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Reaction Dynamics Analysis of Cycloaddition Reactions

Introduction

Figure 1- The reaction coordinate of the Diels-Alder reaction between ethene and butadiene

Computational chemistry is an extremely powerful tool when it comes to understanding how reactants transform into products. Analysis of the mechanism, the features of the transition state, the activation energy barrier and the relative positions of reactants, transition states and products on the potential energy surface are all important aspects when it comes to synthesizing new compounds and using the right catalyst and reaction conditions. This assignment is concerned with cycloaddition reactions, a sub-group of pericyclic reactions, which contribute to a large number of organic synthetic routes. The Diels-Alder reaction in particular was examined where two sigma bonds are formed in a concerted cyclic transition state. A most simple example of a Diels-Alder is the reaction between ethene and butadiene where only one transition state conformation is possible. The computational analysis of a concerted reaction is quite straightforward as it by definition does not involve an intermediate and only one transition state as shown in Figure 1. The same is true for the more complex Diels-Alder reaction of Benzoquinone and Cyclopentadiene: again no intermediate is involved and there is only one concerted TS. However, this time there are two different orientations in which the diene (Cp) can approach the dienophile: In an endo fashion that involves secondary orbital interaction and an exo conformation without such extra orbital interaction. Both pathways will be analyzed in Exercise 2. In the last part - Exercise 3 - the Diels-Alder reaction of sulfur dioxide with o-xylylene is contrasted with a competing reaction: A cheletropic reaction. Again exo and endo pathways are possible for the DA reaction and there is also a choice for the endo reaction to occur at the internal or terminal cis-butadiene.

A minimum is the lowest potential energy configuration of a molecule whereas the transition state is the one of highest potential energy. The gradient is zero at both of these points and the curvature (seconds derivative) is positive for a minimum and negative for a transition state. A negative frequency within the vibrational modes indicates a transition state since all the degrees of freedom are at a minimum except for the reaction coordinate degree of freedom which has a negative curvature - the negative frequency. Only positive frequencies are indicative of a minimum since all the degrees of freedom (3N-6) are minimised and the second derivative - the curvature - is always positive.

Nf710 (talk) 15:38, 8 December 2016 (UTC) Good understanding of TSs

Exercise 1: Diels-Alder reaction of Butadiene and Ethene

The reaction of ethene with butadiene was studied using the PM6 method on Gaussian. This semi-empirical computational approach makes many approximations - such as the zero differential overlap for two-electron repulsion integrals - and obtains some parameters from empirical data. However, this method works well for this reaction since the molecules that are being studied are very simple and thus are part of the database that is used to parametrize the method.

Mechanism

As we can see from Figure 2 the C2-C3 is shorter than an average C-C single bond due to delocalization of the adjacent pi-electrons, giving it some double bond character. The bond length of ethene is an expected sp²- sp² double bond. In the transition state the distance between C1-C6 and C4-C5 is considerably shorter than twice the Van der Waals radius of carbon (1.70Å) (2.11Å as opposed to 2.40Å), indicating that the molecule is already in a reacting confirmation. The double bonds C1-C2 C3-C4 and C5-C6 are now longer whereas C2-C3 has shortened (1.47Å -1.41Å). In the product the double bond is the shortest (1.34Å), followed by the two adjacent single bonds C1-C2/C3-C4 (1.50A), which are shorter than the other three sinlge bonds (1.54Å). This is due to sterics - having a shorter double bond (1.34Å) opposite a longer single bond (1.54Å) requires dC1-C2/C3-C4 to be shorter than average sp³- sp³ single bonds (see Table 1).

Figure 2 - The reaction scheme of the Diels-Alder reaction between ethene and butadiene showing the change in C-C bond lengths

Bond	Reactants	Transition State	Products
C1-C2	1.33344	1.37977	1.49278
C2-C3	1.47097	1.41113	1.33312
C3-C4	1.33321	1.37973	1.49265
C4-C5	-	2.11470	1.53607
C5-C6	1.32733	1.38174	1.53798
C6-C1	-	2.11472	1.53603
Table 1 - The C-C bond lengths (in Å) for reactants, TS and products for the Diels-Alder reaction of ethene and butadiene, PM6 optimised.

Orbital Theory

Figure 3 - The Frontier Molecular Orbital diagram for the Diels-Alder reaction of ethene and butadiene. s=symmetric;a=antisymmetric

Figure 4 - Aninmation of the negative vibrational frequency at the TS

Stereoelectronics teaches us that when assessing a chemical reaction it is important to focus on the Frontier Molecular Orbitals - the best donor and acceptor orbitals. From the Frontier MO diagram in Figure 3 it can be seen how the HOMOs and LUMOs of each reactant combine to form four new molecular orbitals - first in the transition state - and ultimately in the product. For a reaction to be allowed the overlapping orbitals are required to be of the same symmetry. Hence for s-s or a-a interactions the orbital overlap will be non-zero and for a-s interactions it will be zero. Figure 3 also shows how both bonding MOs (1 and 2) are fully occupied whereas the anti-bonding combinations (3 and 4) are not filled - suggesting that the product will be lower in energy than the reactants. The following two jmol objects show the frontier orbitals involved in the Diels-Alder reaction between ethene and butdadiene. Jmol 1 shows the four FMOs that are being formed in the transition state - labelled 1-4 as in line with Figure 3. In Jmol 2 one can look at the orbitals of the reactants that make up these MOs.

Jmol 1 - The FMOs of the transition state structure of the reaction of ethene with butadiene

Jmol 2 - The FMOs of the reactants of the Diels-Alder reaction of ethene with butadiene

Figure 4 illustrates the vibration that corresponds to the reaction path of ethene and butadiene. Since only one negative frequency was associated with the structure it could be confirmed to be the transition state. The animation shows how the bonds lengthen and shorten in a synchronous manner, visualizing how bonds C4-C5 and C1-C6 are formed in a concerted mechanism. The fact that "bonds" C4-C5 and C1-C6 are of the same length in the TS (and so are C1-C2 and C3-C4) underpins that the two new sigma bonds are being formed simultaneously.

Nf710 (talk) 15:43, 8 December 2016 (UTC) Very nice an concise section everything was done well. nice use of buttons in the jmols.

Exercise 2: Diels-Alder reaction of Benzoquinone and Cyclopentadiene

Figure 5- The different approach trajectories leading to the exo and endo products of the Diels-Alder reaction between benzoquinone and cyclopentadiene

Figure 6- The FMO diagram for the Diels-Alder reaction between benzoquinone and cyclopentadiene

The Diels-Alder reaction between benzoquinone and cyclopentadiene can proceed via two different pathways - endo and exo. The difference in approach trajectories, which also leads to a difference in conformation of the product, is illustrated by the reaction scheme in Figure 5. The control of stereochemistry is an important aspect of Organic synthesis, hence it is useful to find the activation energy and relative potential energies associated with each pathway. One then knows what the kinetic and thermodynamic outcome is and can alter the reaction conditions accordingly. As for Exercise 1 the intermolecular distance between the atoms that are forming the new bonds is equal - the bonds are formed in a synchronous and simultaneous manner.

Orbital Theory

As for Exercise 1, the MO diagram has been constructed in order to see how the frontier orbitals interact. Although this reaction appears to be more complex we are only concerned with the frontier orbitals and therefore we can use butadiene and ethene as the basis for this [4+2] cycloaddition. The presence of two electron withdrawing carbonyl groups in benzoquinone causes both its HOMO and LUMO to be lower in energy - see Figure 6. The absence of electron withdrawing groups and the presence of the sp³ carbon in cyclopentadiene causes the diene to be electron-rich thus destabilizing and raising the energy of the HOMO and LUMO. As a result the LUMO of Cp and the HOMO of benzoquinone are far apart in energy and their overlap is less efficient, whereas Cps HOMO is now very close in energy to benzoquinones' LUMO causing this interaction to be dominant. This reaction is classified as a normal electron-demand Diels-Alder reaction, where an electron poor diene reacts with an electron rich dienophile.

By find only one negative vibrational frequency corresponding to the formation of the TS structure it was confirmed that the structure has been correctly identified as the TS. An IRC calculation was performed in order to examine the change in energy that occurs when forming products or reactants from the TS structure. From this it could be concluded that the reaction is exothermic since the reactants were found to be higher in energy than the products.

Jmol 3 - The FMOs of the endo TS structure of the reaction of cyclopentadiene with benzoquinone

Jmol 4 - The FMOs of the exo TS structure of the reaction of cyclopentadiene with benzoquinone

(Good use of code. It's best to set the initial MO to be the same as the first item in the dropdown box (so that you don't need to reload the HOMO before being able to load the LUMO Tam10 (talk) 17:33, 24 November 2016 (UTC))

Nf710 (talk) 15:56, 8 December 2016 (UTC) You must state the level of theory that you are using! You say you have used B3LYP but in the table you have used the PM6 energies, hence giving you a less accurate result. Very nice jmols showing the SSO, but they are also in PM6

Potential Energy

Figure 7- Secondary orbital interactions in the HOMO of the endo TS

After finding the intrinsic reaction coordinate (IRC) at the PM6 level, the geometries of the reactants and products were optimised using the density functional theory (DFT) method B3LYP on a 631-G(d) basis set. This method is more accurate but also computationally more expensive since it uses functionals (functions of functions) which are related to the elctron density. The activation energy associated with the exo pathway was found to be 123.1 kJmol^-1 and therefor ca.6.5k Jmol^-1 greater than that of the endo pathway (116.6 kJmol^-1). The literature activation energies of the exo and endo pathways were found to be 95.8 and 88.3 kJmol^-1 respectively. This is in line with theory, which predicted that the endo product will be the kinetic product due to stabilising secondary orbital interactions (in addition to primary orbital interactions) resulting from the overlap of cyclopentadiene p-orbitals with the empty pi* orbitals of the carbonyl groups in benzoquinone. The exo trajectory is only stabilised by primary orbital interactions, but these are stronger than secondary ones and hence the exo adduct can also form as the minor product. Both products were found to be very close in energy with the endo product being slightly more stable than the exo, making it also the thermodynamic reaction outcome. This is despite the fact that the endo product is expected to suffer from greater steric repulsion than the exo.

	[Hartree/particle]			[kJmol-1]
	Reactants	Transition State	Products	Activation Energy	Reaction Energy
Exo	0.131353	0.178239	0.120191	123.0992024	29.30583323
Endo	0.135834	0.180251	0.127261	116.6168424	22.50841321
Table 2 - Thermal Energies of reactants, TS and products and calculated activation and reaction energies

Exercise 3: o-Xylylene and SO2 -Diels-Alder vs Cheletropic

Figure 8- Overview of the four different TS trajectories for sulfur dioxide and o-xylylene

This part is concerned with the reaction of sulfur dioxide and o-xylylene and the analysis of four possible reaction outcomes - depicted in the reaction schemes in Figure 8. Again endo and exo (Figure 9) products result from a [4+2] Diels-Alder reaction but this time there are two different endo products possible - internal (Figure 11) and terminal (Figure 10). A cheletropic reaction (Figure 12) competes with the Diels-Alder addition and yields the fourth outcome of this discussion. For this exercise semi-empirical PM6 optimised structures have been compared.

Mechanism

Whilst the previous Diels-Alder reaction were shown to proceed via a synchronous mechanism with both sigma bonds being formed at the same rate, for the Diels-Alder reaction between sulfur dioxide and o-xylylene the carbon-oxygen bond is formed before the carbon-sulfur bond (Figure 9-11). One explanation for this could be the difference in electronegativity of oxygen and sulfur, however, also the cheletropic reaction at sulfur is shown to be asynchronous, with one of the carbon-sulfur bonds forming faster than the other - shown in Figure 12.

Figure 9- Animation of the exo Diels-Alder reaction at the TS

Figure 10- Animation of the terminal endo Diels-Alder reaction at the TS

Figure 11- Animation of the internal endo Diels-Alder reaction at the TS

Figure 12- Animation of the Cheletropic reaction at the
TS

Potential Energy

The transition states of all four reaction pathways have been located and confirmed to possess only one negative frequency that corresponds to the vibration at the transition state. Then IRCs have been run, from which the reactants and products have been optimized to a minimum (confirmed by only positive vibrational frequencies and full convergence), and the relative thermal energies extracted. These have been used to determine the activation energy associated with each of the four pathways as well as the change in Gibbs Free Energy - the reaction energy. The results are summarized in Table 3 and visualized in Figure 13 below. Rather than taking the reactants from the IRC path one could also sum the individual energies from each reacting species, however this would neglect intermolecular interactions between reactants.

The data shows that the terminal endo Diels-Alder reaction has the lowest activation energy associated with the TS making its product the kinetic outcome. Again this is likely to be caused by stabilising secondary orbital interactions. The exo product has a slightly higher activation barrier associated than the terminal endo product but turns out to be slightly lower in energy. The Cheletropic reaction has a much higher activation energy but the products is far lower in energy than the other products and it therefore is the thermodynamic product. The internal endo Diels-Alder requires the highest activation energy of all four pathways and the resulting product is of higher energy than the reactants thus it is an endothermic process. The high exothermic reaction energies for the three other reactions are due the gain of aromatizity, allowing the elctrons to delocalize in the heteroaromatic ring. The internal endo-product is non-aromatic and no such stabilization is possible. The remaining presence of two strong sulfur-oxygen double bonds is likely to contribute to the stability of the cheletropic product.

(Heteroaromatic ring? Tam10 (talk) 17:33, 24 November 2016 (UTC))

Figure 13- Relative Activation- and Reaction Energies of DA and Cheletropic reactions

	[Hartree/particle]			[kJmol-1]
	Reactants	Transition State	Products	Activation Energy	Reaction Energy
Exo	0.067720	0.092075	0.021455	63.944057	-121.468767
Endo (terminal)	0.067929	0.090562	0.021695	59.422946	-121.387376
Endo (internal)	1.333211	1.379731	1.492650	97.857643	10.008407
Cheletropic	0.067930	0.099073	0.000000	81.765953	-178.350229
Table 3 - Thermal Energies of reactants, TS and products and calculated activation and reaction energies

(The entry for Endo (internal) seems a bit dodgy. Not only should the reactants have a similar energy to the other reactants, but the activation energy and reaction energy don't correspond Tam10 (talk) 17:33, 24 November 2016 (UTC))

Conclusion

Achieving precise stereospecificity remains a challenge in Organic synthesis. Howerver, the control of stereoselectivity is of great importance since different isomers can have vastly different chemical and biological properties. Computational chemistry can help to tackle these problems especially because it is often impossible to determine whether steric or electronic effects dominate the reactive behaviour of molecules and this is where a computational approach can lead to clarification.

In the above exercises the activation energy and change in free energy was calculated in order to determine the kinetic and thermodynamic outcome of the reactions. This information is essential when designing reactions conditions to achieve high selectivity. To obtain the kinetic product, for example, one would carry out the reaction at lower temperature, hoping that the activation energy of the thermodynamic product will not be supplied. Conversely, to obtain the thermodynamic product one would choose a higher temperature. The mechanisms of cycloaddition reactions was also investigated, finding that ethene and butdadiene as well as benzoquinone and cyclopentadiene react in a highly synchronous fashion whereas the reaction of sulfur dioxide and ‘’o-‘’xylylene showed asynchrous bond breaking and forming. Knowing the order of bond formation one can design catalyst that enhances the stability of the conformation after the first bond has been formed, thus increasing the probability of the second bond being formed. One should note that there is a trade-off between accuracy end computational cost, the more accurate the results (the more complex the wave equation that is being solved, for example by using a greater basis set) the more computationally expensive the method. With more time it would be useful to compare the Thermochemistry results obtained with different methods and basis sets to validate the obtained data. In further work it would be interesting to study other electrocyclic reactions in larger molecules to see how complexity affects the results.