Question

Explain the difference between the σ and π MOs for homonuclear diatomic molecules. How are bonding orbitals and antibonding orbitals different? Why are there two π MOs and one σ MO? Why are the π MOs degenerate?

Short answer

$\sigma$orbital is formed by the direct overlap of $s-s$orbital or $p-p$orbitals overlap whereas $\mathrm{\pi }$orbital is formed by the lateral overlap of $p-p$orbitals overlap of homonuclear diatomic molecules.

Bonding orbitals are lower in energy since it is formed by constructive interference of atomic orbitals whereas antibonding orbitals are higher in energy since it is formed by destructive interference.

One $\sigma$MO is formed by the direct overlap of $p_z-p_z$orbitals overlap whereas the remaining degenerate $p_x,p_y$orbitals form lateral overlap forming two $\mathrm{\pi }$Mos.

$\mathrm{\pi }$MOs are degenerate since $p_x,p_y$orbitals are${90}^0$to the sigma bond and form a lateral overlap of atomic orbitals with the same energy.

Step-by-step solution

Step 1. Formation of sigma orbitals.

$\sigma$orbitals are formed by the direct overlap of $s-s$orbitals and $p_z-p_z$orbitals.

Sigma molecular orbitals are formed by the overlapping of two atomic orbitals from head-to-head along the internuclear axis. In a sigma molecular orbital, the electron density at the middle of the molecular orbital is high in case the two atoms from which the atomic orbitals are overlapping, are identical.

Step 2. Formation of degenerate pi molecular orbitals.

The remaining degenerate $p_x,p_y$orbitals form a lateral overlap with $p_x-p_x$and $p_y-p_y$atomic orbitals forming degenerate $\mathrm{\pi }$Mos.They are degenerate because they have been formed by using the same orbital interactions.