5.4. Degenerate Orbitals

Before we move on to the molecular orbital plots, we should consider degenerate MOs briefly. Confusion often arises because we have been taught, for instance, to expect the degenerate HOMOs of benzene to have nodal planes through two opposite carbon atoms and perpendicular thereto (Figure 5.14):

Figure 5.14 HOMOs of benzene (optimised within D_2h symmetry).

However, if we use the full D_6h symmetry of the molecule, there are an infinite number of combinations of these two orbitals that all have the same energy and are equally good ways to represent the MOs. The HOMOs shown in Figure 5.15 below are just one possibility:

Figure 5.15 HOMOs of benzene (optimised within D_6h symmetry).

Note that these MOs do not even look as if the have the correct symmetry for the molecule. This is because they must be considered as a degenerate pair and not individually. The sums of the two different depictions of the degenerate MOs are identical. The MO plots in Figure 5.14 have been made by slightly reducing the symmetry of the molecule to obtain the familiar orientations of degenerate MOs. In real calculations using the full symmetry, however, less recognisable forms are usually found.

Symmetry Elements
Point Groups
Irreducible Representations and Character Tables
Degenerate Orbitals