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

We need to determine the mathematical representation of an antibonding sigma molecular orbital ($$\sigma^*$$).

Recall the LCAO (Linear Combination of Atomic Orbitals) method

When two atomic orbitals $$\psi_A$$ and $$\psi_B$$ combine, they form two molecular orbitals:

- Bonding MO ($$\sigma$$): formed by constructive (in-phase) combination

- Antibonding MO ($$\sigma^*$$): formed by destructive (out-of-phase) combination

Write the mathematical expressions

The bonding molecular orbital is formed by the addition of the two wave functions:

$$\sigma = \psi_A + \psi_B$$

(with a normalisation constant, which is omitted here for simplicity)

The antibonding molecular orbital is formed by the subtraction of the two wave functions:

$$\sigma^* = \psi_A - \psi_B$$

Understand the physical meaning

In the bonding MO, the wave functions reinforce each other in the internuclear region, leading to increased electron density between the nuclei and a stable bond. In the antibonding MO ($$\sigma^*$$), the wave functions cancel in the internuclear region, creating a node (region of zero electron density) between the nuclei. This results in a destabilising effect that weakens bonding.

The correct answer is Option (2): $$\psi_A - \psi_B$$.