# Diels-Alder Reaction

The Diels-Alder reaction is a [$4+2$] cycloaddition in which a diene (4 $\pi$ electrons) and a dienophile (2 $\pi$ electrons) combine to form a cyclohexene molecule (or a cyclohexadiene if an alkyne is used as the dienophile).

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. Bond multiplicity is the number of bonds that form, depending on the number of bonding electrons in molecular orbitals. An example of a cycloaddition reaction is the Diels-Alder reaction, a concerted reaction in which two new $\sigma$ bonds are formed at the expense of two $\pi$ bonds of the conjugated diene and dienophile. A dienophile is a compound containing a double bond (or a two $\pi$-electron system). The reaction product contains a new six-membered ring with a double bond.

The Diels-Alder reaction is also known as a [$4+2$] cycloaddition, where the 4 refers to the four $\pi$ electrons contributed by the diene and the 2 refers to the two $\pi$ electrons contributed by the dienophile. The diene must be conjugated and must be in the s-cis conformation to react with the dienophile and form the new six-membered ring. If the diene is not in the s-cis position, it needs to be able to rotate into that conformation. If it cannot rotate to the s-cis conformation, then the reaction will not occur. In the s-trans conformation, the two ends of the diene are too far apart to be bridged by the diene. If the diene is locked in the s-cis conformation, the reaction will occur very rapidly.

#### Diels-Alder Reaction

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. For example, chemical interactions and resonance are explained by overlap between the filled HOMO and the empty LUMO. The highest occupied molecular orbital (HOMO) is the highest energy level that is occupied by electrons. The lowest unoccupied molecular orbital (LUMO) is the lowest energy level that is not occupied by electrons. This theory may be used to explain why the Diels-Alder reaction occurs; it can also explain the stereoselectivity that is seen in the product. The key to the theory is that the molecular orbitals used are the highest occupied molecular orbital (containing the least tightly held electrons) and the lowest unoccupied molecular orbital that will result in the lowest energy transition state. In the [$4+2$] cycloaddition of 1,3-butadiene and ethene, there is constructive overlap between the similar phases of both orbitals in the HOMO and the LUMO when lining up the HOMO of 1,3-butadiene with the LUMO of ethene. This results in a reaction that is symmetry allowed, which means the set of orbitals line up in the ground states. Additionally, the way the overlap occurs explains the resulting stereochemistry of the product. The diene approaches the dienophile from one of its faces (above or below the plane), leaving its substituents untouched in the plane.

#### Bonding of 1,3-butadiene with Ethene Using HOMO and LUMO Orbitals

The [$2+2$] cycloaddition of ethene to ethene is symmetry forbidden, which means the set of orbitals do not line up in the ground state. When lining up the HOMO of one ethene molecule and the LUMO of the other ethene, there is constructive overlap between similar phases on one set of orbitals but not the other orbital. Because there is not constructive overlap of both orbitals, the cycloaddition of ethene to ethene is symmetry forbidden and can only occur if one electron of an ethene is excited from the ground to the excited state. When lining up the excited state HOMO of ethene and the LUMO of the other ethene, there is constructive overlap between the two sets of orbitals, and this reaction is symmetry allowed.

#### Bonding Ethene with Ethene Using HOMO and LUMO Orbitals

In the Diels-Alder $4+2$ reaction, the product, cyclohexene, will retain the stereochemistry of the dienophile. This means if the substituents on the dienophile are cis-, they will be cis- on the cyclohexene. If they are trans- on the dienophile, they will be trans on the cyclohexene. Additionally, if the two diene substituents have the same stereochemistry (E or Z), they will be on the same face of the cyclohexene. If the substituents have opposite stereochemistry, they will be on opposite faces of the cyclohexene. This may lead to a mix of enantiomers depending on the substituents present.

Additionally, when combining a cyclic diene with a cyclic dienophile to generate a bicyclic product, the substituents of the diene will generally follow the endo rule. The endo rule is the stereochemical preference for the electron-withdrawing substituent to appear in the endo position rather than the exo position. In the bicyclic products, the electron-withdrawing substituent(s) on the dienophile occupies the stereochemical position (or the endo position) closest to the $\pi$ system of the diene. The endo position refers to a substituent in a bicyclic system oriented toward the larger ring. The reason for preference of the endo product is generally considered to be because of a favorable interaction between the diene's $\pi$ system and the dienophile's substituent $\pi$ system. These interactions are known as secondary orbital interactions.

Finally, an asymmetric dienophile may react in either orientation. Regioselectivity is based on the charge distribution of both diene and dienophile. Regioselectivity is the preference of one direction of chemical bond making or breaking over all other possible directions. The orientation that lines up opposing charges in their resonance forms will lead to the major product. If the diene and dienophile are on the same chain of carbons, an intramolecular Diels-Alder reaction may occur.