[Mark S 2014]

Hi Everyone,

Just going over a couple of inorganic past papers on group theory. When I check the C2v and D2h character tables to find the representations of the d orbitals, I can't seem to find x²-y². However, there is x², y², z². My guess is that x², y², z² can be interpreted as x²-y² and z². I have flicked through recommended books but nothing seems to give me a definite answer, can anyone confirm this for me ?

Thanks.

[Corribus]

Confirmed. In C_2v, dx²-y² orbital has A1 symmetry. But you should be able to determine this even without those extra columns in the character table, just by analyzing how the orbital polarity transforms under the C_2v symmetry operations. You'll notice that none of the symmetry elements change the orbital polarity, which is compatible with A1 symmetry representation (1 1 1 1). A good exercise is to confirm that d_xy has A2 symmetry using this same kind of treatment.