[ptryon]

Are all the d-orbitals truely degenerate? (dxy dxz dzy dx²-y² and dz²) If so is does that mean that the diferent d-orbitals fill can fill in any order for any given TM atom? How would this effect the shape of TM complexes? 

[cth]

In an isolated TM atom, with nothing around, all d-orbitals are indeed degenerate.

However, the presence of ligands changes that situation.
For example, I take the case of octahedral coordination: 6 ligands around the metal centre. Two orbitals, dx²-y² and dz², are pointing towards the ligands and are more destabilised (higher in energy) than the three other orbitals dxy, dxz and dyz which are not pointing directly towards the ligands. So, in this case, the d orbitals are now distributed into 2 groups named:
  e_g contains dx²-y² and dz² which are still degenerate with one another
  t_2g contains dxy, dxz and dyz which are still degenerate with one another

[Rudi]

Are all the d-orbitals truely degenerate? (dxy dxz dzy dx²-y² and dz²)

They are degenerated for isolated ions (in the gas phase) and would also be degenerated in a spherical ligand field.

PS: I'm somewhat late with my post.

[ptryon]

That's great! Thank you!!