The Diels-Alder Reaction

The group of [4 + 2] cycloaddition reactions referred to as the Diels-Alder reaction constitute one of the most versatile and widely used synthetic methods. Stripped to its most basic components, this reaction is represented by the addition of 1,3-butadiene to ethene shown below. The standard state thermodynamic functions for this reaction may be calculated from the heats of formation and entropies of the components.

ΔHº = -40 kcal/mole	ΔSº = -43.6 cal/ ºK mole	ΔGº = -27 kcal/mole kcal/mole

The exothermic nature of this reaction is the result of converting two weak π-bonds into two stronger σ-bonds. The large negative entropy reflects the change from two independent reactant molecules to one product molecule, and the necessity of fixing the diene in a cisoid conformation. Both impose increasing order on the system. Because the entropy factor opposes the enthalpy change, the calculated ΔGº is smaller than ΔHº by 298*ΔSº/1000, but it still represents a strongly exergonic reaction. Despite the favorable overall energy change, this reaction has a substantial free energy of activation, and requires heating to take place. At 200 ºC the TΔSº component increases to 20.6 kcal/mole, but ΔGº remains a strongly exergonic -19.4 kcal/mole. The calculated equilibrium constant favoring cyclohexene at this temperature is therefore greater than 10¹².
Functional substituents on the dienophile or diene reactants often lower the activation barrier, and in some cases spontaneous [4 + 2] additions may occur. Examples include: 1,3-butadiene + maleic anhydride, 1,3-cyclopentadiene + propenal, and 1,3-cyclohexadiene + dimethyl acetylenedicarboxylate.

It is interesting to note that a commercial process for preparing 1,3-butadiene consists of passing gaseous cyclohexene over a red hot metal coil (ca. 900 ºC), as shown in the following equation.

ΔG¹¹⁷³ = +40 – (1173 * 43.6/1000) = -11.1 kcal/mole

This is the reverse of the Diels-Alder cycloaddition, and the thermodynamic functions for this reaction will have opposite signs to those defined above. Using these standard state functions, the success of this procedure can be explained. At 900 ºC (1173 ºK) the entropy component is larger than the enthalpy component, so the ΔG for the decomposition is an exergonic -11.1 kcal/mole. This is equivalent to an equilibrium constant of 10⁸, favoring the desired butadiene, which is easily separated from ethene thanks to its higher boiling point (-4.5 ºC ). It should be noted that ΔH and ΔS are not constant at all temperatures, but do not normally suffer large changes.

Dimerization of Cyclopentadiene

A similar Diels-Alder system that is more easily studied is the dimerization of 1,3-cyclopentadiene shown below. The ΔHº for this reaction is almost 10 kcal/mole lower than that of the butadiene + ethene addition, reflecting strain in the tricyclic product. The ΔSº, on the other hand, is roughly 10 eu less negative as a result of the fixed cisoid orientation of the diene.

ΔHº = -18.4 kcal/mole
ΔSº = -34 cal/ ºK mole
ΔGº = -8.3 kcal/mole kcal/mole

ΔH^‡ = +15 kcal/mole
ΔS^‡ = -32 cal/ ºK mole
ΔG^‡ = +24.5 kcal/mole kcal/mole

At room temperature cyclopentadiene slowly dimerizes, the exergonic ΔGº corresponding to an equilibrium constant of 10⁶ in favor of the dimer. The ΔG^‡ prohibits immediate reaction, but a sample of pure cyclopentadiene at room temperature slowly dimerizes over a week or two. Consequently, the short shelf life of the synthetically important monomer demands that it be freshly prepared just before it is used in a reaction. This is easily accomplished by heating the dimer to just below its boiling point (170 ºC) and collecting the lower boiling monomer (b.p. 42 ºC) as it is formed. Although the ΔG for dimerization is still negative at 170 ºC (-3.3 kcal/mole), it has been substantially lowered by the TΔSº factor, permitting a significant equilibrium concentration of the monomer to be achieved.

The availability of activation parameters for this reaction makes it possible to explore further details of the reaction path. The stereospecificity of the Diels-Alder reaction implies a single step transformation, and the exothermic character of the reaction requires an enthalpy profile similar to that shown on the right. The Hammond Postulate, which uses ΔHº as an indicator, suggests that the transition state would resemble the reactants more than the products. However, the similar magnitude and sign of ΔSº and ΔS^‡ requires the transition state to have a structure very similar to the dimer product. This disagreement is a warning that the Hammond postulate was intended to be used for reaction profiles involving high energy intermediates., and is probably inappropriate for single step reactions such as S_N2 substitutions and the Diels-Alder cycloaddition.