In the hybrid 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

In the hybrid orbital model, sigma (σ) bonds are formed by the direct overlap of orbitals along the internuclear axis (z-axis), such as s-s, s-p, or p-p overlaps. On the other hand, pi (π) bonds are formed by the sideways overlap of parallel p orbitals (either p_x or p_y), resulting in electron density above and below the internuclear axis. Sigma bonds are generally stronger and allow for free rotation of bonded atoms, while π bonds are weaker and restrict rotation due to the parallel orientation of overlapping orbitals. Additionally, σ bonds have symmetrical electron density distribution along the internuclear axis, while π bonds have electron density distributed above and below the internuclear axis.