17.5: Structure of Benzene: Molecular Orbital Model
According to the molecular orbital (MO) model, benzene has a planar structure with a regular hexagon of six sp2 hybridized carbons. As shown in Figure 1, each carbon is bonded to three other atoms with C–C–C and H–C–C bond angles of 120°. The C–H bond length is 109 pm, and the C–C bond length is 139 pm which is midway between the single bond length of sp3 hybridized carbons (154 pm) and sp2 hybridized carbons (133 pm).
The carbon atoms also have an unhybridized 2p atomic orbital with one electron, perpendicular to the plane of the ring, which overlaps with the p orbitals of neighboring carbons, forming a continuous loop of π electrons above and below the plane of the ring. According to molecular orbital (MO) theory, these six 2p orbitals combine to form six π cyclic molecular orbitals (MOs) ψ1, ψ2, ψ3, ψ4, ψ5, and ψ6, as shown in the figure below. Among them, ψ1, ψ2, and ψ3 are bonding, whereas ψ4, ψ5 and ψ6 are antibonding MOs. Generally, the energy of the MOs and the number of nodes increases from ψ1 to ψ6, whereas the bonding interaction decreases. However, these MOs of cyclic systems differ from the linear systems such as 1,3-butadiene by having two degenerate MOs.
The lowest energy bonding MO, ψ1, has no nodes where all the orbitals are in phase. The next lowest MO has one node and can be represented in two ways, where the nodal plane passes through a bond or an atom. These two bonding MOs are degenerate and represented as ψ2 and ψ3. Similarly, the two nodal planes can pass through bonds or atoms, providing two degenerate antibonding MOs of ψ4 and ψ5. The final MO, ψ6, has the highest energy, with three nodal planes representing the out-of-phase combination of all p orbitals.
The six π electrons that form a closed shell of delocalized π electron density above and below the plane of the ring occupy the three bonding MOs, ψ1, ψ2, and ψ3, whose energies are lower than that of the isolated p orbital, thus leading to unusual stability of benzene.
