Pictorial Diagram of Pi Antibonding Molecular Orbital

To determine the correct pictorial diagram representing the $\pi^*$ ($\pi$-antibonding) molecular orbital, we analyze the formation and symmetry of $\pi$-antibonding orbitals using Molecular Orbital Theory (MOT):

1. Formation of $\pi^*$ Molecular Orbital

When two parallel atomic orbitals (such as $p_x$ or $p_y$ orbitals) overlap laterally (perpendicular to the internuclear $z$-axis), they combine to form $\pi$ molecular orbitals.

The antibonding molecular orbital ($\pi^*$) is formed by the out-of-phase combination (destructive interference) of the two atomic orbital wavefunctions: $\psi_{\pi^*} = \psi_A - \psi_B$

2. Phase Distribution and Nodal Planes

• Let atomic orbital $A$ have a positive phase ($+$) in its upper lobe and a negative phase ($-$) in its lower lobe.
• Subtracting atomic orbital $B$ inverts its phases, resulting in a negative phase ($-$) in its upper lobe and a positive phase ($+$) in its lower lobe.

Therefore, the phase distribution across the four lobes of the $\pi^*$ orbital is:

• Upper-left lobe: $(+)$
• Lower-left lobe: $(-)$
• Upper-right lobe: $(-)$
• Lower-right lobe: $(+)$

This configuration creates two nodal planes (where electron density is zero):

1. Horizontal nodal plane: Along the internuclear axis ($z$-axis), separating the upper and lower lobes.
2. Vertical nodal plane: Perpendicular to the internuclear axis, passing midway between the two nuclei and separating the left and right lobes.

3. Visual Representation

In orbital diagrams, different phases ($+$ and $-$) are represented by shaded and unshaded regions, respectively:

• Diagonally opposite lobes share the same phase (both shaded or both unshaded).
• Adjacent lobes have opposite phases (one shaded and one unshaded).

Looking at the options:

• Diagram C correctly shows four lobes with alternating phases: the top-left and bottom-right lobes are shaded, while the top-right and bottom-left lobes are unshaded. It clearly depicts the two perpendicular nodal planes characteristic of a $\pi^*$ orbital.

Correct Option: C