Rep:Mod:TRANJS8812

The Cope Rearrangement

Introduction

Pericyclic Reactions

Pericyclic reactions are highly useful and versatile rearrangment methods in organic synthesis. The appeal of these reactions is the lack of need of extra reagents and specific solvents; only heat or electromagnetic light is required to drive the reaction. These reactions are also useful for forming rings from unsaturated compounds.

One useful example of a pericyclic reaction is the Cope Rearrangment of 1,5-dienes. This is a [3,3]-sigmatropic rearrangement which occurs on heating the diene.

Scheme 1: Mechanism of Cope Rearrangement

In this example, the Cope Rearrangement can progress via a chair or boat transition state, based on the conformations of cyclohexanes.

Computational methods will be used to optimise the reactants and the transition states, using the Hartree-Fock method of calculation or the B3LYP method of calculation.

1,5-hexadiene Conformations

1,5-hexadiene can exist in several different conformations, dependent on the four central atoms being gauche or antiperiplanar.

Optimisation of an Antiperiplanar 1,5-hexadiene Conformation

A molecule of 1,5-hexadiene was drawn, with the four central carbon atoms all in the anti-periplanar conformation. Using the Hartree-Fock model and the 3-21G basis set, the drawn molecule was optimised to a minimum, using Gaussian.

An anti conformation of 1,5-hexadiene (anti2)
Calculation Type	FOPT
Calculation Method	RHF
Basis Set	3-21G
Total Energy	-231.69253528 a.u
RMS Gradient Norm	0.00001891 a.u.
Dipole Moment	0.0000 Debye
Point Group	Ci

The calculation was successful and the molecule was found to possess a center of inversion.

Optimisation of a Gauche 1,5-hexadiene Conformation

This time, a molecule of 1,5-hexadiene was drawn, but with the four central carbon atoms in a gauche conformation. Again, using the Hartree-Fock model and the 3-21G basis set, this molecule was optimised.

A gauche conformation of 1,5-hexadiene (gauche4)
Calculation Type	FOPT
Calculation Method	RHF
Basis Set	3-21G
Total Energy	-231.69153032 a.u.
RMS Gradient Norm	0.00001866 a.u.
Dipole Moment	0.1281 Debye
Point Group	C2

As expected, the minimum energy of the gauche conformation is higher than the minimum energy for the anti conformation drawn. It is expected that there is a more repulsive force between the methylene groups in the gauche conformation than in the anti conformation, and steric hindrance from flagpole interactions between hydrogen atoms on adjacent carbon atoms.

The Most Thermodynamically Stable Conformer

The most stable (lowest energy) conformation of 1,5-hexadiene is predicted to be an anti conformation, as generally, anti conformers are more stable than gauche conformers due to less steric hindrance and less unfavourable interactions between neeigbouring protons.

The anti1 conformation was found to be the most stable of all the anti conformers.

In fact, there is a gauche conformation which is more stable than any of the anti conformers (This is true at the level of theory you did the computation. Is the difference in energy big? Would it hold true at another level of theory? João (talk) 12:37, 22 April 2015 (BST)). There is less steric hindrance and less pronounced flagpole interatcions, decreasing any steric hindrance, making this conformer the most stable overall (Could there be an orbital effect as well? João (talk) 12:37, 22 April 2015 (BST)).

Minimum energy conformation of 1,5-hexadiene (gauche3)
Calculation Type	FOPT
Calculation Method	RHF
Basis Set	3-21G
Total Energy	-231.69266120 a.u
RMS Gradient Norm	0.00001535 a.u.
Dipole Moment	0.3409 Debye
Point Group	C1

The value of -231.69266120 for the total internal energy of the molecule is the lowest of all conformers of 1,5-hexadiene. This is the gauche3 conformation.

Comparing the Hartree-Fock/3-21G and B3LYP/6-31G* Levels of Theory

There are many types of theories, calculation methods and orbital basis sets that can be used to fine-tune and ameliorate the minimum optimisations. Investigated below is the comparison between the Hartree-Fock/3-21G and B3LYP/6-31G* levels of theory and basis sets.

The first confomer optimised, the anti2 confomer, was reoptimised to a minimum using the B3LYP method and the 6-31G* basis set. Below is a comparison of values between the two results.

	An anti conformation of 1,5-hexadiene (anti2)	An anti conformation calculated using B3LYP/6-31G* methods.
Method/Basis Set	HF/3-21G	B3LYP/6-31G*
Calculation Type	FOPT	FOPT
Total Energy	-231.69253528 a.u	-234.61171063 a.u.
RMS Gradient Norm	0.00001891 a.u.	0.00001249 a.u.
Dipole Moment	0.0000 Debye	0.0000 Debye
Point Group	Ci	Ci

Observed is a further reduction in energy using the B3LYP/6-31G* level of theory, meaning that the 6-31G* orbital basis set is a slightly more effective in optimisations (How do you know this is not simply due to DFT calculations giving a lower energy value? In general absolute energies calculated with different levels of energy cannot be compared. João (talk) 12:37, 22 April 2015 (BST)). There is a reduction in energy of 2.91917535 a.u. and a reduction in the RMS gradient norm. There is, however, no visible difference in structure and geometry between both results.

A More Detailed Study of the Energy of 1,5-hexadiene

The energy calculated via Gaussian is the energy of the molecule according to the potential energy surface. Using a molecule optimised to a minimum using the B3LYP/6-31G method, a frequency calculation can be performed on this molecule. Four different types of energies are ultimately calculated:

Simulation of IR vibration spectrum, highlighting maximum peak - vibrational mode #13

1. E₁: Sum of Electronic and Zero-Point Energies (E₁ = E_elec + E_zp)
2. E₂: Sum of Electronic and Thermal Energies (E₂ = E_elec + E_vib + E_rot + E_trans)
3. E₃: Sum of Electronic and Thermal Enthalpies (H = E + RT)
4. E₄: Sum of Electronic and Thermal Free Energies (G = H - TS)

Using the previuosly B3LYP/6-31G* optimised anti2 confomer of 1,5-hexadiene, a frequency calculation was performed, yielding a list of vibration frequencies. The calculation was confirmed to be successful, as there were no negative (imaginary) vibrational frequencies present.

An IR spectrum of all vibrational modes was simulated, showing major peaks at 940.00 cm^-1 - the highest peak (vibrational mode #13), 3030.78 cm^-1 - (vibrational mode #34) and 3136.02 cm^-1 - (vibrational mode #38).

List of vibrations from the frequency calculation of 1,5-hexadiene anti2

As a result of this calculation the values for all aforementioned energies were determined, at 298.15 K.

1. E₁: Sum of Electronic and Zero-Point Energies = -234.469219 a.u.
2. E₂: Sum of Electronic and Thermal Energies = -234.461869 a.u.
3. E₃: Sum of Electronic and Thermal Enthalpies = -234.460925 a.u.
4. E₄: Sum of Electronic and Thermal Free Energies = -234.500809 a.u.

(How would these values vary with temperature? João (talk) 12:37, 22 April 2015 (BST))

The lowest value of energy from this list is the sum of the electronic and thermal free energy.

Optimising the Chair and Boat Transition Structures

The chair and boat transition structures of these reactions are based on the respective conformations of cyclohexane. Here these structures are predicted, and further optimised.

Optimising the Chair Transition Structure

The 'chair' conformation of the Cope transition structure can be shown as a biradical transition state, with two specifically positioned allyl radical fragments. (Note: This is not the accepted intermediate for this reaction but its geometry is highly useful in optimisations).

Biradical 'chair' transition state of Cope rearrangement

To begin with optimising the 'chair' conformation of the cope transition structure, the allyl fragment itself must first be optimised.

Allyl Fragment Optimisation

An allyl fragment (CH₂CHCH₂) was drawn and optimised to a minimum using the HF/3-21G level of theory.

Optimised allyl fragment
Calculation Type	FOPT
Calculation Method	UHF
Basis Set	3-21G
Total Energy	-115.82303830 a.u.
RMS Gradient Norm	0.00018761 a.u.
Dipole Moment	0.0299 Debye
Point Group	C2v

Notable is the fact that the total energy of the optimised allyl fragment is close to half of the value of the total energy for the previously optimised 1,5-hexadiene confomers.

A Pair of Allyls - The Next Step Towards Optimising the 'Chair'

Chair transition state guess

Two allyl separate allyl fragments were drawn, positioning them so they are similar in appearance to the chair conformation of cyclohexane. The distance between terminal carbons of separate allyl fragments were guessed to be 2.2 Å.

This prototype structure was then optimised straight away. In this optimisation, a frequency calculation was included, and the structure was optimised, this time to a transition state, using the Berny algorithm. The Hessian force constants were calculated just once throughout.

Optimised to transition state: allyl fragment pair
Calculation Type	FREQ
Calculation Method	RHF
Basis Set	3-21G
Total Energy	-231.61932237 a.u.
RMS Gradient Norm	0.00003062 a.u.
Dipole Moment	0.0003 Debye
Point Group	C2h

Animation of the imaginary vibrational frequency of the optimised transition state

Observed is one imaginary vibrational frequency, at -818.04 cm^-1. An imaginary vibrational frequency is associated with a transition state, here in the case of the intermediate formation of new C-C σ-bonds. The

This optimised structure has a slightly higher value of total energy than twice the total energy of a single allyl fragment. This is expected, due to the extra interactions between the allyl fragments.

Notable in this optimised transition state is that the distance between terminal carbon atoms of separate allyl fragments were reduced to 2.02 Å, which is overall undesired (Why is this undesired? You were optimizing a transition state structure and you just found it. João (talk) 12:37, 22 April 2015 (BST)). To counter this result during the optimisation, atoms and bonds can be frozen in place during the calculations, and this was taken into account in the next optimisation.

The distances between terminal carbons of separate allyl fragments were both frozen at 2.2 Å, allowing just the central carbon atoms of each allyl fragment to be free to move during the optimisation. This allows a more precise and fine-tuned optimisation overall.

Once the atoms were frozen, this time, the transition state was optimised to a minimum, using the HF/3-21G level of theory, as the transition state structure was already optimised.

Optimised to transition state: allyl fragment pair
Calculation Type	FOPT
Calculation Method	RHF
Basis Set	3-21G
Total Energy	-231.61346000 a.u.
RMS Gradient Norm	0.00558446 a.u. a.u.
Point Group	C2h

Observed is a slight increase in total energy, due to the increase in bond length from 2.02 Å from the previously optimised transition state to 2.2 Å.

Vibrational animation of the transition state optimised through freezing atom positions

The next step for the complete optimisation of the 'chair' conformation transition state is to optimise the distances between the allyl fragments. This was done by incorporating the derivative option within the redundant co-ordinates, for both inter-fragment distances. The structure was then optimised to a transition state via the Berny algorithm.

Fully optimised chair transition state
Calculation Type	FTS
Calculation Method	RHF
Basis Set	3-21G
Total Energy	-231.61518500 a.u.
RMS Gradient Norm	0.00326133 a.u.
Point Group	C2h

Animation of final optimised 'chair' transition state

As a result of this optimisation, there is a further reduction in total energy. The distance between fragments of the terminal carbon atoms is now 2.197 Å, and the distance between the central carbon atoms has increased from 2.88 Å to 2.94 Å. The C₁-C₂-C₃ angle has as a result reduced from 122.9° to 121.9°.

(There is something wrong in the procedure you followed. You should have obtained the same structure as the transition state optimization calculating the force constants for all the molecule as you did above. The frozen coordinate method is an alternative method to optimize the transition state that can be more convenient in some circumstances. It does not require the calculation of the force constants for the all molecule, but just that of the reaction coordinate (for which you need to have a good guess a priori). João (talk) 12:37, 22 April 2015 (BST))

Optimising the Boat Transition State

The 'boat' transition state is the other possible transition state that the Cope rearrangement can progress through. It is expected to be higher in energy than the chair transition state, mirroring the energy profiles of the different conformers of cyclohexane.

The transition state is not based on allyl fragments; instead the original 1,5-hexadiene molecule and the desired product can be drawn, which is used to generate a transition state.

To begin, the anti2 conformer of 1,5-hexadiene was drawn. This particular rearrangement will yield another molecule of 1,5-hexadiene, so this molecule was duplicated and used as the product for the calculation.

To discern between the reacting molecule and the final product, it is essential to label each carbon atom, and take into account their position in the product molecule. The atoms for this calculation were therefore labelled as such:

There is now enough information for an optimisation to a transition state, using the QST2/QST3 method. The QST2 method was chosen for this calculation; (the QST3 allows for the possibility of including a 'guess' transition state but this is not required here.)

The calculation completed without any errors, but the transition state did not have any geometry with resemblance to a boat.

Failed 'boat' optimisation
Calculation Type	FREQ
Calculation Method	RHF
Basis Set	3-21G
Total Energy	-231.61932232 a.u.
RMS Gradient Norm	0.00003274 a.u.
Dipole Moment	0.0003 Debye
Point Group	C2h

Animation of the unsuccessful optimisation

The calculation produces a transition state resembling a chair, but there are interactions between opposite ends of the allyl fragments (What interactions would that be? The dashed lines drawn in your structure don't actually have any particular meaning (the calculation only depends on atoms' positions), the dashed lines connect the atoms which were bonded in your reactants/products. João (talk) 12:37, 22 April 2015 (BST)). This transition state has an imaginary vibrational frequency of -817.91cm^-1, similar to the 'guess' transition structure for the 'chair' conformation.

The reason this calculation fails is because it does not consider the possibility of the central carbon atoms rotating. As shown in the mechanism for the Cope rearrangement, the reaction occurs when the terminal carbon atoms are closer to each-other, in effect, almost forming a complete ring. A straighter chain will not allow the formation of a new σ C-C bond as the two carbon atoms will be too far away to interact. This calculation does not take into account the fact that the central carbon atoms can rotate around to accommodate the possibility of the sigmatropic rearrangement. It is therefore necessary to manually re-orient the reactant and product molecule so that they are more 'C'-shaped.

The reactant and product molecules were then re-orientated by reducing the dihedral angle of the four central carbon atoms from 180° to 0°. The C²-C³-C⁴ and C³-C⁴-C⁵ angles were reduced from 109° to 100°, as shown in the corresponding table:

Animation of the vibration of the boat transition state

These conformations of 1,5-hexadiene look much more likely to re-arrange and it is therefore more likely that the calculation will successfully yield the boat transition state.

The transition structure optimisation was performed, again using the QST2 method.

Successful boat optimimsation
Calculation Type	FREQ
Calculation Method	RHF
Basis Set	3-21G
Total Energy	-231.60280200 a.u.
RMS Gradient Norm	0.00007080 a.u.
Dipole Moment	0.1579 Debye
Point Group	C2v

The boat structure was successfully optimised, with the expected C_2v point group. There is indeed only one vibration frequency of -839.94 cm_-1, more negative than the previous failed transition state calculated.

Tracking the Optimisation with Intrinsic Reaction Coordinates

It is useful to track the steps of the optimisation (You can indeed see the IRC as being such, when the optimization is done by a steepest descent method. Note however, that when you perform an optimization you use more sophisticated and efficient algorithms, in which case tracking different optimization steps would not give you such relevant chemical information. João (talk) 12:37, 22 April 2015 (BST)). A method of performing this in Gaussian is to run an Intrinsic Reaction Coordinate (IRC) calculation. The calculation then plots the minimum energy path throughout an optimisation, and the resulting graph will level off to a minimum energy (if the number of steps allows it to). The IRC calculation will also aid in predicting the 1,5-hexadiene conformer product.

Chair Conformation IRC

The previously optimised chair was used to perform an IRC calculation, 65 steps being specified. The calculation was only computed in the forward direction. The force constants were also computed for each step.

The energy was found to minimise to -231.692 a.u. after 44 steps, so it was not necessary to recompute another IRC.

IRC graph showing the reduction in total energy through calculation steps

Animation of 'transition state'

The IRC calculation did not converge to a transition state; for the final step, there is no imaginary vibrational frequency (the lowest value of the vibrational frequency is 61.84 cm^-1.) (Do you expect the final structure in an IRC calculation to be a transition state or a local minimum? What structure did you use to start your IRC calculation? What conformations does the chair transition state connect? João (talk) 12:37, 22 April 2015 (BST))

Boat Conformation IRC

The previously optimised boat was used to perform an IRC calculation, 65 steps being specified. The calculation was only computed in the forward direction. The force constants were also computed for each step.

The energy was found to minimise to -231.686 a.u. after 45 steps.

IRC graph showing the reduction in total energy through calculation steps

Animation of transition state

Here a transition state had been reached; the imaginary vibrational frequency has a wavenumber of -150.83 cm^-1

Boats, Chairs, Basis Sets and Energies

The 'chair' and 'boat' transition states were previously optimised using the Hartree-Fock/3-21G level of theory. It was previously concluded, through the optimisations of 1,5-hexadienes, that the B3LYP/6-31G* level of theory is more effective at lowering the total energy of a molecule. The re-optimised transition states can be further used to obtained more accurate values for their intrinsic energy properties, more accurately than using the HF/3-21G level of theory.

It is in fact useful to use a lower level of theory to obtain a good prototype optimisation structure to work from, higher levels of theory can be conducted more quickly and accurately afterwards.

The 'chair' and 'boat' transition state were therefore re-optimised using the B3LYP/6-31G* level of theory.

Comparison of Chair Optimisations

Method/Basis Set	HF/3-21G	B3LYP/6-31G*
Calculation Type	FREQ	FREQ
Total Energy	-231.61518500 a.u.	-232.98235323 a.u.
RMS Gradient Norm	0.00326133 a.u.	0.00000760 a.u.
Dipole Moment	0 Debye	0.3960 Debye
Point Group	C2h	C2h

There is an expected reduction of total energy through this re-optimisation. There is also no visible change in geometry.

There is, however an increase in dipole moment, which is an unexpected result. It has not been conjectured on why this drastic change in dipole moment has taken place. (This is indeed surprising, and the energy you obtain also seems too high and I would expect a much too high activation energy. This suggest there is some error in your calculation. João (talk) 12:37, 22 April 2015 (BST))

Comparison of Boat Optimisations

Method/Basis Set	HF/3-21G	B3LYP/6-31G*
Calculation Type	FREQ	FREQ
Total Energy	-231.60280200 a.u.	-234.54045615 a.u.
RMS Gradient Norm	0.00007080 a.u.	0.00488727 a.u.
Dipole Moment	0.1579 Debye	0.0562 Debye
Point Group	C2v	C2v

The energy difference for this reoptimisation is more drastic than in the reoptimisation for the 'chair' conformation. Through the HF/3-21G basis set, it was the 'chair' conformation that had the lowest value of total energy. After the reoptimsations with B3LYP/6-31G* basis set, the 'boat' conformation is now lower in energy than the 'chair' conformation. The level of theory is therefore very important in certain calculations. (Did you confirm your structure is still a transition state at the higher level of theory? João (talk) 12:37, 22 April 2015 (BST))

There is also a reduction in total dipole moment from HF/3-21G to B3LYP/6-31G*.

Activation Energies

The activation energies of both transition structures can be calculated from the optimisations. A value for the zero-point energy is calculated which is then used to work out the activation energy (Why did you separate out the zero-point energy? João (talk) 12:37, 22 April 2015 (BST)). Below is the comparison between experimental and optimisation:

Conformation	Experimental Ea (0K)	Optimisation Ea (0K
Chair	33.5 ± 0.5 kcal/mol	33.561 kcal/mol
Boat	44.7 ± 2.0 kcal/mol	42.592 kcal/mol

The values are relatively similar for the chair conformation, but drastically different for the boat conformation (Calling it a drastic difference is a bit pessimistic. See for instance how your HF/3-21G activation energies compare. João (talk) 12:37, 22 April 2015 (BST)).

The energies were also calculated at 298.15 K:

Conformation	Ea (298.15 K)
Chair	31.105 kcal/mol
Boat	41.822 kcal/mol

The energies reduce at a higher temperature - expected as atmospheric energy contributes more to the activation at a higher tempeature.

Conclusion

Through all this data, it is the chair transition state which this reaction proceeds via, as the chair transition state has the lowest activation energy, even though the boat transition state is more thermodynamically stable. (That would be inconsistent. I think there might be an error in you calculation of the activation energy somewhere. João (talk) 12:37, 22 April 2015 (BST))

The Diels-Alder Cycloaddition

Introduction

The Diels-Alder cycloaddition is a synthesis classic - a highly versatile, simple pericyclic reaction which allows the formation of cyclohexene rings, which can be further reacted as part of long synthetic routes.

Mechanism of Diels-Alder cycloaddition

The Diels-Alder cycloaddition is a [4+2]-cycloaddition, involving the formation of two new C-C σ-bonds. Two reactants are required, an s-cis-diene and a dienophile (which doesn't necessarily have to be a C=C double bond). To form the desired product, the reaction must be heated.

An example of endo and exo products of Diels-Alder reactions

The simplest example is the reaction between s-cis butadiene and ethylene to form cyclohexene. If the dienophile is unsymmetrical structure, there are two types of products that may form, exo-products and endo-products. Exo-products are thermodynamically more stable, as endo-products suffer from more severe steric effects, but usually the endo-product predominates in Diels-Alder cycloadditions, as it is the kinetic product and is formed faster. Refer to the diagram of the reaction between cyclohexa-1,3,-diene and maleic anhydride to view the structure of these products.

Simple Diels-Alder Optimisations

To understand the reaction through optimisations, the simplest example of a Diels-Alder reaction, the reaction between s-cis-butadiene and ethylene was modelled. To begin with, the semi-empirical AM1 method, lower in sophistication than the HF/3-21G model, was used for these optimisations.

Ethylene and Butadiene

S-Cis Butadiene Optimisation and MO Visualisation

Optimisation of s-cis-butadiene
Calculation Type	FOPT
Calculation Method	RAM1
Basis Set	ZDO
Total Energy	0.04879718 a.u.
RMS Gradient Norm	0.00001429 a.u.
Dipole Moment	0.0414 Debye
Point Group	C2v

Once optimised, the list of molecular orbitals can be calculated and visualised. The HOMO and LUMO are visualised as they are the most important in determining how the reaction with ethylene will take place.

Molecular Orbital	Visualisation	Symmetry	Energy of MO
Butadiene HOMO		Anti-symmetric	-0.34382 a.u.
Butadiene LUMO		Symmetric	0.01708 a.u.

Ethylene Optimisation and MO Visualisation

Optimisation of ethylene
Calculation Type	FOPT
Calculation Method	RAM1
Basis Set	ZDO
Total Energy	0.02619028 a.u.
RMS Gradient Norm	0.00003649 a.u.
Dipole Moment	0 Debye
Point Group	D2h

The HOMO and LUMO are then calculated and visualised:

Molecular Orbital	Visualisation	Symmetry	Energy of MO
Ethylene HOMO		Symmetric	-0.38775 a.u.
Ethylene LUMO		Anti-Symmetric	0.05283 a.u.

Towards Cyclohexene - The Diels-Alder Transition State

Diels Alder reaction including 'envelope' transition state

The Diels-Alder cycloaddition proceeds via an 'envelope' transition state, which will be optimised. This conformation is favourable as there is a large overlap between the π-systems of both reactants. The distance between the butadiene and ethylene is estimated at 2.0 Å, but the value is found via the optimised strucutre.

6-31G* cyclohexene transition state
Calculation Type	FOPT
Calculation Method	RAM1
Basis Set	ZDO
Total Energy	0.02795804 a.u.
RMS Gradient Norm	0.00004317 a.u.
Dipole Moment	0.4558 Debye
Point Group	C2v

The envelope transition state drawn has unexpectedly been optimised into an almost-planar hexagon, and not the unexpected envelope; meaning that this optimisation may have gone beyond the transition state, and closer to the cyclohexene product. The ethylene is now optimised to be closer to the butadiene, with a distance of 1.48 Å (slightly longer than the σ C-C bonds of butadiene itself.) (Indeed this structure is unexpected. Did you check if it was a transition state? Perhaps you set up the calculation to optimize to a minimum? João (talk) 14:29, 22 April 2015 (BST))

The HOMO and LUMO are calculated and visualised:

Molecular Orbital	Visualisation	Symmetry	Energy of MO
Transition State HOMO		Anti-Symmetric	-0.32074 a.u.
Transition State LUMO		Symmetric	0.01693 a.u.

The LUMO for this transition state is essentially very similar to the LUMO of s-cis-butadiene (though it is slightly lower in energy, due to slightly favourable interactions between the MOs of ethylene).

The HOMO of this transition state is the combination of the HOMO of the cis-butadiene and the LUMO of the ethylene.

Maleic Acid and Cyclohexadiene: A Study in Regioselectivity

This transition structure is first optimised using the Semi-Empirical/AM1 level of theory, then further optimised using the more sophisticated B3LYP/6-31G* level of theory for comparison. There is a noticeable difference in the time taken to perform the optimisation calculations between the almost instantaneous AM1 method and the longer B3LYP method.

Optimisation of Maleic Anhydride

	Semi-Empirical/AM1	B3LYP/6-31G*
Visual	AM1 optimised maleic anhydride	6-31G* optimised maleic acid
Calculation Type	FOPT	FOPT
Calculation Method	RAM1	RB3LYP
Basis Set	ZDO	6-31G(D)
Total Energy	-0.12182418 a.u.	-379.28953540 a.u.
RMS Gradient Norm	0.00003683 a.u.	0.00003415 a.u.
Dipole Moment	4.5779 Debye	4.0720 Debye
Point Group	C2v	C2v

Optimisation of Cyclohexa-1,3-diene

	Semi-Empirical/AM1	B3LYP/6-31G*
Visual	AM1 optimised cyclohexa-1,3-diene	6-31G* optimised cyclohexa-1,3-diene
Calculation Type	FOPT	FOPT
Calculation Method	RAM1	RB3LYP
Basis Set	ZDO	6-31G(D)
Total Energy	0.02771129 a.u.	-233.41891660 a.u.
RMS Gradient Norm	0.00000562 a.u.	0.00000664 a.u.
Dipole Moment	0.4313 Debye	0.3777 Debye
Point Group	C2	C2

(Your endo and exo products below are exactly the same molecule: you have too many hydrogen atoms in your cyclohexene ring. Are these product or transition state structures? João (talk) 14:29, 22 April 2015 (BST))

The Endo Product Optimisation

	Semi-Empirical/AM1	B3LYP/6-31G*
Visual	AM1 optimised endo product	6-31G* optimised endo product
Calculation Type	FOPT	FOPT
Calculation Method	RAM1	RB3LYP
Basis Set	ZDO	6-31G(D)
Total Energy	-0.21387277 a.u.	-613.70918462 a.u.
RMS Gradient Norm	0.00001592 a.u.	0.03275780 a.u.
Dipole Moment	5.5057 Debye	7.8200 Debye
Point Group	Cs	Cs

The Exo Product Optimisation

	Semi-Empirical/AM1	B3LYP/6-31G*
Visual	AM1 optimised exo product	6-31G* optimised exo product
Calculation Type	FOPT	FOPT
Calculation Method	RAM1	RB3LYP
Basis Set	ZDO	6-31G(D)
Total Energy	-0.21387281 a.u.	-613.99106865 a.u.
RMS Gradient Norm	0.00001101 a.u.	0.00006005 a.u.
Dipole Moment	5.5059 Debye	4.9382 Debye
Point Group	Cs	Cs

Molecular Orbitals of the Diels-Alder Products

Molecular Orbital	Visualisation	Energy of MO
Endo Product HOMO		-0.23810 a.u.
Endo Product LUMO		-0.02076 a.u.
Exo Product HOMO		-0.27495 a.u.
Exo Product LUMO		-0.02649 a.u.

The energies of the molecular orbitals are lower for the exo product than the endo product. All-in-all, through these optimisations and calculations, the energy of the exo product is calculated to be lower in energy than the endo product.

In fact, the endo product predominates, even though it is higher in energy due to less favourable interactions, as it is formed faster. (The point of the exercise was exactly to study the transition states of the reaction and check if/why that is the case. João (talk) 14:29, 22 April 2015 (BST))

Conclusion

In conclusion, the calculations point towards the exo transition state as the more stable transition state - leading to the exo product. The program however doesn't consider the fact that the kinetic product can be formed faster than the thermodynamic product (If you expect the endo product to be formed faster, how should the endo transition state compare with the exo? João (talk) 14:29, 22 April 2015 (BST)).