For metal dxy, dyz, and dxz orbitals, what are the symmetry labels and degeneracy?

The metal dxy, dyz, and dxz orbitals are considered to have specific symmetry properties in crystal field theory, particularly within octahedral complexes. In such complexes, the d orbitals split into different energy levels based on their symmetry with respect to the ligands surrounding the metal ion.

The dxy, dyz, and dxz orbitals belong to the symmetry category known as t2g. This designation reflects how these orbitals transform under the symmetry operations of the octahedral point group. Specifically, the t2g set of orbitals exhibits a lower energy than the eg set, which includes the dz2 and dx2-y2 orbitals. The term "degeneracy" refers to the number of orbitals that share the same energy level. In this case, there are three orbitals (dxy, dyz, and dxz), making the degeneracy of this set equal to 3.

The other choices refer to different types of orbital symmetry or their corresponding degeneracies that do not apply to the dxy, dyz, and dxz set of orbitals in the context of octahedral complexes. For example, the e1 designation relates to a different symmetry characteristic and would imply two orbitals