File:Movie IRC ENDO INTERNAL PM6 cl8614 zoom.gif

2016-11-18T09:24:39Z

Cl8614:

2016-11-18T04:40:57Z

Cl8614: /* Potential Energy */

'''Reaction Dynamics Analysis of Cycloaddition Reactions'''
= Introduction =
[[File:Intro Reaction Coordinate.png|thumb|x400px|400px|'''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 - 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 very simple example is the reaction between ethene and butadiene where only one transition state conformation is possible.<ref name=":0">Houk, K. N., Lin, Y. T., & Brown, F. K. (1986). Evidence for the concerted mechanism of the Diels-Alder reaction of butadiene with ethylene. J. Am. Chem. Soc., 108(3), 554–556. '''doi:10.1021/ja00263a059''' </ref> 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.

= 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 sp<sup>2</sup>- sp<sup>2</sup> 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 a carbon atom (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 sp<sup>3</sup>- sp<sup>3</sup> single bonds (see '''Table 1''').

[[File:Bond-Lengths.png|thumb|x700px|700px|'''Figure 2''' - The reaction scheme of the Diels-Alder reaction between ethene and butadiene showing the change in C-C bond lengths]]

{| class="wikitable"
|-
!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
|-
|colspan="4"|'''Table 1''' - The C-C bond lengths (in Å) for reactants, TS and products<br>for the Diels-Alder reaction of ethene and butadiene, PM6 optimised.
|}

== Orbital Theory ==
[[File:MO Diagram ethene+butdaiene.png|thumb|x520px|520px|'''Figure 3''' - The Frontier Molecular Orbital diagram for the Diels-Alder reaction of ethene and butadiene. s=symmetric;a=antisymmetric]]
[[File:Vibration Exercise1.gif|thumb|x400px|400px|'''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>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>TS FREEZE OPTFREQ2 JMOL PM6 CL8614.LOG</uploadedFileContents>
<title>Jmol 1 - The FMOs of the transition state structure of the reaction of ethene with butadiene</title>
<name>DielsAlder_TS</name>
</jmolApplet>
</jmol>
<jmol>
<jmolmenu>
<target>DielsAlder_TS</target>
<item>
<script>mo 19;</script>
<text>HOMO butadiene + LUMO ethene(4)</text>
</item>
<item>
<script>mo 18;</script>
<text>HOMO ethene + LUMO butadiene(3)</text>
</item>
<item>
<script>mo 17;</script>
<text>HOMO ethene + LUMO butadiene(2)</text>
</item>
<item>
<script>mo 16;</script>
<text>HOMO butadiene + LUMO ethene(1)</text>
</item>
</jmolmenu>
</jmol>
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat "";</script>
<uploadedFileContents>REACTANTS JMOL WIKI2 OPT CL8614.LOG</uploadedFileContents>
<title>Jmol 2 - The FMOs of the reactants of the Diels-Alder reaction of ethene with butadiene</title>
<name>DielsAlder_reactants</name>
</jmolApplet>
</jmol>
<jmol>
<jmolmenu>
<target>DielsAlder_reactants</target>
<item>
<script>mo 16;</script>
<text>Ethene HOMO</text>
</item>
<target>DielsAlder_reactants</target>
<item>
<script>mo 19;</script>
<text>Ethene LUMO</text>
</item>
<target>DielsAlder_reactants</target>
<item>
<script>mo 17;</script>
<text>Butadiene HOMO</text>
</item>
<target>DielsAlder_reactants</target>
<item>
<script>mo 18;</script>
<text>Butadiene LUMO</text>
</item>
</jmolmenu>
</jmol>

'''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.

= Exercise 2: Diels-Alder reaction of Benzoquinone and Cyclopentadiene =
[[File:Exercise2-endo-exo-Cp BQ.png|thumb|x500px|500px|'''Figure 5'''- The different approach trajectories leading to the exo and endo products of the Diels-Alder reaction between benzoquinone and cyclopentadiene]]
[[File:MO Diagram NED.png|thumb|x500px|500px|'''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 condition accordingly.

== 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.<ref name=":3">Fukui, K., Yonezawa, T., & Shingu, H. (1952). A molecular orbital theory of reactivity in aromatic hydrocarbons. J. Chem. Phys., 20(4), 722–725. https://doi.org/10.1063/1.1700523</ref> The presence of two electron withdrawing carbonyl groups in benzoquinone causes both its HOMO and LUMO to be lower in energy. The absence of electron withdrawing groups and the presence of the sp<sup>3</sup> 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 looking at all vibrational frequencies it was confirmed that the structure has been correctly identified as the TS. Visualization of the single negative frequency ('''Figure 6''') shows that it corresponds to the vibration that leads to the formation of the transition state structure. 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>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 33; mo cutoff 0.015; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>TS IRC JMOL CP BENZOQUINONE TS PM6 CL8614 ENDO.LOG</uploadedFileContents>
<title>Jmol 3 - The FMOs of the endo TS structure of the reaction of cyclopentadiene with benzoquinone</title>
<name>DielsAlder2_TS</name>
</jmolApplet>
</jmol>

<jmol>
<jmolmenu>
<target>DielsAlder2_TS</target>
<item>
<script>mo 34;</script>
<text>LUMO in the endo TS</text>
</item>
<item>
<script>mo 33;</script>
<text>HOMO in the endo TS</text>
</item>
</jmolmenu>
</jmol>

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 33; mo cutoff 0.015; mo nodots nomesh fill translucent; mo titleformat "";</script>
<uploadedFileContents>TS IRC JMOL CP BENZOQUINONE TS PM6 CL8614 EXO.LOG</uploadedFileContents>
<title>Jmol 4 - The FMOs of the exo TS structure of the reaction of cyclopentadiene with benzoquinone</title>
<name>DielsAlder2_reactants</name>
</jmolApplet>
</jmol>
<jmol>
<jmolmenu>
<target>DielsAlder2_reactants</target>
<item>
<script>mo 34;</script>
<text>LUMO in the exo TS</text>
</item>
<item>
<script>mo 33;</script>
<text>HOMO in the exo TS</text>
</item>
</jmolmenu>
</jmol>

== Potential Energy ==
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.<ref name=":2">Parr, R. G.; Yang, W. (1989). Density-Functional Theory of Atoms and Molecules. New York: Oxford University Press. ISBN 0-19-504279-4</ref>
The activation energy associated with the exo pathway was found to be '''XXX''' greater than that of the endo pathway. The literature activation energies of the exo and endo pathways were found to be 95.8 and 88.3 kJmol<sup>-1</sup> respectively.<ref name=":1">Tormena, C. F., Lacerda, V., & De Oliveg, K. T. (2010). Revisiting the stability of endo/exo diels-alder adducts between cyclopentadiene and 1,4-benzoquinone. Journal of the Brazilian Chemical Society, 21(1), 112–118. '''doi:10.1590/S0103-50532010000100017'''</ref> 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.<ref name=":3">Fukui, K., Yonezawa, T., & Shingu, H. (1952). A molecular orbital theory of reactivity in aromatic hydrocarbons. J. Chem. Phys., 20(4), 722–725. https://doi.org/10.1063/1.1700523</ref> The exo trajectory is only stabilised by primary orbital interactions, but these are stronger than secondary ones and hence the exo adduct will also form as the minor product. Both products were found to be very close in energy with the endo product being slightly lower than the exo, making it also the thermodynamic reaction outcome.
[[File:Exo DielsAlder Movie.gif|thumb|x500px|500px|'''Figure 7'''- The vibration that corresponds to the reaction path at the transition state]]
{| class="wikitable"
!
!Energy (Hartree/particle)
|-
! style="text-align: left;" | Cyclopentadiene
| -194.1010626
|-
! style="text-align: left;" | Benzoquinone
| -381.4516816
|-
! style="text-align: left;" | Sum of reactants
| '''-575.5527442'''
|-
! style="text-align: left;" | Endo TS
| -575.5769643
|-
! style="text-align: left;" | Exo TS
| -575.5208852
|-
! style="text-align: left;" | Endo Product
|2.11472
|-
! style="text-align: left;" | Exo Product
|2.11472
|-
|colspan="4"|'''Table 2''' - The activation energy and change in free energy associated with the endo and exo pathway.
|}

= Exercise 3: ''o''-Xylylene and SO2 -Diels-Alder vs Cheletropic =
[[File:Reaction scheme All 4.png|thumb|x500px|500px|'''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 yield the fourth outcome that is being computed. For this exercise PM6 optimised structures have been compared.
<br>[[File:Movie IRC Exo PM6 cl8614 wrong way.gif|left|thumb|x400px|330px|'''Figure 9'''- Animation of the exo Diels-Alder reaction at the TS]]
[[File:Movie IRC ENDO_PM6 cl8614.gif|center|thumb|x420px|330px|'''Figure 10'''- Animation of the terminal endo Diels-Alder reaction at the TS]]
[[File:Movie IRC ENDO INTERNAL PM6 cl8614.gif|left|thumb|x400px|330px|'''Figure 11'''- Animation of the internal endo Diels-Alder reaction at the TS]]
[[File:Movie IRC Cheletropic PM6 cl8614.gif|center|thumb|x420px|330px|'''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, 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'''. Rather than taking the reactants from the IRC path one could also sum the individual energies from each reacting species, however this would neglect interactions between these that will be present in reality.
[[File:Relative Ea RE new.png|right|thumb|x500px|500px|'''Figure 15'''- Relative Activation- and Reaction Energies of DA and Cheletropic reactions]]
{| class="wikitable"
!
!colspan="3"|[Hartree/particle]
!colspan="3"|[kJmol<sup>-1</sup>]
|-
!
!Reactants
!Transition State
!Products
!Activation Energy
!Reaction Energy
|-
! style="text-align: left;" | Exo
|0.067720
|0.092075
|0.021455
|63.944057
| -121.468767
|-
! style="text-align: left;" | Endo (terminal)
|0.067929
|0.090562
|0.021695
|59.422946
| -121.387376
|-
! style="text-align: left;" | Endo (internal)
|1.333211
|1.379731
|1.492650
|97.857643
|10.008407
|-
! style="text-align: left;" | Cheletropic
|0.067930
|0.099073
|0.000000
|81.765953
| -178.350229
|-
|colspan="6"|'''Table 3''' - Thermal Energies of reactants, TS and products and calculated activation and reaction energies
|}

= Conclusion =

= References =