Bond energy has been defined in the text as the amount of energy required to break a chemical bond, so we have come to think of the addition of energy as breaking bonds. However, in some cases the addition of energy can cause the formation of bonds. For example, in a sample of helium gas subjected to a high-energy source, some He_ molecules exist momentarily and then dissociate. Use MO theory (and diagrams) to explain why \(\mathrm{He}_{2}\) molecules can come to exist and why they dissociate.

Molecular Orbital Theory (MO theory) is a method to describe the electronic structure of molecules. It combines atomic orbitals from individual atoms to form molecular orbitals that belong to the entire molecule. These molecular orbitals can have different shapes, energies, and their occupation by electrons determines the stability of the molecule.

For constructing the MO diagram, we need to consider atomic orbitals of the two Helium atoms (He). Each He atom has two electrons, occupying the 1s orbital. When the two He atoms come close to each other, their atomic orbitals interact, and due to their overlapping, they form two molecular orbitals: 1. Bonding Molecular Orbital (σ): This molecular orbital has lower energy than the parent atomic orbitals and is formed by the in-phase combination of the atomic orbitals. 2. Antibonding Molecular Orbital (σ*): This molecular orbital has higher energy than the parent atomic orbitals and is formed by the out-of-phase combination of the atomic orbitals. The MO diagram for He2 molecule is shown as follows: - Atomic orbitals from two He atoms are on the left and right sides. - Molecular orbitals are represented in the middle. The lower energy bonding molecular orbital (σ) is at the bottom and the higher energy antibonding molecular orbital (σ*) is at the top.

Each Helium atom has 2 electrons in its 1s orbital. When forming He2, there are a total of 4 electrons to be placed in the molecular orbitals. According to Aufbau principle, electrons fill the molecular orbitals in order of increasing energy. So, two electrons will go into the bonding molecular orbital (σ) and the remaining two electrons will go into the antibonding molecular orbital (σ*). Hence, electron configuration of He2 is: σ2σ*2

From the electron configuration of He2 (σ2σ*2), we can observe that the number of electrons in bonding orbital is equal to the number of electrons in antibonding orbital. This means that the stabilization energy provided by the electrons in bonding molecular orbital is exactly canceled by the destabilization energy due to electrons in the antibonding molecular orbital. So, when Helium gas is subjected to a high-energy source, some He2 molecules can come to exist momentarily due to the formation of σ bonding molecular orbital. However, the destabilizing effect of the electrons in σ* antibonding molecular orbital leads to the rapid dissociation of these He2 molecules. In conclusion, MO theory and MO diagrams help us understand the momentary existence and dissociation of He2 molecules under high-energy conditions. The formation of bonding and antibonding molecular orbitals and their occupation by electrons dictate the overall stability of the molecule.