What do 2C2 and σh mean in XeF4 symmetry?

[ampakine]

In my lecture notes the symmetry elements for XeF₄ are listed as:
[PLAIN]http://img690.imageshack.us/img690/7216/syms.png
but nowhere does it explain what 2C₂ or σ_h means. What are these symmetry operations?

 

[SpectraCat]

In my lecture notes the symmetry elements for XeF₄ are listed as:
[PLAIN]http://img690.imageshack.us/img690/7216/syms.png
but nowhere does it explain what 2C₂ or σ_h means. What are these symmetry operations?

Well, XeF₄ has D_4h symmetry, which is pretty high, so there are a lot of elements. The 2C₂ notation means that there are 2 C₂ axes perpendicular to the principal axis .. there are actually two sets of these, which is why there is a primed and double-primed notation as well. The σ_h notation just means that there is a plane of symmetry perpendicular to the principal axis.

 

[ampakine]

Ah right, thanks a lot. Is there a sure shot way to know which is the principle rotation axis? For example in XeF₄ why is the C₄ the principle rotation axis? Why not the C₂ axis perpendicular to it or why not the C₂ rotation axis that goes from one F to the other F diagonally opposite it?

Also I didn't want to start a new thread for this so I'll ask it here. In MO theory for octahedral coordination complexes there are 6 ligand atomic orbitals which split into 3 sets of degenerate orbitals: a_1g, t_1u and e_g. I keep seeing them referred to as symmetries. Does this mean the orbitals in these sets have a distinct shape or something? Are these point groups? I found this diagram:
[PLAIN]http://img852.imageshack.us/img852/6572/symm.png
but I'm not too sure what to make of it. I can see how each of the ligand orbitals corresponds to a 4s, 4p or an e_g d orbital and I'm guessing these are the orbitals that they merge with to form MOs but I'm pretty confused about the shapes of these ligand orbitals. Does the t_1u orbital have 6 lobes or something?