[Winga]

According to my two lecture notes, one said the HOMO of CO is a sigma "bonding" orbital formed by C's 2p and O's 2p orbitals (e.g. both are 2px orbitals). While another one said the HOMO is a sigma "antibonding" orbital formed by C's 2s and O's 2s orbitals.

So, which one is correct? (or which one is more preferable?)

[Mitch]

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[Albert]

According to my two lecture notes, one said the HOMO of CO is a sigma "bonding" orbital formed by C's 2p and O's 2p orbitals (e.g. both are 2px orbitals). While another one said the HOMO is a sigma "antibonding" orbital formed by C's 2s and O's 2s orbitals.

So, which one is correct? (or which one is more preferable?)

In my opinion, the former is the correct one.

[Winga]

The energy level of C's and O's atomic orbitals in this diagram are quite similar.

But another one shows that the energy difference is quite large that gives another pattern.

As you know, it is due to electronegative difference between C and O, but in what extent?
If small, properly, it's just same as your case, if large, it will be another case.

[Albert]

Carbon and oxygen belong to the same period and are quite close to each other.
According to that, I'd say their atomic orbitals have similar energies.

[Winga]

Here is another version...

[Winga]

After comparing them, I drew a conclusion...

If CO ligand donates e- density to metal centre through sigma bonding (from sigma* orbital), the bond order of CO will greater than 3 (neglect back pi bonding).

I have never heard about such a bond order of CO, I think yours is correct.