For metal px, py, and pz orbitals, what are the symmetry labels and degeneracy?

In the context of molecular symmetry and group theory, the metal px, py, and pz orbitals are associated with specific symmetry labels and degeneracy due to their behavior under symmetry operations of the given point group. The correct label for these three orbitals when considering their symmetry properties in a typical octahedral environment is indeed t1u.

The "t" in the label indicates that this is a triply degenerate representation, which means there are three orbitals with the same energy level (or symmetry) that can be transformed into each other through symmetry operations such as rotation and reflection. These orbitals correspond to the spatial distributions of electron density that are invariant under certain symmetry operations, characterizing them as part of a degenerate set.

In molecular systems, a degeneracy of 3 is indicative of how these orbitals can form combinations (like linear combinations of the atomic orbitals, or LCAO) that yield the overall electronic structure of complexes. This degeneracy is essential to understanding bonding in transition metal complexes, where such orbitals interact with ligands.

This labeling aligns well with the properties of the dx or d orbitals in an octahedral environment, but for p-type orbitals, the designation reflects their specific symmetry