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.

σ bonds (sigma bonds) are formed by end-on overlapping of bonding orbitals along the internuclear axis (usually considered along the z-axis). These bonds have cylindrical symmetry about the internuclear axis and tend to be stronger due to greater overlap compared to π bonds. π bonds (pi bonds) are formed by the side-on overlapping of bonding orbitals along the internuclear axis. These bonds have a nodal plane along the internuclear axis, and the electron density is distributed above and below this plane. Due to less effective overlapping, π bonds are generally weaker than σ bonds. It's important to note that a double bond is composed of one σ bond and one π bond, while a triple bond has one σ bond and two π bonds.

Atomic orbitals such as s, p_z, and hybridized orbitals (sp, sp^2, sp^3, etc.) can contribute to form σ bonds. For example, an s-s overlap, s-p_z overlap, and a p_z - p_z overlap can all result in σ bonds, as long as the overlapping occurs along the internuclear axis.

Atomic orbitals like p_x, p_y, and hybridized orbitals (if necessary) can form π bonds. It is essential to remember that p_x and p_y orbitals lie perpendicular to the internuclear axis (z-axis), which allows for side-on overlapping and π bond formation. In summary, σ bonds are characterized by end-on overlapping of bonding atomic orbitals (such as s, p_z, and hybrids) along the internuclear axis and tend to be stronger due to more significant overlap. In contrast, π bonds result from side-on overlapping of atomic orbitals (mainly p_x and p_y) perpendicular to the internuclear axis and are generally weaker due to less effective overlapping.