Chapter 14, Problem 14.15P

Interpretation Introduction

Interpretation:

Whether benzene dication and benzene dianion are aromatic, antiaromatic, or nonaromatic is to the determined on the basis the characteristics of their MO diagrams.

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 molecule is oriented with one vertex pointing straight down. Each vertex then represents the energy of a $\text{π}$ MO, and the center of the (molecular) polygon represents the energy of the original noninteracting p atomic orbitals. The number of $\text{π}$ MOs equals the number of contributing AOs. If this number is even, half are bonding and half antibonding. If the number is odd, one MO is nonbonding, of the same energy as the original p orbitals. Of the remaining, half are bonding and half antibonding.

If the number of $\text{π}$ electrons in such a system fits the formula $\text{4n+2 (n = 0, 1, 2,}\mathrm{...}\text{)}$, the molecule is aromatic. If it fits the formula $\text{4n (n = 0, 1, 2,}\mathrm{...}\text{)}$, the molecule is antiaromatic. All other species are nonaromatic.