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, ψ_5, 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, ψ_6, 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.