Question

Consider the following molecular orbitals formed from the combination of two hydrogen \(1 s\) orbitals: a. Which is the bonding molecular orbital and which is the antibonding molecular orbital? Explain how you can tell by looking at their shapes. b. Which of the two molecular orbitals is lower in energy? Why is this true?

Short answer

a. The bonding molecular orbital is the one with increased electron density between the nuclei, while the antibonding molecular orbital has a node between the nuclei, resulting in decreased electron density. By looking at their shapes, we can identify which one shows a high concentration of shading or lobe density between the nuclei (bonding) and which one has a node (antibonding). b. The bonding molecular orbital is lower in energy due to the stronger bond it creates, whereas the antibonding molecular orbital has a higher energy level because of the weak or non-existent bond.

Step-by-step solution

Understanding Molecular Orbitals

Molecular orbitals are formed when atomic orbitals, in this case, two hydrogen 1s orbitals, combine during the formation of a chemical bond. There are mainly two types of molecular orbitals: bonding molecular orbitals and antibonding molecular orbitals. Bonding molecular orbitals have lower energy compared to the constituent atomic orbitals and are formed when the overlapping atomic orbitals have the same phase. This leads to an increase in electron density in the region between the two nuclei and, as a result, creates a strong bond. On the other hand, antibonding molecular orbitals have higher energy than the constituent atomic orbitals and are formed when atomic orbitals with different phases overlap. This results in decreased electron density in the region between the two nuclei, leading to a weak bond or no bond at all.

Identifying Bonding vs. Antibonding Molecular Orbitals

To identify the bonding molecular orbital and the antibonding molecular orbital among the given molecular orbitals, we need to look at their shapes. In a bonding molecular orbital, the overlapping atomic orbitals have the same phase (positive or negative), hence their overlap leads to an increased electron density between the two nuclei, which creates a strong bond. In these orbitals, you will notice a high concentration of shading or lobe density (electron density) in the region between the two nuclei. On the other hand, an antibonding molecular orbital will have the overlapping atomic orbitals with different phases (one positive and one negative) leading to the cancellation of the phases, reducing the electron density in the region between the two nuclei. In these orbitals, you will observe a node, which is an area of zero electron density, between the two nuclei. From the given shapes, you can identify which molecular orbital is bonding and which one is antibonding by looking at the distribution of electron density between the nuclei.

Comparing Energy Levels

As mentioned earlier, bonding molecular orbitals have lower energy than their constituent atomic orbitals, while antibonding molecular orbitals have higher energy. Since the bonding molecular orbital results in a stronger bond, it will have a lower energy level. The antibonding molecular orbital, due to the weak or non-existent bond, will have a higher energy level. Therefore, the molecular orbital with the lower energy level is the bonding MO, and the one with higher energy is the antibonding MO.