Hybrid orbitals are constructed from valence atomic orbitals and used to make sigma bonds between atoms.
Sigma bonds are formed by the overlap of orbitals that are pointing directly towards one another. If two atoms are connected by a sigma bond, rotating one of the atoms around the bond axis doesn't break the bond.
If a bond between two atoms is broken when one atom is rotated around the bond axis, that bond is called a pi bond.
Pi bonds are formed from the overlap of parallel p orbitals on adjacent atoms. They are not formed from hybrid orbitals.
Ethene, sp2 hybridization with a pi bond
The Lewis structure of the molecule CH2CH2 is below. Each carbon forms 3 sigma bonds and has no lone pairs.
As with borane, make 2sp2 hybrid orbitals on each carbon from the 2s, 2px, and 2py atomic orbitals. A 2pz orbital remains on each carbon.
Combine each H(1s) orbital with a C(2sp2) orbital to make a sigma bonding and a sigma antibonding molecular orbital. (C-H bonds)
Combine the 2 C(2sp2) orbitals to make a sigma bonding and a sigma antibonding molecular orbital. (C-C bond)
There are no remaining hybrid orbitals.
There remains a 2p orbital on each carbon. These can combine to make a pi bonding and a pi antibonding molecular orbital. The stabilization (decrease in energy) in going from the p orbital to pi bonding orbital equals the destabilization (increase in energy) in going from the p orbital to the pi antibonding orbital. The stabilization and destabilization in forming a pi bond are much less than for a sigma bond.
Finally, add the valence electrons to the molecular orbital diagram. Each carbon has 4 and each hydrogen 1 for a total of 12 electrons.
Ethyne, sp hybridization with two pi bonds
Ethyne, HCCH, is a linear molecule. Each carbon atom makes 2 sigma bonds and has no lone pairs of electrons.
The carbon atoms in ethyne use 2sp hybrid orbitals to make their sigma bonds. After hybridization, a 2px and a 2py orbital remain on each carbon atom.
Combine each H(1s) orbital with a C(2sp) orbital to make a sigma bonding and a sigma antibonding molecular orbital. (C-H bonds)
Combine the other 2 C(2sp) orbitals to make a sigma bonding and a sigma antibonding molecular orbital. (C-C bond)
There are no remaining hybrid orbitals.
The 2px orbitals on each atom combine to make 2 pi symmetry orbitals. The 2py orbitals on each carbon combine to make another 2 pi symmetry orbitals, 90 degrees from the first set.
Add the valence electrons to the molecular orbital diagram. Each carbon has 4 and each hydrogen 1 for a total of 10 electrons.
Professor Patricia Shapley, University of Illinois, 2012