The process is straightforward:

• Draw a circle of radius 2b.

• Inside the circle, inscribe the regular polygon corresponding to the molecule of interest
  • One vertex must be pointed downward

  • All vertices must just touch the circle

The positions of the vertices then describe the energies of the molecular orbitals.

• Orbitals with negative energies are bonding; those with positive energies are antibonding

• Orbitals of zero (or a) energy are non bonding

For example:

The diagram on the left represents benzene. The six p-electrons then may be placed in the orbitals with spins paired, beginning with the lowest. The six electrons just fill all the bonding orbitals.

• Note the degeneracy of both HOMO and LUMO.

Notice that the 4n + 2 rule falls naturally out of this diagram: two electrons for the single orbital of lowest energy, and four for each doubly degenerate level.

On the right is cyclobutadiene, with four p-electrons.

• Again, the HOMO is degenerate.

• Since Hund's rule won't let us pair electrons in an orbital until there is no other option, Frost's circle predicts cyclobutadiene to be a diradical.

Note that this scheme only works for regular polygons. If cyclobutadiene is not square, it doesn't have to be a diradical.

• In fact, the Jahn-Teller effect predicts that such a species should distort so as to remove the degeneracy of the half-filled orbitals.

• When finally synthesized at 77 K in an argon glass, cyclobutadiene was found to be rectangular, with all electrons paired.