Match the entries of column I with appropriate entries of column II and choose the correct option out of the four options given.

(a)-(iii), (b)-(i), (c)-(ii), (d)-(iv)

The correct answer is option 3. (a)-(iii), (b)-(i), (c)-(ii), (d)-(iv).

Let us delve deeper into the concept of crystal field stabilization energy (CFSE) and its relationship with the electronic configuration of transition metal ions in coordination complexes.

1. Crystal Field Stabilization Energy (CFSE):

CFSE is a term used to describe the energy difference between the d-orbitals in a free ion compared to their energy in a coordination complex where they are affected by the surrounding ligands. In transition metal complexes, the interaction between the metal ion and the ligands creates a crystal field. This field splits the degenerate d-orbitals into two sets: \(e_g\) (higher energy) and \(t_{2g}\) (lower energy). The energy difference between these sets is denoted by Δo. CFSE arises from the difference in energy between the lower and higher energy sets of d-orbitals. CFSE is a crucial factor in determining the stability and reactivity of transition metal complexes.

2. Effect of Electronic Configuration on CFSE:

The electronic configuration of the metal ion influences the magnitude of CFSE. Specifically, the number of d-electrons plays a significant role. For a given coordination geometry and ligand field, the CFSE varies depending on whether the d-orbitals are fully filled, half-filled, or partially filled. Different configurations have different CFSE values, leading to varying stabilities of oxidation states in transition metal complexes.

Now, let's relate this to the entries in the question:

(a) \(d^4\) Configuration:

In a \(d^4\) configuration, there are four d-electrons. This configuration corresponds to an incomplete \( t_{2g} \) set and an empty \( e_g \) set. The CFSE is negative, indicating that energy is released when the d-orbitals split. The magnitude of CFSE for \(d^4\) is -0.6Δo.

(b) \(d^5\) Configuration:

In a \(d^5\) configuration, there are five d-electrons. This configuration results in exactly half-filled \( t_{2g} \) and \( e_g \) sets. There is no energy difference between the sets, so the CFSE is zero.

(c) d^6 Configuration:

In a \(d^6\) configuration, there are six d-electrons. This configuration corresponds to a fully filled \( t_{2g} \) set and an empty \( e_g \) set. The CFSE is negative, but less so than for \(d^4\), with a magnitude of -0.4Δo.

(d) \(d^7\) Configuration:

In a \(d^7\) configuration, there are seven d-electrons. This configuration results in a fully filled \( t_{2g} \) set and one electron in the \( e_g \) set. The CFSE is more negative than for\( d^6\), with a magnitude of -0.8Δo.

Finally, the correct match between column I and II is:

(a) \(d^4\): (iii) -0.6Δo

(b) \(d^5\): (i) 0.0Δo

(c) \(d^6\): (ii) -0.4Δo

(d) \(d^7\): (iv) -0.8Δo

This demonstrates how the electronic configuration of transition metal ions influences CFSE and, consequently, their stability in coordination complexes.