Which of the following configuration will not give John- teller distortion ( In both HS & LS complexes ) ?

Options

A. `d^(8)`
B. `d^(7)`
C. `d^(6)`
D. `d^(4)`

Explanation

To determine which configuration will not exhibit Jahn-Teller distortion (JTD) in both high-spin (HS) and low-spin (LS) complexes, we need to analyze the electron configurations of transition metal complexes and their corresponding d-electron counts.

### Step-by-Step Solution:

1. **Understand Jahn-Teller Distortion**:
- Jahn-Teller distortion occurs in coordination complexes when there is an asymmetry in the distribution of electrons in the d-orbitals. Specifically, if either the eg or t2g orbitals are unsymmetrical, JTD is likely to occur.

2. **Identify Electron Configurations**:
- We need to examine the d-electron counts for different configurations, particularly focusing on d8, d7, and d4 complexes.

3. **Analyze d8 Configuration**:
- **High-Spin (HS)**: In a d8 high-spin configuration, the electrons fill the orbitals as follows:
- t2g: ↑ ↑ ↑
- eg: ↑ ↑
- Here, both eg and t2g orbitals are symmetrical, hence no JTD occurs.
- **Low-Spin (LS)**: In a d8 low-spin configuration, the filling is:
- t2g: ↑ ↑ ↑ ↑
- eg: ↑ ↑
- Again, both orbitals remain symmetrical, indicating no JTD.

4. **Analyze d7 Configuration**:
- **High-Spin (HS)**:
- t2g: ↑ ↑ ↑
- eg: ↑ ↑
- The t2g is unsymmetrical, leading to JTD.
- **Low-Spin (LS)**:
- t2g: ↑ ↑ ↑
- eg: ↑ ↑
- The eg is unsymmetrical, leading to JTD.

5. **Analyze d4 Configuration**:
- **High-Spin (HS)**:
- t2g: ↑ ↑
- eg: ↑ ↑ ↑
- The eg is unsymmetrical, leading to JTD.
- **Low-Spin (LS)**:
- t2g: ↑ ↑
- eg: ↑ ↑ ↑
- The t2g is unsymmetrical, leading to JTD.

6. **Conclusion**:
- The only configuration that does not exhibit Jahn-Teller distortion in both high-spin and low-spin states is the **d8 configuration**.

### Answer:
**The configuration that will not give Jahn-Teller distortion in both high-spin and low-spin complexes is d8.**