Diels-Alder Reaction

  1. Introduction
  2. Conjugated dienes undergo a cycloaddition reaction with multiple bonds to form unsaturated six-membered rings. In conventional terminology, this is a 1,4-addition of a diene and a dienophile. This reaction has a great synthetic importance and was discovered by two German chemists, Otto Diels and Kurt Alder, who received the 1950 Nobel Prize.

    The simplest Diels-Alder Reaction is the reaction of 1,3-butadiene and ethylene to yield cyclohexene (Figure 1).

Figure 1 : Diels-Alder addition of ethylene and butadiene


  1. Reaction mechanism
  2. The Diels-Alder reaction is a thermal cycloaddition whose mechanism involves the sigma-overlap of the pi-orbitals of the two unsaturated systems. There is not a single mechanism for all Diels-Alder reactions[4]. At first approximation, we can divide them into two classes : Real mechanisms are a mixture of these two extremes, one bond being more properly formed and thus shorter than the other.

    More O'Ferral-Jencks Diagram for the Diels-Alder Reaction

    Figure 2 : Mechanisms of the Diels-Alder Reaction

    To have an idea of the mechanism and to calculate the activation energy of a reaction, we have to find its transition state, using a gradient minimization. The transition state of the Diels-Alder Addition of butadiene and ethylene shows that it looks like the reactants. It is called an early transition state.

  3. Reaction study
  4. Here are the different computation results that we can get with the different computational methods :

    Unit : kCal/mol Activation Energy
    H
    Reaction Enthalpy
    H
    MM2 23.76 -56.45
    PM3 27.04 -52.55
    AM1 23.76 -56.45

    Table 1 : Computation results for the Diels Alder additin of ethylene and butadiene

    Experiments[7] give us the Arrhenius Activation Energy : 27.5 kCal/mol for a temperature between 760K and 921K. The Activation Enthalpy is then 27.5-(RT/4180)=25.83 kCal/mol (equation 10). Two remarks can be made on this result :


Endo - Exo  Selectivity

    When both the diene and the dienophile are suitably substituted, a stereochemical feature arises because the reactants may approach each other in two distinct orientations. The substituent on the dienophile may be directed away from the diene (exo  approach) or toward the diene (endo  approach). This stereochemical difference is often found with cyclic compounds. One very simple exemple is the Diels-Alder addition of two cyclopentadiene(1) (Figure 3).

Figure 3 : Diels-Alder addition of two cyclopentadienes


    1. Mechanisms
    In most Diels-Alder reactions, when the product distribution is under kinetic control, the endo adduct is preferentially, sometimes exclusively, formed. Several hypotheses have been made to explain this selectivity :

    Exo-Attack Endo-Attack

    Figure 4 : HOMO-LUMO interactions in the Diels-Alder addition of two cyclopentadienes


    In the above figure :
    • Red lines represent single bonds
    • Yellow lines represens double bonds
    • Hydrogen have been omitted
    • Red and yellow orbitals represent the LUMOs
    • Blue and green orbitals represent the HOMOs

exo Transition State
endo Transition State

Figure 5 : Transition states in the Diels-Alder addition of two cyclopentadienes


    1. Results of calculations
Unit : kCal/mol Activation Energy
H
Reaction Enthalpy
Hr
endo exo endo exo
AM1 34.21 33.17 -22.69 -24.43
PM3 37.40 36.61 -19.34 -21.20

Table 2 : Calculation results for the Diels-Alder reaction of two cyclopentadienes


    We have here the opportunity to calibrate the results given by the semi-empirical program MOPAC that we used to calculate the activation energy, the reaction enthalpy and the geometry of the molecules and transition states. We see that calculation gives a small exo preference whereas only the endo-adduct is formed. We should be aware of this during the other experiments.

    1. Influence of the entropy
Hr
(kCal/mol)
Sr
(Cal/K/mol)
Gr
(kCal/mol)
H
(kCal/mol)
S
(kCal/K/mol)
G
(kCal/mol)
PM3 exo -21.20 -48.39 -6.80 36.61 -44.18 49.85
endo -19.34 -48.31 -4.92 37.40 -44.43 50.57

Table 3 : Diels-Alder Addition of two cyclopentadiene
Detailed thermochemical parameters at 298K

    The reaction entropy and activation entropy differences are very small and we can neglect their effect on the Gibbs Free-Energies Gr and G (calculated using equation (2') and (9)). This is not surprising because the exo and the endo reactions are very similar. In both cases, we have the addition of two reagents that yield one product, and the bond transformations are identical. To compare Diels-Alder reactions, it is a good approximation to study only the reaction enthalpies (Hess' law (3) enables us to calculate them easily with the outputs of the calculations which are often heats of formation). The reaction enthalpy differences are almost the same as those of Gibbs free energy.

    1. Influence of the temperature
Hr
(kCal/mol)
Sr
(Cal/K/mol)
Gr
(kCal/mol)
H
(kCal/mol)
S
(kCal/K/mol)
G
(kCal/mol)
200 K
PM3
exo -20.93 -47.19 -11.49 36.61 -44.39 45.49
endo -19.06 -47.25 -9.61 37.41 -44.12 46.24
400 K
PM3
exo -21.33 -48.70 -1.85 36.73 -44.08 54.36
endo -19.47 -48.80 0.05 37.52 -43.85 55.06

Table 4 : Diels-Alder Addition of two cyclopentadiene
Detailed thermochemical parameters at 200K and 400K

    We have a confirmation that the yield of the Diels-Alder addition decreases with the temperature. With a temperature higher than 400K, we would favour the reverse reaction. This is due to the negative entropy that favours dissociation, and its importance increases with temperature. We observe that there is no change in the endo-exo selectivity, and that the entropy differences between endo and exo products and transition states are so small that we do not need to take them into account.

    We conclude that we only need to deal with the heats of formation at 298K to predict endo-exo selectivity in the Diels-Alder additions. This does not let us have any ideas about the yield of such reactions, but only on the selectivity.


    (1) Cyclopentadiene is a volatile hydrocarbon (b.p. 46C), available commercially as a dimer that can be cracked thermally. The dimer boils at 170C. When the free monomer has been prepared by slow distillation of the dimer, it must be used immediately as it re-dimerizes on standing to give the Diels-Alder endo-addition product.

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