What are the symmetry labels and degeneracy for metal dx2-y2 and dz2 orbitals?

The metal dx2-y2 and dz2 orbitals are part of the d orbitals that are relevant in coordination chemistry and crystal field theory. In the context of octahedral symmetry, the d orbitals can be categorized into groups based on their symmetry properties and degeneracy.

For transition metals in an octahedral field, the d orbitals split into two sets: the eg set (which includes the dx2-y2 and dz2 orbitals) and the t2g set (comprising the dxy, dxz, and dyz orbitals). In this configuration, the dx2-y2 and dz2 orbitals are known to have the same symmetry characteristics and are both associated with the eg symmetry.

The symmetry labels for eg orbitals in an octahedral field include 'e', and since both the dx2-y2 and dz2 orbitals can be described with this label, their degeneracy is 2. This means that there are two orbitals that share the same energy level in this field of symmetry.

Therefore, identifying these symmetries correctly, both the dx2-y2 and dz2 orbitals exhibit an e type symmetry with a degeneracy of 2. This makes the selected answer accurate in aligning