Question

In the molecular orbital model, compare and contrast \(\sigma\) bonds with \(\pi\) bonds. What orbitals form the \(\sigma\) bonds and what orbitals form the \(\pi\) bonds? Assume the \(z\) -axis is the internuclear axis.

Short answer

In the molecular orbital model, σ bonds are formed by the direct overlap of atomic orbitals along the internuclear axis (z-axis), involving s and p orbitals, whereas π bonds are formed by the side-to-side overlap of atomic orbitals, typically involving only p orbitals. Sigma bonds are stronger and allow for more free rotation around the bond axis, while pi bonds result in a more rigid molecular structure. The presence of a π bond often indicates a double or triple bond, as the first bond formed between atoms will always be a σ bond.

Step-by-step solution

Definition of σ (sigma) and π (pi) Bonds

Sigma (σ) and Pi (π) are types of covalent bonds that occur between atoms in a molecule. These bonds are formed due to the overlapping of atomic orbitals. Sigma bonds result from the end-to-end, or head-on overlapping of orbitals, while pi bonds result from the side-to-side overlapping.

Formation of σ (sigma) bonds

Sigma bonds are formed by the direct overlap of atomic orbitals along the internuclear axis. They can be formed by the following combinations of atomic orbitals: 1. s-s Orbital overlap: When two s orbitals from two separate atoms overlap, a σ bond is formed. 2. s-p Orbital overlap: When an s orbital from one atom overlaps with a p orbital from another atom, a σ bond is formed. 3. p-p Orbital overlap: When two p orbitals from two separate atoms overlap along their axes, a σ bond is formed. In general, any atomic orbital can participate in the formation of a sigma bond as long as they overlap along the internuclear axis (z-axis in this case).

Formation of π (pi) bonds

Pi bonds are formed by the side-to-side overlap of atomic orbitals, which occurs perpendicular to the internuclear axis. Pi bonds are usually formed by the following combinations of atomic orbitals: 1. p-p Orbital overlap: When two p orbitals from two separate atoms overlap side-by-side (not along their axes), a π bond is formed. Please note that s orbitals cannot form π bonds due to their spherical symmetry. In the case of other orbitals, like d orbitals, they can form Pi bonds but are rarely found in simple molecular systems.

Comparison between σ and π Bonds

1. Sigma bonds are stronger than pi bonds due to the direct overlapping along the internuclear axis, resulting in greater electron density between atoms. 2. Sigma bonds allow for more free rotation around the bond axis, while pi bonds limit the rotation due to the side-by-side configuration, leading to a more rigid molecular structure when pi bonds are present. 3. The presence of a pi bond often indicates that a double or triple bond exists because the first bond formed between any two atoms in a molecule will always be a sigma bond. In conclusion, sigma bonds are formed by the direct overlap of atomic orbitals along the internuclear axis and can involve s and p orbitals, while pi bonds are formed by the side-to-side overlap of atomic orbitals, typically involving only p orbitals. Sigma bonds are stronger and allow for more free rotation around the bond axis, while pi bonds result in a more rigid molecular structure.

Key concepts

Sigma Bonds

Sigma (\(\sigma\)) bonds are a fundamental component of molecular bonding. They occur when atomic orbitals overlap in a direct, end-to-end manner along the internuclear axis, usually designated as the \(z\)-axis. This type of overlap allows for a high density of electron sharing directly between the two nuclei.
Sigma bonds can be formed by various combinations of atomic orbitals:

• s-s orbital overlap: This occurs when two s orbitals from different atoms come together.
• s-p orbital overlap: Here, an s orbital from one atom overlaps with a p orbital from another.
• p-p orbital overlap: This involves two p orbitals aligning along their axes.

Because of their direct nature, sigma bonds have a robust electron cloud between the nuclei, making them the strongest type of covalent bonds. They also allow for free rotation of atoms around the bond axis, giving molecules a degree of flexibility.

Pi Bonds

Pi (\(\pi\)) bonds introduce a different type of orbital overlap. These bonds are formed through the side-to-side alignment of p orbitals, occurring perpendicular to the internuclear axis. In contrast to sigma bonds, this configuration does not establish high electron density directly between the nuclei.
Pi bonds typically involve only p-p orbital overlap. Two p orbitals can overlap across the \(z\)-axis (the internuclear axis), creating an electron cloud that lies above and below this axis. Because of the required alignment, s orbitals, with their spherical symmetry, are not involved in forming pi bonds.
Pi bonds add rigidity to molecular structures by restricting rotation around the bond axis. Their presence is common in double and triple bonds where, after the initial sigma bond, any additional bonds are pi bonds. While weaker than sigma bonds, because of their lateral overlap, pi bonds play a crucial role in the chemistry of unsaturated hydrocarbons, such as alkenes and alkynes.

Orbital Overlap

Orbital overlap is the concept that explains the formation of both sigma and pi bonds. It describes how atomic orbitals merge to allow electrons to be shared between atoms, thereby forming covalent bonds.
There are two main types of orbital overlap:

• End-to-end overlap: This is characteristic of sigma bonds. Here, orbitals align along the internuclear axis, providing a strong and stable overlap.
• Side-to-side overlap: This is seen in pi bonds. The orbitals overlap parallelly to one another, creating an electron cloud above and below the bond axis.

Understanding orbital overlap helps explain the differences in bond strengths and the resultant molecular geometry. The type of overlap not only dictates the bond's strength but also its flexibility, as seen in the freedom of rotation allowed by sigma bonds compared to the restricted rotation in pi bonds.

Covalent Bonds

Covalent bonds form the foundation of chemistry by involving the sharing of electron pairs between atoms. This process is central in both sigma and pi bonding. In simple terms, covalent bonds are the glue that holds molecules together by establishing electron density between nuclei.
Sigma and pi bonds represent two principal kinds of covalent bonds:

• Sigma bonds: These covalent bonds result from direct overlapping, leading to single bonds that form the backbone of molecular structures.
• Pi bonds: These form additional bonds beyond the initial sigma bond, developing from side-to-side orbital overlaps.

The combination of sigma and pi bonds determines the overall bond order and strength of the molecule. It's important to understand that every covalent connection starts as a sigma bond, with additional pi bonds bringing more stability and precise structural configurations. Such bonding plays a key role in shaping the physical and chemical properties of molecules.