What is the symmetry label and degeneracy of a metal s orbital?

The metal s orbital is an important topic in molecular and solid-state symmetry and its associated labels. The symmetry label for an s orbital is a1g, which indicates that it is symmetric with respect to inversion through the center of the molecule or crystal. The "a" stands for symmetry under the identity operation, and "g" indicates that it is a gerade representation, meaning it is symmetric with respect to inversion (the wave function does not change sign).

The degeneracy of the s orbital is 1, as it has only one energy level associated with it. This is in contrast to orbitals with higher angular momentum, which can have multiple orientations in space, thus leading to higher degeneracy. The s orbital does not have any directional characteristics and is spherical, reinforcing the idea of its single degeneracy.

The other options refer to different symmetries or degeneracies that apply to other types of orbitals or representations, such as p or d orbitals, which can possess multiple orientations and thus result in higher degeneracies. For instance, t2g represents a set of d orbitals with degeneracy of 3, corresponding to their specific geometric arrangements. However, the s orbital is distinct in both symmetry label and degeneracy, solidifying