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I need help understanding the molecule FHF-'s molecular orbital diagram: enter image description here

So I know that "ag" refers to the 2pz and 2s orbitals of fluorine atoms...but I am not sure why "ag" is labeled for the topmost orbital level? I don't really know what that is...but it's interacting with both hydrogen's 1s orbital and fluorine's 2p orbital, so does it imply that it's either antibonding or bonding orbital? And the one right below the topmost orbital--would that be the antibonding sigma 2pz orbital?

Thanks, I'd appreciate the help!

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So we are treating the two fluorines as ligand groups on the right hand side and we introduce a Hydrogen on the left. We observe that each fluorine has a 2S, 2px, 2py and 2pz. If we take the 2pz as being along the internuclear axis then we assign it with sigma symmetry, while the x and y p orbitals have pi symmetry.

It is the 2pz that can interact with the Hydrogens 1S because it has the correct symmetry. It turns out that the symmetry of that orbital is ag. This creates as you say the bonding and anti bonding pair with the H's 1S. It is important to note that the bonding and anti bonding pair are of the same symmetry.

The hydrogen only has the 1S orbital (symmetry ag) and no others, so every other orbital of a symmetry that is not ag is non-bonding since it has no respective partner in the FHF environment.

With regard to the assignation of symmetry to an orbital you must have an understanding of SALCs (symmetry adapted linear combinations of molecular orbitals), if you perform a projection operator method then you will generate the symmetrys ... however this is a bit advanced and not something expected at undergraduate level (to my knowledge).

I hope that helps :)

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