# How could you predict degenerate pi molecular orbitals just knowing what symmetry point group a molecule belongs to?

If you were to apply the Huckel method to some molecules which belonged to, say, $C_{2v}, D_{2h},$ and $D_{4h}$, which ones would you expect to have degeneracies?

I'm not sure if this is mixing up math jargon with chemistry jargon here, but I know the Mulliken symbol E is doubly degenerate and T is triply degenerate. So would the $D_{4h}$ molecule have degeneracies because it has the irreducible representations $E_g$ and $E_u$?

• This might be interesting for you. Apr 24 '15 at 7:03

Which orbital symmetries you can get in a molecule always depends on the molecule’s point group. Only for those point groups which have degenerate irreducible representations can you get degenerate orbitals; so out of your examples only the $D_{4h}$ molecule could. This is entirely independent of Hückel’s method to determine energy levels.
But just because your molecule has the irreducible representations, doesn’t mean that a $\pi$ orbital has to have that degeneracy. Instead, it again depends on what you get when following symmetry rules.
You can calculate whether you will get $\pi$ degeneracies by drawing your molecule of interest, including all the p atomic orbitals and determining the molecule’s point group. Once you have that, for each symmetry operation, check how many p orbitals would be transformed onto themselves by said operation (and note whether with or without a phase change). Add that up. Once you’ve done that, you basically have the representation of the p-orbitals of the molecule that you can reduce to irreducible representations, finding out how many discrete and degenerate energy levels you have (albeit not including energy values).
• Agreed. In some cases, it could be easier than this. Let's say you have a central atom (e.g, $\ce{Pt}$). You can then look in the character table to see the representations of the p and d orbitals and know if there's a degenerate orbital set for those atomic orbitals. Generally, though you need to perform the symmetry analysis you describe. Jun 12 '15 at 17:00