4.10 Problems
99
to the composite nature of the molecule being considered, with several fragments
bound to one central atom.
4.10 Problems
4.1 A Schlegel diagram of a polyhedron is a projection into a plane figure. The figure below shows the Schlegel diagram for a dodecahedron. As was explained
in the preceding chapter (see Fig. 3.8(a)), a dodecahedron contains five cubes,
e.g., the cube based on the nodes 1, 3, 9, 10,a,c,i,j. Symmetry elements of
I h permute these cubes. Construct the set of the five cubes and determine the
irreps of this set. Can you obtain this result by induction?
4.2 Consider the set of eight tangential π -orbitals on a tetrahedron. Derive the
irreducible representations in the T d point group. How would you label the
canonical symmetry of the combinations that are shown in the figure below?
4.3 Consider the set of perpendicular p z -orbitals in the polyaromatic planar
molecule coronene shown below. This set gives rise to a symmetry of molecular orbitals of a 1u and b 1g . Can you draw both these orbitals? (Use the standard orientation of the central benzene frame, as shown in Fig. 3.10)
99
to the composite nature of the molecule being considered, with several fragments
bound to one central atom.
4.10 Problems
4.1 A Schlegel diagram of a polyhedron is a projection into a plane figure. The figure below shows the Schlegel diagram for a dodecahedron. As was explained
in the preceding chapter (see Fig. 3.8(a)), a dodecahedron contains five cubes,
e.g., the cube based on the nodes 1, 3, 9, 10,a,c,i,j. Symmetry elements of
I h permute these cubes. Construct the set of the five cubes and determine the
irreps of this set. Can you obtain this result by induction?
4.2 Consider the set of eight tangential π -orbitals on a tetrahedron. Derive the
irreducible representations in the T d point group. How would you label the
canonical symmetry of the combinations that are shown in the figure below?
4.3 Consider the set of perpendicular p z -orbitals in the polyaromatic planar
molecule coronene shown below. This set gives rise to a symmetry of molecular orbitals of a 1u and b 1g . Can you draw both these orbitals? (Use the standard orientation of the central benzene frame, as shown in Fig. 3.10)