Rep:Mod:tsch3114
Introduction
During this lab, computational techniques were used to locate and characterise transition state structures of pericyclic reactions. A transition state is the configuration that corresponds to the highest energy point along a reaction coordinate. It is a maximum that links the reactants and the products. Knowing the location of a transition state gives important information regarding how a reaction progresses. Information on the mechanism (stepwise or concerted?), thermodynamics and kinetics can be obtained.
A reaction coordinate is an abstract one-dimensional representation of how far a reaction has progressed. In reality, all reactions have multiple degrees of freedom that will determine the energy of the system as all atoms involved are able to move in three directions. The reaction coordinate is an abstraction of all degrees of freedom. A potential energy surface (PES) is a 3D plot that includes two dimensions or coordinates. In a PES, the transition state is a saddle point between the reactants and products. It is a better representation of a real system as it shows that there can be many possible pathways between reactants and products.
Gaussian and Gaussview were used to explore transitions state structures. Two computational techniques were used throughout the lab. The semi-empirical PM6 method, which is much faster as it relies on experimental data but is consequently less accurate, and the ab initio density functional theory (DFT) method which was used later on in each exercise as it gives a more accurate result but requires much more computation and time.
Throughout the lab, carbon atoms involved in bond formation were held at 2.2 Å. This value is found in-between an sp3 C-C bond and 2x carbon Van der Waals radii. Hence it is a good approximation for the transition state carbon-carbon distance.
Nf710 (talk) 17:23, 21 March 2017 (UTC)Good understanding of the TSs on the PES but it would have been nice if you could have described it with second derivatives
Exercise 1: Reaction of Butadiene with Ethylene
Method
This reaction is the simplest possible example of a [4+2] cycloaddition reaction, known as a Diels-Alder reaction between a diene and a dienophile. It is a concerted pericyclic reaction that involves the formation of 2 σ-bonds and 1 π-bond and breaking 3 π-bonds, or the reverse. For this reaction, no regioselectivity needs to be considered because there are no addition groups bonded to either reactant.
Method 2 was used to calculate the TS structure for this reaction. It was decided that not enough information was known of the transition state structure to make an accurate guess. Initially reactants were constructed separately in Gaussian and optimised to a minimum to a PM6 level. They were confirmed to have no imaginary (i.e. negative) frequencies.
The reactants were then combined. Reacting carbons were held approximately 2.2 Å apart and the system was optimised to a minimum at a PM6 level. The transitions state (TS(berny)) was then optimised and the frequency was found at a PM6 level. It was confirmed that a transition state had been obtained by the presence of a single imaginary frequency. The transition state was then determined more accurately using DFT B3LYP/6-31G(d) technique. From this, transition state MOs were determined. An intrinsic reaction coordinate (IRC) calculation was carried out with 200 steps which further confirmed that the correct TS had been obtained.
IRC
| Intrinsic Reaction Coordinate | RMS Gradient Norm | |
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It can be seen that the transition state is found at a maximum and that the products and the reactants are found at minima. This can be used to confirm the success of the computation.
MOs
(Fv611 (talk) 17:02, 15 March 2017 (UTC) You used the wrong symmetry labels (we asked for a discussion on symmetric/antisymmetric orbitals). Additionally, you haven't drawn out the MOs for the transition state. If you had, you would have realised they do not match your calculated orbitals: you state that the symmetric MOs have the highest and lowest energies, and yet in your MO table the HOMO-1 and LUMO+1 are antisymmetric, while HOMO and LUMO are symmetric.)
The MO diagrams shows that there has been a net destabalisation of reactants in order to form the transition state. This is expected as the transition state is found at an energy maximum.
Only fragment orbitals with the same symmetry label (gerade or ungerade) are able to combine to form MOs. Combinations of orbitals with opposite symmetry labels results in an overlap integral equal to zero. The given arrangement allows for constructive overlap (i.e. non-zero overlap integral) of orbitals found at the end of both pi system.
| HOMO Butadiene | LUMO Butadiene | HOMO Ethylne | LUMO Ethylne | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| HOMO-1 -TS | HOMO -TS | LUMO -TS | LUMO+1 -TS | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
Normal vs. Inverse electron-demand Diels-Alder Reactions
This is an example of a normal electron-demand Diels-Alder reaction. Electrons are donated from the diene HOMO to the dienophile LUMO. This is the case for the majority of Diels-Alder reactions. Inverse electron-demand Diels-Alder reactions occur when the diene fragment orbitals are found lower in energy with respect to the dienophile. This is the result of an electron withdrawing group found on the diene and an electron donating group bonded to the dienophile.
C-C Bond Lengths
Carbons are labelled on the MO diagram above.
| C-C Bond Lengths/Å | |||
| C-C bond | Reactants | Transition State | Products |
| 1-2 | 1.33344 | 1.38307 | 1.50901 |
| 2-3 | 1.47083 | 1.40721 | 1.33697 |
| 3-4 | 1.33344 | 1.38307 | 1.50901 |
| 4-5 | infinite | 2.27215 | 1.54961 |
| 5-6 | 1.32731 | 1.38607 | 1.55524 |
| 6-1 | infinite | 2.27215 | 1.54961 |
Bond lengths changes as expected throughout the reaction. In the reactants, the three π-bonds (1-2, 3-4, 5-6) are shorter than the σ-bond (2-3). At the transition structure, the π-bonds are elongated as the π-bond interaction is broken to give a σ-bond. The σ-bond is shorter as it begins to form a π-bond. 3-4 and 6-1 are no longer an infinite distance apart. They are close enough to have a begin to form a bonding interaction in the transition structure. For the product, it can be seen that 1-2 and 3-4 are the same length, as are 4-5 and 6-1. σ-bond. This reflects the symmetric nature of the cyclohexene product. 2-3 is the only π-bond that remains. It is a similar length to π-bonds in reactants, reflecting the similar bonding environment.
Typically, sp2–sp2 CC bonds are 1.34 Å and sp3-sp3 CC bonds are 1.54 Å. Computational data is in good agreement with this. It is suggested that the butadiene σ-bond is shorter than expected due to a small amount of delocalisation.
(Fv611 (talk) 17:02, 15 March 2017 (UTC) You didn't mention the relationship between your calculated TS bond lengths and the Van der Waals radius of Carbon atoms.)
Imaginary Vibration
A single imaginary vibration is found at the transition state of a reaction that corresponds to the reaction pathway. In this reaction, it is highly symmetrical, with both sets of carbons approaching each other at once. This is indicative of a single synchronous or concerted bond forming step.
Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole
This is another example of a Diels-Alder Reaction. Regioselectivity had to be taken into account as both endo and exo products are possible depending on the angle of approach of the reactants. Both isomers were computed using the same method as in excercise 1. Imaginary frequencies (endo: i520.87 cm-1; exo: i528.84 cm-1) were used to confirm that transition state structures had been obtained. The product structure was obtained by minimising the final structure of the forwards reaction of a PM6 IRC calculation using DFT to a B3lyp-631(g) level.
MOs
The MOs involved in bonding of the reactants and TSs are shown below.
| Cyclohexadiene HOMO | Cyclohexadiene LUMO | 1,3-Dioxole HOMO | 1,3-Dioxole LUMO | ||||||||||||
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| HOMO-1 | HOMO | LUMO | LUMO+1 | ||||||||||||
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| HOMO-1 | HOMO | LUMO | LUMO+1 | ||||||||||||
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(There isn't an MO diagram here. You have to show the TS MOs are formed from the reactants Tam10 (talk) 15:38, 15 March 2017 (UTC))
This is an example of an inverse electron-demand Diels-Alder reaction. Two oxygen atoms bonded to the π-bond are electron-withdrawing groups. This raises the HOMO energy enough to change how bonding occurs.
Nf710 (talk) 17:12, 21 March 2017 (UTC) The oxygens in this case are electron donating groups
Thermochemistry
Thermochemistry data were taken from computations made using DFT and semi-empirical techniques. They gave very different values but showed the same trends. All computations are at room temperature and pressure.
| DFT | Reactants kJ/mol | Transition State kJ/mol | Product kJ/mol | Activation Energy kJ/mol | Gibbs Free Energy of reaction kJ/mol |
|---|---|---|---|---|---|
| Exo reaction | -1313780.527 | -1313614.231 | -1313845.679 | 166.2965445 | -65.1517825 |
| Endo reaction | -1313780.527 | -1313622.057 | -1313849.273 | 158.469929 | -68.746092 |
| Semi-empirical | Reactants kJ/mol | Transition State kJ/mol | Product kJ/mol | Activation Energy kJ/mol | Gibbs Free Energy of reaction kJ/mol |
|---|---|---|---|---|---|
| Exo reaction | 169.602049 | 364.697703 | 99.700737 | 195.095654 | -69.901312 |
| Endo reaction | 169.602049 | 362.166721 | 99.2622785 | 192.564672 | -70.3397705 |
The thermochemistry data shows that the endo Diels-Alder reaction is kinetically more favoured than the exo reaction as the transition state has a lower energy. This can be explained by considering the through-space interaction of the O atom p-orbital lone pairs and the forming π-bond. This secondary orbital interaction is a positive interaction that lowers the energy of the transition state structure so the endo product is formed faster. It can be seen in the Jmol of the endo HOMO. In the exo transition state, the oxygen atoms face away from the π-bond so no stabalising interaction can take place. It is usually the case that the exo product has a lower energy transition state as it is less sterically congested.
The endo product is also thermodynamically more favoured as the Gibbs Free Energy of reaction is more negative. Both reactions have a negative Gibbs so the forwards reaction is more favoured. It is evident that they should have similar Gibbs values as they are structurally very similar.
Nf710 (talk) 17:16, 21 March 2017 (UTC) Your energies are correct. you haven't explained why the thermo product is the thermo product. A diagram would have been nice.
Exercise 3: Diels-Alder vs Cheletropic
A Cheletropic reaction is another example of a pericylic reaction. It differs from a Diels-Alder reaction as both new bonds are bonded to the same atom.
IRC
| Exo DA | Endo DA | Cheletropic |
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 https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:CH3114_2_3_ENDO_IRC.gif |
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Thermochemistry
| Reactants kJ/mol | Transition State kJ/mol | Product kJ/mol | Activation Energy kJ/mol | Gibbs Free Energy of reaction kJ/mol | |
|---|---|---|---|---|---|
| Exo reaction | 153.470977 | 241.7481635 | 56.3301025 | 88.2771865 | -97.1408745 |
| Endo reaction | 153.470977 | 237.76528 | 56.962848 | 84.294303 | -96.508129 |
| Cheletropic reaction | 153.470977 | 260.0846555 | 0.0078765 | 106.6136785 | -153.4631005 |
(It would be good to see what you used for reactants. You have a slightly different energy. Tam10 (talk) 15:38, 15 March 2017 (UTC))
(Best to normalise energies to the reactants. This makes reading off activation and reaction energies easy Tam10 (talk) 15:38, 15 March 2017 (UTC))
It can be seen that the cheletropic reaction is has the highest activation energy so is the kinetically least favoured. It is however the most thermodynamically favoured.
The Exo Diels-Alder reaction is less kinetically favoured and more thermodynamically favoured. This is for the same reasons as in exercise 2.
(Not much detail in the written answer Tam10 (talk) 15:38, 15 March 2017 (UTC))
Xylylene stability
All three reactions involve the aromatisation of the 6-member ring. Xylylene is highly unstable because it is not aromatic but can easily react to form an aromatic compound. This is a large thermodynamic driving force for the reaction and it can be used to explain the large Gibbs free energy for the reaction.
It is possible that attack could occur on the other side of the ring. However, this reaction would result in sterically congested transition states and products and most importantly, would not involve the formation of an aromatic 6-member ring. Analysis of this alternative endo Diels-Alder reaction computed an activation energy off 115 kJ/mol and a Gibbs free energy of reaction of 18 kJ/mol. Hence this reaction is thermodynamically disfavoured, and has a high activation energy so will occur much more slowly than competing reaction pathways. It is not a spontaneous process.
Conclusion
It was successfully shown that computational techniques can be used to locate and characterise transition state structures using both semi-empirical and ab initio techniques. From computed thermochemistry data, it was possible to determine the kinetic and thermo products without . These could then be rationalised by studying the transition state and product structures. These techniques are limited to relatively simple systems. It is not possible to carry out bulk analysis of many reactions using these techniques. They are better suited to analysing known simple reactions.