oxidation state has a \(3d^3\) electron configuration. This means there are three electrons in the \(3d\) orbitals.

Crystal Field Theory:

Octahedral Field: In an octahedral crystal field, the d-orbitals split into two sets: \( t_{2g} \) (lower energy) and \( e_g \) (higher energy). For Cr³⁺ (\(3d^3\)), three electrons occupy the \( t_{2g} \) orbitals, which is a stable configuration due to the favorable crystal field stabilization energy (CFSE).

Tetrahedral Field: In a tetrahedral crystal field, the splitting of d-orbitals is different (\( t_{2} \) and \( e \)). The CFSE in tetrahedral complexes is generally lower than in octahedral complexes for \(3d\) electrons, making tetrahedral complexes less stable.

Crystal Field Stabilization Energy (CFSE):

CFSE refers to the overall energy difference between the high-energy and low-energy sets of d-orbitals in a crystal field. For \(Cr^{3+}\), the CFSE is more favorable in an octahedral field due to the higher energy splitting between \( t_{2g} \) and \( e_g \) orbitals, which provides greater stabilization.

Comparison with Other Metal Ions:

\(Ti^{3+}\), \(V^{3+}\), \(Fe^{3+}\), \(Co^{2+}\): These ions can form both octahedral and tetrahedral complexes, but their preferences may differ based on their electron configurations and the ligand field they encounter.

\(Cr^{3+}\): Specifically, \(Cr^{3+}\) has a \(3d^3\) configuration, which is particularly stable in an octahedral field due to the favorable arrangement of electrons in the \( t_{2g} \) orbitals.

Conclusion:

The main reason why \(Cr^{3+}\) does not typically form tetrahedral complexes, unlike \(Ti^{3+}\), \(V^{3+}\), \(Fe^{3+}\), and \(Co^{2+}\), is due to the significantly higher crystal field stabilization energy (CFSE) it experiences in octahedral complexes compared to tetrahedral complexes. This CFSE difference arises from the specific electronic structure of \(Cr^{3+}\) and the energy levels of its d-orbitals in different ligand environments. Therefore, the correct answer remains: Crystal field stabilization energy in octahedral vis-à-vis tetrahedral Cr³⁺ system plays the deciding role.