Chapter 12.20, Problem 23P

Interpretation Introduction

Interpretation:

The adaptation of Frost's circleto generate the orbital energy level diagram is to beshown for cycloheptantrienyl cation.

Concept introduction:

The number of $\text{π}$ electrons for a given polyene cation are first determined.

These $\text{π}$ electrons are assigned to the molecular orbitals in accordance with the rule that states that the lowest energy orbitals fill first and the maximum number of electrons in one orbital is two. In case of the two orbitals having comparable energies, each gets one electron before either orbital gets two.

Frost's circle is used to set up the Huckel's molecular orbitals of planar, monocyclic, and completely conjugated polyenes.

The energy levels can be superimposed on a polygon with appropriate sides with the vertex pointing down.

By inscribing a polygon having appropriate number of sides within a circle so that one of its corners lies at the bottom, each of the polygon's corners defines a $\text{π}$ electron energy level.

A horizontal dotted line drawn through the center of the circle separates the bonding and anti-bonding molecular orbitals.

The bonding orbitals are shown by the vertices below the halfway mark of the circle.The antibonding orbitals are shown by the vertices above the halfway mark. If the vertices lie exactly in the middle, then they represent non-bonding orbitals.