[Mitch]

Anyone know why the 3sigma orbital in CO has such a large coefficient on Carbon. I would expect it on Oxygen because Oxygen is more electronegative and because the 3sigma orbital is somewhat low in energy. I suppose it's just one of those gray lines.

[movies]

The next lowest energy MO has a very large coefficient on oxygen (lower in energy because it has lots of electron density on oxygen, which is electronegative).  To make up for the large coefficient on oxygen in the NHOMO, the HOMO has to have a small coefficient on oxygen.  The opposite is true for carbon: small coefficient in the NHOMO, large coefficient in the HOMO.

[Demotivator]

To make up for the large coefficient on oxygen in the NHOMO, the HOMO has to have a small coefficient on oxygen.  

Is that right? I'm not so sure about NHOMO affecting a HOMO of a different atomic orbital set, though it's true that  to make up for a large coefficient in a bonding MO, the antibonding version gets a small coefficient.

My take is that it's mostly due to some mixing of s character from the carbon  with the pz orbitals of C (sp hybrid) and pz of O to form the sigma bond MO.
The O exercises its electronegativity mostly through the pi bonds as movies observed.

Interestingly, the large HOMO C coefficient  explains why CO bonds through the C in metal carbonyls.

[Mitch]

movies: I don't believe that logic is valid for all cases of heteronuclear diatomic molecules. Because the higher energy MOs will have the larger coefficient on the less electronegative atom. Also, you are comparing the pi-set to the sigma-set and that might not be valid from symmetry considerations.

Demotivator: That is an interesting approach. I think the way I will settle it is simply like this. Although, we've all learned that the lower energy MOs will have the largest coefficient on the most electronegative atom, and that the higher energy MOs will have the largest coefficient on the most electropositive atom. I think the 3(sigma) level is where we see this crossing into the electropositive atom having the larger coefficient. At least that's what I'm going with unless someone has something better.

[movies]

Doh!  My bad.  You guys are right.  The polarization of the pi orbitals won't affect the coefficients in the sigma series.

I checked in my inorganic textbook and it seems to suggest essentially what Demotivator said.  The 3-sigma MO arises from the p_z AO on oxygen and the 2s and 2p_z AOs on carbon.  

It seems that the 1-sigma MO represents a lone pair on oxygen (essentially non-bonding) and the 2-sigma MO represents the sigma bond between C and O.  The 1-pi MO only involves p-orbitals on the C and the O, so it won't affect the 3-sigma orbital.

Any population of the 3-sigma orbital would be a bonding interaction with respect to the p AOs involved, but anti-bonding with respect to the s AO on carbon (the bonding sigma interaction is accounted for in the 2-sigma MO).  Since the s AO on carbon is lower energy than both the p AOs on carbon and on oxygen, the lowest energy MO will be primarily composed of the s AO on carbon, suggestive of the localization of those electrons on carbon.

Thanks for catching my error guys.

[Mitch]

It's good to know these things, thanks guys.