# Other Pericyclic Reactions

Frontier molecular orbital (FMO) theory dictates whether a reaction will occur naturally or will need to have the electrons excited to form a product. The Woodward-Hoffmann rules predict the stereochemistry and activation energy of pericyclic reactions.

A pericyclic reaction is a reaction in which bonds are made or broken in a concerted cyclic transition state. Several categories of reactions are pericyclic. The three most common types of pericyclic reactions are cycloaddition, electrocyclic, and sigmatropic. A cycloaddition reaction is a concerted reaction in which two or more unsaturated molecules (or parts of the same molecule) combine to form a cyclic product, with a net reduction of bond multiplicity. An electrocyclic reaction is a reversible reaction that involves ring closure of a conjugated polyalkene to a cycloalkene or ring opening of a cycloalkene to a conjugated polyalkene. A sigmatropic reaction is a reaction in which the net result is that one $\sigma$ bond is changed to another $\sigma$ bond in an uncatalyzed intramolecular process. These reactions are governed by the Woodward-Hoffmann rules, or pericyclic selection rules, a set of rules used to rationalize or predict certain aspects of the stereochemical outcome and activation energy of pericyclic reactions.

The Woodward-Hoffmann rules are based on frontier molecular orbital theory and the conservation of orbital symmetry. The frontier molecular orbital theory is the concept that the highest-energy occupied orbitals of one molecule interact with the highest-energy unoccupied orbitals of another molecule. Conservation of symmetry requires the orbital symmetry of the products to be the same as that of the reactants. When orbital symmetry is discussed in reference to $\pi$ bonds, it refers to the fact that a $\pi$ bond orbital is symmetrical, with the carbon-carbon bond acting as a plane of reflection. An idealized bond has a bonding (or symmetric) phase on one side of the plane and an antibonding (or antisymmetric) phase on the other side of the plane. Electrons reside in the bonding phase, and like phases interact.

Pericyclic reactions will not occur if they are symmetry forbidden, such as when orbitals of opposite phases overlap, and electrocyclic reactions are no different. To make (or break) a ring, the bonding phases of the $\pi$ orbitals on the terminal carbons must overlap or rotate. This need explains why under one set of conditions some molecules will rotate one direction but will rotate another direction under different conditions. All pericyclic reactions may be promoted by either thermal (heat) conditions or photochemical (light energy) conditions. Thermal condition is a condition of a reaction where heat is the deciding factor in the distribution of products. Photochemical change refers to a chemical change initiated by light. The conditions used to promote a reaction, however, influence the product obtained.

### Woodward-Hoffmann Rules for Electrocyclic Reactions

$n$ Electron Pairs Thermal Photochemical
$4n$ (even) Conrotatory Disrotatory
$4n+2$ (odd) Disrotatory Conrotatory

Electrocyclic reactions will form via either a conrotatory or disrotatory movement of the molecular orbital to form new $\sigma$ bonds in the cyclization reaction. These reactions, however, will not occur if they are symmetry forbidden (for example, if orbitals of opposite phases overlap). To make (or break) a ring, the bonding phases of the $\pi$ orbitals on the terminal carbons must be able to overlap or rotate so that they may overlap.

Electrocyclic reactions will form via either a conrotatory or disrotatory movement. Conrotatory is a classification that describes when the two ends of the polyalkene rotate in the same direction during the movement of the molecular orbital to form new $\sigma$ bonds in the cyclization reaction. Disrotatory is a classification that describes when the two ends of the polyalkene rotate in opposite directions during the movement of the molecular orbital to form new $\sigma$ bonds in the cyclization reaction. The rotation pathway will dictate the stereochemical outcome of the reaction. Either thermal conditions or photochemical conditions may be employed to complete the electrocyclic reactions.

In addition to the need to rotate individual carbons to maintain orbital symmetry, some classes of pericyclic reactions also require the rotation of whole $\pi$ systems. This often happens when the reaction is intermolecular rather than intramolecular (such as with an electrocyclic reaction). With intermolecular reactions, such as a cycloaddition, bonding may take place in one of two ways: suprafacial or antarafacial. Suprafacial is having like phases of the p orbitals of two molecules on the same side of the $\pi$ systems so that two bonding interactions occur. Antarafacial describes when one $\pi$ system must twist to align like phases of the p orbitals so that two bonding interactions will occur.

### Woodward-Hoffmann Rules for Cycloaddition Reactions and Sigmatropic Rearrangements

$m+n=q$ Electron Pairs from Reactants
($m$, $n$ are electron pairs from each component)
Thermal Photochemical
$4q$ (odd) Supra/supra Supra/antara
$4q+2$ (even) Supra/antara Supra/supra

Bonding involving $\pi$ systems as a whole requires designations for the sides of these $\pi$ systems. These designations are suprafacial, which is when the like phases of the $\pi$ orbitals of the two molecules are on the same side of the $\pi$ systems so that two bonding interactions occur, or antarafacial, which is when one $\pi$ system must twist to align like phases of the $\pi$ orbitals so that two bonding interactions will occur.

A sigmatropic rearrangement is a reaction where one $\sigma$ bond is changed to another $\sigma$ bond in an uncatalyzed intramolecular process. This essentially means that a $\sigma$ bond is broken, a $\pi$ bond is relocated, and a new $\sigma$ bond is formed, but the movement of bonds does not involve a cyclization. The numbering used to designate the reactions is an indicator of where the original $\sigma$ bond starts and where it ends up.

These rearrangements employ the same Woodward-Hoffmann rules as cycloadditions. This means two molecules provide electron pairs or $\pi$ systems. The stereochemistry of the final product depends on the reaction conditions as well as whether the total number of pairs provided are even or odd. In the case of sigmatropic rearrangements, this means that the migrating hydrogen atom is initially designated suprafacial and then, as it passes through the transition state, it may end in the same suprafacial orientation or in the opposite orientation.

#### Sigmatropic Rearrangement Numbering System

Sigmatropic rearrangements are the unique class among pericyclic reactions. At first glance, these reactions may look simplistic and a bit redundant. However, when applied to asymmetric molecules, it is easy to see the usefulness of these rearrangements. Two examples of these rearrangements are the Cope and Claisen rearrangements. A Cope rearrangement is a [3,3]-sigmatropic rearrangement that involves the rearrangement of 1,5-dienes to a regioisomer, an isomer based on the location of a functional group. A Claisen rearrangement is a [3,3]-sigmatropic rearrangement that involves the rearrangement of vinyl allyl ethers (phenyl allyl ethers) to unsaturated carbonyls. Vinyl allyl ethers have the general formula ${\rm{CH}}_2={\rm {CH{-}O{-}CH_2{-}CH}}={\rm{CH}}_2$, while phenyl allyl ethers have the general formula ${\rm {C_6H_5{-}O{-}CH_2{-}CH}}={\rm{CH}}_2$. Both rearrangements are thermally driven and generally result in the more thermodynamically stable isomer. The main difference between the two is that the Claisen rearrangement involves an oxygen in the process, while the Cope rearrangement does not. Additionally, Cope rearrangements are reversible, but the equilibrium favors the more stable isomer.