Polygon Rule

The polygon rule predicts that the MO energy diagrams for these annulenes will resemble the polygonal shapes of the annulenes. 

Q Explain how to construct the molecular orbitals of a conjugated cyclic system similar to benzene and cyclobutadiene. Use the polygon rule to draw the energy diagram, and fill in the electrons to show whether a given compound or ion is aromatic or antiaromatic. 

Pinacol rearrangement, 292, 299, 309, 326 Piperidine, 455 Planck s constant, 231 Plane of symmetry, 69 Polar bonds. 27 Polarity, 21 Polarizability, 121 Polar molecules, 27 Polycyclic compounds, 162 Polygon rule, 197 Polymerization, alkenes, 102 116 dienes, 153//... 

The polygon rule gives you a fast way to draw an electronic configuration. It also provides a quick check on molecular orbitals you might draw, to see which are bonding, antibonding, and nonbonding. 

The shape formed by connecting the different energy levels of the pi MOs for any conjugated ring system will always be identical to the shape of the ring system standing on one of its points (the polygon rule). 

Example 10-12. Using the polygon rule and Equation (10.49), sketch the one-electron MO diagram for the pi MOs in benzene. Use group theory to determine the symmetries and shapes of these MOs. 

---