# What can visual observations of pi-bonding MOs explain about LCAO expansion coefficients?

For examples of CO and N2, what can their MOs tell us about their expansion coefficients?

I've thought that in N2, its symmetric so the expansion coefficients would be equal from the pi-bonding MO due to the symmetry as shown in the image below.

And for CO, the coefficients could be different with the oxygen having less character due to it being more electronegative?

I'm thinking like this because I know each AO of an atom is multiplied by an expansion coefficient to build MOs. But I don't entirely know what the expansion coefficient is or where it really comes from so I can't answer the question fully. Any help is appreciated.

I've thought that in N2, its symmetric so the expansion coefficients would be equal from the pi-bonding MO

Yes, that's right; symmetric molecules have symmetric MOs which have symmetric coefficients of the constituent AOs.

And for CO, the coefficients could be different ...

And yes, conversely for unsymmetric molecules, the coefficients are going to be different.

... with the oxygen having less character due to it being more electronegative?

This is where it starts to get rather murky.

In this specific case, where the π MOs are formed from carbon and oxygen 2p orbitals only, then you can say that the bonding π MO has more oxygen character (not less!). This is because the oxygen 2p orbitals are lower in energy, so the bonding MO (which is lower in energy than antibonding) will take on more of the oxygen 2p than the carbon 2p. On the other hand, the π* antibonding MO will have more carbon character.

(You could say that this is because of electronegativity, but I think that effective nuclear charge is a slightly better rationalisation. That said, they're all interrelated, of course.)

However, this line of logic only works when you have the case of two AOs combining to form two MOs. The moment you have more than two, you need to be very careful about claiming which one has greater contribution. For example, the σ framework of the same molecule, CO, turns out to be pretty complicated, and it's not obvious at all which combination of carbon 2s, carbon 2p, oxygen 2s, and oxygen 2p forms any given MO.

Also, even in the 2 AOs/2 MOs case, the electronegativity argument must be applied with caution. We could say above that oxygen 2p is lower in energy than carbon 2p, but if you're not comparing the same orbitals, then there's no guarantee that the more electronegative element has orbitals that are lower in energy.

Generally, if you wanted to make definitive statements about which atom had a greater contribution, you'd have to actually use a computer programme to calculate these actual contributions. This is known as electronic structure theory, which is a fairly prominent subfield of computational chemistry. If you don't have something like this, then the conclusions you can draw in a qualitative fashion are fairly limited.

• Orthocresol, this has nothing to do with the post, but I am unable to find it in Stack Exchange. How do you make those vertical lines, and the text citing the OP at the right, while writing your answer? Thanks in advance. Commented Mar 21, 2023 at 12:38
• @MetalStorm They're blockquotes: chemistry.stackexchange.com/editing-help#simple-blockquotes If you're new to Markdown then the other pages on there will be useful too. Alternatively, you can click 'edit' on my post to see the original source code that I typed. (If you don't save it then nothing will be edited.) Commented Mar 21, 2023 at 14:21