Chapter 14, Problem 14.12P

Interpretation Introduction

Interpretation:

The complete MO energy diagram for benzene similar to Figures 14-6 and 14-12, including the MOs of $\text{σ}$ symmetry, is to be drawn.

Concept introduction:

Frost's method is used to obtain the relative energies of the $\text{π}$ MOs of a completely conjugated cyclic $\text{π}$ system. The benzene hexagon is oriented so that one vertex is pointed directly downward. Each of the six vertices then represents the energy of $\text{π}$ molecular orbitals ${\text{( π}}_{\text{1}}{\text{, π}}_{\text{2}}{\text{, π}}_{\text{3}}{\text{, π}}_{\text{4}}^{\text{*}}{\text{, π}}_{\text{5}}^{\text{*}}{\text{, π}}_{\text{6}}^{\text{*}}\text{)}$. The center of the polygon represents the energy of each noninteracting p atomic orbitals. Benzene has $\text{π}$ molecular orbitals ${\text{(π}}_1)$ with the lowest energy and a pair of degenerate orbitals, ${\text{π}}_{\text{2}}{\text{ and π}}_3$, at somewhat higher energy. The second pair of degenerate orbitals are ${\text{ π}}_{\text{4}}^{\text{*}}{\text{, π}}_{\text{5}}^{\text{*}}$, at still higher energy. Finally, the ${\text{π}}_{\text{6}}^{\text{*}}$ orbital has the highest energy.