Explain the difference between the \(\sigma\) and \(\pi\) MOs for homonuclear diatomic molecules. How are bonding and antibonding orbitals different? Why are there two \(\pi\) MOs and one \(\sigma\) MO? Why are the \(\pi\) MOs degenerate?

In homonuclear diatomic molecules, σ orbitals form when atomic orbitals overlap along the internuclear axis, leading to greater electron density between the nuclei and cylindrical symmetry. π orbitals form when atomic orbitals overlap above and below, or in front and behind the internuclear axis, creating a nodal plane and concentrated electron density. Bonding orbitals arise from constructive interference of atomic orbitals and have lower energy, while antibonding orbitals arise from destructive interference and have higher energy. The two π MOs and one σ MO occur due to the combination of s- and p-orbitals in molecular orbital formation. Finally, π MOs are degenerate because they have the same energy level, resulting from their similar electron density distribution and electrostatic interactions.