Procedure for Constructing Molecular Orbital Diagrams Based on Hybrid Orbitals
Begin with the Lewis structure.
Decide how many orbitals each atom needs to make its sigma bonds and to hold its non-bonding electrons. Draw the atomic and hybrid orbitals on on side of the page.
For each sigma bond, take a hybrid (or atomic) orbital from each atom. Use these to generate a sigma bonding and a sigma antibonding molecular orbital. The average energy of the molecular orbitals must be the same as the average energy of the two orbitals you used to make them.
Use any hybrid orbitals left after after making the sigma orbitals for non-bonding molecular orbitals (without a change in energy).
Combine any parallel p orbitals on adjacent atoms into a set of pi molecular orbitals.
Total the valence electrons from all atoms and add these to the molecular orbital diagram, filling the lowest energy orbitals first.
Sigma Bonds with sp3 Hybrid Orbitals
Atoms that have 4 bonds, 3 bonds and 1 lone pair, 2 bonds and 2 lone pairs, or 1 bond and 3 lone pairs need four hybrid orbitals 109 degrees apart. Combining an s orbital, a px orbital, a py orbital, and a pz orbital makes four, sp3 orbitals in a tetrahedral array.
Molecular Orbital of Methane, CH4
The Lewis structure shows us that the carbon atom makes 4 sigma bonds to hydrogen and has no non-bonding electron pairs.
The central carbon atom combines its 2s, 2px, 2py, and 2pz valence orbitals to make four, 2sp3 hybrid orbitals.
Each one of these combines with a 1s atomic orbital from a hydrogen atom. These 2 atomic and hybrid orbitals form 2 molecular orbitals, a sigma bonding orbital and a sigma antibonding orbital.
After we combine all 4 H(1s) orbitals with the 4 C(2sp3) orbitals, the diagram looks like this.
There are no remaining hybrid orbitals.
There are no p orbitals.
The total number of electrons is 8, 4 from carbon and 1 from each hydrogen atom
Molecular Orbital of Water, H2O
The Lewis structure shows that the oxygen in water has two bonding pairs and two lone pairs of electrons around it.
Oxygen makes four 2sp3 hybrid orbitals from its valence orbitals. Each hydrogen atom has a 1s orbital.
Two of the O(2sp3) hybrid orbitals and 2 of the H(1s) orbitals combine to make 2 sigma bonding and 2 sigma antibonding molecular orbitals.
The remaining 2 O(2sp3) hybrid orbitals become non-bonding molecular orbitals.
There are no p orbitals. All orbitals have been used to make the sigma and non-bonding molecular orbitals.
The molecule has a total of 8 electrons, 6 from oxygen and 1 from each hydrogen atom.
Professor Patricia Shapley, University of Illinois, 2012