According to molecular theory, the species among the following that does not exist is:

Options

A. `He_(2^+)`
B. `He_(2^-)`
C. `Be_2`
D. `O_2^(2-)`

Answer

To determine which species among the given options does not exist, we need to calculate the bond order for each species. The bond order can be calculated using the formula:

\[ \text{Bond Order} = \frac{(\text{Number of bonding electrons} - \text{Number of antibonding electrons})}{2} \]

If the bond order is 0, the molecule does not exist.

### Step 1: Analyze BE2

1. **Electron Configuration**: For two beryllium (Be) atoms, each has the configuration 1s² 2s². Therefore, for BE₂, we have:
- Total electrons = 2 (from each Be) = 4 electrons.
- Molecular orbital configuration:
- σ(1s)², σ*(1s)², σ(2s)².

2. **Count Electrons**:
- Bonding electrons = 4 (σ(1s)² + σ(2s)²)
- Antibonding electrons = 2 (σ*(1s)²)

3. **Calculate Bond Order**:
\[ \text{Bond Order} = \frac{(4 - 2)}{2} = \frac{2}{2} = 1 \]
- Since the bond order is 1, BE₂ exists.

### Step 2: Analyze O2²⁻

1. **Electron Configuration**: For O₂²⁻, we have 8 electrons from each O atom and 2 additional electrons due to the 2- charge, giving us a total of 18 electrons.
- Molecular orbital configuration:
- σ(1s)², σ*(1s)², σ(2s)², σ*(2s)², σ(2p)², π(2p)², π*(2p)².

2. **Count Electrons**:
- Bonding electrons = 10 (σ(1s)² + σ(2s)² + σ(2p)² + π(2p)²)
- Antibonding electrons = 8 (σ*(1s)² + σ*(2s)² + π*(2p)²)

3. **Calculate Bond Order**:
\[ \text{Bond Order} = \frac{(10 - 8)}{2} = \frac{2}{2} = 1 \]
- Since the bond order is 1, O₂²⁻ exists.

### Step 3: Analyze He₂⁻

1. **Electron Configuration**: For He₂⁻, we have 2 electrons from each He atom and 1 additional electron due to the negative charge, giving us a total of 5 electrons.
- Molecular orbital configuration:
- σ(1s)², σ*(1s)², σ(2s)¹.

2. **Count Electrons**:
- Bonding electrons = 3 (σ(1s)² + σ(2s)¹)
- Antibonding electrons = 2 (σ*(1s)²)

3. **Calculate Bond Order**:
\[ \text{Bond Order} = \frac{(3 - 2)}{2} = \frac{1}{2} = 0.5 \]
- Since the bond order is 0.5, He₂⁻ exists.

### Step 4: Analyze He₂⁺

1. **Electron Configuration**: For He₂⁺, we have 4 electrons (2 from each He) minus 1 due to the positive charge, giving us a total of 3 electrons.
- Molecular orbital configuration:
- σ(1s)², σ*(1s)¹.

2. **Count Electrons**:
- Bonding electrons = 2 (σ(1s)²)
- Antibonding electrons = 1 (σ*(1s)¹)

3. **Calculate Bond Order**:
\[ \text{Bond Order} = \frac{(2 - 1)}{2} = \frac{1}{2} = 0.5 \]
- Since the bond order is 0.5, He₂⁺ exists.

### Conclusion

After analyzing all the species, we find that:

- BE₂ has a bond order of 1 (exists).
- O₂²⁻ has a bond order of 1 (exists).
- He₂⁻ has a bond order of 0.5 (exists).
- He₂⁺ has a bond order of 0.5 (exists).

Thus, the species that does not exist among the given options is **BE₂**.