3.3. p-Systems

Much of the pioneer work using MO-theory was limited to p-systems. One reason was technical - early MO-techniques only treated the p-system and ignored s-bonds - and another was the fact that many chemical reactions occur by reaction with one or more double bonds. Figure 3.11 shows typical energy levels for the different types of molecular orbitals:

Figure 3.13 Schematic diagram of typical MO energy levels.

The most stable orbitals are generally s-bonds, whereas p-bonding orbitals lie higher in energy because of the overlap effect described in the previous section. Note that this energetic sequence also explains the reactivity of p-systems. Frontier orbital theory (see Sect. 4.2) suggests that MOs close to the HOMO-LUMO border are more important in determining reactivity than more stable occupied or less stable virtual orbitals. Nonbonding lone pairs generally lie higher in energy than MOs from the p-system. The order is reversed for the unoccupied, or virtual orbitals. Here nonbonding acceptors, such as those found for carbocations or Lewis acids in general, are lowest in energy (often with negative energies, which means that the system can accept an electron with a gain in energy according to Koopmans' theorem). The antibonding orbitals of the p-system come next, followed by the s-antibonds, which are often very high in energy. Note that this orbital ordering, and the p-overlap arguments given in Sect. 3.2, suggest that p-bonds can be regarded as very strained and reactive s-bonds. One consequence of this is that electrocyclic reactions usually occur in the direction in which two p-bonds are converted into two new s-bonds.

In the following, we will describe two simple techniques for determining the character of p-orbitals in linear and cyclic systems.

3.3.1. Linear Systems

The character of the p-MOs in a linear conjugated system can be determined using three simple rules:

1. The lowest energy orbital is bonding throughout, and therefore symmetrical relative to a central nodal plane.
2. The symmetry of the MOs relative to a central nodal plane alternates as the energy increases.
3. The number of nodal planes between p-orbitals (not the plane of the p-system itself) increases by one for each MO as the energy increases.

This principle is illustrated for 1,3,5-hexatriene in Figure 3.14:

Figure 3.14 Schematic diagram of the p-MOs of 1,3,5-hexatriene. S and A denote symmetry and antisymmetry relative to a central nodal plane.

Such a simple scheme does not give the magnitudes of the AO-coefficients, but is useful simply to determine the nature and symmetry of the individual MOs.

3.3.2. Cyclic Systems

Similar principles apply to cyclic p-systems, with the slight modification that degenerate orbitals can occur and that there is a very simple technique, proposed by Frost and Martin, to determine the MO-pattern and Hückel theory energy levels. These can be obtained simply by drawing a circle and then placing a regular polygon with the correct number of sides with one corner at 6 o'clock within it. The energy levels are then given by the positions of the corners, as illustrated in Figure 3.15 below for benzene.

Figure 3.15 Frost and Martin's technique illustrated for benzene.

We thus find the familiar pattern of a single low lying MO followed by two doubly degenerate sets and a final single high energy orbital.

The nature of the MOs can now be determined qualitatively using the fact that the number of nodal planes starts at zero for the lowest orbital and increases by one for each energy level, giving the well-known benzene MOs (note that the degenerate sets are portrayed as symmetric and antisymmetric relative to a vertical plane perpendicular to the page (Figure 3.16).

Figure 3.16 The p-MOs of benzene.

The p-MO patterns for the common cyclic conjugated systems can all be determined in this way. The resulting MOs are given in Chapter 6 and the patterns of the energy levels in the figure below:

Figure 3.17 Energy levels for simple annulenes.

Ethylene
Cyclopropane
p-Systems
Next:
Hyperconjugation