Question

Match List - I with List - II. Match the number of d-electrons and CFSE in tetrahedral complexes (ignore pairing) 

Choose the correct answer from the options given below : 
 

• A. A-III, B-I, C-IV, D-II
• B. A-III, B-I, C-II, D-IV
• C. A-IV, B-I, C-II, D-III
• D. A-II, B-III, C-IV, D-I

Hint:

Remember the inversion between octahedral and tetrahedral field splitting: Octahedral is $t_{2g}$ (lower, -0.4) and $e_g$ (upper, +0.6). Tetrahedral is $e$ (lower, -0.6) and $t_2$ (upper, +0.4). Tetrahedral complexes are essentially always high-spin!

Answer 1

The Correct Option is C

Step 1: Concept:
The question asks for the Crystal Field Stabilization Energy (CFSE) of tetrahedral complexes for various $d^n$ configurations. Tetrahedral complexes almost exclusively form high-spin complexes because the tetrahedral splitting parameter ($\Delta_t$) is very small ($\Delta_t \approx \frac{4}{9}\Delta_o$).

Step 2: Key Formula or Approach:
In a tetrahedral crystal field, the $d$-orbitals split into two sets:
- A lower energy doubly degenerate $e$ set.
- A higher energy triply degenerate $t_2$ set.
The energy of the $e$ orbitals is lowered by $-0.6 \Delta_t$, and the energy of the $t_2$ orbitals is raised by $+0.4 \Delta_t$ relative to the barycenter.
\[ \text{CFSE} = [(-0.6 \times n_e) + (0.4 \times n_{t_2})] \Delta_t \]
where $n_e$ and $n_{t_2}$ are the number of electrons in the $e$ and $t_2$ levels, respectively. The problem asks us to ignore pairing energy.

Step 3: Step-by-step Explanation:
Since they are high-spin, we fill the 5 orbitals singly before any pairing occurs:

• A. $d^6$: Configuration is $e^3 t_2^3$ (first 5 electrons singly occupy all orbitals, the 6th pairs in the lower $e$ set).
$\text{CFSE} = [3(-0.6) + 3(0.4)]\Delta_t = [-1.8 + 1.2]\Delta_t = -0.6 \Delta_t$. (Matches IV).

• B. $d^4$: Configuration is $e^2 t_2^2$ (all 4 electrons unpaired).
$\text{CFSE} = [2(-0.6) + 2(0.4)]\Delta_t = [-1.2 + 0.8]\Delta_t = -0.4 \Delta_t$. (Matches I).

• C. $d^7$: Configuration is $e^4 t_2^3$.
$\text{CFSE} = [4(-0.6) + 3(0.4)]\Delta_t = [-2.4 + 1.2]\Delta_t = -1.2 \Delta_t$. (Matches II).

• D. $d^8$: Configuration is $e^4 t_2^4$.
$\text{CFSE} = [4(-0.6) + 4(0.4)]\Delta_t = [-2.4 + 1.6]\Delta_t = -0.8 \Delta_t$. (Matches III).
The complete matching sequence is A-IV, B-I, C-II, D-III.

Step 4: Final Answer:
The correctly matched sequence corresponds to option (C).