Question

Using cartoon representations, draw a molecular orbital mixing diagram for a \(\mathrm{C}-\mathrm{O}\) \(\sigma\) bond. In your picture, consider the relative energies of \(\mathrm{C}\) and \(\mathrm{O}\) and how this changes the resulting bonding and antibonding molecular orbitals relative to a \(\mathrm{C}-\mathrm{C} \sigma\) bond.

Short answer

Answer: The energies of the σ and σ* MOs for the C-O σ bond are more stabilizing (lower energy) for the bonding interaction and more destabilizing (higher energy) for the antibonding interaction compared to the MOs in a C-C σ bond. This is due to the larger energy difference between the C and O atomic orbitals compared to the energy difference between two C atomic orbitals.

Step-by-step solution

Identify the atomic orbitals involved

For a σ bond between Carbon and Oxygen, we consider the 2p_z atomic orbitals of both atoms. This is because the 2p_z orbitals of both atoms are oriented along the internuclear axis and can form an effective σ bond.

Draw the MO energy diagram

To draw the MO energy diagram, follow these steps: 1. Draw a vertical axis representing the energy levels, with lower energies towards the bottom and higher energies towards the top. 2. Place the 2p_z atomic orbitals of C and O along the axis according to their relative energies. The 2p_z orbital of Oxygen is lower in energy than that of Carbon. Therefore, place the C 2p_z orbital higher up on the axis than the O 2p_z orbital. 3. Draw lines connecting the atomic orbitals of C and O to the resulting MOs along the energy axis. The lower MO represents the bonding orbital (σ), while the higher MO represents the antibonding orbital (σ*). 4. Label each atomic orbital (2p_z of C and 2p_z of O) and molecular orbital (σ and σ*) accordingly.

Compare MO energies with a C-C σ bond

Now, we need to compare the C-O σ bond's MO energies with the MO energies of a C-C σ bond: 1. Draw a separate MO energy diagram for the C-C σ bond, placing the 2p_z atomic orbitals of each Carbon symmetrically along the energy axis. 2. Connect the Carbon 2p_z orbitals with lines to show the resulting bonding (σ) and antibonding (σ*) MOs for the C-C σ bond. 3. Compare the energies of C-O σ and σ* MOs with the energies of the C-C σ and σ* MOs. Since the energy difference between C and O atomic orbitals is larger than between two C atomic orbitals, it results in a more stabilizing bonding interaction and a more destabilizing antibonding interaction for the C-O σ bond relative to the C-C σ bond.