(Solved): [21 pts] Consider the hypothetical pentagonal planar molecule \( \mathrm{PH}_{5} \), which has \( \ ...

[21 pts] Consider the hypothetical pentagonal planar molecule \( \mathrm{PH}_{5} \), which has \( \boldsymbol{D}_{5 h} \) symmetry. a. Determine the symmetries and degeneracies of the valence \( s \) and \( p \) orbitals on the central phosphorus atom. (How does each phosphorus valence orbital transform in this point group?) Label the orbitals accordingly. b. Draw the unique symmetry adapted orbitals (SAO) for the five terminal \( \mathrm{H} \) atoms. Note: This is a pentagon with an \( \mathrm{H} \) atom at each corner.