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.

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.

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).

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.

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.