Question

When $\psi_A$ and $\psi_B$ are the wave functions of atomic orbitals, then $\sigma^*$ is represented by :

• A. $\psi_A - 2\psi_B$
• B. $\psi_A - \psi_B$
• C. $\psi_A + 2\psi_B$
• D. $\psi_A + \psi_B$

Answer 1

The Correct Option is B

In molecular orbital theory, molecular orbitals form from the linear combination of atomic orbitals. When dealing with diatomic molecules, these combinations form bonding and antibonding orbitals.

The symbols \(\psi_A\) and \(\psi_B\) represent the wave functions of atomic orbitals from atoms A and B, respectively.

To form molecular orbitals, atomic orbitals can combine constructively or destructively:

• Constructive combination results in a bonding molecular orbital, which is generally represented as \(\psi_A + \psi_B\).
• Destructive combination results in an antibonding molecular orbital, denoted by \(\sigma^*\), which is typically represented as \(\psi_A - \psi_B\).

The antibonding molecular orbital, \(\sigma^*\), is formed when the wave functions interfere destructively, leading to a nodal plane between the nuclei where the electron density is low.

Given these explanations, the correct representation of \(\sigma^*\) is:

Correct Answer: \(\psi_A - \psi_B\)

Let's rule out the other options:

• \(\psi_A - 2\psi_B\): This does not correspond to a standard form for molecular orbitals.
• \(\psi_A + 2\psi_B\): This would enhance constructive interference and does not represent an antibonding orbital.
• \(\psi_A + \psi_B\): This is typically the expression for a bonding orbital, not an antibonding one.

Answer 2

The bonding ($\sigma$) and anti-bonding ($\sigma^*$) molecular orbitals are formed by the constructive and destructive interference of atomic orbitals' wave functions.
For an anti-bonding molecular orbital ($\sigma^*$):
\[ \psi_{\sigma^*} = \psi_A - \psi_B. \]
This occurs due to the out-of-phase overlap of the wave functions, leading to a node between the nuclei and a higher energy state.
Thus, $\sigma^*$ is represented by:
\[ \psi_A - \psi_B. \]