[mycotheologist]

I am aware that it is called the "parity" but what does parity mean in this case?

[cth]

It comes from the German word "gerade". It means the system is symmetric in respect to the inversion center.

If you have something like T_2u, the "u" means the system is antisymmetric (symmetric but with inversion of the signs + and -) in respect to the inversion center.

If there is no "u" and "g", it means there is no inversion center, like in T₂.

[mycotheologist]

Thanks, its starting to make a lot more sense now. How do these orbitals produce an inversion center though? From what I read, the p orbitals become the t_1u set in an octahedral field. p orbitals are symmetrically distributed around the atom though so wouldn't they have an inversion center? As for the e_g set, it contains a d_z² orbital, I can't really see how an inversion center could apply to that at all.

[cth]

For p orbitals, you have two lobes with different signs (+ and -) and the nucleus located just in between them. The inversion center is at the nucleus. Both lobes are symmetrical to one another in respect to the inversion center, but there signs are changed: + becomes - and - becomes +. They are antisymmetric by the inversion center and are noted "u" in T_1u.

The same for d_z² with the inversion center located at the nucleus.
By the way, E_g contains both d_z² and d_x²-y².

[mycotheologist]

That explains it, thanks. Did you say the e_g orbitals "aren't" symmetrically distributed though?

[cth]

That explains it, thanks. Did you say the e_g orbitals "aren't" symmetrically distributed though?

No. The "g" of E_g indicates it is symmetrical in respect to the inversion center. Both d_z² and d_x²-y² have an inversion center.

[mycotheologist]

Ah yeah, thats what I was thinking. That explains everything, thanks a lot!