Sketch the molecular orbital and label its type ( \(\sigma\) or \(\pi ;\) bonding or antibonding) that would be formed when the following atomic orbitals overlap. Explain your labels.

To decide the interaction type, assess whether the overlapping atomic orbitals interfere constructively (bonding interaction) or destructively (antibonding interaction). When the wave functions of the atomic orbitals have the same sign, they result in a bonding interaction, and when they have opposite signs, they create an antibonding interaction.

Now, it's necessary to identify whether the bond being formed is a \(\sigma\) bond or a \(\pi\) bond. Recall the primary distinctions: - \(\sigma\) bond: The electron density is symmetrical surrounding the bond axis (internuclear axis) - \(\pi\) bond: The electron density is distributed above and below the plane of the bond axis (internuclear axis) Examine the overlap geometry of the atomic orbitals to determine which bond type is being formed. For example, the overlap of two s orbitals or the end-to-end overlap of two p orbitals (along the internuclear axis) will result in a \(\sigma\) bond. On the other hand, the side-to-side overlap of two p orbitals will form a \(\pi\) bond.

Sketch the molecular orbital in a manner that reflects the bond type and interaction type. If a \(\sigma\) bond is being formed, show the electron density symmetrically distributed around the internuclear axis. If a \(\pi\) bond is being formed, draw the electron density above and below the internuclear axis. Finally, for bonding interactions, indicate constructive interference between the two atomic orbitals, while for antibonding interactions, show destructive interference. In conclusion, to sketch and label the type of molecular orbital formed when atomic orbitals overlap: 1. Determine whether the interaction is bonding or antibonding based on the wave functions of the atomic orbitals 2. Identify the bond type (\(\sigma\) or \(\pi\)) based on the overlap geometry 3. Sketch and label the molecular orbital according to the bond and interaction types.