Question

How do the bonding and antibonding MOs formed from a given pair of AOs compare to each other with respect to

(a) Energy

(b) Presence of nodes

(c) Inter-nuclear electron density

Short answer

1. The energy of the anti-bonding molecular orbital is higher than the energy of the bonding molecular orbital formed from the atomic orbitals.
2. The presence of nodes (no electron density) can be seen in the anti-bonding orbitals as they are present at higher energy whereas in the bonding molecular orbitals the bond formation between the atomic orbitals takes place at a lower energy level comparatively.
3. The inter-nuclear electron density of the bonding molecular orbitals is greater than the anti-bonding molecular orbitals.

Step-by-step solution

Molecular Bonding Orbitals.

Molecular Bonding Orbitals can be formed from the atomic orbitals of atoms involved. The atomic orbitals are of similar energy which attracts each other and from a molecular having similar energy. The molecular orbitals formed can be:

• Anti-Bonding Molecular Orbitals
• Bonding Molecular Orbitals

The difference between both the molecular is that the anti-bonding molecular orbital is formed because of the side-wise overlapping whereas the bonding molecular orbital is formed as a result of the head-on overlapping.

Subpart (a) The energy of bonding and antibonding MOs formed from a given pair of AOs.

The energy of the anti-bonding molecular orbital is higher than the energy of the bonding molecular orbital formed from the atomic orbitals. The anti-bonding is formed by the atomic orbitals which have different energy.

The energy difference in the atomic orbital of the anti-bonding orbital (A.B.O) is higher than the atomic orbitals involved in the bonding orbitals (B.O).

Subpart (b) The presence of nodes in the bonding and antibonding MOs formed from a given pair of AOs.

There is a combination of p-orbital to form molecular orbital having bonding and anti-bonding orbital. Molecular orbital describes the distribution of electrons of molecules such as the distribution of electrons of an atomic orbital. In this molecule, two bonding atomic orbitals and two anti-bonding atomic orbitals formed a molecular orbital.

Subpart (c) The Inter-nuclear electron density in the bonding and antibonding MOs formed from a given pair of AOs.

The inter-nuclear electron density of the bonding molecular orbitals is greater than the anti-bonding molecular orbitals. The energy of the anti-bonding molecular orbital is higher than the bonding atomic orbitals. That is why the electron is bound to the nucleus in bonding orbitals due to lower energy and stability.

The anti-bonding orbitals have lower electron density between the atoms and therefore forms node (no electron density) in the formation of bond.