[xshadow]

I have to discuss water polarity using this MO diagram:
https://upload.wikimedia.org/wikipedia/commons/d/d4/H2O-MO-Diagram.svg


I don't understand what I have to say seeing this diagram.
I know water is polar becasue of O-H bond (different electronegativitiy)

Here the bonding orbitals  where I have electrons seems developed  around oxygen but also around the two hydrogen (except for the non bonding orbital ..but that carrespond to its lone pair...not to the O-H  bond polarity) . How can I explain water polarity only lookink this diagram !?

Thanks

[Corribus]

Molecular orbital theory basically creates molecular orbitals as linear combinations of atomic orbitals, and the contribution of the atomic orbital from each inclusive atom in the molecular is weighted to some degree. So, for instance, you can see the homo in this case has no contribution from the orbitals centered on the hydrogens - meaning all the electron density of electrons in the HOMO is centered on the oxygen. The total electron density centered on any atom in the molecule is determined by summing up the electron density contribution on that atom from each molecular orbital. Not always easy to do this qualitatively by just inspection, but it is clear in the case of water that the three lower energy MOs have electron density more or less evenly distributed among the oxygen and hydrogen atoms (because the AO contributions are more or less even). But the HOMO as noted above has zero AO contribution from the hydrogens, and therefore no electron density. So, the oxygen will have, again approximately, more electron density than the hydrogens, thus creating a dipole.

Of course, a real MO treatment can do this quantitatively because you'll know the exact AO contribution percentages for each MO. I don't really like doing it by inspection because you are trying to judge "by eye" how "big" the AO contributions are - usually represented as how big they are drawn on the diagram. But, it is clear they are zero on the H centers of the HOMO, so I think this is what the problem is getting at.

[NDW]

Corribus - Wouldn't your answer also indicate that a CO2 molecule would have a dipole?

[Corribus]

Well you also have to consider where the atomic orbitals are situated in physical space. I.e., the molecular symmetry. So no, CO2 would not be dipolar by the same argument. The MOs for carbon dioxide are also quite a bit different, again because of the symmetry-adapted mixing of atomic orbitals (and the p-orbitals of oxygen get involved).