For which of the followng `d^(n)` configuration complexes, can not exist in both high spin and low spin forms:
(I) `d^(3)`
(II) `d^(5)`
(III) `d^(6)`
(IV) `d^(8)`

Options

A. I, II & III
B. II, III & IV
C. I & IV
D. none of these

Explanation

To determine which of the given `d^(n)` configuration complexes cannot exist in both high spin and low spin forms, we need to analyze the behavior of the d-electrons in the presence of strong and weak field ligands.

### Step-by-Step Solution:

1. **Understanding High Spin and Low Spin Configurations**:
- High spin complexes occur when the splitting energy (Δ) is less than the pairing energy (P). Electrons occupy higher energy orbitals before pairing occurs.
- Low spin complexes occur when the splitting energy (Δ) is greater than the pairing energy (P). Electrons pair up in lower energy orbitals before occupying higher ones.

2. **Analyzing Each Configuration**:
- **(I) `d^(3)` Configuration**:
- For `d^(3)`, there are three electrons. They will fill the three available orbitals (t2g) without pairing. This configuration is independent of the ligand field strength, meaning it cannot exist in both high spin and low spin forms. It will always be high spin.

- **(II) `d^(5)` Configuration**:
- For `d^(5)`, the electrons can either fill the t2g orbitals (low spin) or occupy the eg orbitals (high spin). Therefore, `d^(5)` can exist in both high spin and low spin forms depending on the ligand field strength.

- **(III) `d^(6)` Configuration**:
- For `d^(6)`, similar to `d^(5)`, it can either have all six electrons in the t2g orbitals (low spin) or fill the t2g and start filling eg orbitals (high spin). Thus, `d^(6)` can also exist in both forms.

- **(IV) `d^(8)` Configuration**:
- For `d^(8)`, the electrons will fill the orbitals in a way that they will always pair up in the t2g orbitals before occupying the eg orbitals. This configuration can also exist in both high spin and low spin forms depending on the ligand field.

3. **Conclusion**:
- The only configuration that cannot exist in both high spin and low spin forms is `d^(3)`. Therefore, the answer is:
- **Answer**: (I) `d^(3)`