5.8 Stability of Conjugated Dienes: Molecular Orbital Theory

Conjugated dienes can be prepared by some of the methods previously discussed for preparing alkenes (Section 5.1–Section 5.2). The base-induced elimination of HX from an allylic halide is one such reaction.

Simple conjugated dienes used in polymer synthesis include 1,3-butadiene, chloroprene (2-chloro-1,3-butadiene), and isoprene (2-methyl-1,3-butadiene). Isoprene has been prepared industrially by several methods, including the acid-catalyzed double dehydration of 3-methyl-1,3-butanediol.

One of the properties that distinguishes conjugated from nonconjugated dienes is that the central single bond is shorter than might be expected. The C2–C3 single bond in 1,3- butadiene, for instance, has a length of 147 pm, some 6 pm shorter than the C2–C3 bond in butane (153 pm).

According to molecular orbital theory, the stability of conjugated dienes arises because of an interaction between the π orbitals of the two double bonds. To review briefly, when two p atomic orbitals combine to form a π bond, two π molecular orbitals (MOs) result. One is lower in energy than the starting p orbitals and is therefore bonding; the other is higher in energy, has a node between nuclei, and is antibonding. The two π electrons occupy the low-energy, bonding orbital, resulting in formation of a stable bond between atoms (Figure 5.9).Figure 5.9 Two p orbitals combine to form two π molecular orbitals. Both electrons occupy the low-energy, bonding orbital, leading to a net lowering of energy and formation of a stable bond. The asterisk on ψ* indicates an antibonding orbital.

Now let’s combine four adjacent p atomic orbitals, as occurs in a conjugated diene. In so doing, we generate a set of four π molecular orbitals, two of which are bonding and two of which are antibonding (Figure 5.10). The four π electrons occupy the two bonding orbitals, leaving the antibonding orbitals vacant.

Figure 5.10 Four π molecular orbitals in 1,3-butadiene. Note that the number of nodes between nuclei increases as the energy level of the orbital increases.

The lowest-energy π molecular orbital (denoted ψ1, Greek psi) has no nodes between the nuclei and is therefore bonding. The π MO of next-lowest energy, ψ2, has one node between nuclei and is also bonding. Above ψ1 and ψ2 in energy are the two antibonding π MOs, ψ3^* and ψ4^* (The asterisks indicate antibonding orbitals). Note that the number of nodes between nuclei increases as the energy level of the orbital increases. The ψ3^* orbital has two nodes between nuclei, and ψ4^*, the highest-energy MO, has three nodes between nuclei.

Comparing the π molecular orbitals of 1,3-butadiene (two conjugated double bonds) with those of 1,4-pentadiene (two isolated double bonds) shows why the conjugated diene is more stable. In a conjugated diene, the lowest-energy π MO (ψ1) has a favorable bonding interaction between C2 and C3 that is absent in a nonconjugated diene. As a result, there is a certain amount of double-bond character to the C2–C3 single bond, making that bond both stronger and shorter than a typical single bond. Electrostatic potential maps show clearly the additional electron density in the central single bond (Figure 5.11).

Figure 5.11 Electrostatic potential maps of 1,3-butadiene (conjugated) and 1,4- pentadiene (nonconjugated). Additional electron density is present in the central C−C bond of 1,3-butadiene, corresponding to partial double-bond character.

In describing 1,3-butadiene, we say that the π electrons are spread out, or delocalized, over the entire π framework, rather than localized between two specific nuclei. Delocalization allows the bonding electrons to be closer to more nuclei, thus leading to lower energy and greater stability.