Question

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.

Short answer

In order to sketch and label the molecular orbital formed when atomic orbitals overlap: 1. Determine if the interaction is bonding or antibonding based on the signs of the wave functions of the atomic orbitals. 2. Identify the bond type (\(\sigma\) or \(\pi\)) based on the geometry of the atomic orbital overlap. 3. Sketch and label the molecular orbital according to the bond type (\(\sigma\) or \(\pi\)) and the interaction type (bonding or antibonding).

Step-by-step solution

Determine the interaction type (bonding or antibonding)

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.

Identify the bond type (\(\sigma\) or \(\pi\))

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 and label the molecular orbital

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.

Key concepts

Understanding Bonding Interactions

In molecular orbital theory, bonding interactions occur when the atomic orbitals from two atoms overlap in a manner that is constructive. This means that the wave functions associated with the atomic orbitals add up, enhancing electron density between the two nuclei.
This increased electron density helps to hold the two atoms together, creating a stable bond.
If the wave functions have the same sign, constructive interference occurs, leading to a bonding interaction.
Bonding interactions are essential for forming strong chemical bonds, and they play a crucial role in the molecule's stability.

• Constructive interference enhances electron density.
• Results in a stable interaction between atoms.
• Wave functions with the same sign lead to bonding interactions.

The Importance of Orbital Overlap

Orbital overlap is a key component in determining how atomic orbitals combine to form molecular orbitals. When two atomic orbitals overlap, they can interfere in ways that either strengthen or weaken the bond that forms between two atoms.
In ideal situations, effective overlap between the orbitals leads to the formation of a stronger bond.
Depending on the geometry of this overlap, the resulting bonds can be different.
For example, a strong overlap often results in a double bond, which might involve both a sigma bond and a pi bond.

• Effective overlap is crucial for strong bonds.
• Variety of bond types result from different overlap scenarios.
• Geometry of overlap affects bond strength and type.

Exploring Antibonding Interactions

Antibonding interactions occur when atomic orbitals overlap in a destructive manner. Here, the wave functions of the orbitals have opposite signs, leading to cancellation—known as destructive interference.
This type of interaction decreases electron density between nuclei, destabilizing the bond and often resulting in increased energy and reduced bond strength.
Antibonding molecular orbitals are usually indicated by a star (*) notation, as in \(\sigma^*\) or \(\pi^*\).

• Destructive interference reduces electron density.
• Opposite sign wave functions lead to antibonding.
• Indicated by a star notation, signaling instability.

Understanding Sigma and Pi Bonds

Sigma (\(\sigma \)) and pi (\(\pi \)) bonds are the two main types of covalent bonds characterized based on electron distribution and orbital overlap. A sigma bond forms from the end-to-end overlap of orbitals along the internuclear axis, resulting in a symmetrical electron distribution.
This type of bond is usually strong and represents the first bond formed between two atoms.
In contrast, a pi bond arises from the side-to-side overlap of orbitals, creating an electron cloud above and below the plane of the nuclei.
It's usually formed after the sigma bond in double or triple bonds.

• Sigma bonds have symmetrical distribution along the internuclear axis.
• They usually indicate strong, primary interaction.
• Pi bonds form additional bonds with side-to-side orbital overlap.

Deciphering Wave Function Interference

Wave function interference is a pivotal concept in molecular orbital theory and chemistry in general. It describes how wave functions of atomic orbitals combine. In constructive interference, wave functions with the same sign merge, enhancing electron density between atoms, which stabilizes the bond.
On the other hand, destructive interference occurs when wave functions with opposite signs overlap, causing a decrease in electron density due to cancellation, which destabilizes the bond.
This concept determines whether a molecular orbital will be bonding or antibonding.

• Constructive interference strengthens bonds.
• Destructive interference leads to instability.
• Plays a critical role in defining molecular orbital types.