Overview

The Frost circle or the inscribed polygon method is a graphical method for determining the relative energies of π molecular orbitals (MOs) for planar, fully conjugated, and monocyclic compounds. This method was first described by A. A. Frost and Boris Musulin in 1953.

A Frost circle is constructed by drawing a polygon whose number of edges is equal to the number of carbons of the given cyclic system, with one of the vertices pointing down. Then, a circle is drawn enclosing the polygon so that all the polygon's vertices touch the circle. The points where the circle touches the polygon are marked with short horizontal lines, representing the energy levels of π molecular orbitals.

Subsequently, a dashed horizontal line is drawn through the center of the circle, bisecting the polygon. The energy levels below this line represent bonding molecular orbitals, and above this line represent antibonding molecular orbitals. The energy levels on the line represent non-bonding molecular orbitals, with the energy equal to p orbitals from which the molecular orbitals are formed. 

Finally, the π electrons are added to the energy levels starting from the lowest and moving upwards. The degenerate orbitals are filled first with a single electron and then paired with another electron if available, following Pauli’s exclusion principle and Hund’s rules.

Procedure

The Frost circle or the inscribed polygon method is a graphical method based on Hückel's rule to determine the number and relative energies of the π molecular orbitals of planar, monocyclic, and conjugated systems.

A Frost circle is drawn by inscribing a polygon, representing the cyclic compound, inside a circle with one of the vertices pointing down.

The intersections where the circle touches the polygon are marked by short horizontal lines representing the number and the relative energies of π molecular orbitals.

Next, a dashed horizontal line is drawn through the circle's center, bisecting the polygon. This line represents the energy of the participating p orbitals.

All the molecular orbitals with energies below this line are bonding, those above the line are antibonding, and those on the line are non-bonding molecular orbitals.

Lastly, the π electrons are added to the energy levels according to Hund's rule and Pauli's exclusion principle.