Overview

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.

Procedure

The molecular orbital model describes benzene as a regular planar hexagon with six sp² hybridized carbons.

Adjacent carbon atoms form σ bonds via sp²–sp²  orbital overlap. Each carbon atom also forms a σ bond with hydrogen by sp²–1s orbital overlap. All the bond angles are 120°.

In addition, each carbon has a half-filled unhybridized 2p atomic orbital perpendicular to the plane of the ring.

These six 2p orbitals combine to form three bonding and three antibonding molecular orbitals.

The bonding orbitals are completely filled by the six π electrons, while the antibonding orbitals are empty, giving benzene a closed-shell configuration that confers stability.

Consequently, the π electron density is delocalized in the form of doughnut-shaped regions above and below the plane of the ring.

Delocalization also explains why just one carbon–carbon bond length is observed for benzene, with a value between typical carbon–carbon single and double bond lengths.