Bonding, Nonbonding and Antibonding MOs

[Stratosphere]

Homework Statement

Ignoring any orbitals not in the valence shell how many orbitals are in each of the following molecules? How many are bonding, nonbonding, and antibonding? How many orbitals are occupied?
Co2

Homework Equations

The Attempt at a Solution

The answer it gives in the book is 4 of each. I tried it and I got confused. The solution it gives is this.

"Carbon dioxide has one carbon and two oxygens. Each of these three atoms contribute one 2s orbital and three 2p orbitals. Thus, there are a total of twelve atomic orbitals in the valence shells of these atoms and twelve molecular orbitals in the molecule. Each atom obeys the octet rule. There are a total of four each of bonding, nonbonding and antibonding molecular orbitals so eight orbitals are filled."

Can someone explain it a little bit clearer than that?

 

[x12179x]

Wikipedia has Carbon Dioxide as one of it's examples in the MO article:
http://en.wikipedia.org/wiki/Molecular_orbital_diagram#Carbon_Dioxide_MO_DiagramHere is my summary using the images from the wiki article:
The first image in the CO2 section is of the atomic orbitals (AO) of Carbon and Oxygen
The 2nd image are the Molecular Obritals (MO) when Carbon and Oxygen combine to become Carbon dioxide.

In the 2nd image, the 1st column shows which AOs the MO came from. The last column shows which MOs are Bonding, Anit-bonding and Non bonding.

For example:
Take AO1 (which is Carbon's 2s orbital) and AO8 (which are the two Oxygen's 2pz orbital)

When you combine an AO1 and two AO8 to make O=C=O (Carbon dioxide), you can either get what looks like MO1 or MO2.

In the image the AO1 orbital is blue (lets call it +)

Each of the AO8 orbital has 2 phases (red and blue, or - and +). When same phase overlap, it is called bonding, if opposite phase, it is anti-bonding.

With AO1 + 2 AO8, you can get:
O ===== C ===== O
(-)(+)... (+) ... (+)(-) Bonding
or
(+)(-) ...(+) ...(-)(+) Anti-bondingThe other MOs work the same way (from combining the AOs of C and O into O=C=O using the different possible phase orientations that exists)s orbital can only overlap with Pz orbital only because of it's orientation, so oxygen's two Py's and 2 Px's orbitals combine with carbon's 2s orbital to form a nonbonding orbital.