Why Does Benzene Possess a D_6h Symmetry? A Quasiclassical State Approach for Probing π-Bonding and Delocalization Energies

In response to a recent controversy over the issue of whether the π-electrons of benzene do or do not possess a distortive tendency away from a D_6h symmetry, we have developed a new approach based on the quasiclassical (QC) state, which is the spin-alternant state of a chemical species and which allows definition of the π-bonding energy in a manner which does not depend on energy partition and is free of the dilemma of assignment of the nuclear repulsion. The QC state concept is applied to probe bonding energies in H₂ and C₂H₄ and then used to quantify delocalization energies of H₆ and benzene. It is shown that the π-bonding energy of benzene is stabilized by a localizing B_2u distortion. As such, the π-system of benzene behaves precisely like the delocalized H₆ hexagon which is a transition state more stable in a distorted D_3h, geometry. The analogy between the delocalized π-electrons of benzene and H6 is further highlighted by demonstrating, computationally, that they both possess exalted diamagnetic susceptibilities associated with ring currents. While H₆ simply falls apart to three H₂ molecules, the π-electrons of benzene are held together by the a-frame. Benzene is therefore the site of two opposing driving forces. The π driving force tends to distort the molecule while the stronger σ driving force of the QC state acts in the opposite direction and imposes a regular geometry. As such, benzene possesses a unique delocalized π-component which has a dual nature; at any geometry of the C₆H₆ structure, the π-electrons are strongly stabilized by the quantum mechanical resonance energy (QMRE), and at the same time, they possess a global distortive tendency toward a D_3h structure. It is demonstrated that this dual picture of benzene is in perfect agreement with the “aromatic” behavior of benzene. Applications are presented to the Stanger model of bent benzene, tricyclobutabenzene, and naphthalene.