Catalysis of a Diels-Alder Addition with a Porphyrin Trimer

  1. Introduction
  2. They are as yet few effective enzyme mimics for biomolecular reactions because we do not understand the design rules governing their operations. Enzyme catalysed reactions on a single bound substrate are now understood and imitated by synthesic chemistry. However one of the major goals of supramolecular chemistry remains to imitate the ability of enzymes to bind two substrate molecules and catalysis stereospecific reactions between them. In a recent paper, C. Walter and J. Sander[10] report the catalyse of the Diels-Alder addition of a furan-based diene (1) and a maleimide based dienophile (2). They use a porphyrin trimer catalyst that is inspired by biological enzymes. We will try to see how different models can fit the experiments.

Figure 2.1 : Diels Alder Addition of the 1 and 2

  1. Calculation Results
    1. Addition of 1 and 2 without catalyst
    2. Calculations were first carried out without any catalyst. Both molecular mechanics (MM2) and semi-empirical calculations (MOPAC 93, PM3 and AM1) were performed. Results are given in table 2.1.

Table 2.1 : Endo/Exo selectivity without Catalyst
kCal.mol-1 H°f(reactants) H°f(T.S.) H°f(products) Reaction Enthalpy Activation Energy
Semi-Empirical MOPAC 93 PM3 endo 17.76 41.81 -4.73 -22.48 24.05
exo 38.65 -7.88 -25.63 20.90
AM1 endo 55.33 73.44 25.80 -29.53 18.11
exo 70.62 23.53 -31.80 15.29
MM2 endo -27.50 8.80 -13.51 13.99 36.30
exo 8.19 -11.55 15.94 35.69

    Here we can see that there is an exo preference : the difference between exo and endo Activation Energy is about 3 kCal/mol (PM3). The exo product is more stable, too. When we refer to the value we have computed for the Diels-Alder addition of two cyclopentadienes, these values are more in favor of an exo product and we can conclude that there is an exo selectivity, which corroborates with experiment[11] (table 2.2).

kCal.mol-1 Reaction Enthalpy Activation Energy
Experimental endo -27.0 26.3
exo -29.2 25.1

Table 2.2 : Experimental results

With the MM2 Force Field we get an endo thermodynamic selectivity. Experience has shown that is is not, and we will have to keep this correction in mind to compare with the calculation in the presence of a catalyst. The value we get for the transition state is not very useful because we cannot describe the hybridization of the different atoms. For example, the oxygen atom on the diene is sp2 in the reactants and sp3 in the product. We cannot model it in the transition state in a way that can be treated correctly in a molecular mechanic calculation. Furthermore, the transition state is not a minimum of energy. The algorithms that are used to find the geometry of the ground state do not converge rapidly to the transition state.

  1. Catalysts
The two catalysts we decided to study are built with a porphyrin trimer motif. The shape of this trimer is described in figure 2.2. The first catalyst (1) has been synthesized[12] and already usedfor the catalysis of the reaction of 1 and 2. The second catalyst (2) is smaller than the other and we wondered if it could catalyse the formation of the endo product.

The planes represent the porphyrins and the bold lines represent the links between them.

The Zinc-porphyrin

Links used in Catalyst 1

Links used in Catalyst 2

Figure 2.2 : Catalysts 1 and 2

    Thanks to Dr. James Stewart, the catalyst 1 has been optimized using semi-empirical calculations : Mopac 93 (H°f = 849.63 kCal/mol, Gradient Norm = 2.48) and Mozyme[21], a new program he is developing (H°f = 849.69 kCal/mol).

    1. Catalyst 1
    In our first simulation, we used the catalyst with a side chain of length two. The results are given in tables 2.3 and 2.4. The Heat of formation refers to the products linked by the pyridines to two Zinc atoms on the catalyst. Mopac calculations were also carried out on the exo and endo adduct. Due to the time required to handle such big molecules (325 atoms), the transition states could not been calculated with Mopac. We can estimate that we would need at least one month to find the transition state and to carry out a vibrational analysis on a Silicon graphics INDY Workstation, with 96 Mbytes memory.

Table 2.3 : Endo/Exo selectivity with Catalyst 1 (MM2)
kCal.mol-1 H°f(reactants) H°f(T.S.) H°f(products) Reaction Enthalpy Activation Energy
MM2 endo -129.00 -40.72 -98.42 30.58 88.28
exo -90.69 -108.82 20.18 38.51

endo adductexo adduct
Mopac 93
Gradient Norm H°f
Gradient Norm
850.1 8.47 842.0 6.74

Table 2.4 : Semi-Empirical (PM3) results

kCal.mol-1 Reaction Enthalpy Activation Energy
Experiments endo -27.7 27.3
exo -28.9 24.2

Table 2.5 : Experimental results[11]

    It is obvious that the mechanics calculations results for the transition states are very bad. As it has been said before, this is due to the fact that mechanics are designed to find ground states and not transition states. However we can see that the MM2 force field gives more or less the same exoselectivity (about 10 kCal/mol) as the PM3 calculations.
    The selectivity seems to be better with Mopac calculations than is found with experiment. This could be due to fact that the endo addition does not imply the fixation of both reactants on the catalyst.

    1. Catalyst 2
    Due to time shortage, we only carried out mechanical calculations (a single optimization has been computed with catalyst 1, but needed about 10 days to be accurate enough). Results are given in table 2.6.

Table 2.6 : Endo/Exo selectivity with Catalyst 2
kCal.mol-1 H°f(reactants) H°f(T.S.) H°f(products) Reaction Enthalpy Activation Energy
PM3 endo 136.02 105.23 -116.21 19.82 68.08
exo -90.93 -117.06 18.96 43.08

    With catalyst 1, we have observed that the difference between the endo and the exo reaction enthalpies was close to the semi-empirical value. If we have the same behavior with the second simulation, we can conclude that there is no endo-exo selectivity at a first approximation (and even an endo selectivity if we take into account the correction we have shown with cyclopentadienes). We can reasonably think that the endo-addition is here more favoured: The endo transition state and product are more compact and so require a smaller catalyst.

  1. Substrate Strain and Catalyst Deformation
  2. In order to understand how the catalyst works, we need to study its deformation and the substrate strain when they are bound together. We separate the substrate and the catalyst by cutting the Zinc-pyrimidine bonds. After that we calculate the current energy of the catalyst and the substrate. The results are given in table 2.7., the square brackets indicating that this geometries are not these optimized geometries for either the catalyst or the substrate alone.

Table 2.7 : Strain analysis
Molecular Mechanics MM2 (CAChe)
kCal.mol-1 [ Catalyst ] Catalyst
Ground State
Deformation [ Substrate ] Substrate
Ground State
Catalyst 1 Reactants -87.70 -89.30 1.60 12.19 -27.50 39.69
Exo Product -87.86 1.44 29.12 -11.56 40.68
Endo Product -87.48 1.82 40.80 -13.51 54.31
Catalyst 2 Reactants -85.99 -90.04 4.05 25.33 -27.50 52.83
Exo Product -79.22 10.82 28.66 -11.56 40.22
Endo Product -82.60 7.44 29.14 -13.51 42.65

    The MM2 force field does not describe the dative bond between nitrogen and zinc. We require CAChe Mechanics to estimate the missing parameters : using the augmented option, the calculation was extended to all elements by applying simple empirical rules to estimate parameters for elements not in the MM2 set. This explains why the strain energies for the substrates are very high. We are only interested in the difference between these numerical values. For example, it is obvious that the endo adduct is much more strained than the exo adduct (about 14 kCal/mol). We note that for catalyst 1, the deformation is not important (less than 2 kCal/mol) whereas with catalyst 2, the smaller one, it is more significant. Catalyst 2 is probably too small for catalysing either the endo or the exo additions.

    The same experiment was carried out using the PM3 semi-empirical method for catalyst 1. The single point energies of the two parts of each catalyst+substrate complex are shown in Table 2.8 :

Table 2.8 : Strain analysis
Mopac 93 PM3/RHF
kCal.mol-1 [ Catalyst ] Catalyst
Ground State
Deformation [ Substrate ] Substrate
Ground State
Exo Product 867.5 849.7 17.8 -6.2 -7.9 0.8
Endo Product 865.3 15.6 5.2 -4.7 9.9

    We first have to check the validity of this analysis : the energy of the two dative bonds is

    These two values are close enough to confirm that the same operation has been made on the two fragments.

    These results partially invalidate the deduction we could have made with the MM2 experiments. We find here that the exo adduct is practically unstrained, whereas there is a strain energy at about 10 kCal/mol for the endo adduct. This confirms that the porphyrin trimer has exactly the right size to bind the exo product. The deformation of the catalyst is more important than has been found with mechanics calculations, but it remains very small in comparison with the size of the catalyst: the deformation is spread out over the 285 atoms and the 315 bonds.

  1. Conclusion
  2. We have shown here that is is very difficult to use molecular mechanics to analyse kinetic effects. Since transition states cannot be found without modelling the electrons, we cannot measure small effects such as the difference between the activation energies of the endo and exo addition. We have to carry out calculations at a higher level.

    Semi-empirical calculations are a solution to this problem, but they require so much time that we have to be sure of the interest of the computation. In the near future, with the increase in the capacities of the computers, it will probably be possible to carry out these calculations within a week or less. Another solution may lie in running Mozyme. Mozyme is a semi-empirical quantum chemical program for the study of large systems. The methods in Mozyme are similar to those in Mopac. The fundamental difference is that, whereas MOPAC uses matrix algebra for the solution of the self-consistent field equations, Mozyme uses localized molecular orbitals (Lewis structures).

    The idea of trying to model new catalysts can be applied to other classes of reactions. We could, for example, try to build an asymmetric trimer that could yield the endo product. We have not dealt with entropies. We have already seen that the entropy is not important when we compare two similar reactions like endo and exo additions. If we want to prove that a catalyst accelerates a reaction, we will have to take it into account, because catalysts often act as "entropic-traps" and freeze degrees of freedom. Unfortunately, the estimation of the entropy of formation for each molecule requires much more CPU-time than the heat of formation. That explains why we cannot verify the importance of entropy factors in this system.

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