Which of the following pictorial diagram most correctly represents the \( \pi^* \) (\( \pi \) - antibonding) molecular orbital between two atoms if the internuclear axis is taken to be in the z-direction ( \( \xrightarrow{\text{z-axis}} \) )?}
Step 1: Understanding the Concept:
Molecular orbitals form by the overlap of atomic orbitals. \( \pi \) - orbitals form by lateral (sideways) overlap. Bonding \( \pi \) orbitals have constructive interference, while antibonding \( \pi^* \) orbitals have destructive interference, resulting in a nodal plane between the two nuclei.
Step 2: Key Formula or Approach:
Identify the characteristics of \( \pi^* \) MO:
1. Lateral overlap of p-orbitals.
2. Destructive overlap results in a nodal plane perpendicular to the internuclear axis.
3. Opposite phases are adjacent across the vertical node.
Step 3: Detailed Explanation:
Looking at the provided diagrams:
- Diagram (A) shows side-on constructive overlap (bonding \( \pi \)).
- Diagram (B) shows end-on destructive overlap (antibonding \( \sigma^* \)).
- Diagram (C) shows lateral p-orbitals with opposite phases (\( + \) and \( - \)) adjacent to each other across a nodal plane between the atoms. This is the hallmark of a \( \pi^* \) orbital.
- Diagram (D) shows a different sigma overlap.
Step 4: Final Answer:
Diagram (C) correctly represents the \( \pi^* \) molecular orbital.
