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The Cope Rearrangement Tutorial

Optimising the Reactants and Products

In this section, the reactants and products for the Cope rearrangement are built and optimised using Gaussview. The reactant and product in this reaction are, coincidentally, the same: 1,5-hexadiene (however a [3,3]-sigmatropic rearrangement does take place). Initially, a gauche conformer of this molecule is constructed , in which the torsional angle between the bulkier R groups surrounding the innermost carbon-carbon bond of the molecule is 60°. This conformer is then optimised at the HF/3-21G level (ie. using the Hartree Fock method and the 3-21G basis set). This optimisation allows the determination of the energy of the structure, at -231.69166700 au, and also the symmetry of the structure (C1 point group). This confirms that the gauche conformer evaluated in this step was the gauche 3 conformer.

  • gauche3 conformer
    gauche3 conformer

Then, an anti conformer of this molecule is constructed (in which the torsional angle between the bulkier R groups is now between 90° and 180°) and optimised, at the same level as previously. This resulted in an energy of -231.69253496 au for the anti conformer, and a Ci point group, revealing that this is the anti 2 conformer. This shows that the energy of the anti conformer is slightly lower (more negative) than that of the gauche conformer, which can easily be rationalised: in the anti conformer the torsional angle between the bulkier groups is larger, meaning the steric clash between them is reduced. This can also be thought of in terms of electronic contributions: the R groups contain more electrons than the hydrogens, and an increased torsional angle between them reduces the electrostatic repulsion between the two electron rich R groups, thus reducing the energy. It would therefore be expected that the lowest energy conformer of this molecule would be an anti conformer, in which the torsional angle between the R groups is the closest to 180°. This conformer is in fact the anti 1 conformer, which has a torsional angle that is slightly closer to 180° than that of the anti 2 conformer, giving it a slightly lower energy. Upon construction and optimisation (at the same level) of this conformer, the point group is determined to be C2 and the energy -231.69260232 au. This means that the minimum energy for this compound is -231.69260232 au, and thus this conformer will be used in the calculation of any activation energies or enthalpies for this compound.

  • anti2 conformer
    anti2 conformer

For the anti 2 conformer, the calculated energy is -231.69253496 au, while the given energy for this same compound is -231.69254 au: this gives an energy difference of 0.00000504 au which is the same as 1.3 J mol-1. For these purposes, this energy difference is very small, and it can be considered that this energy difference is negligible.

Nf710 (talk) 12:36, 19 November 2015 (UTC) This is just about acceptable

The anti 2 conformer is then reoptimised at a higher level- the B3LYP/6-31G* level (using the DFT method with the B3LYP functional and the 6-31G basis set). The energy of the conformer is now calculated as -234.55970548 au, while the point group remains the same (as the symmetry has not changed). Nf710 (talk) 12:40, 19 November 2015 (UTC) This energy is incorrect it shoudl be something like 234.61171166, perhaps you are using a different basis set. However, the bond lengths in the structure optimised at the higher level are longer than in that optimised at the lower level. Furthermore, the bond angles in the more highly optimised structure are further from the "ideal angles" for the hybridisation of the carbons involved, which is unexpected as one would assume the opposite would be the case. For example, the carbons at either end of the chain are sp2 hybridised and would have an ideal angle of 120°, however improved optimisation changes the calculated bond angle from 116.312° to 116.282°. This is also the case for the central sp3 carbons, which would have an ideal bond angle of 109.5°, however in the case of further optimisation this bond angle changes from 107.728° to 106.744°. This implies that the real structure does not feature ideal bond angles: it is obvious that in reality the ideal bond angles are never actually observed as other factors contribute to real structures, however it appears that in this case, the Lewis structure for 1,5-hexadiene really is inadequate and the real structure is much more delocalised. This also accounts for the increased bond lengths in the structure?

Nf710 (talk) 12:43, 19 November 2015 (UTC) interesting point. The best way to test this theory would be to compare to x ray structures. But good analysis of geoms but it would have been better if you had tabulated it.

Finally, a frequency calculation is carried out in order to obtain energies which can be compared to experimentally determined data. The optimised B3LYP/6-31G* structure has a frequency calculation (still using the DFT method with the B3LYP functional and the 6-31G basis set) carried out, giving the frequencies of the 42 vibrational modes for this compound, at 298.15K. The results also give various energies for this structure. This same procedure is then run again, but this time specifying the temperature to be 0 Kelvin.

Nf710 (talk) 12:45, 19 November 2015 (UTC) You need to include the fact that because there was no imaginary frequencies then we must have found a local minimum

The sum of the electronic and zero point energies is calculated as 234.360347 at 298.15K, and 234.360344 at 0K. This makes sense as both results are the same for all practical purposes, as would be expected since this result is the same as the potential energy at 0K, and so should be the same regardless of the temperature at which the frequency analysis is carried out.

The sum of the electronic and thermal energies is calculated as 234.354911 at 298.15K and 234.354904 at 0K. Once again, these results are broadly similar, which once again is expected as this result corresponds to the energy at 298.15K and so should be the same regardless of the temperature at which the frequency analysis is conducted.

The sum of the electronic and thermal enthalpies is calculated as 234.353967 at 298.15K and 234.354904 at 0K. This energy relates once again to the energy of the structure at 298.15K but with an additional term, so it makes sense that, once again, the energies are comparable for both temperatures.

The sum of the electronic and thermal energies is calculated as 234.389289 at 298.15K and 234.389292 at 0K. These energies once again are similar, as is expected since they relate to the energy at 298.15K, but this time with a further entropic contribution.

Optimising the Chair and Boat Transition States

Once the reactants and products have been constructed and optimised, it is possible to begin the construction and optimisation of the transition state for the Cope Rearrangement. Since the reaction is concerted, the transition state will be a 6 membered ring of carbons and hydrogens, and can thus adopt two different structures: the chair conformation and the boat conformation. The chair structure is lower in energy than the boat structure (obviously since this is a transition state, both of these structures are much higher in energy than the reactants or products), as in the chair conformation every bond angle can be the perfect 109.5° and there is no torsional strain, since there are no eclipsing carbon-carbon interactions as these bonds are staggered. The boat conformation is the next lowest energy conformation of a 5 membered ring, however it does still feature torsional strain and so is a slightly higher energy conformer.

Initially, the chair transition state is built, by combining two allyl fragments (optimised to the HF/32-1G level) such that they resemble a chair structure, with the terminal ends being 2.21724Å apart (the closest that could be achieved by eye). Initially, the two allyl fragments were simply lined up by eye, giving the distance between one pair of terminal carbons as 2.18985Å and that between the other pair as 2.23034Å, however when this structure was optimised the calculation crashed, so it was instead necessary to line up the fragments again by eye and using the symmetrise function to make the two distances equal (as this is a very important feature of a chair transition state), by reducing the tolerance such that the molecule can adopt a Ci point group. After this had been performed, the molecule was optimised using two different methods.

Firstly, the transition state was optimised using a Gaussian calculation in which the transition state was optimised to a TS (Berny), using the Hartree Fock method and the 3-21G basis set. This gave an imaginary vibration at -817.91 cm-1, indicating that the achieved structure was in fact a transition state, as these always feature imaginary (ie. negative) vibrations. This is because a transition state corresponds to a local maximum on the potential energy surface, which the reactants must go over in order to reach a lower energy state. Therefore the curvature at this point is negative, and the tendency at the transition state is to fall down either side (either returning to the reactants or forming products). The animation of this vibration clearly corresponds to the cope rearrangement, as it shows the each terminus of the fragments moving closer together in turn, and adopting an sp3 hybridisation rather than its initial sp2 hybridisation, such as would be the result of the Cope rearrangement.

Nf710 (talk) 12:53, 19 November 2015 (UTC)Good understanding of the way the TS optimisations work. however teh curvature is the second derivative of the PES which then goes into the quantum harmonic oscilator equation. hence a negative curvature gives a imaginary freq.

  • Animation of the Cope Rearranegment
    Animation of the Cope Rearranegment

After this, the same transition state is optimised again, using the frozen coordinate method. In this method, the bonds which will form/break (between the two termini of the allyl fragments) are identified as bonds and frozen. This is then optimised at the HF/32-1G level, producing a structure very similar to that in the previous part (since they correspond to the same structure), with bond lengths (between the termini) set at 2.21724Å. These are then optimised again in the same fashion, now giving these bond lengths as 2.02052Å, which is shorter than that expected in the chair conformer. In the previous optimisation, the final bond lengths obtained were 2.02047Å, which is quite similar to this, and once again, shorter than that expected. This indicates that the chair like transition state is not a perfect chair, and the terminal bond lengths are shorter than expected as they correspond to bonds being broken/formed in the reaction, and so are not proper bonds during the transition state, as they are in the process of transitioning. The frozen coordinate method once again featured a vibration at -817.85 cm-1, indicating that a transition state was in fact found.

Nf710 (talk) 13:00, 19 November 2015 (UTC) Correct frequency

After this, the boat transition state was constructed and optimised, once again, using a different method of optimisation. In order to do this, the anti2 conformer of 1,5-cyclohexadiene was used to construct the transition state using the QST2 method. In this method, the reactant and the product are specified, and the programme interpolates between the two to generate a reasonable transition state. Initially, the optimised anti2 conformer is copied, as this can also represent the product of the reaction (since the reactant and product of this reaction are the same), and then the atom numbers are altered such that they correspond to each other. The QST2 calculation is then run, however it fails, generating a transition state similar to a dissociated chair. This is because the calculation did not consider the possibility of a rotation around the central carbon bonds, which is necessary to form the boat transition state. The solution to this problem was to modify the starting and finishing structures such that they are already rotated, by modifying the dihedral angles for the central 4 carbons. The calculation was then repeated and gave a boat transition structure, with one imaginary frequency. The motion for this corresponded to the two ends of the structure moving together and apart, indicating that it represents the Cope rearrangement.

Nf710 (talk) 13:00, 19 November 2015 (UTC) Where is your frequency, where are your numbers?

Comparison of the chair and boat transition structures shows that it is very difficult to postulate exactly which conformers have produced which transition states, therefore it is necessary to use the Intrinsic Reaction Coordinate method to trace the lowest energy path from a local maximum (the transition state), to the local minimum (the original structure) on the potential energy surface. An IRC was computed for the chair transition structure, using 50 points on the IRC and calculating the reaction only in the forwards direction. However, this does not yield a minimum geometry, indicating that there were not enough points on the IRC. In order to obtain a minimum after this, one can redo the calculation using more points, do a simple optimisation to a minimum for the last point on the IRC, or calculate force constants at each stage.

Nf710 (talk) 13:00, 19 November 2015 (UTC) you havent provided your IRC I cant give you marks for this, neither have you tried to identify the conformer it connects.

After this, the activation energies for the chair and boat transition structures were compared by reoptimising both structures at the B3LYP/6-31G* level of theory, These reoptimised structures had similar geometries but the energy differences at the different levels of theory were very different. The energies for the transition structures and the anti2 reactant at both levels of theory are summarised below:

HF/3-21G B3LYP/6-31G*
Chair Transition Structure -231.618910 au -234.557021 au
Boat Transition Structure -231.602714 au -234.543110 au
anti2 conformer -231.69166700 au -234.55970548 au

At the HF/3-21G level of theory, the energy difference between the anti2 conformer and the chair and boat transition structures were 0.072757 au and 0.088953 au respectively. At the B3LYP/6-31G* level of theory, however, these energy differences were instead 0.002049548 au and 0.01659548 au. It can be seen that, at the higher level of theory, the energy difference between the reactive conformer and the respective transition states are much smaller.

Nf710 (talk) 13:11, 19 November 2015 (UTC) your electronic energies here are correct however you havent worked out the activation energies in kcal or compared it to experimental values or provided the thermal values. It is good that you have come to the conclusion that lower basis sets are good for geoms but not energies. however in future please tabulate your results. It is very hard and annoying to read block text. It would have been good if you could have put some more info about the methods that you have used here. like the theory behind DFT and HF.

The Diels Alder Reaction

The construction and optimisation of the transition states for the Diels Alder reaction is carried out in the same way as for the Cope Rearrangement: by constructing an estimate of the transition structure geometry and then optimising it. This was done using the Berny transition state method at the AM1 semi-empirical level of theory. Furthermore, some of the important MO's of the reactants and products were visualised. The Berny transition state method was chosen as it was the most simple method, given that reasonable structures for the transition states could be constructed.

Cis butadiene and ethylene

Initially, one of the simplest Diels Alder reactions is modeled, in which cis butadiene is the diene and ethylene is the dienophile. The cis butadiene was constructed and optimised under the AM1 semi-empirical molecular orbital method, and the MO's visualised. The HOMO was found to be the 11th MO which had an a2 symmetry and an energy of -0.34381 au, while the LUMO was the 12th MO with b1 symmetry and an energy of 0.01707 au. Both of these MOs are antisymmetric with respect to the plane of the molecule, as it can be seen that the MOs both have different phase patterns on either side of this plane, so reflection in the plane will change the MO, hence they are ungerade and antisymmetric. After this, the transition state was constructed and optimised. This was done by starting with the bicyclo [2,2,2] octane structure and removing the extra ethyl fragment, to give an "envelope" shaped structure, in which the bonds were modified, to give a structure with half formed bonds between the ethylene and the alkene carbons of the cis butadiene, and the alkene bonds reduced to an order of 1.5.This structure was then optimised using the Berny transition state method at the AM1 semi-empirical level of theory. This gave a structure with one imaginary vibrational frequency at -956.27 cm-1, thus confirming it to be a transition state. The animation for this vibration shows the terminal ends of the cis butadiene and the carbons of the ethylene moving together and apart again: this corresponds to the Diels Alder reaction, and demonstrates that the formation of the two new bonds is synchronous. This supports the idea of a pericyclic, concerted mechanism for the reaction. The vibration of the lowest positive frequency for this structure occurs at 147.18 cm-1, and when animated shows a vibration in which bond formation would instead be asynchronous, as each set of termini vibrate towards each other in an asynchronous manner.

(You should include images showing the MOs to help the reader understand what you're describing Tam10 (talk) 16:11, 17 November 2015 (UTC))

(The lowest positive frequency isn't related to a bond forming or breaking mode. If you looks carefully you should be able to see that the termini aren't coming together. Unfortunately it isn't animated so I'm not sure if you're seeing something else Tam10 (talk) 16:11, 17 November 2015 (UTC))

  • Animation of the Diels Alder reaction
    Animation of the Diels Alder reaction

The transition structure then had its HOMO and LUMO visualised, demonstrating the HOMO to be the 17th MO with an energy of -0.32395 au, and the LUMO to be the 18th MO with an energy of 0.02316 au. The HOMO is antisymmetric with respect to the reflection plane of the molecule, while the LUMO is symmetric with respect to this plane. The HOMO is thus labelled as a (antisymmetric): it is formed by combining the π* MO of ethylene with the HOMO of cis butadiene, as modelled in the previous part. The π* MO of ethylene is formed from the out-of-phase overlap of the p orbitals on the carbons, creating a high energy, anti bonding MO. The HOMO of cis butadiene consists of the out-of-phase overlap of the p orbitals on the central carbons, but an in-phase overlap of the p orbitals of the carbons at either end. This leads to an MO which is bonding with respect to the carbons at the the ends, but anti bonding with respect to the central carbons. These MO's then overlap with each other in an in phase interaction, creating an MO which is bonding between the ethylene fragment and the cis butadiene fragment, but partially antibonding within the cis butadiene fragment, and antibonding within the ethylene fragment. In this way, it can be seen that in the transition state, the HOMO represents the weakening of the double bonds within the reactants, as well as the formation of bonds between these molecules, which is in fact a way of describing the Diels Alder reaction itself. The reaction is allowed as it involves the interaction of the HOMO of cis butadiene with the LUMO of ethylene (the π* MO). These MOs are both antisymmetric with respect to the reflection plane, hence the overlap can occur and the HOMO which is generated is also antisymmetric (labelled a).

  • Diels Alder transition state HOMO visualisation
    Diels Alder transition state HOMO visualisation

(You have only included the HOMO here Tam10 (talk) 16:11, 17 November 2015 (UTC))

  • Diels Alder transition state with labelled bond lengths
    Diels Alder transition state with labelled bond lengths

The optimised transition structure retains its original envelope geometry. In this structure however, the bond lengths are no longer equal, which makes sense as they are no longer equivalent. The partially formed C-C sigma bonds now have bond lengths of 2.11929Å and 2.11914Å. A typical sp3 carbon-carbon bond length would be 1.54Å while that of an sp2 carbon-carbon bond is 1.40140Å. The Van der Waals radius of a carbon atom is 170pm, thus that for two carbon atoms is 340pm or 3.4Å. This demonstrates that while the partially formed C-C sigma bonds in the transition state are still quite a bit longer than standard C-C sigma bonds, they are still shorter than the sum of the Van der Waals radii of the two atoms, and therefore there is definitely a bonding interaction occurring. Furthermore, the bond lengths are much closer to that of a traditional sigma bond length than the sum of the Van der Waals radii, meaning that it is closer to being a typical bond than being a non-bonding interaction, in the transition state. As for the other bonds, the partially broken pi bonds have lengths of 1.38291Å, 1.38173Å and 1.39747Å, which are all slightly shorter than typical C-C pi bonds, but reasonably close. This seems unusual as these bonds will all become single sigma bonds in the product, which are actually longer than double bonds. However, it must be considered that in the transition state there aren't really any single or double bonds, as the entire system is delocalised due to the reaction being concerted. These shortened bond lengths suggest that there is increased electron density between these carbons at this point, shortening the bonds. The last carbon-carbon bond in the system is the carbon-carbon sigma bond which will become a double bond. This has a bond length of 1.39747Å, which is once again shorter than a typical double bond, further enhancing the idea of enhanced delocalisation in the transition state. It seems that the transition state consists of multiple bonds between all of the interacting carbons, as fits in with the idea of a concerted reaction mechanism. It could also be postulated that as these bond lengths are shorter than expected, there is an increased repulsion between the carbon nuclei involved, increasing the energy of the system, as is expected in a transition state, which serves as a local maximum on the potential energy surface.

Cyclohexa-1,3-diene and maleic anhydride

After the modelling of a simple Diels Alder reaction, a more complex one was attempted, in which there are two different potential products: the exo and the endo product. In this scenario, it is necessary to also consider affects such as the secondary orbital overlap effect, as well as sterics. The Diels Alder reaction used for this purpose was the reaction between the diene cyclohexa-1,3-diene and the dienophile maleic anhydride. In order to model this reaction, the transition state was constructed, once again using a molecule of bicyclo [2,2,2] octane as the basis for the structure. In this case, it was not necessary to remove a CH2-CH2 fragment, as one of the reagents already contained a six membered ring. The conjoined ring was modified to give one bond with a bond order of 1.5, while the two opposite bonds were modified so as to have bond order of 0.5. Affixed to the two carbons opposite the 1.5 bond order bond, the maleic anhydride was added. This could either be done in an endo fashion, in which the maleic anhydride points in the opposite direction to the bridging ethyl group, or in an exo fashion in which it points in the same direction. Both forms were created. These structures were then optimised using the Berny transition state method once again, at the semi empirical AM1 level of theory. Both the endo and the exo form displayed imaginary vibrations, at wavelengths of -230.77 cm-1 and -230.76 cm-1, respectively. The animation for both of these vibrations were similar to that in the previous Diels Alder simulation, showing a vibration corresponding to the reaction, hence proving that these were two transition states. The energies of both structures were measured: the endo form had an energy of -0.00699435 au, while the exo form had an energy of -0.00699436 au. The energy difference between the exo and the endo form is 10-8 au, which initially appears to be negligible, however this value also corresponds to an energy difference of 2.6255 kJ mol-1 which is not negligible, it is a significant enough energy difference to explain the preference for the endo form under kinetic control, as this transition state is lower in energy.

The main difference in structure between the exo and endo forms is the position of the CH2-CH2 bridge relative to the maleic anhydride. When they are on the same side of the newly formed ring, the product is exo, while when they are on opposite sides the product is endo. In the exo form, the distances between the CH2-CH2 carbons and the carbonyl carbons of the maleic anhydride are 3.44798Å and 3.44799Å, while in the endo form, the distances between the carbonyl carbons of the maleic anhydride and the carbons between which the double bond is forming (these are the closer carbons in this form) are 3.44801Å and 3.44828Å. These distances are reasonably similar, although in the exo form these carbons are slightly closer. The reason that the exo form is more strained than the endo form is that the CH2-CH2 fragment can be thought of as being bulkier than the CH=CH fragment, as the hydrogens in the ethylene fragment will be pointing away from the maleic anhydride, while in the ethyl fragment this is not the case. Furthermore, in the endo form, the maleic anhydride fragment and the CH2-CH2 fragment end up on opposite sides of the forming six membered ring, helping to avoid steric congestion, while in the exo form these two bulky substituents end up on the same side of the ring. This is not usually the case: generally in Diels Alder reactions, the endo product dominates when under kinetic control due to it having the lowest activation energy (as the transition state is stabilised by secondary orbital interactions), however the thermodynamic product tends to be the exo product, which is usually the least sterically hindered product. This specific reaction is a special case in which the endo form is favoured both sterically and electronically.

(It appears that you have the wrong model for the Jmols. In addition, they both have additional hydrogens, so you are in fact trying to perform calculations on a system that doesn't exist Tam10 (talk) 16:11, 17 November 2015 (UTC))

(Because you have these additional hydrogens, your endo and exo are actually the same thing. This means you're drawing the wrong conclusions Tam10 (talk) 16:11, 17 November 2015 (UTC))

As for the bond lengths within the forming six membered ring, they are all slightly longer in both the exo and endo adduct for this reaction than they are in the previous Diels Alder reaction discussed. The forming C-C sigma bonds have lengths 2.66808Å in the exo adduct, and lengths of 2.66807Å and 2.66810Å in the endo adduct. These values are very similar, and once again suggest that these are definitely already bonding interactions at this stage, as they are still shorter than the sum of the Van der Waals radii for the carbons involved. However they are longer than those observed in the previous Diels Alder reaction, suggesting that in this Diels Alder reaction, the bonds are less formed in the transition state than in the other reactions. The previous double bonds in the structure have lengths of 1.44062Å, 1.44063Å and 1.35928Å in the exo adduct, and 1.44143Å, 1.4413Å and 1.35928Å in the endo adduct. These are reasonably similar to each other, however the bond within the maleic anhydride is significantly shorter than the other two bonds of this type in both adducts. This could be a result of decreased electron density in this bond as a result of the electron withdrawing carbonyls adjacent to it, which results in the bond. The bond that is becoming a double has a bond length of 1.58750Å in the exo form and 1.58361Å in the endo form, both of which are significantly longer than in the previous Diels Alder reaction where this bond had a length of 1.39747Å. This suggests that

For both the exo and the endo adducts, the HOMOs were visualised. In both adducts, the HOMO was found to be the 35th MO (hence the LUMO in both was found to be the 36th MO). For both adducts, the energy of the HOMO was calculated as -0.26887 au, while the energy of the LUMO's was calculated as having a magnitude of 0.05615 au in both adducts. However, in the endo adduct, the LUMO had a positive energy while in the exo adduct it had a negative energy. This means that in the exo adduct there is a smaller HOMO-LUMO energy gap than in the endo adduct

The visualisation of the HOMOs of both the exo and endo adducts revealed that the HOMOs for both adducts are essentially the same: they consist of the in phase overlap of the pi orbitals on the double bond in the maleic anyhydride fragment with those of the diene. The orbitals involved on the diene are bonding with respect to the alkene bonds (due to in-phase weak overlap of the p orbitals on the carbons involved), but anti-bonding between these alkenes, as there is a node between them. The MO involved on the maleic anhydride is the antibonding π* orbital of the alkene. The bottom lobes of these orbitals overlap in-phase with those of the diene, creating a bonding interaction between the maleic anhydride fragment and the diene fragment, hence the HOMO is bonding between the two fragments (and hence bonding for the newly forming six membered ring), but slightly antibonding within the fragments themselves This is the case for both the exo and the endo forms, as the MO's under consideration are the same, it is simply the orientation of the molecule that is different. The difference, however, arises from the fact that on the maleic anhydride, other orbitals are involved. The p orbitals on the carbonyl oxygens also contribute: they are arranged such as to be out-of-phase with the adjacent p orbitals on the maleic anhydride double bond. In the exo adduct, this does not add much to the overall character of the HOMO, as these carbonyl oxygens are too far from the diene orbitals to interact with them. In the endo form, however, these oxygen p orbitals are close enough to the π orbitals of the diene to interact, in an in-phase manner, resulting in what is known as the secondary orbital overlap effect. This effect helps to stabilise the transition state, as it adds another bonding interaction between the maleic anhydride fragment and the diene fragment, thus lowering the energy of the endo transition state relative to the exo transition state. In both conformations, there is a node between the maleic anhydride fragment and the rest of the molecule as the phase changes across the plane of the (flat) maleic anhydride molecule. This is a strongly antibonding feature, and thus destabilises the transition state. In the endo form, however, the secondary orbital interactions help to overcome this, hence lowering the endo form of the transition state and making it the kinetic product.

Conclusion

This computational experiment has allowed the optimisation of the transition states for two important pericyclic processes: the Cope rearrangement and the Diels Alder reaction. In the case of the Diels Alder reaction, issues of selectivity were also considered, in terms of whether the exo or endo product and the reasons behind this. There is much scope for further work in this field however, as many factors can influence the outcome of a Diels Alder reaction: for example, solvent effects and temperature. Furthermore, it would be interesting to examine the impact of highly bulky substituents which destabilise the endo form, on the outcome of the reaction. This can all be achieved by further modelling using computational techniques.

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