Which of the following combination is not allowed in the `LCAO` method for the formation of molecular orbital (consider Z-axis as the molecular axis) ? .

Options

A. `s +p_(x)`
B. `s +p_(z)`
C. `p_(x) +p_(x)`
D. `p_(z) +p_(z)`

Explanation

To determine which combination is not allowed in the Linear Combination of Atomic Orbitals (LCAO) method for the formation of molecular orbitals, we need to analyze the symmetry and orientation of the atomic orbitals involved.

### Step-by-Step Solution:

1. **Understanding LCAO Method**: The LCAO method states that atomic orbitals can combine to form molecular orbitals if they have the proper symmetry and orientation for effective overlap.

2. **Identifying the Orbitals**: We have the following combinations to analyze:
- Option 1: s + px
- Option 2: s + pz
- Option 3: px + px
- Option 4: pz + pz

3. **Analyzing Each Combination**:
- **Option 1: s + px**: The s orbital is spherical and has no directional preference, while the px orbital has a directional lobe along the x-axis. Since they do not have the same orientation for effective overlap, this combination is **not allowed**.
- **Option 2: s + pz**: The s orbital can effectively overlap with the pz orbital, which has a lobe along the z-axis. This combination is **allowed**.
- **Option 3: px + px**: Both px orbitals have the same orientation along the x-axis, allowing for effective overlap. This combination is **allowed**.
- **Option 4: pz + pz**: Similar to the px orbitals, both pz orbitals have the same orientation along the z-axis, allowing for effective overlap. This combination is **allowed**.

4. **Conclusion**: The combination that is not allowed in the LCAO method is **Option 1: s + px**.

### Final Answer:
The combination that is not allowed in the LCAO method for the formation of molecular orbitals is **Option 1: s + px**.

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