In an anti-bonding MO the electron density is minimum

between the nuclei

The correct answer is option 2. between the nuclei.

Let us delve into the nature of molecular orbitals, particularly focusing on anti-bonding molecular orbitals and their electron density distribution.

Molecular Orbitals (MO)

When atomic orbitals combine during the formation of a molecule, they form molecular orbitals. These molecular orbitals can be classified as either bonding or anti-bonding based on the phase relationship of the combining atomic orbitals.

Bonding Molecular Orbitals

Formation: Constructive interference of atomic orbitals.

Electron Density: High electron density between the nuclei.

Stability: Electrons in bonding MOs stabilize the molecule as they create an attractive force between the nuclei.

Anti-Bonding Molecular Orbitals

Formation: Destructive interference of atomic orbitals.

Electron Density: A node (region of zero electron density) forms between the nuclei.

Stability: Electrons in anti-bonding MOs destabilize the molecule since the electron density between the nuclei is minimized, leading to a lack of attractive force in that region.

Understanding the Electron Density in Anti-Bonding MOs

Destructive Interference : When two atomic orbitals combine out of phase (meaning their wave functions have opposite signs), they create an anti-bonding MO. This out-of-phase combination results in destructive interference where the wave functions cancel each other out.

Node Formation: The destructive interference leads to a node, a plane or region where the probability of finding an electron is zero. This node is typically located between the nuclei of the bonding atoms.

Electron Density Distribution: In an anti-bonding MO, electron density is not uniformly distributed. The presence of the node means that the electron density is particularly low or zero at the point between the two nuclei, which is in contrast to bonding MOs where electron density is maximized between the nuclei.

Analyzing the Options

1. Around one atom of the molecule: This is not accurate for anti-bonding MOs, as the node is specifically between the nuclei, not localized around a single atom.

2. Between the nuclei: This is correct. The hallmark of an anti-bonding MO is the node between the nuclei, where the electron density is minimized or zero. This node results from the destructive interference of the atomic orbitals.

3. At a point away from the nuclei of the molecule: While the electron density can be higher away from the nuclei in anti-bonding MOs, this does not capture the key feature of the minimized electron density between the nuclei. The important concept is the node (zero electron density) between the nuclei

4. At no place: This is incorrect because there is a specific region where the electron density is minimized, which is the node between the nuclei.

Visual Representation

Consider the simplest case of molecular orbitals formed from \(1s\) atomic orbitals, like in the hydrogen molecule ion (\(H_2^+\)):

Bonding MO (\(\sigma_{1s}\)): Constructive interference leads to increased electron density between the nuclei.

Anti-Bonding MO (\(\sigma_{1s}^*\)): Destructive interference creates a node between the nuclei where the electron density is zero.

Therefore, the correct and detailed explanation confirms that in an anti-bonding molecular orbital, the electron density is minimized between the nuclei: 2. between the nuclei.