ChemWiki - User contributions [en]

Rep:Transition states (st4215)

2017-10-25T10:50:37Z

St4215: /* Exercise 3: Diels-Alder vs Cheletropic */

== Introduction ==
In a chemical reaction, reactants can change into the products via a multitude of different configurations of atoms, each with a different energy. These energies corresponds to a energy profile (when there is 1 degree of freedom), or a Potential Energy Surface (PES) (when there are two degrees of freedom). An example of the PES for a reaction can be seen below.

[[File:st4215_Pes.jpeg|thumb|250px|right| A possible potential energy surface (PES) for a reaction. (Source: [http://www.kf.elf.stuba.sk/~ballo/piatok/prezentacia/hartree-fock/hf_2.html Department of Physics, Slovak University of Technology in Bratislava])]]

As illustrated in the PES, the reactants and products correspond to energy minima - where energy increases in all directions, meaning that the reactants and products sit in a well. At this point, the gradient of the PES curve is zero, and the second derivative yields a positive value, indicating it is a minimum.

The reaction coordinate is hence the minimum energy pathway that leads from the reactants to the products, where the maximum energy along this pathway corresponds to the transition state. In terms of the PES, this corresponds to a first-order saddle point - where energy increases in all directions but one. At this point, the gradient of the PES curve is also zero - it is both a maximum and a minimum. However, the second derivative leads a negative value, indicating that energy is a maximum in one direction but a minimum in all other directions. This value is a negative force constant which corresponds to the imaginary frequency in the vibration spectrum of the transition state. The normal mode corresponding to this imaginary frequency usually show the relevant atoms of the reactants moving towards each other to form the product.

Hence the presence of a negative imaginary frequency in the transition state calculation confirms that the structure at a saddle point and hence corresponds to the transition state. However, energy minima where reactants and products lie should not contain any imaginary frequencies, as the second derivative only yields positive force constant values. The lack of imaginary frequencies in a frequency calculation can confirm that the structures lie in energy minima, and correspond to either the reactants or products.

In this module, computational methods were used to locate and characterise transition states for various pericyclic reactions, including Diels-Alder and cheletropic reactions. An overview of the various methods that were used in the calculations are detailed [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial here].

== Exercises ==
The instructions for the exercises can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_exercise here].

=== Exercise 1: Reaction of Butadiene with Ethylene ===
The reaction between butadiene and ethylene is a [4+2] cycloaddition reaction, or more specifically, a Diels-Alder reaction - a reaction involving a conjugated diene in the s-cis conformation, and a dienophile containing a double bond. In this simple Diels-Alder reaction, butadiene is the diene and ethylene is the dienophile. The reaction scheme for this reaction is shown below:
[[File:st4215_Ex1_reactionscheme.png|thumb|center|300px| Reaction of butadiene with ethylene [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_exercise (Source)]]]

In this exercise, we use this Diels-Alder reaction to determine the orbital symmetry requirements for a reaction to take place, and to show the effect of hybridisation and bond order on the length of C-C bonds. We also probe into the mechanism of the reaction, and determine if bond formation is synchronous or asynchronous.

The link to this completed exercise can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_states_(st4215):_Exercise_1 here].

=== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ===
The reaction of cyclohexadiene and 1,3-dioxole is also a Diels-Alder reaction, in which cyclohexadiene is the diene and 1,3-dioxole is the dienophile. However, unlike the simple Diels-Alder reaction between butadiene and ethylene, this reaction is slightly more complex - 1,3-dioxole can approach the diene at different orientations, leading to the formation of the endo- and exo- Diels-Alder products. This can be seen in the reaction scheme below:
[[File:st4215_Ex2_reactionscheme.png|thumb|center|400px| Reaction of butadiene with ethylene [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_exercise (Source)]]]

The endo- product is formed from a transition state where the substituents on the dienophile point towards the π system of the diene, while the exo- product is formed from a transition state where the substituents are pointing away.

In this exercise, we take a closer look at a different aspect of the Diels-Alder reaction - whether it is normal or inverse electron demand. We also consider the Diels-Alder reaction when an unsymmetrical diene is involved, and compare the endo- and exo- DA reactions in terms of which is more kinetically or thermodynamically favourable. In the process, we confirm that the orbital symmetry requirements as elucidated in Exercise 1 still apply, and illustrate that there are differences between the PM6 and B3LYP calculation methods, with one being more suitable than the other in this case.

The link to this completed exercise can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_states_(st4215):_Exercise_2 here].

=== Exercise 3: Diels-Alder vs Cheletropic ===
In this exercise, we examine the possible reactions between o-xylylene and SO<sub>2</sub> - the Diels-Alder reaction and the cheletropic reaction, as illustrated in the reaction scheme below.
[[File:st4215_Ex3_reactionscheme.png|thumb|center|600px| Reaction of o-xylylene and SO<sub>2</sub>
[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_exercise (Source)]]]

Again, in the Diels-Alder reaction, the dienophile SO<sub>2</sub> can approach the diene o-xylylene at different orientations, resulting in the endo- and exo- DA products. The cheletropic reaction, which is a pericyclic reaction in which the new bonds formed are made to the same atom, results in a single product.

In this exercise, we compare the three different reaction pathways - both Diels-Alder reactions and the cheletropic reaction - in terms of their reaction coordinates, as well as which is the most thermodynamically or kinetically favoured. We also investigate the possibility of a Diels-Alder reaction at a second site in xylylene.

The link to this completed exercise can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_states_(st4215):_Exercise_3 here].

== Conclusion ==
<small><i>Note: Please see each exercise for conclusions pertaining to that exercise</i></small><br>Computational methods allowed us to successfully examine the various pericyclic reactions, by locating and characterising their transition states via a variety of methods. In the process, we were able to determine the kinetic and thermodynamic products of each reaction, prove that orbitals must share the same symmetry in order to interact, and construct MO diagrams based on calculations, among others.

Rep:Transition states (st4215): Exercise 3

2017-10-25T10:50:18Z

St4215: /* Exercise 3: Diels-Alder vs Cheletropic */

== Exercise 3: Diels-Alder vs Cheletropic ==
In this exercise, we examine the possible reactions between o-xylylene and SO<sub>2</sub> - the Diels-Alder reaction and the cheletropic reaction, as illustrated in the reaction scheme below.
[[File:st4215_Ex3_reactionscheme.png|thumb|center|600px| Reaction of o-xylylene and SO<sub>2</sub>
[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_exercise (Source)]]]

Again, in the Diels-Alder reaction, the dienophile SO<sub>2</sub> can approach the diene o-xylylene at different orientations, resulting in the endo- and exo- DA products. The cheletropic reaction, which is a pericyclic reaction in which the new bonds formed are made to the same atom, results in a single product.

In this exercise, we compare the three different reaction pathways - both Diels-Alder reactions and the cheletropic reaction - in terms of their reaction coordinates, as well as which is the most thermodynamically or kinetically favoured. We also investigate the possibility of a Diels-Alder reaction at a second site in xylylene.

=== Calculations ===
Calculations were performed at the PM6 level. Method 3 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial#Method_3 tutorial]) was used to locate the transition state.

The optimised molecules can be seen here:

{| class="wikitable"
! colspan="2" | Reactants
|-
| style="text-align: center;" | o-xylylene
| style="text-align: center;" | SO<sub>2</sub>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16</script>
<uploadedFileContents>st4215_XYLYLENE_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16</script>
<uploadedFileContents>st4215_SO2_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo || style="text-align: center;" | Exo
|-
| style="text-align: center;" | Transition state
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>St4215_ex3_ENDO_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_ex3_ENDO_TS_IRC2_PM6.LOG | IRC file]]
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>st4215_ex3_Exo_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_ex3_Exo_TS_IRC_PM6.LOG | IRC file]]
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>st4215_ex3_CHEL_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_ex3_CHEL_TS_IRC_PM6.LOG | IRC file]]
|-
| style="text-align: center;" | Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>St4215_ex3_ENDO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>st4215_ex3_EXO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>st4215_ex3_CHEL_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Reaction coordinate ===
<small><i>Visualise the reaction coordinate with an IRC calculation for each path. Include a .gif file in the wiki of these IRCs.</i></small>

The formation of the products for each of the endo- and exo- Diels-Alder reactions, as well as the cheletropic reaction, can be visualised below.

{| class="wikitable"
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
|-
| [[File:st4215_ENDO_TS_IRCmovie.gif]]
| [[File:st4215_Exo_TS_IRCmovie.gif]]
| [[File:st4215_Chel_TS_IRCmovie.gif]]
|}

We can see that SO<sub>2</sub> approaches xylylene at a different orientation and angle for each of these reactions. This difference in approach trajectories hence lead to the formation of different products.

It can also be observed that in each of the reactions, as the product is formed, the 6-membered ring in xylylene becomes aromatic. This means that there is a strong driving force for the formation of the products. In contrast, the reactant xylylene is highly unstable as it is non-aromatic, and as can be seen in these reactions, can readily react with unsaturated bonds to form a more stable aromatic product.

=== Energy analysis ===
<small><i>Calculate the activation and reaction energies (converting to kJ/mol) for each step as in Exercise 2 to determine which route is preferred. Using Excel or Chemdraw, draw a reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels-Alder reactions and the cheletropic reaction. You can set the 0 energy level to the reactants at infinite separation.</i></small>

==== Free energies ====
The free energies of the reactants, transition states and products for each of the 3 reactions are tabulated below. The reaction barriers and energies are also calculated.

{| class="wikitable"
! rowspan="2" scope="col" style="width: 150px;" |
! colspan="2" scope="col" style="width: 300px;" | Energy at 298 K (PM6)
|-
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
|-
| colspan="3" style="background: #B7C3D0" | <b>Reactants</b>
|-
| Xylylene || style="text-align: center;" | 0.17876 || style="text-align: center;" | 469.34
|-
| SO<sub>2</sub> || style="text-align: center;" | -0.11927 || style="text-align: center;" | -313.14
|-
| Total reactants || style="text-align: center;" | 0.059496 || style="text-align: center;" | 156.21
|-
| colspan="3" style="background: #B7C3D0" | <b>Endo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | 0.090560 || style="text-align: center;" | 237.77
|-
| Product || style="text-align: center;" | 0.021704 || style="text-align: center;" | 56.984
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0311 || style="text-align: center;" | 81.6
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0378 || style="text-align: center;" | -99.2
|-
| colspan="3" style="background: #B7C3D0" | <b>Exo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | 0.092078 || style="text-align: center;" | 241.75
|-
| Product || style="text-align: center;" | 0.021455 || style="text-align: center;" | 56.330
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0326 || style="text-align: center;" | 85.5
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0380 || style="text-align: center;" | -99.9
|-
| colspan="3" style="background: #B7C3D0" | <b>Cheletropic</b>
|-
| Transition state || style="text-align: center;" | 0.099058 || style="text-align: center;" | 260.08
|-
| Product || style="text-align: center;" | -0.000002 || style="text-align: center;" | -0.0052510
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0396 || style="text-align: center;" | 104
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0595 || style="text-align: center;" | -156
|}
<small><i>^Note that all values from the calculations are reported to 5 s.f. unless more decimal places are needed to differentiate between each reaction type. Derived quantities (reaction barrier and reaction energy) are reported to 3 s.f.</i></small>

==== Thermodynamic and kinetic products ====
From the values above, a combined reaction profile showing the reaction barriers and reaction energies can also be plotted as seen below.
[[File:st4215_ex3_Reaction_profile2.PNG|600px|thumb|center|Reaction profile diagram for the 3 Diels-Alder and cheletropic reactions, setting the energy of the reactants to zero]]

We can clearly see that the endo- Diels-Alder product is the kinetic product as it has the lowest reaction barrier of +81.6 kJmol<sup>-1</sup>, while the cheletropic product is the thermodynamic product as it is most stable as has the lowest energy of -156 kJmol<sup>-1</sup>. This is consistent with experimental and computational data.<ref name="chel_3"/><ref name="chel_1"/>

The high stability of the cheletropic product is likely due to its high symmetry, which minimises steric clash, as well as the preference of S to adopt a five-membered compared to 6-membered ring structure. This is in contrast to saturated carbon rings, where 6-membered cyclohexane is more stable than 5-membered cyclopentane due to deviation from tetrahedral bond angles of 109° in cyclopentane, resulting in angle strain. However, due to the larger size of the S atom, C-C<sub>tet</sub>-S bond angles in a 5-membered unsaturated sulfur ring (like in the cheletropic product) are much closer to the tetrahedral bond angle, at 105°. In comparison, the 6-membered heterocycle in the Diels-Alder products have C-C<sub>tet</sub>-S bond angles of around 114°, which are comparatively larger than 109°. This is illustrated below:

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
|-
| Products
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; measure 3 16 11</script>
<uploadedFileContents>St4215_ex3_ENDO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; rotate y 180; measure 3 16 11</script>
<uploadedFileContents>st4215_ex3_EXO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; measure 1 7 15</script>
<uploadedFileContents>st4215_ex3_CHEL_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

It is also expected that one of the Diels-Alder products (the endo- product) is the kinetic product instead of the cheletropic product.<ref name="chel_3"/> While the reaction barriers for both endo- and exo- Diels-Alder reactions are similar, the reaction barrier for the cheletropic reaction is much higher. Examining their transition states (see below) allows us to infer why.

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
|-
| Transition state HOMO
| style="text-align: center;" | [[File:st4215_ex3_Endo_TS_HOMO.PNG]]
| style="text-align: center;" | [[File:st4215_ex3_Exo_TS_HOMO.PNG]]
| style="text-align: center;" | [[File:st4215_ex3_Chel_TS_HOMO.PNG]]
|-
| Discussion
| colspan="2" | Some stabilising secondary orbital interactions can be seen in the HOMOs of the endo- and exo- transition states, hence lowering its energy and reducing the reaction barriers for these reactions.
| No stabilising secondary orbital interactions are present here - in fact, the HOMO of the transition state is highly antisymmetric with many nodes, and hence likely to be high in energy.
|}

Like most Diels-Alder reactions, the endo and not the exo- product is the kinetic product due to more or greater stabilising secondary orbital interactions in the transition state. However, in this reaction, both the endo- and exo- transition states seem to have an approximately equal but not significant amount of stabilising orbital interactions in the HOMO. This explains why the endo- and exo- transition states are relatively close in energy.

== Extra: Diels-Alder reaction at a different site ==
O-xylylene also contains a cis-butadiene fragment that can act as the diene in another Diels-Alder reaction. However, this reaction is very kinetically and thermodynamically favourable, as proven by computational methods.

=== Calculations ===
Calculations were performed at the PM6 level. Method 3 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial#Method_3 tutorial]) was used to locate the transition state.

The optimised molecules can be seen here. Optimised reactants (o-xylylene and SO<sub>2</sub>) from the earlier reaction were used.

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder (2)
|-
| style="text-align: center;" | Endo || style="text-align: center;" | Exo
|-
| style="text-align: center;" | Transition state
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>st4215_BAD_ENDO_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_BAD_ENDO_IRC_PM6.LOG | IRC file]]
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>st4215_BAD_EXO_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_BAD_EXO_IRC_PM6.LOG | IRC file]]
|-
| style="text-align: center;" | Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 64</script>
<uploadedFileContents>st4215_BAD_ENDO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_BAD_EXO_PDT_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Energy analysis ===
The free energies of the reactants, transition states and products for both the endo- and exo- Diels Alder reactions are tabulated below. The reaction barriers and energies are also calculated.

{| class="wikitable"
! rowspan="2" scope="col" style="width: 150px;" |
! colspan="2" scope="col" style="width: 300px;" | Energy at 298 K (PM6)
|-
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
|-
| colspan="3" style="background: #B7C3D0" | <b>Reactants</b>
|-
| Xylylene || style="text-align: center;" | 0.17876 || style="text-align: center;" | 469.34
|-
| SO<sub>2</sub> || style="text-align: center;" | -0.11927 || style="text-align: center;" | -313.14
|-
| Total reactants || style="text-align: center;" | 0.059496 || style="text-align: center;" | 156.21
|-
| colspan="3" style="background: #B7C3D0" | <b>Endo- Diels-Alder (2)</b>
|-
| Transition state || style="text-align: center;" | 0.10207 || style="text-align: center;" | 267.99
|-
| Product || style="text-align: center;" | 0.065613 || style="text-align: center;" | 172.27
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0426 || style="text-align: center;" | 112
|-
| Reaction energy (ΔG) || style="text-align: center;" | +0.00612 || style="text-align: center;" | +16.1
|-
| colspan="3" style="background: #B7C3D0" | <b>Exo- Diels-Alder (2)</b>
|-
| Transition state || style="text-align: center;" | 0.10505 || style="text-align: center;" | 275.82
|-
| Product || style="text-align: center;" | 0.067305 || style="text-align: center;" | 176.71
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0456 || style="text-align: center;" | 120
|-
| Reaction energy (ΔG) || style="text-align: center;" | +0.00781 || style="text-align: center;" | +20.5
|}
<small><i>^Note that all values from the calculations are reported to 5 s.f. unless more decimal places are needed to differentiate between each reaction type. Derived quantities (reaction barrier and reaction energy) are reported to 3 s.f.</i></small>

We can hence see that this reaction is both kinetically and thermodynamically unfavourable compared to the other Diels-Alder reaction (previously discussed) and the cheletropic reaction.

Comparing the reaction barriers, the activation energies of 112 kJmol<sup>-1</sup> (endo) and 120 kJmol<sup>-1</sup> (exo) are much higher than that of the other DA reaction, at 81.6 kJmol<sup>-1</sup> (endo) and 85.5 kJmol<sup>-1</sup> (exo), as well as the cheletropic reaction, at 104 kJmol<sup>-1</sup>. Hence this Diels-Alder reaction is the most kinetically unfavourable reaction.

Comparing the reaction energies, we can see that both the endo- and exo- reactions are endothermic - compared to the other two DA reactions as well as the cheletropic reaction, which are exothermic. This indicates that this Diels-Alder reaction is also highly thermodynamically unfavourable as ΔG<0 and it is not spontaneous.

=== Conclusion ===
While there are several possible reactions between o-xylylene and SO<sub>2</sub>, including a Diels-Alder reaction at two different sites and a cheletropic reaction, not all are comparable in terms of kinetic and thermodynamic favourability. Calculations show that the cheletropic reaction is the most thermodynamically favoured due to the higher stability of a 5-membered S ring, and the Diels-Alder reaction between the two terminal alkene carbons of xylylene is much more kinetically and thermodynamically favourable compared to the Diels-Alder reaction involving the cis-butadiene fragment in the aromatic 6-membered ring. This is because the aromaticity of the ring is not broken in the former reaction.

== References ==

<references>
<ref name="chel_1">F. Monnat, P. Vogel, J. A. Sordo. [http://onlinelibrary.wiley.com/doi/10.1002/1522-2675(200203)85:3%3C712::AID-HLCA712%3E3.0.CO;2-5/epdf <i>Hetero-Diels-Alder and Cheletropic Additions of Sulfur Dioxide to 1,2-Dimethylidenecycloalkanes. Determination of Thermochemical and Kinetics Parameters for Reactions in Solution and Comparison with Estimates From Quantum Calculations</i>] Helv. Chim. Acta. <b>85</b> (3), 712–732 (2002).</ref>
<ref name="chel_3">D. Suarez, T. L. Sordo, J. A. Sordo. [http://pubs.acs.org/doi/pdf/10.1021/jo00114a039 <i>A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls</i>] J. Org. Chem., <b>60</b> (9), 2848–2852 (1995).</ref>

</references>

File:St4215 Ex3 reactionscheme.png

2017-10-25T10:49:13Z

St4215:

Rep:Transition states (st4215): Exercise 1

2017-10-25T10:47:42Z

St4215: /* Exercise 1: Reaction of Butadiene with Ethylene */

== Exercise 1: Reaction of Butadiene with Ethylene ==
The reaction between butadiene and ethylene is a [4+2] cycloaddition reaction, or more specifically, a Diels-Alder reaction - a reaction involving a conjugated diene in the s-cis conformation, and a dienophile containing a double bond. In this simple Diels-Alder reaction, butadiene is the diene and ethylene is the dienophile. The reaction scheme for this reaction is shown below:

[[File:st4215_Ex1_reactionscheme.png|thumb|center|300px| Reaction of butadiene with ethylene [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_exercise (Source)]]]

In this exercise, we use this Diels-Alder reaction to determine the orbital symmetry requirements for a reaction to take place, and to show the effect of hybridisation and bond order on the length of C-C bonds. We also probe into the mechanism of the reaction, and determine if bond formation is synchronous or asynchronous.

=== Calculations ===
Calculations were performed at the PM6 level. Method 1 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial#Method_1 tutorial]) was used to locate the transition state.

The optimised molecules can be seen here:

{| class="wikitable"
! colspan="2" | Reactants
! Transition state
! Product
|-
|<jmol>
<jmolApplet>
<title>Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_CYCLOHEXENE_TS_IRC3_PM6.LOG | IRC file]]
| <jmol>
<jmolApplet>
<title>Cyclohexene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_CYCLOHEXENE_PDT_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Molecular orbitals ===

==== MO diagram ====
<small><i>Construct an MO diagram for the formation of the butadiene/ethene TS, including basic symmetry labels (symmetric/antisymmetric or s/a).</i></small><br>

The MO diagram for this cycloaddition reaction was constructed as shown below. We first assume based on prior knowledge that only orbitals of the same symmetry can combine; however, this is proven in a later section.

The MOs have been labelled accordingly with their numbers according to the calculations, and can be visualised in the section below.<br>
[[File:st4215_ex1_MO_diagram.PNG]]

Considering the actual energy levels of the MOs computed from the calculations, a more accurate MO diagram can be constructed, as seen [[Media:st4215_ex1_MO_diagram_actual.PNG|here]]. However, this does not affect the relative energy levels of the MOs (within each molecule) or the interactions between these MOs.

==== Computed MOs ====
<small><i>Include images (or Jmol objects) for each of the HOMO and LUMO of butadiene and ethene, and the four MOs these produce for the TS. Correlate these MOs with the ones in your MO diagram to show which orbitals interact.</i></small><br>

The HOMOs and LUMOs for each reactant, butadiene and ethylene, as well as the 4 MOs that these produce for the TS, were calculated and can be visualised below. The MO numbers correspond to that labelled on the MO diagram, allowing us to see which orbitals interact. We can also observe that these computed MOs bear physical resemblance to that drawn in the MO diagram, in terms of the bonding and antibonding phases in each MO.

{| class="wikitable"
! rowspan="2" | Symmetry
! colspan="2" | Reactants
! rowspan="2" colspan="2"| Transition state
|-
| style="text-align: center;" | Butadiene
| style="text-align: center;" | Ethylene
|-
| Antisymmetric
| <b>MO 11</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 7</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 16</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 19</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Symmetric
| <b>MO 12</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 6</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 17</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 18</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Symmetry requirements ====
<small><i>What can you conclude about the requirements for symmetry for a reaction (when is a reaction 'allowed' and when is it 'forbidden')? Write whether the orbital overlap integral is zero or non-zero for the case of a symmetric-antisymmetric interaction, a symmetric-symmetric interaction and an antisymmetric-antisymmetric interaction.</i></small><br>

From the table above as well as the MO diagram, we can see that the HOMO/LUMO of butadiene interact with the corresponding LUMO/HOMO in ethylene respectively. These interactions can occur as each pair of orbitals share the same symmetry. The HOMO of butadiene (MO 11) and the LUMO of ethylene (MO 7) are both antisymmetric, and interact to give two antisymmetric MOs in the TS (MOs 16 and 19). Similarly, the LUMO of ethylene (MO 12) and the HOMO of butadiene (MO 6) are both symmetric, and interact to give two symmetric MOs in the TS (MOs 17 and 18). Hence we can conclude that a reaction is only allowed when the relevant orbitals share the same symmetry, as this would allow orbitals to overlap and thus interact. This is illustrated in the following table:

{| class="wikitable"
! Symmetry of interaction
! Orbital overlap integral
|-
| style="text-align: center;" | Symmetric-antisymmetric
| style="text-align: center;" | Zero
|-
| style="text-align: center;" | Symmetric-symmetric
| style="text-align: center;" | Non-zero
|-
| style="text-align: center;" | Antisymmetric-antisymmetric
| style="text-align: center;" | Non-zero
|}

=== C-C bond lengths ===
<small><i>Include measurements of the 4 C-C bond lengths of the reactants and the 6 C-C bond lengths of the TS and products. How do the bond lengths change as the reaction progresses? What are typical sp3 and sp2 C-C bond lengths? What is the Van der Waals radius of the C atom? How does this compare with the length of the partly formed C-C bonds in the TS.</i></small>

The C-C bond lengths in the reactants, TS and products are tabulated below.

{| class="wikitable"
! rowspan="2" colspan="2" |
! colspan="2" | Reactants
! rowspan="2" | Transition state
! rowspan="2" | Product
|-
| style="text-align: center;" | Butadiene
| style="text-align: center;" | Ethylene
|-
| colspan="2" style="text-align: center;"| Labelled C atoms
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7; label display</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4; label display</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>st4215_CYCLOHEXENE_PDT_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| rowspan="6" style="text-align: center;" | C-C bond<br> length / Å
| style="width: 50px;" | Bond A || <center> C1-C4: 1.34 </center>|| || <center> C1-C4: 1.38 </center> || <center> C1-C4: 1.50 </center>
|-
| Bond B || <center> C4-C6: 1.47 </center> || || <center> C4-C6: 1.41 </center> || <center> C4-C6: 1.34 </center>
|-
| Bond C || <center> C6-C7: 1.34 </center> || || <center> C6-C7: 1.38 </center> || <center> C6-C7: 1.50 </center>
|-
| Bond D || || <center> C1-C4: 1.33 </center> || <center> C11-C14: 1.38 </center> || <center> C11-C14: 1.54 </center>
|-
| Bond E || || || <center> C7-C14: 2.11 </center> || <center> C7-C14: 1.54 </center>
|-
| Bond F || || || <center> C1-C11: 2.11 </center> || <center> C1-C11: 1.54 </center>
|}

From the values above, we can observe the following changes in bond length as the reaction progresses.

{| class="wikitable" style="width: 750px;"
! Bond
! Trend in bond length as reaction progresses
! Graph
|-
| A || As the reaction progresses, the length of Bond A increases. This is because Bond A is initially a C=C double bond in butadiene, which becomes a sp<sup>2</sup>-sp<sup>3</sup> C-C single bond in cyclohexene. These lengths are similar to typical values of 1.34 Å for alkenes and 1.50 Å sp<sup>2</sup>-sp<sup>3</sup> C-C bonds.<ref name="bondlength"/>
| [[File:st4215_BondA.JPG|200px]]
|-
| B || As the reaction progresses, the length of Bond B decreases. This is because Bond B is initially an sp<sup>2</sup>-sp<sup>2</sup> C-C single bond in butadiene, which becomes a C=C double bond in cyclohexene. These lengths are similar to typical values of 1.47 Å for sp<sup>2</sup>-sp<sup>2</sup> C-C bonds and 1.34 Å for alkenes.<ref name="bondlength"/>
| [[File:st4215_BondB.JPG|200px]]
|-
| C || Similar to Bond A, as the reaction progresses, the length of Bond C increases. This is due to the same reason as explained for Bond A.
| [[File:st4215_BondC.JPG|200px]]
|-
| D || As the reaction progresses, the length of Bond D increases. This is because Bond B is initially an C=C single bond in ethylene, which becomes a sp<sup>3</sup>-sp<sup>3</sup> C-C single bond in cyclohexene. These lengths are similar to typical values of 1.34 Å for alkenes and 1.54 Å for sp<sup>3</sup>-sp<sup>3</sup> C-C bonds.<ref name="bondlength"/>
| [[File:st4215_BondD.JPG|200px]]
|-
| E || Bond E is formed in this reaction. Hence as the reaction progresses from the transition state to the product, the length of Bond E increases. The length of the fully formed Bond E in the product, an sp<sup>3</sup>-sp<sup>3</sup> C-C single bond, corresponds to the typical value of 1.54 Å.<ref name="bondlength"/> The distance between the C atoms in the TS (2.11 Å) falls between twice the van der Waal radius of C (2 x 1.70 Å<ref name="vdw_c"/> = 3.40 Å) and the length of the fully formed Bond E, indicating that the atoms are approaching each other.
| [[File:st4215_BondE.JPG|200px]]
|-
| F || Like Bond E, Bond F is also formed in this reaction. Hence as the reaction progresses from the transition state to the product, the length of Bond F increases, due to the same reasons as explained above.
| [[File:st4215_BondF.JPG|200px]]
|}

We can hence conclude that bond lengths in the reactants and product do not deviate from typical values. Additionally, we can also show that an increase in bond order from 1 to 2 indeed shortens the C-C bond, while an increase in hybridisation from sp<sup>2</sup> to sp<sup>3</sup> does lengthen the C-C bond, as seen in the comparison of theoretical values.

=== Transition state ===
<i><small>Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous?</small></i>
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 7; rotate x -40; select atomno=1, atomno=7, atomno=11, atomno=14; label display </script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
<name>cyclohexeneTS</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>cyclohexeneTS</target>
</jmolbutton>
<jmolbutton>
<script>measure 1 11; measure 7 14</script>
<text>C-C Distances</text>
<target>cyclohexeneTS</target>
</jmolbutton>
</jmol>
<br><br>
As illustrated above, the formation of the two bonds are synchronous as the relevant pairs of atoms (C1/C11 and C7/C14) are moving towards each other at the same time, with the distance between the two atoms being approximately equal in both pairs. This is to be expected as evidence shows that the Diels-Alder reaction can proceed via a concerted, synchronous mechanism.<ref name="DA_1"/> However, it is important to note that this may also be the result of the calculation method used, as studies with other calculation methods (DFT/B3LYP) have also shown that other mechanisms are feasible.<ref name="DA_2"/>

=== Conclusion ===
By examining this simple Diels-Alder reaction between butadiene and ethylene, we can conclude from computational data that only orbitals need to share the same symmetry to be able to overlap and hence interact. This knowledge will be useful in Exercise 2, where we again construct a MO diagram for a another Diels-Alder reaction. By following the change in C-C bond lengths over the course of the reaction, it can also be concluded that as per theoretical data, bond lengths shorten when bond order increases and hybridisation decreases. Lastly, based on this calculation, we can conclude that the Diels-Alder reaction between butadiene and ethylene proceeds via synchronous bond formation in the transition state.

== References ==
<references>
<ref name="bondlength">M. A. Fox, J. K. Whitesell, E. Buchholz. <i>Organische Chemie: Grundlagen, Mechanismen, bioorganische Anwendungen</i> (1995).</ref>
<ref name="vdw_c">A. Bondi. [http://pubs.acs.org/doi/pdf/10.1021/j100785a001 <i>van der Waals Volumes and Radii </i>] J. Phys. Chem. <b>68</b>(3), 441–451 (1996).</ref>
<ref name="DA_1">K. N. Houk, Y. T Lin & F. K. Brown. [http://pubs.acs.org/doi/pdf/10.1021/ja00263a059 <i>Evidence for the Concerted Mechanism of the Diels-Alder Reaction of Butadiene with Ethylene.</i>] J. Am. Chem. SOC. <b>108</b>, 554-556 (1986).</ref>
<ref name="DA_2">E. Goldstein, B. Beno & K. N. Houk. [http://pubs.acs.org/doi/pdf/10.1021/ja9601494 <i>Density Functional Theory Prediction of the Relative Energies and Isotope Effects for the Concerted and Stepwise Mechanisms of the Diels-Alder Reaction of Butadiene and Ethylene</i>] J. Am. Chem. Soc. <b>118</b>, 6036-6043 (1996).
</ref>
</references>

Rep:Transition states (st4215)

2017-10-25T10:47:26Z

St4215: /* Exercise 1: Reaction of Butadiene with Ethylene */

== Introduction ==
In a chemical reaction, reactants can change into the products via a multitude of different configurations of atoms, each with a different energy. These energies corresponds to a energy profile (when there is 1 degree of freedom), or a Potential Energy Surface (PES) (when there are two degrees of freedom). An example of the PES for a reaction can be seen below.

[[File:st4215_Pes.jpeg|thumb|250px|right| A possible potential energy surface (PES) for a reaction. (Source: [http://www.kf.elf.stuba.sk/~ballo/piatok/prezentacia/hartree-fock/hf_2.html Department of Physics, Slovak University of Technology in Bratislava])]]

As illustrated in the PES, the reactants and products correspond to energy minima - where energy increases in all directions, meaning that the reactants and products sit in a well. At this point, the gradient of the PES curve is zero, and the second derivative yields a positive value, indicating it is a minimum.

The reaction coordinate is hence the minimum energy pathway that leads from the reactants to the products, where the maximum energy along this pathway corresponds to the transition state. In terms of the PES, this corresponds to a first-order saddle point - where energy increases in all directions but one. At this point, the gradient of the PES curve is also zero - it is both a maximum and a minimum. However, the second derivative leads a negative value, indicating that energy is a maximum in one direction but a minimum in all other directions. This value is a negative force constant which corresponds to the imaginary frequency in the vibration spectrum of the transition state. The normal mode corresponding to this imaginary frequency usually show the relevant atoms of the reactants moving towards each other to form the product.

Hence the presence of a negative imaginary frequency in the transition state calculation confirms that the structure at a saddle point and hence corresponds to the transition state. However, energy minima where reactants and products lie should not contain any imaginary frequencies, as the second derivative only yields positive force constant values. The lack of imaginary frequencies in a frequency calculation can confirm that the structures lie in energy minima, and correspond to either the reactants or products.

In this module, computational methods were used to locate and characterise transition states for various pericyclic reactions, including Diels-Alder and cheletropic reactions. An overview of the various methods that were used in the calculations are detailed [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial here].

== Exercises ==
The instructions for the exercises can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_exercise here].

=== Exercise 1: Reaction of Butadiene with Ethylene ===
The reaction between butadiene and ethylene is a [4+2] cycloaddition reaction, or more specifically, a Diels-Alder reaction - a reaction involving a conjugated diene in the s-cis conformation, and a dienophile containing a double bond. In this simple Diels-Alder reaction, butadiene is the diene and ethylene is the dienophile. The reaction scheme for this reaction is shown below:
[[File:st4215_Ex1_reactionscheme.png|thumb|center|300px| Reaction of butadiene with ethylene [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_exercise (Source)]]]

In this exercise, we use this Diels-Alder reaction to determine the orbital symmetry requirements for a reaction to take place, and to show the effect of hybridisation and bond order on the length of C-C bonds. We also probe into the mechanism of the reaction, and determine if bond formation is synchronous or asynchronous.

The link to this completed exercise can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_states_(st4215):_Exercise_1 here].

=== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ===
The reaction of cyclohexadiene and 1,3-dioxole is also a Diels-Alder reaction, in which cyclohexadiene is the diene and 1,3-dioxole is the dienophile. However, unlike the simple Diels-Alder reaction between butadiene and ethylene, this reaction is slightly more complex - 1,3-dioxole can approach the diene at different orientations, leading to the formation of the endo- and exo- Diels-Alder products. This can be seen in the reaction scheme below:
[[File:st4215_Ex2_reactionscheme.png|thumb|center|400px| Reaction of butadiene with ethylene [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_exercise (Source)]]]

The endo- product is formed from a transition state where the substituents on the dienophile point towards the π system of the diene, while the exo- product is formed from a transition state where the substituents are pointing away.

In this exercise, we take a closer look at a different aspect of the Diels-Alder reaction - whether it is normal or inverse electron demand. We also consider the Diels-Alder reaction when an unsymmetrical diene is involved, and compare the endo- and exo- DA reactions in terms of which is more kinetically or thermodynamically favourable. In the process, we confirm that the orbital symmetry requirements as elucidated in Exercise 1 still apply, and illustrate that there are differences between the PM6 and B3LYP calculation methods, with one being more suitable than the other in this case.

The link to this completed exercise can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_states_(st4215):_Exercise_2 here].

=== Exercise 3: Diels-Alder vs Cheletropic ===
In this exercise, we examine the possible reactions between o-xylylene and SO<sub>2</sub> - the Diels-Alder reaction and the cheletropic reaction, as illustrated in the reaction scheme below.
(insert chemdraw diagram)

Again, in the Diels-Alder reaction, the dienophile SO<sub>2</sub> can approach the diene o-xylylene at different orientations, resulting in the endo- and exo- DA products. The cheletropic reaction, which is a pericyclic reaction in which the new bonds formed are made to the same atom, results in a single product.

In this exercise, we compare the three different reaction pathways - both Diels-Alder reactions and the cheletropic reaction - in terms of their reaction coordinates, as well as which is the most thermodynamically or kinetically favoured. We also investigate the possibility of a Diels-Alder reaction at a second site in xylylene.

The link to this completed exercise can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_states_(st4215):_Exercise_3 here].

== Conclusion ==
<small><i>Note: Please see each exercise for conclusions pertaining to that exercise</i></small><br>Computational methods allowed us to successfully examine the various pericyclic reactions, by locating and characterising their transition states via a variety of methods. In the process, we were able to determine the kinetic and thermodynamic products of each reaction, prove that orbitals must share the same symmetry in order to interact, and construct MO diagrams based on calculations, among others.

Rep:Transition states (st4215)

2017-10-25T10:47:15Z

St4215: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

== Introduction ==
In a chemical reaction, reactants can change into the products via a multitude of different configurations of atoms, each with a different energy. These energies corresponds to a energy profile (when there is 1 degree of freedom), or a Potential Energy Surface (PES) (when there are two degrees of freedom). An example of the PES for a reaction can be seen below.

[[File:st4215_Pes.jpeg|thumb|250px|right| A possible potential energy surface (PES) for a reaction. (Source: [http://www.kf.elf.stuba.sk/~ballo/piatok/prezentacia/hartree-fock/hf_2.html Department of Physics, Slovak University of Technology in Bratislava])]]

As illustrated in the PES, the reactants and products correspond to energy minima - where energy increases in all directions, meaning that the reactants and products sit in a well. At this point, the gradient of the PES curve is zero, and the second derivative yields a positive value, indicating it is a minimum.

The reaction coordinate is hence the minimum energy pathway that leads from the reactants to the products, where the maximum energy along this pathway corresponds to the transition state. In terms of the PES, this corresponds to a first-order saddle point - where energy increases in all directions but one. At this point, the gradient of the PES curve is also zero - it is both a maximum and a minimum. However, the second derivative leads a negative value, indicating that energy is a maximum in one direction but a minimum in all other directions. This value is a negative force constant which corresponds to the imaginary frequency in the vibration spectrum of the transition state. The normal mode corresponding to this imaginary frequency usually show the relevant atoms of the reactants moving towards each other to form the product.

Hence the presence of a negative imaginary frequency in the transition state calculation confirms that the structure at a saddle point and hence corresponds to the transition state. However, energy minima where reactants and products lie should not contain any imaginary frequencies, as the second derivative only yields positive force constant values. The lack of imaginary frequencies in a frequency calculation can confirm that the structures lie in energy minima, and correspond to either the reactants or products.

In this module, computational methods were used to locate and characterise transition states for various pericyclic reactions, including Diels-Alder and cheletropic reactions. An overview of the various methods that were used in the calculations are detailed [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial here].

== Exercises ==
The instructions for the exercises can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_exercise here].

=== Exercise 1: Reaction of Butadiene with Ethylene ===
The reaction between butadiene and ethylene is a [4+2] cycloaddition reaction, or more specifically, a Diels-Alder reaction - a reaction involving a conjugated diene in the s-cis conformation, and a dienophile containing a double bond. In this simple Diels-Alder reaction, butadiene is the diene and ethylene is the dienophile. The reaction scheme for this reaction is shown below:
[[File:st4215_Ex1_reactionscheme.png|thumb|center|400px| Reaction of butadiene with ethylene [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_exercise (Source)]]]

In this exercise, we use this Diels-Alder reaction to determine the orbital symmetry requirements for a reaction to take place, and to show the effect of hybridisation and bond order on the length of C-C bonds. We also probe into the mechanism of the reaction, and determine if bond formation is synchronous or asynchronous.

The link to this completed exercise can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_states_(st4215):_Exercise_1 here].

=== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ===
The reaction of cyclohexadiene and 1,3-dioxole is also a Diels-Alder reaction, in which cyclohexadiene is the diene and 1,3-dioxole is the dienophile. However, unlike the simple Diels-Alder reaction between butadiene and ethylene, this reaction is slightly more complex - 1,3-dioxole can approach the diene at different orientations, leading to the formation of the endo- and exo- Diels-Alder products. This can be seen in the reaction scheme below:
[[File:st4215_Ex2_reactionscheme.png|thumb|center|400px| Reaction of butadiene with ethylene [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_exercise (Source)]]]

The endo- product is formed from a transition state where the substituents on the dienophile point towards the π system of the diene, while the exo- product is formed from a transition state where the substituents are pointing away.

In this exercise, we take a closer look at a different aspect of the Diels-Alder reaction - whether it is normal or inverse electron demand. We also consider the Diels-Alder reaction when an unsymmetrical diene is involved, and compare the endo- and exo- DA reactions in terms of which is more kinetically or thermodynamically favourable. In the process, we confirm that the orbital symmetry requirements as elucidated in Exercise 1 still apply, and illustrate that there are differences between the PM6 and B3LYP calculation methods, with one being more suitable than the other in this case.

The link to this completed exercise can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_states_(st4215):_Exercise_2 here].

=== Exercise 3: Diels-Alder vs Cheletropic ===
In this exercise, we examine the possible reactions between o-xylylene and SO<sub>2</sub> - the Diels-Alder reaction and the cheletropic reaction, as illustrated in the reaction scheme below.
(insert chemdraw diagram)

Again, in the Diels-Alder reaction, the dienophile SO<sub>2</sub> can approach the diene o-xylylene at different orientations, resulting in the endo- and exo- DA products. The cheletropic reaction, which is a pericyclic reaction in which the new bonds formed are made to the same atom, results in a single product.

In this exercise, we compare the three different reaction pathways - both Diels-Alder reactions and the cheletropic reaction - in terms of their reaction coordinates, as well as which is the most thermodynamically or kinetically favoured. We also investigate the possibility of a Diels-Alder reaction at a second site in xylylene.

The link to this completed exercise can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_states_(st4215):_Exercise_3 here].

== Conclusion ==
<small><i>Note: Please see each exercise for conclusions pertaining to that exercise</i></small><br>Computational methods allowed us to successfully examine the various pericyclic reactions, by locating and characterising their transition states via a variety of methods. In the process, we were able to determine the kinetic and thermodynamic products of each reaction, prove that orbitals must share the same symmetry in order to interact, and construct MO diagrams based on calculations, among others.

Rep:Transition states (st4215): Exercise 2

2017-10-25T10:47:09Z

St4215: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
The reaction of cyclohexadiene and 1,3-dioxole is also a Diels-Alder reaction, in which cyclohexadiene is the diene and 1,3-dioxole is the dienophile. However, unlike the simple Diels-Alder reaction between butadiene and ethylene, this reaction is slightly more complex - 1,3-dioxole can approach the diene at different orientations, leading to the formation of the endo- and exo- Diels-Alder products. This can be seen in the reaction scheme below:
[[File:st4215_Ex2_reactionscheme.png|thumb|center|400px| Reaction of cyclohexadiene and 1,3-dioxole [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_exercise (Source)]]]

The endo- product is formed from a transition state where the substituents on the dienophile point towards the π system of the diene, while the exo- product is formed from a transition state where the substituents are pointing away.

In this exercise, we take a closer look at a different aspect of the Diels-Alder reaction - whether it is normal or inverse electron demand. We also consider the Diels-Alder reaction when an unsymmetrical diene is involved, and compare the endo- and exo- DA reactions in terms of which is more kinetically or thermodynamically favourable. In the process, we confirm that the orbital symmetry requirements as elucidated in Exercise 1 still apply, and illustrate that there are differences between the PM6 and B3LYP calculation methods, with one being more suitable than the other in this case.

=== Calculations ===
Calculations were performed at both the PM6 and B3LYP/6-31G(d) level. Method 2 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial#Method_2 tutorial]) was used to locate the transition state.

The optimised molecules can be seen here:

{| class="wikitable"
! rowspan="2" | Calculation method
! colspan="2" | Reactants
! colspan="2" | Endo
! colspan="2" | Exo
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-dioxole
| style="text-align: center;" | Transition state
| style="text-align: center;" | Product
| style="text-align: center;" | Transition state
| style="text-align: center;" | Product
|-
| style="text-align: center;" | B3LYP
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18</script>
<uploadedFileContents>st4215_CYCLOHEXADIENE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26</script>
<uploadedFileContents>st4215_DIOXOLE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18</script>
<uploadedFileContents>st4215_ENDO_PDT_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>st4215_EXO_PDT_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" | PM6
| style="text-align: center;" | [[Media:st4215_CYCLOHEXADIENE_OPTFREQ_PM6.LOG| Cyclohexadiene (PM6)]]
| style="text-align: center;" | [[Media:st4215_DIOXOLE_OPTFREQ_PM6.LOG| 1,3-dioxole (PM6)]]
| style="text-align: center;" | [[Media:st4215_ENDO_TS_OPTFREQ_PM6.LOG| Endo-TS (PM6)]] <br> [[Media:st4215_ENDO_TS_IRC2_PM6ONPM6.LOG| IRC file]]
| style="text-align: center;" | [[Media:st4215_ENDO_PDT_OPTFREQ_PM6.LOG| Endo-product (PM6)]]
| style="text-align: center;" | [[Media:st4215_EXO_TS_OPTFREQ_PM6.LOG| Exo-TS (PM6)]] <br> [[Media:st4215_EXO_TS_IRC_PM6ONPM6.LOG| IRC file]]
| style="text-align: center;" | [[Media:st4215_EXO_PDT_OPTFREQ_PM6.LOG| Exo-product(PM6)]]

|}

=== Molecular orbitals ===

==== Computed MOs ====
<small><i>Using your MO diagram for the Diels-Alder reaction, locate the occupied and unoccupied orbitals associated with the DA reaction for both TSs by symmetry. Find the relevant MOs and add them to your wiki (at an appropriate angle to show symmetry).</i></small>

The MOs involved in this reaction - the HOMOs and LUMOs for the reactants (cyclohexadiene and 1,3-dioxole), as well as the 4 MOs that these produce in each of the endo and exo transition states - are shown below. As determined in Exercise 1, which is also a Diels-Alder reaction, only orbitals of the same symmetry are able to interact. This is illustrated in the table below, where the symmetry or antisymmetry of each orbital can be clearly seen.

{| class="wikitable"
! rowspan="2"| Symmetry
! colspan="2" | Reactants
! colspan="2" rowspan="2"| Transition state (Endo)
! colspan="2" rowspan="2"| Transition state (Exo)
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
|-
| Antisymmmetric
| <b>MO 22</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXADIENE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 20</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26; mo 20; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_DIOXOLE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 40</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 40; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 43</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 43; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 40</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 43</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Symmetric
| <b>MO 23</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXADIENE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 19</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26; mo 19; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_DIOXOLE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 41</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 41; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 42</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 42; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 41</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 42</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

It is important to note that these MOs were generated from the B3LYP and not the PM6 calculation. While both calculation methods were used, the B3LYP calculation proved to be a better choice in visualising the MOs as it allowed us to see the symmetry of the orbitals more clearly, and corresponded more closely to the graphical representation of the orbitals in the MO diagram (see next section).

==== MO diagrams ====
<i><small>Construct a new MO diagram using these new orbitals, adjusting energy levels as necessary. Is this a normal or inverse demand DA reaction?</small></i>

MO diagrams for both the endo- and exo- Diels-Alder reactions were constructed as shown below. Energy levels of the MOs have been adjusted to reflect their actual values, as calculated in the B3LYP calculation.

{| class="wikitable"
! Endo- Diels-Alder
! Exo- Diels-Alder
|-
| [[File:st4215_Endo_MO_diagram.PNG|500px]]
| [[File:st4215_Exo_MO_diagram.PNG|500px]]
|}

From the MO diagrams above, we can conclude that both the endo- and exo- reactions are inverse demand DA reactions. In contrast to a normal electron demand DA reaction, where the diene is electron rich with a high LUMO and the dienophile is electron poor with a low HOMO, cyclohexadiene (the diene) is electron poor with a low HOMO and 1,3-dioxole (the dienophile) is electron rich with a high LUMO. Hence we can classify these reactions as inverse demand.

This is likely due to the nature of the dienophile, 1-3-dioxole, which has an electron-donating O atom. The lone pairs on the two adjacent O atoms are able to donate electron density into the double bond, making the dienophile more electron rich and raising the energy of its MOs, including its LUMO. In contrast, cyclohexadiene does not have any electron-donating substituents and is relatively electron poor. Hence, considering the Frontier Molecular Orbitals (FMOs), the LUMO<sub>dienophile</sub> is relatively high-energy and closer in energy to the low-energy HOMO<sub>diene</sub>, as compared to HOMO<sub>dienophile</sub> and LUMO<sub>diene</sub>. Thus the interaction between the LUMO<sub>dienophile</sub> and HOMO<sub>diene</sub> is the strongest and dominates in this reaction, causing it to be inverse demand.<ref name="inverse"/>

=== Energy analysis ===
<small><i>Tabulate the energies and determine the reaction barriers and reaction energies (in kJ/mol) at room temperature (the corrected energies are labelled "Sum of electronic and thermal Free Energies", corresponding to the Gibbs free energy). Which are the kinetically and thermodynamically favourable products? Look at the HOMO of the TSs. Are there any secondary orbital interactions or sterics that might affect the reaction barrier energy?</i></small>

==== Free energies ====
The free energy of the reactants as well as the endo- and exo- Diels-Alder transition states and products are tabulated below. The reaction barriers and energies are also calculated.

{| class="wikitable"
! rowspan="3" scope="col" style="width: 150px;" |
! colspan="4" scope="col" style="width: 500px;" | Energy at 298 K
|-
| colspan="2" style="text-align: center;" | B3LYP
| colspan="2" style="text-align: center;" | PM6
|-
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
|-
| colspan="5" style="background: #B7C3D0" | <b>Reactants</b>
|-
| Cyclohexadiene || style="text-align: center;" | -233.32 || style="text-align: center;" | -6.1259 x 10<sup>5</sup> || style="text-align: center;" | 0.11688 || style="text-align: center;" | 306.86
|-
| 1,3-dioxole || style="text-align: center;" | -267.07 || style="text-align: center;" | -7.0119 x 10<sup>5</sup> || style="text-align: center;" | -0.052279 || style="text-align: center;" | -137.26
|-
| Total reactants || style="text-align: center;" | -500.39 || style="text-align: center;" | -1.3138 x 10<sup>6</sup> || style="text-align: center;" | 0.064598 || style="text-align: center;" | 169.60
|-
| colspan="5" style="background: #B7C3D0" | <b>Endo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | -500.332 || style="text-align: center;" | -1.3136 x 10<sup>6</sup> || style="text-align: center;" | 0.13794 ||style="text-align: center;" | 362.17
|-
| Product || style="text-align: center;" | -500.419 || style="text-align: center;" | -1.3138 x 10<sup>6</sup> || style="text-align: center;" | 0.037807 || style="text-align: center;" | 99.26
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0609 || style="text-align: center;" | 160 || style="text-align: center;" | 0.0733 || style="text-align: center;" | 193
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0257 || style="text-align: center;" | -67.4 || style="text-align: center;" | -0.0268 || style="text-align: center;" | -70.3
|-
| colspan="5" style="background: #B7C3D0" | <b>Exo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | -500.329 || style="text-align: center;" | -1.3136 x 10<sup>6</sup> || style="text-align: center;" | 0.13890 || style="text-align: center;" | 364.68
|-
| Product || style="text-align: center;" | -500.417 || style="text-align: center;" | -1.3138 x 10<sup>6</sup> || style="text-align: center;" | 0.037977 || style="text-align: center;" | 99.71
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0639 || style="text-align: center;" | 168 || style="text-align: center;" | 0.0743 || style="text-align: center;" | 195
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0243 || style="text-align: center;" | -63.8 || style="text-align: center;" | -0.0266 || style="text-align: center;" | -69.9
|}
<small><i>^Note that all values from the calculations are reported to 5 s.f. unless more decimal places are needed to differentiate between endo- and exo- geometries. Derived quantities (reaction barrier and reaction energy) are reported to 3 s.f.</i></small>

==== Thermodynamic and kinetic products ====
From the table above, we can conclude that the endo- product is both the kinetic and thermodynamic product. This is because it has a lower reaction barrier, meaning that less activation energy is required for the reaction, making it the kinetic product. The endo- product also has a lower reaction energy (ΔG), meaning that the endo- product is lower in energy and more stable than the exo- product, hence making it the thermodynamic product.

This is in contrast to most Diels-Alder reactions, in which the exo- product is the thermodynamic product as it is less sterically hindered and more stable, while the endo- product is the kinetic product due to stabilising orbital interactions in the transition state.<ref name="fmo"/> However, the difference for this reaction can be explained.

As seen in the jmols below, the endo- TS indeed has stabilising secondary orbital interactions between the p orbitals of O in 1,3-dioxole and the p orbitals of C in cyclohexadiene, which are absent in the exo- TS. The presence of these interactions lower the energy of the transition state, hence lowering the reaction barrier and making the endo-product the kinetic product.

Comparing the endo- and exo- products, we can also see that these stabilising orbital interactions are also in present in the endo- product. Additionally, the endo- product is less sterically hindered compared to the exo-product, in which there is steric clash between the hydrogens which are pointing towards each other. These two factors cause the energy of the endo- product to be lower than that of the exo- product, hence lowering the reaction energy and making the endo- product the thermodynamic product as well.

{| class="wikitable"
!
! Endo
! Exo
|-
| Transition state
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 41; rotate x 90; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; rotate x 90; rotate y 180; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 41; rotate x 90; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>st4215_ENDO_PDT_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 41; rotate x 90; rotate y 180; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>st4215_EXO_PDT_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Conclusion ===
As per Exercise 1, MO calculations and visualisation for this Diels-Alder reaction prove that only orbitals with the same symmetry can overlap and interact, hence showing that this is not unique to a singular reaction. A closer examination of the MO diagram also allows us to determine that this reaction is an inverse electron demand DA reaction, due to the presence of electron-donating groups on the dienophile (1,3-dioxole) which raises the energy of its LUMO. Analysing the energy levels of the reactants, TSs and products also reveal that the endo- product is both the kinetic and thermodynamic product, due to greater stability of the transition state (due to stabilising secondary orbital interactions) and the final product (due to lesser steric clash).

== References ==
<references>
<ref name="inverse">D. Boger. <i>Progress in heterocyclic chemistry. (1st ed.).</i> (1989).</ref>
<ref name="fmo">I. Fleming. <i>Frontier Orbitals and Organic Chemical Reactions.</i> (1976).</ref>
</references>

Rep:Transition states (st4215): Exercise 2

2017-10-25T10:46:00Z

St4215: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
The reaction of cyclohexadiene and 1,3-dioxole is also a Diels-Alder reaction, in which cyclohexadiene is the diene and 1,3-dioxole is the dienophile. However, unlike the simple Diels-Alder reaction between butadiene and ethylene, this reaction is slightly more complex - 1,3-dioxole can approach the diene at different orientations, leading to the formation of the endo- and exo- Diels-Alder products. This can be seen in the reaction scheme below:
[[File:st4215_Ex2_reactionscheme.png|thumb|center|500px| Reaction of cyclohexadiene and 1,3-dioxole [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_exercise (Source)]]]

The endo- product is formed from a transition state where the substituents on the dienophile point towards the π system of the diene, while the exo- product is formed from a transition state where the substituents are pointing away.

In this exercise, we take a closer look at a different aspect of the Diels-Alder reaction - whether it is normal or inverse electron demand. We also consider the Diels-Alder reaction when an unsymmetrical diene is involved, and compare the endo- and exo- DA reactions in terms of which is more kinetically or thermodynamically favourable. In the process, we confirm that the orbital symmetry requirements as elucidated in Exercise 1 still apply, and illustrate that there are differences between the PM6 and B3LYP calculation methods, with one being more suitable than the other in this case.

=== Calculations ===
Calculations were performed at both the PM6 and B3LYP/6-31G(d) level. Method 2 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial#Method_2 tutorial]) was used to locate the transition state.

The optimised molecules can be seen here:

{| class="wikitable"
! rowspan="2" | Calculation method
! colspan="2" | Reactants
! colspan="2" | Endo
! colspan="2" | Exo
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-dioxole
| style="text-align: center;" | Transition state
| style="text-align: center;" | Product
| style="text-align: center;" | Transition state
| style="text-align: center;" | Product
|-
| style="text-align: center;" | B3LYP
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18</script>
<uploadedFileContents>st4215_CYCLOHEXADIENE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26</script>
<uploadedFileContents>st4215_DIOXOLE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18</script>
<uploadedFileContents>st4215_ENDO_PDT_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>st4215_EXO_PDT_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" | PM6
| style="text-align: center;" | [[Media:st4215_CYCLOHEXADIENE_OPTFREQ_PM6.LOG| Cyclohexadiene (PM6)]]
| style="text-align: center;" | [[Media:st4215_DIOXOLE_OPTFREQ_PM6.LOG| 1,3-dioxole (PM6)]]
| style="text-align: center;" | [[Media:st4215_ENDO_TS_OPTFREQ_PM6.LOG| Endo-TS (PM6)]] <br> [[Media:st4215_ENDO_TS_IRC2_PM6ONPM6.LOG| IRC file]]
| style="text-align: center;" | [[Media:st4215_ENDO_PDT_OPTFREQ_PM6.LOG| Endo-product (PM6)]]
| style="text-align: center;" | [[Media:st4215_EXO_TS_OPTFREQ_PM6.LOG| Exo-TS (PM6)]] <br> [[Media:st4215_EXO_TS_IRC_PM6ONPM6.LOG| IRC file]]
| style="text-align: center;" | [[Media:st4215_EXO_PDT_OPTFREQ_PM6.LOG| Exo-product(PM6)]]

|}

=== Molecular orbitals ===

==== Computed MOs ====
<small><i>Using your MO diagram for the Diels-Alder reaction, locate the occupied and unoccupied orbitals associated with the DA reaction for both TSs by symmetry. Find the relevant MOs and add them to your wiki (at an appropriate angle to show symmetry).</i></small>

The MOs involved in this reaction - the HOMOs and LUMOs for the reactants (cyclohexadiene and 1,3-dioxole), as well as the 4 MOs that these produce in each of the endo and exo transition states - are shown below. As determined in Exercise 1, which is also a Diels-Alder reaction, only orbitals of the same symmetry are able to interact. This is illustrated in the table below, where the symmetry or antisymmetry of each orbital can be clearly seen.

{| class="wikitable"
! rowspan="2"| Symmetry
! colspan="2" | Reactants
! colspan="2" rowspan="2"| Transition state (Endo)
! colspan="2" rowspan="2"| Transition state (Exo)
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
|-
| Antisymmmetric
| <b>MO 22</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXADIENE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 20</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26; mo 20; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_DIOXOLE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 40</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 40; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 43</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 43; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 40</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 43</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Symmetric
| <b>MO 23</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXADIENE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 19</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26; mo 19; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_DIOXOLE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 41</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 41; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 42</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 42; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 41</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 42</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

It is important to note that these MOs were generated from the B3LYP and not the PM6 calculation. While both calculation methods were used, the B3LYP calculation proved to be a better choice in visualising the MOs as it allowed us to see the symmetry of the orbitals more clearly, and corresponded more closely to the graphical representation of the orbitals in the MO diagram (see next section).

==== MO diagrams ====
<i><small>Construct a new MO diagram using these new orbitals, adjusting energy levels as necessary. Is this a normal or inverse demand DA reaction?</small></i>

MO diagrams for both the endo- and exo- Diels-Alder reactions were constructed as shown below. Energy levels of the MOs have been adjusted to reflect their actual values, as calculated in the B3LYP calculation.

{| class="wikitable"
! Endo- Diels-Alder
! Exo- Diels-Alder
|-
| [[File:st4215_Endo_MO_diagram.PNG|500px]]
| [[File:st4215_Exo_MO_diagram.PNG|500px]]
|}

From the MO diagrams above, we can conclude that both the endo- and exo- reactions are inverse demand DA reactions. In contrast to a normal electron demand DA reaction, where the diene is electron rich with a high LUMO and the dienophile is electron poor with a low HOMO, cyclohexadiene (the diene) is electron poor with a low HOMO and 1,3-dioxole (the dienophile) is electron rich with a high LUMO. Hence we can classify these reactions as inverse demand.

This is likely due to the nature of the dienophile, 1-3-dioxole, which has an electron-donating O atom. The lone pairs on the two adjacent O atoms are able to donate electron density into the double bond, making the dienophile more electron rich and raising the energy of its MOs, including its LUMO. In contrast, cyclohexadiene does not have any electron-donating substituents and is relatively electron poor. Hence, considering the Frontier Molecular Orbitals (FMOs), the LUMO<sub>dienophile</sub> is relatively high-energy and closer in energy to the low-energy HOMO<sub>diene</sub>, as compared to HOMO<sub>dienophile</sub> and LUMO<sub>diene</sub>. Thus the interaction between the LUMO<sub>dienophile</sub> and HOMO<sub>diene</sub> is the strongest and dominates in this reaction, causing it to be inverse demand.<ref name="inverse"/>

=== Energy analysis ===
<small><i>Tabulate the energies and determine the reaction barriers and reaction energies (in kJ/mol) at room temperature (the corrected energies are labelled "Sum of electronic and thermal Free Energies", corresponding to the Gibbs free energy). Which are the kinetically and thermodynamically favourable products? Look at the HOMO of the TSs. Are there any secondary orbital interactions or sterics that might affect the reaction barrier energy?</i></small>

==== Free energies ====
The free energy of the reactants as well as the endo- and exo- Diels-Alder transition states and products are tabulated below. The reaction barriers and energies are also calculated.

{| class="wikitable"
! rowspan="3" scope="col" style="width: 150px;" |
! colspan="4" scope="col" style="width: 500px;" | Energy at 298 K
|-
| colspan="2" style="text-align: center;" | B3LYP
| colspan="2" style="text-align: center;" | PM6
|-
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
|-
| colspan="5" style="background: #B7C3D0" | <b>Reactants</b>
|-
| Cyclohexadiene || style="text-align: center;" | -233.32 || style="text-align: center;" | -6.1259 x 10<sup>5</sup> || style="text-align: center;" | 0.11688 || style="text-align: center;" | 306.86
|-
| 1,3-dioxole || style="text-align: center;" | -267.07 || style="text-align: center;" | -7.0119 x 10<sup>5</sup> || style="text-align: center;" | -0.052279 || style="text-align: center;" | -137.26
|-
| Total reactants || style="text-align: center;" | -500.39 || style="text-align: center;" | -1.3138 x 10<sup>6</sup> || style="text-align: center;" | 0.064598 || style="text-align: center;" | 169.60
|-
| colspan="5" style="background: #B7C3D0" | <b>Endo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | -500.332 || style="text-align: center;" | -1.3136 x 10<sup>6</sup> || style="text-align: center;" | 0.13794 ||style="text-align: center;" | 362.17
|-
| Product || style="text-align: center;" | -500.419 || style="text-align: center;" | -1.3138 x 10<sup>6</sup> || style="text-align: center;" | 0.037807 || style="text-align: center;" | 99.26
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0609 || style="text-align: center;" | 160 || style="text-align: center;" | 0.0733 || style="text-align: center;" | 193
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0257 || style="text-align: center;" | -67.4 || style="text-align: center;" | -0.0268 || style="text-align: center;" | -70.3
|-
| colspan="5" style="background: #B7C3D0" | <b>Exo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | -500.329 || style="text-align: center;" | -1.3136 x 10<sup>6</sup> || style="text-align: center;" | 0.13890 || style="text-align: center;" | 364.68
|-
| Product || style="text-align: center;" | -500.417 || style="text-align: center;" | -1.3138 x 10<sup>6</sup> || style="text-align: center;" | 0.037977 || style="text-align: center;" | 99.71
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0639 || style="text-align: center;" | 168 || style="text-align: center;" | 0.0743 || style="text-align: center;" | 195
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0243 || style="text-align: center;" | -63.8 || style="text-align: center;" | -0.0266 || style="text-align: center;" | -69.9
|}
<small><i>^Note that all values from the calculations are reported to 5 s.f. unless more decimal places are needed to differentiate between endo- and exo- geometries. Derived quantities (reaction barrier and reaction energy) are reported to 3 s.f.</i></small>

==== Thermodynamic and kinetic products ====
From the table above, we can conclude that the endo- product is both the kinetic and thermodynamic product. This is because it has a lower reaction barrier, meaning that less activation energy is required for the reaction, making it the kinetic product. The endo- product also has a lower reaction energy (ΔG), meaning that the endo- product is lower in energy and more stable than the exo- product, hence making it the thermodynamic product.

This is in contrast to most Diels-Alder reactions, in which the exo- product is the thermodynamic product as it is less sterically hindered and more stable, while the endo- product is the kinetic product due to stabilising orbital interactions in the transition state.<ref name="fmo"/> However, the difference for this reaction can be explained.

As seen in the jmols below, the endo- TS indeed has stabilising secondary orbital interactions between the p orbitals of O in 1,3-dioxole and the p orbitals of C in cyclohexadiene, which are absent in the exo- TS. The presence of these interactions lower the energy of the transition state, hence lowering the reaction barrier and making the endo-product the kinetic product.

Comparing the endo- and exo- products, we can also see that these stabilising orbital interactions are also in present in the endo- product. Additionally, the endo- product is less sterically hindered compared to the exo-product, in which there is steric clash between the hydrogens which are pointing towards each other. These two factors cause the energy of the endo- product to be lower than that of the exo- product, hence lowering the reaction energy and making the endo- product the thermodynamic product as well.

{| class="wikitable"
!
! Endo
! Exo
|-
| Transition state
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 41; rotate x 90; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; rotate x 90; rotate y 180; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 41; rotate x 90; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>st4215_ENDO_PDT_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 41; rotate x 90; rotate y 180; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>st4215_EXO_PDT_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Conclusion ===
As per Exercise 1, MO calculations and visualisation for this Diels-Alder reaction prove that only orbitals with the same symmetry can overlap and interact, hence showing that this is not unique to a singular reaction. A closer examination of the MO diagram also allows us to determine that this reaction is an inverse electron demand DA reaction, due to the presence of electron-donating groups on the dienophile (1,3-dioxole) which raises the energy of its LUMO. Analysing the energy levels of the reactants, TSs and products also reveal that the endo- product is both the kinetic and thermodynamic product, due to greater stability of the transition state (due to stabilising secondary orbital interactions) and the final product (due to lesser steric clash).

== References ==
<references>
<ref name="inverse">D. Boger. <i>Progress in heterocyclic chemistry. (1st ed.).</i> (1989).</ref>
<ref name="fmo">I. Fleming. <i>Frontier Orbitals and Organic Chemical Reactions.</i> (1976).</ref>
</references>

Rep:Transition states (st4215): Exercise 2

2017-10-25T10:45:19Z

St4215: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

File:St4215 Ex2 reactionscheme.png

2017-10-25T10:44:14Z

St4215:

Rep:Transition states (st4215)

2017-10-25T10:43:03Z

St4215: /* Exercise 1: Reaction of Butadiene with Ethylene */

== Introduction ==
In a chemical reaction, reactants can change into the products via a multitude of different configurations of atoms, each with a different energy. These energies corresponds to a energy profile (when there is 1 degree of freedom), or a Potential Energy Surface (PES) (when there are two degrees of freedom). An example of the PES for a reaction can be seen below.

[[File:st4215_Pes.jpeg|thumb|250px|right| A possible potential energy surface (PES) for a reaction. (Source: [http://www.kf.elf.stuba.sk/~ballo/piatok/prezentacia/hartree-fock/hf_2.html Department of Physics, Slovak University of Technology in Bratislava])]]

As illustrated in the PES, the reactants and products correspond to energy minima - where energy increases in all directions, meaning that the reactants and products sit in a well. At this point, the gradient of the PES curve is zero, and the second derivative yields a positive value, indicating it is a minimum.

The reaction coordinate is hence the minimum energy pathway that leads from the reactants to the products, where the maximum energy along this pathway corresponds to the transition state. In terms of the PES, this corresponds to a first-order saddle point - where energy increases in all directions but one. At this point, the gradient of the PES curve is also zero - it is both a maximum and a minimum. However, the second derivative leads a negative value, indicating that energy is a maximum in one direction but a minimum in all other directions. This value is a negative force constant which corresponds to the imaginary frequency in the vibration spectrum of the transition state. The normal mode corresponding to this imaginary frequency usually show the relevant atoms of the reactants moving towards each other to form the product.

Hence the presence of a negative imaginary frequency in the transition state calculation confirms that the structure at a saddle point and hence corresponds to the transition state. However, energy minima where reactants and products lie should not contain any imaginary frequencies, as the second derivative only yields positive force constant values. The lack of imaginary frequencies in a frequency calculation can confirm that the structures lie in energy minima, and correspond to either the reactants or products.

In this module, computational methods were used to locate and characterise transition states for various pericyclic reactions, including Diels-Alder and cheletropic reactions. An overview of the various methods that were used in the calculations are detailed [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial here].

== Exercises ==
The instructions for the exercises can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_exercise here].

=== Exercise 1: Reaction of Butadiene with Ethylene ===
The reaction between butadiene and ethylene is a [4+2] cycloaddition reaction, or more specifically, a Diels-Alder reaction - a reaction involving a conjugated diene in the s-cis conformation, and a dienophile containing a double bond. In this simple Diels-Alder reaction, butadiene is the diene and ethylene is the dienophile. The reaction scheme for this reaction is shown below:
[[File:st4215_Ex1_reactionscheme.png|thumb|center|400px| Reaction of butadiene with ethylene [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_exercise (Source)]]]

In this exercise, we use this Diels-Alder reaction to determine the orbital symmetry requirements for a reaction to take place, and to show the effect of hybridisation and bond order on the length of C-C bonds. We also probe into the mechanism of the reaction, and determine if bond formation is synchronous or asynchronous.

The link to this completed exercise can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_states_(st4215):_Exercise_1 here].

=== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ===
The reaction of cyclohexadiene and 1,3-dioxole is also a Diels-Alder reaction, in which cyclohexadiene is the diene and 1,3-dioxole is the dienophile. However, unlike the simple Diels-Alder reaction between butadiene and ethylene, this reaction is slightly more complex - 1,3-dioxole can approach the diene at different orientations, leading to the formation of the endo- and exo- Diels-Alder products. This can be seen in the reaction scheme below:
(insert chemdraw diagram)

The endo- product is formed from a transition state where the substituents on the dienophile point towards the π system of the diene, while the exo- product is formed from a transition state where the substituents are pointing away.

In this exercise, we take a closer look at a different aspect of the Diels-Alder reaction - whether it is normal or inverse electron demand. We also consider the Diels-Alder reaction when an unsymmetrical diene is involved, and compare the endo- and exo- DA reactions in terms of which is more kinetically or thermodynamically favourable. In the process, we confirm that the orbital symmetry requirements as elucidated in Exercise 1 still apply, and illustrate that there are differences between the PM6 and B3LYP calculation methods, with one being more suitable than the other in this case.

The link to this completed exercise can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_states_(st4215):_Exercise_2 here].

=== Exercise 3: Diels-Alder vs Cheletropic ===
In this exercise, we examine the possible reactions between o-xylylene and SO<sub>2</sub> - the Diels-Alder reaction and the cheletropic reaction, as illustrated in the reaction scheme below.
(insert chemdraw diagram)

Again, in the Diels-Alder reaction, the dienophile SO<sub>2</sub> can approach the diene o-xylylene at different orientations, resulting in the endo- and exo- DA products. The cheletropic reaction, which is a pericyclic reaction in which the new bonds formed are made to the same atom, results in a single product.

In this exercise, we compare the three different reaction pathways - both Diels-Alder reactions and the cheletropic reaction - in terms of their reaction coordinates, as well as which is the most thermodynamically or kinetically favoured. We also investigate the possibility of a Diels-Alder reaction at a second site in xylylene.

The link to this completed exercise can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_states_(st4215):_Exercise_3 here].

== Conclusion ==
<small><i>Note: Please see each exercise for conclusions pertaining to that exercise</i></small><br>Computational methods allowed us to successfully examine the various pericyclic reactions, by locating and characterising their transition states via a variety of methods. In the process, we were able to determine the kinetic and thermodynamic products of each reaction, prove that orbitals must share the same symmetry in order to interact, and construct MO diagrams based on calculations, among others.

Rep:Transition states (st4215): Exercise 1

2017-10-25T10:42:13Z

St4215: /* Exercise 1: Reaction of Butadiene with Ethylene */

== Exercise 1: Reaction of Butadiene with Ethylene ==
The reaction between butadiene and ethylene is a [4+2] cycloaddition reaction, or more specifically, a Diels-Alder reaction - a reaction involving a conjugated diene in the s-cis conformation, and a dienophile containing a double bond. In this simple Diels-Alder reaction, butadiene is the diene and ethylene is the dienophile. The reaction scheme for this reaction is shown below:

[[File:st4215_Ex1_reactionscheme.png|thumb|center|400px| Reaction of butadiene with ethylene [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_exercise (Source)]]]

In this exercise, we use this Diels-Alder reaction to determine the orbital symmetry requirements for a reaction to take place, and to show the effect of hybridisation and bond order on the length of C-C bonds. We also probe into the mechanism of the reaction, and determine if bond formation is synchronous or asynchronous.

=== Calculations ===
Calculations were performed at the PM6 level. Method 1 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial#Method_1 tutorial]) was used to locate the transition state.

The optimised molecules can be seen here:

{| class="wikitable"
! colspan="2" | Reactants
! Transition state
! Product
|-
|<jmol>
<jmolApplet>
<title>Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_CYCLOHEXENE_TS_IRC3_PM6.LOG | IRC file]]
| <jmol>
<jmolApplet>
<title>Cyclohexene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_CYCLOHEXENE_PDT_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Molecular orbitals ===

==== MO diagram ====
<small><i>Construct an MO diagram for the formation of the butadiene/ethene TS, including basic symmetry labels (symmetric/antisymmetric or s/a).</i></small><br>

The MO diagram for this cycloaddition reaction was constructed as shown below. We first assume based on prior knowledge that only orbitals of the same symmetry can combine; however, this is proven in a later section.

The MOs have been labelled accordingly with their numbers according to the calculations, and can be visualised in the section below.<br>
[[File:st4215_ex1_MO_diagram.PNG]]

Considering the actual energy levels of the MOs computed from the calculations, a more accurate MO diagram can be constructed, as seen [[Media:st4215_ex1_MO_diagram_actual.PNG|here]]. However, this does not affect the relative energy levels of the MOs (within each molecule) or the interactions between these MOs.

==== Computed MOs ====
<small><i>Include images (or Jmol objects) for each of the HOMO and LUMO of butadiene and ethene, and the four MOs these produce for the TS. Correlate these MOs with the ones in your MO diagram to show which orbitals interact.</i></small><br>

The HOMOs and LUMOs for each reactant, butadiene and ethylene, as well as the 4 MOs that these produce for the TS, were calculated and can be visualised below. The MO numbers correspond to that labelled on the MO diagram, allowing us to see which orbitals interact. We can also observe that these computed MOs bear physical resemblance to that drawn in the MO diagram, in terms of the bonding and antibonding phases in each MO.

{| class="wikitable"
! rowspan="2" | Symmetry
! colspan="2" | Reactants
! rowspan="2" colspan="2"| Transition state
|-
| style="text-align: center;" | Butadiene
| style="text-align: center;" | Ethylene
|-
| Antisymmetric
| <b>MO 11</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 7</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 16</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 19</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Symmetric
| <b>MO 12</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 6</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 17</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 18</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Symmetry requirements ====
<small><i>What can you conclude about the requirements for symmetry for a reaction (when is a reaction 'allowed' and when is it 'forbidden')? Write whether the orbital overlap integral is zero or non-zero for the case of a symmetric-antisymmetric interaction, a symmetric-symmetric interaction and an antisymmetric-antisymmetric interaction.</i></small><br>

From the table above as well as the MO diagram, we can see that the HOMO/LUMO of butadiene interact with the corresponding LUMO/HOMO in ethylene respectively. These interactions can occur as each pair of orbitals share the same symmetry. The HOMO of butadiene (MO 11) and the LUMO of ethylene (MO 7) are both antisymmetric, and interact to give two antisymmetric MOs in the TS (MOs 16 and 19). Similarly, the LUMO of ethylene (MO 12) and the HOMO of butadiene (MO 6) are both symmetric, and interact to give two symmetric MOs in the TS (MOs 17 and 18). Hence we can conclude that a reaction is only allowed when the relevant orbitals share the same symmetry, as this would allow orbitals to overlap and thus interact. This is illustrated in the following table:

{| class="wikitable"
! Symmetry of interaction
! Orbital overlap integral
|-
| style="text-align: center;" | Symmetric-antisymmetric
| style="text-align: center;" | Zero
|-
| style="text-align: center;" | Symmetric-symmetric
| style="text-align: center;" | Non-zero
|-
| style="text-align: center;" | Antisymmetric-antisymmetric
| style="text-align: center;" | Non-zero
|}

=== C-C bond lengths ===
<small><i>Include measurements of the 4 C-C bond lengths of the reactants and the 6 C-C bond lengths of the TS and products. How do the bond lengths change as the reaction progresses? What are typical sp3 and sp2 C-C bond lengths? What is the Van der Waals radius of the C atom? How does this compare with the length of the partly formed C-C bonds in the TS.</i></small>

The C-C bond lengths in the reactants, TS and products are tabulated below.

{| class="wikitable"
! rowspan="2" colspan="2" |
! colspan="2" | Reactants
! rowspan="2" | Transition state
! rowspan="2" | Product
|-
| style="text-align: center;" | Butadiene
| style="text-align: center;" | Ethylene
|-
| colspan="2" style="text-align: center;"| Labelled C atoms
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7; label display</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4; label display</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>st4215_CYCLOHEXENE_PDT_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| rowspan="6" style="text-align: center;" | C-C bond<br> length / Å
| style="width: 50px;" | Bond A || <center> C1-C4: 1.34 </center>|| || <center> C1-C4: 1.38 </center> || <center> C1-C4: 1.50 </center>
|-
| Bond B || <center> C4-C6: 1.47 </center> || || <center> C4-C6: 1.41 </center> || <center> C4-C6: 1.34 </center>
|-
| Bond C || <center> C6-C7: 1.34 </center> || || <center> C6-C7: 1.38 </center> || <center> C6-C7: 1.50 </center>
|-
| Bond D || || <center> C1-C4: 1.33 </center> || <center> C11-C14: 1.38 </center> || <center> C11-C14: 1.54 </center>
|-
| Bond E || || || <center> C7-C14: 2.11 </center> || <center> C7-C14: 1.54 </center>
|-
| Bond F || || || <center> C1-C11: 2.11 </center> || <center> C1-C11: 1.54 </center>
|}

From the values above, we can observe the following changes in bond length as the reaction progresses.

{| class="wikitable" style="width: 750px;"
! Bond
! Trend in bond length as reaction progresses
! Graph
|-
| A || As the reaction progresses, the length of Bond A increases. This is because Bond A is initially a C=C double bond in butadiene, which becomes a sp<sup>2</sup>-sp<sup>3</sup> C-C single bond in cyclohexene. These lengths are similar to typical values of 1.34 Å for alkenes and 1.50 Å sp<sup>2</sup>-sp<sup>3</sup> C-C bonds.<ref name="bondlength"/>
| [[File:st4215_BondA.JPG|200px]]
|-
| B || As the reaction progresses, the length of Bond B decreases. This is because Bond B is initially an sp<sup>2</sup>-sp<sup>2</sup> C-C single bond in butadiene, which becomes a C=C double bond in cyclohexene. These lengths are similar to typical values of 1.47 Å for sp<sup>2</sup>-sp<sup>2</sup> C-C bonds and 1.34 Å for alkenes.<ref name="bondlength"/>
| [[File:st4215_BondB.JPG|200px]]
|-
| C || Similar to Bond A, as the reaction progresses, the length of Bond C increases. This is due to the same reason as explained for Bond A.
| [[File:st4215_BondC.JPG|200px]]
|-
| D || As the reaction progresses, the length of Bond D increases. This is because Bond B is initially an C=C single bond in ethylene, which becomes a sp<sup>3</sup>-sp<sup>3</sup> C-C single bond in cyclohexene. These lengths are similar to typical values of 1.34 Å for alkenes and 1.54 Å for sp<sup>3</sup>-sp<sup>3</sup> C-C bonds.<ref name="bondlength"/>
| [[File:st4215_BondD.JPG|200px]]
|-
| E || Bond E is formed in this reaction. Hence as the reaction progresses from the transition state to the product, the length of Bond E increases. The length of the fully formed Bond E in the product, an sp<sup>3</sup>-sp<sup>3</sup> C-C single bond, corresponds to the typical value of 1.54 Å.<ref name="bondlength"/> The distance between the C atoms in the TS (2.11 Å) falls between twice the van der Waal radius of C (2 x 1.70 Å<ref name="vdw_c"/> = 3.40 Å) and the length of the fully formed Bond E, indicating that the atoms are approaching each other.
| [[File:st4215_BondE.JPG|200px]]
|-
| F || Like Bond E, Bond F is also formed in this reaction. Hence as the reaction progresses from the transition state to the product, the length of Bond F increases, due to the same reasons as explained above.
| [[File:st4215_BondF.JPG|200px]]
|}

We can hence conclude that bond lengths in the reactants and product do not deviate from typical values. Additionally, we can also show that an increase in bond order from 1 to 2 indeed shortens the C-C bond, while an increase in hybridisation from sp<sup>2</sup> to sp<sup>3</sup> does lengthen the C-C bond, as seen in the comparison of theoretical values.

=== Transition state ===
<i><small>Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous?</small></i>
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 7; rotate x -40; select atomno=1, atomno=7, atomno=11, atomno=14; label display </script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
<name>cyclohexeneTS</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>cyclohexeneTS</target>
</jmolbutton>
<jmolbutton>
<script>measure 1 11; measure 7 14</script>
<text>C-C Distances</text>
<target>cyclohexeneTS</target>
</jmolbutton>
</jmol>
<br><br>
As illustrated above, the formation of the two bonds are synchronous as the relevant pairs of atoms (C1/C11 and C7/C14) are moving towards each other at the same time, with the distance between the two atoms being approximately equal in both pairs. This is to be expected as evidence shows that the Diels-Alder reaction can proceed via a concerted, synchronous mechanism.<ref name="DA_1"/> However, it is important to note that this may also be the result of the calculation method used, as studies with other calculation methods (DFT/B3LYP) have also shown that other mechanisms are feasible.<ref name="DA_2"/>

=== Conclusion ===
By examining this simple Diels-Alder reaction between butadiene and ethylene, we can conclude from computational data that only orbitals need to share the same symmetry to be able to overlap and hence interact. This knowledge will be useful in Exercise 2, where we again construct a MO diagram for a another Diels-Alder reaction. By following the change in C-C bond lengths over the course of the reaction, it can also be concluded that as per theoretical data, bond lengths shorten when bond order increases and hybridisation decreases. Lastly, based on this calculation, we can conclude that the Diels-Alder reaction between butadiene and ethylene proceeds via synchronous bond formation in the transition state.

== References ==
<references>
<ref name="bondlength">M. A. Fox, J. K. Whitesell, E. Buchholz. <i>Organische Chemie: Grundlagen, Mechanismen, bioorganische Anwendungen</i> (1995).</ref>
<ref name="vdw_c">A. Bondi. [http://pubs.acs.org/doi/pdf/10.1021/j100785a001 <i>van der Waals Volumes and Radii </i>] J. Phys. Chem. <b>68</b>(3), 441–451 (1996).</ref>
<ref name="DA_1">K. N. Houk, Y. T Lin & F. K. Brown. [http://pubs.acs.org/doi/pdf/10.1021/ja00263a059 <i>Evidence for the Concerted Mechanism of the Diels-Alder Reaction of Butadiene with Ethylene.</i>] J. Am. Chem. SOC. <b>108</b>, 554-556 (1986).</ref>
<ref name="DA_2">E. Goldstein, B. Beno & K. N. Houk. [http://pubs.acs.org/doi/pdf/10.1021/ja9601494 <i>Density Functional Theory Prediction of the Relative Energies and Isotope Effects for the Concerted and Stepwise Mechanisms of the Diels-Alder Reaction of Butadiene and Ethylene</i>] J. Am. Chem. Soc. <b>118</b>, 6036-6043 (1996).
</ref>
</references>

Rep:Transition states (st4215): Exercise 1

2017-10-25T10:41:46Z

St4215: /* Exercise 1: Reaction of Butadiene with Ethylene */

== Exercise 1: Reaction of Butadiene with Ethylene ==
The reaction between butadiene and ethylene is a [4+2] cycloaddition reaction, or more specifically, a Diels-Alder reaction - a reaction involving a conjugated diene in the s-cis conformation, and a dienophile containing a double bond. In this simple Diels-Alder reaction, butadiene is the diene and ethylene is the dienophile. The reaction scheme for this reaction is shown below:

[[File:st4215_Ex1_reactionscheme.png|thumb|center| Reaction of butadiene with ethylene [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_exercise (Source)]]]<br>

In this exercise, we use this Diels-Alder reaction to determine the orbital symmetry requirements for a reaction to take place, and to show the effect of hybridisation and bond order on the length of C-C bonds. We also probe into the mechanism of the reaction, and determine if bond formation is synchronous or asynchronous.

=== Calculations ===
Calculations were performed at the PM6 level. Method 1 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial#Method_1 tutorial]) was used to locate the transition state.

The optimised molecules can be seen here:

{| class="wikitable"
! colspan="2" | Reactants
! Transition state
! Product
|-
|<jmol>
<jmolApplet>
<title>Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_CYCLOHEXENE_TS_IRC3_PM6.LOG | IRC file]]
| <jmol>
<jmolApplet>
<title>Cyclohexene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_CYCLOHEXENE_PDT_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Molecular orbitals ===

==== MO diagram ====
<small><i>Construct an MO diagram for the formation of the butadiene/ethene TS, including basic symmetry labels (symmetric/antisymmetric or s/a).</i></small><br>

The MO diagram for this cycloaddition reaction was constructed as shown below. We first assume based on prior knowledge that only orbitals of the same symmetry can combine; however, this is proven in a later section.

The MOs have been labelled accordingly with their numbers according to the calculations, and can be visualised in the section below.<br>
[[File:st4215_ex1_MO_diagram.PNG]]

Considering the actual energy levels of the MOs computed from the calculations, a more accurate MO diagram can be constructed, as seen [[Media:st4215_ex1_MO_diagram_actual.PNG|here]]. However, this does not affect the relative energy levels of the MOs (within each molecule) or the interactions between these MOs.

==== Computed MOs ====
<small><i>Include images (or Jmol objects) for each of the HOMO and LUMO of butadiene and ethene, and the four MOs these produce for the TS. Correlate these MOs with the ones in your MO diagram to show which orbitals interact.</i></small><br>

The HOMOs and LUMOs for each reactant, butadiene and ethylene, as well as the 4 MOs that these produce for the TS, were calculated and can be visualised below. The MO numbers correspond to that labelled on the MO diagram, allowing us to see which orbitals interact. We can also observe that these computed MOs bear physical resemblance to that drawn in the MO diagram, in terms of the bonding and antibonding phases in each MO.

{| class="wikitable"
! rowspan="2" | Symmetry
! colspan="2" | Reactants
! rowspan="2" colspan="2"| Transition state
|-
| style="text-align: center;" | Butadiene
| style="text-align: center;" | Ethylene
|-
| Antisymmetric
| <b>MO 11</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 7</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 16</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 19</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Symmetric
| <b>MO 12</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 6</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 17</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 18</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Symmetry requirements ====
<small><i>What can you conclude about the requirements for symmetry for a reaction (when is a reaction 'allowed' and when is it 'forbidden')? Write whether the orbital overlap integral is zero or non-zero for the case of a symmetric-antisymmetric interaction, a symmetric-symmetric interaction and an antisymmetric-antisymmetric interaction.</i></small><br>

From the table above as well as the MO diagram, we can see that the HOMO/LUMO of butadiene interact with the corresponding LUMO/HOMO in ethylene respectively. These interactions can occur as each pair of orbitals share the same symmetry. The HOMO of butadiene (MO 11) and the LUMO of ethylene (MO 7) are both antisymmetric, and interact to give two antisymmetric MOs in the TS (MOs 16 and 19). Similarly, the LUMO of ethylene (MO 12) and the HOMO of butadiene (MO 6) are both symmetric, and interact to give two symmetric MOs in the TS (MOs 17 and 18). Hence we can conclude that a reaction is only allowed when the relevant orbitals share the same symmetry, as this would allow orbitals to overlap and thus interact. This is illustrated in the following table:

{| class="wikitable"
! Symmetry of interaction
! Orbital overlap integral
|-
| style="text-align: center;" | Symmetric-antisymmetric
| style="text-align: center;" | Zero
|-
| style="text-align: center;" | Symmetric-symmetric
| style="text-align: center;" | Non-zero
|-
| style="text-align: center;" | Antisymmetric-antisymmetric
| style="text-align: center;" | Non-zero
|}

=== C-C bond lengths ===
<small><i>Include measurements of the 4 C-C bond lengths of the reactants and the 6 C-C bond lengths of the TS and products. How do the bond lengths change as the reaction progresses? What are typical sp3 and sp2 C-C bond lengths? What is the Van der Waals radius of the C atom? How does this compare with the length of the partly formed C-C bonds in the TS.</i></small>

The C-C bond lengths in the reactants, TS and products are tabulated below.

{| class="wikitable"
! rowspan="2" colspan="2" |
! colspan="2" | Reactants
! rowspan="2" | Transition state
! rowspan="2" | Product
|-
| style="text-align: center;" | Butadiene
| style="text-align: center;" | Ethylene
|-
| colspan="2" style="text-align: center;"| Labelled C atoms
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7; label display</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4; label display</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>st4215_CYCLOHEXENE_PDT_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| rowspan="6" style="text-align: center;" | C-C bond<br> length / Å
| style="width: 50px;" | Bond A || <center> C1-C4: 1.34 </center>|| || <center> C1-C4: 1.38 </center> || <center> C1-C4: 1.50 </center>
|-
| Bond B || <center> C4-C6: 1.47 </center> || || <center> C4-C6: 1.41 </center> || <center> C4-C6: 1.34 </center>
|-
| Bond C || <center> C6-C7: 1.34 </center> || || <center> C6-C7: 1.38 </center> || <center> C6-C7: 1.50 </center>
|-
| Bond D || || <center> C1-C4: 1.33 </center> || <center> C11-C14: 1.38 </center> || <center> C11-C14: 1.54 </center>
|-
| Bond E || || || <center> C7-C14: 2.11 </center> || <center> C7-C14: 1.54 </center>
|-
| Bond F || || || <center> C1-C11: 2.11 </center> || <center> C1-C11: 1.54 </center>
|}

From the values above, we can observe the following changes in bond length as the reaction progresses.

{| class="wikitable" style="width: 750px;"
! Bond
! Trend in bond length as reaction progresses
! Graph
|-
| A || As the reaction progresses, the length of Bond A increases. This is because Bond A is initially a C=C double bond in butadiene, which becomes a sp<sup>2</sup>-sp<sup>3</sup> C-C single bond in cyclohexene. These lengths are similar to typical values of 1.34 Å for alkenes and 1.50 Å sp<sup>2</sup>-sp<sup>3</sup> C-C bonds.<ref name="bondlength"/>
| [[File:st4215_BondA.JPG|200px]]
|-
| B || As the reaction progresses, the length of Bond B decreases. This is because Bond B is initially an sp<sup>2</sup>-sp<sup>2</sup> C-C single bond in butadiene, which becomes a C=C double bond in cyclohexene. These lengths are similar to typical values of 1.47 Å for sp<sup>2</sup>-sp<sup>2</sup> C-C bonds and 1.34 Å for alkenes.<ref name="bondlength"/>
| [[File:st4215_BondB.JPG|200px]]
|-
| C || Similar to Bond A, as the reaction progresses, the length of Bond C increases. This is due to the same reason as explained for Bond A.
| [[File:st4215_BondC.JPG|200px]]
|-
| D || As the reaction progresses, the length of Bond D increases. This is because Bond B is initially an C=C single bond in ethylene, which becomes a sp<sup>3</sup>-sp<sup>3</sup> C-C single bond in cyclohexene. These lengths are similar to typical values of 1.34 Å for alkenes and 1.54 Å for sp<sup>3</sup>-sp<sup>3</sup> C-C bonds.<ref name="bondlength"/>
| [[File:st4215_BondD.JPG|200px]]
|-
| E || Bond E is formed in this reaction. Hence as the reaction progresses from the transition state to the product, the length of Bond E increases. The length of the fully formed Bond E in the product, an sp<sup>3</sup>-sp<sup>3</sup> C-C single bond, corresponds to the typical value of 1.54 Å.<ref name="bondlength"/> The distance between the C atoms in the TS (2.11 Å) falls between twice the van der Waal radius of C (2 x 1.70 Å<ref name="vdw_c"/> = 3.40 Å) and the length of the fully formed Bond E, indicating that the atoms are approaching each other.
| [[File:st4215_BondE.JPG|200px]]
|-
| F || Like Bond E, Bond F is also formed in this reaction. Hence as the reaction progresses from the transition state to the product, the length of Bond F increases, due to the same reasons as explained above.
| [[File:st4215_BondF.JPG|200px]]
|}

We can hence conclude that bond lengths in the reactants and product do not deviate from typical values. Additionally, we can also show that an increase in bond order from 1 to 2 indeed shortens the C-C bond, while an increase in hybridisation from sp<sup>2</sup> to sp<sup>3</sup> does lengthen the C-C bond, as seen in the comparison of theoretical values.

=== Transition state ===
<i><small>Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous?</small></i>
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 7; rotate x -40; select atomno=1, atomno=7, atomno=11, atomno=14; label display </script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
<name>cyclohexeneTS</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>cyclohexeneTS</target>
</jmolbutton>
<jmolbutton>
<script>measure 1 11; measure 7 14</script>
<text>C-C Distances</text>
<target>cyclohexeneTS</target>
</jmolbutton>
</jmol>
<br><br>
As illustrated above, the formation of the two bonds are synchronous as the relevant pairs of atoms (C1/C11 and C7/C14) are moving towards each other at the same time, with the distance between the two atoms being approximately equal in both pairs. This is to be expected as evidence shows that the Diels-Alder reaction can proceed via a concerted, synchronous mechanism.<ref name="DA_1"/> However, it is important to note that this may also be the result of the calculation method used, as studies with other calculation methods (DFT/B3LYP) have also shown that other mechanisms are feasible.<ref name="DA_2"/>

=== Conclusion ===
By examining this simple Diels-Alder reaction between butadiene and ethylene, we can conclude from computational data that only orbitals need to share the same symmetry to be able to overlap and hence interact. This knowledge will be useful in Exercise 2, where we again construct a MO diagram for a another Diels-Alder reaction. By following the change in C-C bond lengths over the course of the reaction, it can also be concluded that as per theoretical data, bond lengths shorten when bond order increases and hybridisation decreases. Lastly, based on this calculation, we can conclude that the Diels-Alder reaction between butadiene and ethylene proceeds via synchronous bond formation in the transition state.

== References ==
<references>
<ref name="bondlength">M. A. Fox, J. K. Whitesell, E. Buchholz. <i>Organische Chemie: Grundlagen, Mechanismen, bioorganische Anwendungen</i> (1995).</ref>
<ref name="vdw_c">A. Bondi. [http://pubs.acs.org/doi/pdf/10.1021/j100785a001 <i>van der Waals Volumes and Radii </i>] J. Phys. Chem. <b>68</b>(3), 441–451 (1996).</ref>
<ref name="DA_1">K. N. Houk, Y. T Lin & F. K. Brown. [http://pubs.acs.org/doi/pdf/10.1021/ja00263a059 <i>Evidence for the Concerted Mechanism of the Diels-Alder Reaction of Butadiene with Ethylene.</i>] J. Am. Chem. SOC. <b>108</b>, 554-556 (1986).</ref>
<ref name="DA_2">E. Goldstein, B. Beno & K. N. Houk. [http://pubs.acs.org/doi/pdf/10.1021/ja9601494 <i>Density Functional Theory Prediction of the Relative Energies and Isotope Effects for the Concerted and Stepwise Mechanisms of the Diels-Alder Reaction of Butadiene and Ethylene</i>] J. Am. Chem. Soc. <b>118</b>, 6036-6043 (1996).
</ref>
</references>

Rep:Transition states (st4215): Exercise 1

2017-10-25T10:41:08Z

St4215: /* Exercise 1: Reaction of Butadiene with Ethylene */

== Exercise 1: Reaction of Butadiene with Ethylene ==
The reaction between butadiene and ethylene is a [4+2] cycloaddition reaction, or more specifically, a Diels-Alder reaction - a reaction involving a conjugated diene in the s-cis conformation, and a dienophile containing a double bond. In this simple Diels-Alder reaction, butadiene is the diene and ethylene is the dienophile. The reaction scheme for this reaction is shown below:

[[File:st4215_Ex1_reactionscheme.png|thumb|center| Reaction of butadiene with ethylene [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_exercise (Source)]]]

In this exercise, we use this Diels-Alder reaction to determine the orbital symmetry requirements for a reaction to take place, and to show the effect of hybridisation and bond order on the length of C-C bonds. We also probe into the mechanism of the reaction, and determine if bond formation is synchronous or asynchronous.

=== Calculations ===
Calculations were performed at the PM6 level. Method 1 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial#Method_1 tutorial]) was used to locate the transition state.

The optimised molecules can be seen here:

{| class="wikitable"
! colspan="2" | Reactants
! Transition state
! Product
|-
|<jmol>
<jmolApplet>
<title>Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_CYCLOHEXENE_TS_IRC3_PM6.LOG | IRC file]]
| <jmol>
<jmolApplet>
<title>Cyclohexene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_CYCLOHEXENE_PDT_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Molecular orbitals ===

==== MO diagram ====
<small><i>Construct an MO diagram for the formation of the butadiene/ethene TS, including basic symmetry labels (symmetric/antisymmetric or s/a).</i></small><br>

The MO diagram for this cycloaddition reaction was constructed as shown below. We first assume based on prior knowledge that only orbitals of the same symmetry can combine; however, this is proven in a later section.

The MOs have been labelled accordingly with their numbers according to the calculations, and can be visualised in the section below.<br>
[[File:st4215_ex1_MO_diagram.PNG]]

Considering the actual energy levels of the MOs computed from the calculations, a more accurate MO diagram can be constructed, as seen [[Media:st4215_ex1_MO_diagram_actual.PNG|here]]. However, this does not affect the relative energy levels of the MOs (within each molecule) or the interactions between these MOs.

==== Computed MOs ====
<small><i>Include images (or Jmol objects) for each of the HOMO and LUMO of butadiene and ethene, and the four MOs these produce for the TS. Correlate these MOs with the ones in your MO diagram to show which orbitals interact.</i></small><br>

The HOMOs and LUMOs for each reactant, butadiene and ethylene, as well as the 4 MOs that these produce for the TS, were calculated and can be visualised below. The MO numbers correspond to that labelled on the MO diagram, allowing us to see which orbitals interact. We can also observe that these computed MOs bear physical resemblance to that drawn in the MO diagram, in terms of the bonding and antibonding phases in each MO.

{| class="wikitable"
! rowspan="2" | Symmetry
! colspan="2" | Reactants
! rowspan="2" colspan="2"| Transition state
|-
| style="text-align: center;" | Butadiene
| style="text-align: center;" | Ethylene
|-
| Antisymmetric
| <b>MO 11</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 7</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 16</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 19</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Symmetric
| <b>MO 12</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 6</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 17</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 18</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Symmetry requirements ====
<small><i>What can you conclude about the requirements for symmetry for a reaction (when is a reaction 'allowed' and when is it 'forbidden')? Write whether the orbital overlap integral is zero or non-zero for the case of a symmetric-antisymmetric interaction, a symmetric-symmetric interaction and an antisymmetric-antisymmetric interaction.</i></small><br>

From the table above as well as the MO diagram, we can see that the HOMO/LUMO of butadiene interact with the corresponding LUMO/HOMO in ethylene respectively. These interactions can occur as each pair of orbitals share the same symmetry. The HOMO of butadiene (MO 11) and the LUMO of ethylene (MO 7) are both antisymmetric, and interact to give two antisymmetric MOs in the TS (MOs 16 and 19). Similarly, the LUMO of ethylene (MO 12) and the HOMO of butadiene (MO 6) are both symmetric, and interact to give two symmetric MOs in the TS (MOs 17 and 18). Hence we can conclude that a reaction is only allowed when the relevant orbitals share the same symmetry, as this would allow orbitals to overlap and thus interact. This is illustrated in the following table:

{| class="wikitable"
! Symmetry of interaction
! Orbital overlap integral
|-
| style="text-align: center;" | Symmetric-antisymmetric
| style="text-align: center;" | Zero
|-
| style="text-align: center;" | Symmetric-symmetric
| style="text-align: center;" | Non-zero
|-
| style="text-align: center;" | Antisymmetric-antisymmetric
| style="text-align: center;" | Non-zero
|}

=== C-C bond lengths ===
<small><i>Include measurements of the 4 C-C bond lengths of the reactants and the 6 C-C bond lengths of the TS and products. How do the bond lengths change as the reaction progresses? What are typical sp3 and sp2 C-C bond lengths? What is the Van der Waals radius of the C atom? How does this compare with the length of the partly formed C-C bonds in the TS.</i></small>

The C-C bond lengths in the reactants, TS and products are tabulated below.

{| class="wikitable"
! rowspan="2" colspan="2" |
! colspan="2" | Reactants
! rowspan="2" | Transition state
! rowspan="2" | Product
|-
| style="text-align: center;" | Butadiene
| style="text-align: center;" | Ethylene
|-
| colspan="2" style="text-align: center;"| Labelled C atoms
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7; label display</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4; label display</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>st4215_CYCLOHEXENE_PDT_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| rowspan="6" style="text-align: center;" | C-C bond<br> length / Å
| style="width: 50px;" | Bond A || <center> C1-C4: 1.34 </center>|| || <center> C1-C4: 1.38 </center> || <center> C1-C4: 1.50 </center>
|-
| Bond B || <center> C4-C6: 1.47 </center> || || <center> C4-C6: 1.41 </center> || <center> C4-C6: 1.34 </center>
|-
| Bond C || <center> C6-C7: 1.34 </center> || || <center> C6-C7: 1.38 </center> || <center> C6-C7: 1.50 </center>
|-
| Bond D || || <center> C1-C4: 1.33 </center> || <center> C11-C14: 1.38 </center> || <center> C11-C14: 1.54 </center>
|-
| Bond E || || || <center> C7-C14: 2.11 </center> || <center> C7-C14: 1.54 </center>
|-
| Bond F || || || <center> C1-C11: 2.11 </center> || <center> C1-C11: 1.54 </center>
|}

From the values above, we can observe the following changes in bond length as the reaction progresses.

{| class="wikitable" style="width: 750px;"
! Bond
! Trend in bond length as reaction progresses
! Graph
|-
| A || As the reaction progresses, the length of Bond A increases. This is because Bond A is initially a C=C double bond in butadiene, which becomes a sp<sup>2</sup>-sp<sup>3</sup> C-C single bond in cyclohexene. These lengths are similar to typical values of 1.34 Å for alkenes and 1.50 Å sp<sup>2</sup>-sp<sup>3</sup> C-C bonds.<ref name="bondlength"/>
| [[File:st4215_BondA.JPG|200px]]
|-
| B || As the reaction progresses, the length of Bond B decreases. This is because Bond B is initially an sp<sup>2</sup>-sp<sup>2</sup> C-C single bond in butadiene, which becomes a C=C double bond in cyclohexene. These lengths are similar to typical values of 1.47 Å for sp<sup>2</sup>-sp<sup>2</sup> C-C bonds and 1.34 Å for alkenes.<ref name="bondlength"/>
| [[File:st4215_BondB.JPG|200px]]
|-
| C || Similar to Bond A, as the reaction progresses, the length of Bond C increases. This is due to the same reason as explained for Bond A.
| [[File:st4215_BondC.JPG|200px]]
|-
| D || As the reaction progresses, the length of Bond D increases. This is because Bond B is initially an C=C single bond in ethylene, which becomes a sp<sup>3</sup>-sp<sup>3</sup> C-C single bond in cyclohexene. These lengths are similar to typical values of 1.34 Å for alkenes and 1.54 Å for sp<sup>3</sup>-sp<sup>3</sup> C-C bonds.<ref name="bondlength"/>
| [[File:st4215_BondD.JPG|200px]]
|-
| E || Bond E is formed in this reaction. Hence as the reaction progresses from the transition state to the product, the length of Bond E increases. The length of the fully formed Bond E in the product, an sp<sup>3</sup>-sp<sup>3</sup> C-C single bond, corresponds to the typical value of 1.54 Å.<ref name="bondlength"/> The distance between the C atoms in the TS (2.11 Å) falls between twice the van der Waal radius of C (2 x 1.70 Å<ref name="vdw_c"/> = 3.40 Å) and the length of the fully formed Bond E, indicating that the atoms are approaching each other.
| [[File:st4215_BondE.JPG|200px]]
|-
| F || Like Bond E, Bond F is also formed in this reaction. Hence as the reaction progresses from the transition state to the product, the length of Bond F increases, due to the same reasons as explained above.
| [[File:st4215_BondF.JPG|200px]]
|}

We can hence conclude that bond lengths in the reactants and product do not deviate from typical values. Additionally, we can also show that an increase in bond order from 1 to 2 indeed shortens the C-C bond, while an increase in hybridisation from sp<sup>2</sup> to sp<sup>3</sup> does lengthen the C-C bond, as seen in the comparison of theoretical values.

=== Transition state ===
<i><small>Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous?</small></i>
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 7; rotate x -40; select atomno=1, atomno=7, atomno=11, atomno=14; label display </script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
<name>cyclohexeneTS</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>cyclohexeneTS</target>
</jmolbutton>
<jmolbutton>
<script>measure 1 11; measure 7 14</script>
<text>C-C Distances</text>
<target>cyclohexeneTS</target>
</jmolbutton>
</jmol>
<br><br>
As illustrated above, the formation of the two bonds are synchronous as the relevant pairs of atoms (C1/C11 and C7/C14) are moving towards each other at the same time, with the distance between the two atoms being approximately equal in both pairs. This is to be expected as evidence shows that the Diels-Alder reaction can proceed via a concerted, synchronous mechanism.<ref name="DA_1"/> However, it is important to note that this may also be the result of the calculation method used, as studies with other calculation methods (DFT/B3LYP) have also shown that other mechanisms are feasible.<ref name="DA_2"/>

=== Conclusion ===
By examining this simple Diels-Alder reaction between butadiene and ethylene, we can conclude from computational data that only orbitals need to share the same symmetry to be able to overlap and hence interact. This knowledge will be useful in Exercise 2, where we again construct a MO diagram for a another Diels-Alder reaction. By following the change in C-C bond lengths over the course of the reaction, it can also be concluded that as per theoretical data, bond lengths shorten when bond order increases and hybridisation decreases. Lastly, based on this calculation, we can conclude that the Diels-Alder reaction between butadiene and ethylene proceeds via synchronous bond formation in the transition state.

== References ==
<references>
<ref name="bondlength">M. A. Fox, J. K. Whitesell, E. Buchholz. <i>Organische Chemie: Grundlagen, Mechanismen, bioorganische Anwendungen</i> (1995).</ref>
<ref name="vdw_c">A. Bondi. [http://pubs.acs.org/doi/pdf/10.1021/j100785a001 <i>van der Waals Volumes and Radii </i>] J. Phys. Chem. <b>68</b>(3), 441–451 (1996).</ref>
<ref name="DA_1">K. N. Houk, Y. T Lin & F. K. Brown. [http://pubs.acs.org/doi/pdf/10.1021/ja00263a059 <i>Evidence for the Concerted Mechanism of the Diels-Alder Reaction of Butadiene with Ethylene.</i>] J. Am. Chem. SOC. <b>108</b>, 554-556 (1986).</ref>
<ref name="DA_2">E. Goldstein, B. Beno & K. N. Houk. [http://pubs.acs.org/doi/pdf/10.1021/ja9601494 <i>Density Functional Theory Prediction of the Relative Energies and Isotope Effects for the Concerted and Stepwise Mechanisms of the Diels-Alder Reaction of Butadiene and Ethylene</i>] J. Am. Chem. Soc. <b>118</b>, 6036-6043 (1996).
</ref>
</references>

File:St4215 Ex1 reactionscheme.png

2017-10-25T10:39:10Z

St4215:

Rep:Transition states (st4215)

2017-10-25T10:34:50Z

St4215: /* Conclusion */

== Introduction ==
In a chemical reaction, reactants can change into the products via a multitude of different configurations of atoms, each with a different energy. These energies corresponds to a energy profile (when there is 1 degree of freedom), or a Potential Energy Surface (PES) (when there are two degrees of freedom). An example of the PES for a reaction can be seen below.

[[File:st4215_Pes.jpeg|thumb|250px|right| A possible potential energy surface (PES) for a reaction. (Source: [http://www.kf.elf.stuba.sk/~ballo/piatok/prezentacia/hartree-fock/hf_2.html Department of Physics, Slovak University of Technology in Bratislava])]]

As illustrated in the PES, the reactants and products correspond to energy minima - where energy increases in all directions, meaning that the reactants and products sit in a well. At this point, the gradient of the PES curve is zero, and the second derivative yields a positive value, indicating it is a minimum.

The reaction coordinate is hence the minimum energy pathway that leads from the reactants to the products, where the maximum energy along this pathway corresponds to the transition state. In terms of the PES, this corresponds to a first-order saddle point - where energy increases in all directions but one. At this point, the gradient of the PES curve is also zero - it is both a maximum and a minimum. However, the second derivative leads a negative value, indicating that energy is a maximum in one direction but a minimum in all other directions. This value is a negative force constant which corresponds to the imaginary frequency in the vibration spectrum of the transition state. The normal mode corresponding to this imaginary frequency usually show the relevant atoms of the reactants moving towards each other to form the product.

Hence the presence of a negative imaginary frequency in the transition state calculation confirms that the structure at a saddle point and hence corresponds to the transition state. However, energy minima where reactants and products lie should not contain any imaginary frequencies, as the second derivative only yields positive force constant values. The lack of imaginary frequencies in a frequency calculation can confirm that the structures lie in energy minima, and correspond to either the reactants or products.

In this module, computational methods were used to locate and characterise transition states for various pericyclic reactions, including Diels-Alder and cheletropic reactions. An overview of the various methods that were used in the calculations are detailed [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial here].

== Exercises ==
The instructions for the exercises can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_exercise here].

=== Exercise 1: Reaction of Butadiene with Ethylene ===
The reaction between butadiene and ethylene is a [4+2] cycloaddition reaction, or more specifically, a Diels-Alder reaction - a reaction involving a conjugated diene in the s-cis conformation, and a dienophile containing a double bond. In this simple Diels-Alder reaction, butadiene is the diene and ethylene is the dienophile. The reaction scheme for this reaction is shown below:
(insert chemdraw diagram)

In this exercise, we use this Diels-Alder reaction to determine the orbital symmetry requirements for a reaction to take place, and to show the effect of hybridisation and bond order on the length of C-C bonds. We also probe into the mechanism of the reaction, and determine if bond formation is synchronous or asynchronous.

The link to this completed exercise can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_states_(st4215):_Exercise_1 here].

=== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ===
The reaction of cyclohexadiene and 1,3-dioxole is also a Diels-Alder reaction, in which cyclohexadiene is the diene and 1,3-dioxole is the dienophile. However, unlike the simple Diels-Alder reaction between butadiene and ethylene, this reaction is slightly more complex - 1,3-dioxole can approach the diene at different orientations, leading to the formation of the endo- and exo- Diels-Alder products. This can be seen in the reaction scheme below:
(insert chemdraw diagram)

The endo- product is formed from a transition state where the substituents on the dienophile point towards the π system of the diene, while the exo- product is formed from a transition state where the substituents are pointing away.

In this exercise, we take a closer look at a different aspect of the Diels-Alder reaction - whether it is normal or inverse electron demand. We also consider the Diels-Alder reaction when an unsymmetrical diene is involved, and compare the endo- and exo- DA reactions in terms of which is more kinetically or thermodynamically favourable. In the process, we confirm that the orbital symmetry requirements as elucidated in Exercise 1 still apply, and illustrate that there are differences between the PM6 and B3LYP calculation methods, with one being more suitable than the other in this case.

The link to this completed exercise can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_states_(st4215):_Exercise_2 here].

=== Exercise 3: Diels-Alder vs Cheletropic ===
In this exercise, we examine the possible reactions between o-xylylene and SO<sub>2</sub> - the Diels-Alder reaction and the cheletropic reaction, as illustrated in the reaction scheme below.
(insert chemdraw diagram)

Again, in the Diels-Alder reaction, the dienophile SO<sub>2</sub> can approach the diene o-xylylene at different orientations, resulting in the endo- and exo- DA products. The cheletropic reaction, which is a pericyclic reaction in which the new bonds formed are made to the same atom, results in a single product.

In this exercise, we compare the three different reaction pathways - both Diels-Alder reactions and the cheletropic reaction - in terms of their reaction coordinates, as well as which is the most thermodynamically or kinetically favoured. We also investigate the possibility of a Diels-Alder reaction at a second site in xylylene.

The link to this completed exercise can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_states_(st4215):_Exercise_3 here].

== Conclusion ==
<small><i>Note: Please see each exercise for conclusions pertaining to that exercise</i></small><br>Computational methods allowed us to successfully examine the various pericyclic reactions, by locating and characterising their transition states via a variety of methods. In the process, we were able to determine the kinetic and thermodynamic products of each reaction, prove that orbitals must share the same symmetry in order to interact, and construct MO diagrams based on calculations, among others.

Rep:Transition states (st4215)

2017-10-25T10:33:43Z

St4215:

== Introduction ==
In a chemical reaction, reactants can change into the products via a multitude of different configurations of atoms, each with a different energy. These energies corresponds to a energy profile (when there is 1 degree of freedom), or a Potential Energy Surface (PES) (when there are two degrees of freedom). An example of the PES for a reaction can be seen below.

[[File:st4215_Pes.jpeg|thumb|250px|right| A possible potential energy surface (PES) for a reaction. (Source: [http://www.kf.elf.stuba.sk/~ballo/piatok/prezentacia/hartree-fock/hf_2.html Department of Physics, Slovak University of Technology in Bratislava])]]

As illustrated in the PES, the reactants and products correspond to energy minima - where energy increases in all directions, meaning that the reactants and products sit in a well. At this point, the gradient of the PES curve is zero, and the second derivative yields a positive value, indicating it is a minimum.

The reaction coordinate is hence the minimum energy pathway that leads from the reactants to the products, where the maximum energy along this pathway corresponds to the transition state. In terms of the PES, this corresponds to a first-order saddle point - where energy increases in all directions but one. At this point, the gradient of the PES curve is also zero - it is both a maximum and a minimum. However, the second derivative leads a negative value, indicating that energy is a maximum in one direction but a minimum in all other directions. This value is a negative force constant which corresponds to the imaginary frequency in the vibration spectrum of the transition state. The normal mode corresponding to this imaginary frequency usually show the relevant atoms of the reactants moving towards each other to form the product.

Hence the presence of a negative imaginary frequency in the transition state calculation confirms that the structure at a saddle point and hence corresponds to the transition state. However, energy minima where reactants and products lie should not contain any imaginary frequencies, as the second derivative only yields positive force constant values. The lack of imaginary frequencies in a frequency calculation can confirm that the structures lie in energy minima, and correspond to either the reactants or products.

In this module, computational methods were used to locate and characterise transition states for various pericyclic reactions, including Diels-Alder and cheletropic reactions. An overview of the various methods that were used in the calculations are detailed [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial here].

== Exercises ==
The instructions for the exercises can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_exercise here].

=== Exercise 1: Reaction of Butadiene with Ethylene ===
The reaction between butadiene and ethylene is a [4+2] cycloaddition reaction, or more specifically, a Diels-Alder reaction - a reaction involving a conjugated diene in the s-cis conformation, and a dienophile containing a double bond. In this simple Diels-Alder reaction, butadiene is the diene and ethylene is the dienophile. The reaction scheme for this reaction is shown below:
(insert chemdraw diagram)

In this exercise, we use this Diels-Alder reaction to determine the orbital symmetry requirements for a reaction to take place, and to show the effect of hybridisation and bond order on the length of C-C bonds. We also probe into the mechanism of the reaction, and determine if bond formation is synchronous or asynchronous.

The link to this completed exercise can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_states_(st4215):_Exercise_1 here].

=== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ===
The reaction of cyclohexadiene and 1,3-dioxole is also a Diels-Alder reaction, in which cyclohexadiene is the diene and 1,3-dioxole is the dienophile. However, unlike the simple Diels-Alder reaction between butadiene and ethylene, this reaction is slightly more complex - 1,3-dioxole can approach the diene at different orientations, leading to the formation of the endo- and exo- Diels-Alder products. This can be seen in the reaction scheme below:
(insert chemdraw diagram)

The endo- product is formed from a transition state where the substituents on the dienophile point towards the π system of the diene, while the exo- product is formed from a transition state where the substituents are pointing away.

In this exercise, we take a closer look at a different aspect of the Diels-Alder reaction - whether it is normal or inverse electron demand. We also consider the Diels-Alder reaction when an unsymmetrical diene is involved, and compare the endo- and exo- DA reactions in terms of which is more kinetically or thermodynamically favourable. In the process, we confirm that the orbital symmetry requirements as elucidated in Exercise 1 still apply, and illustrate that there are differences between the PM6 and B3LYP calculation methods, with one being more suitable than the other in this case.

The link to this completed exercise can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_states_(st4215):_Exercise_2 here].

=== Exercise 3: Diels-Alder vs Cheletropic ===
In this exercise, we examine the possible reactions between o-xylylene and SO<sub>2</sub> - the Diels-Alder reaction and the cheletropic reaction, as illustrated in the reaction scheme below.
(insert chemdraw diagram)

Again, in the Diels-Alder reaction, the dienophile SO<sub>2</sub> can approach the diene o-xylylene at different orientations, resulting in the endo- and exo- DA products. The cheletropic reaction, which is a pericyclic reaction in which the new bonds formed are made to the same atom, results in a single product.

In this exercise, we compare the three different reaction pathways - both Diels-Alder reactions and the cheletropic reaction - in terms of their reaction coordinates, as well as which is the most thermodynamically or kinetically favoured. We also investigate the possibility of a Diels-Alder reaction at a second site in xylylene.

The link to this completed exercise can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_states_(st4215):_Exercise_3 here].

== Conclusion ==
Computational methods allowed us to successfully examine the various pericyclic reactions, by locating and characterising their transition states via a variety of methods. In the process, we were able to determine the kinetic and thermodynamic products of each reaction, prove that orbitals must share the same symmetry in order to interact, and construct MO diagrams based on calculations, among others.

Rep:Transition states (st4215)

2017-10-25T10:22:33Z

St4215: /* Exercises */

== Introduction ==
In a chemical reaction, reactants can change into the products via a multitude of different configurations of atoms, each with a different energy. These energies corresponds to a energy profile (when there is 1 degree of freedom), or a Potential Energy Surface (PES) (when there are two degrees of freedom). An example of the PES for a reaction can be seen below.

[[File:st4215_Pes.jpeg|thumb|250px|right| A possible potential energy surface (PES) for a reaction. (Source: [http://www.kf.elf.stuba.sk/~ballo/piatok/prezentacia/hartree-fock/hf_2.html Department of Physics, Slovak University of Technology in Bratislava])]]

As illustrated in the PES, the reactants and products correspond to energy minima - where energy increases in all directions, meaning that the reactants and products sit in a well. At this point, the gradient of the PES curve is zero, and the second derivative yields a positive value, indicating it is a minimum.

The reaction coordinate is hence the minimum energy pathway that leads from the reactants to the products, where the maximum energy along this pathway corresponds to the transition state. In terms of the PES, this corresponds to a first-order saddle point - where energy increases in all directions but one. At this point, the gradient of the PES curve is also zero - it is both a maximum and a minimum. However, the second derivative leads a negative value, indicating that energy is a maximum in one direction but a minimum in all other directions. This value is a negative force constant which corresponds to the imaginary frequency in the vibration spectrum of the transition state. The normal mode corresponding to this imaginary frequency usually show the relevant atoms of the reactants moving towards each other to form the product.

Hence the presence of a negative imaginary frequency in the transition state calculation confirms that the structure at a saddle point and hence corresponds to the transition state. However, energy minima where reactants and products lie should not contain any imaginary frequencies, as the second derivative only yields positive force constant values. The lack of imaginary frequencies in a frequency calculation can confirm that the structures lie in energy minima, and correspond to either the reactants or products.

In this module, computational methods were used to locate and characterise transition states for various pericyclic reactions, including Diels-Alder and cheletropic reactions. An overview of the various methods that were used in the calculations are detailed [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial here].

== Exercises ==
The instructions for the exercises can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_exercise here].

=== Exercise 1: Reaction of Butadiene with Ethylene ===
The reaction between butadiene and ethylene is a [4+2] cycloaddition reaction, or more specifically, a Diels-Alder reaction - a reaction involving a conjugated diene in the s-cis conformation, and a dienophile containing a double bond. In this simple Diels-Alder reaction, butadiene is the diene and ethylene is the dienophile. The reaction scheme for this reaction is shown below:
(insert chemdraw diagram)

In this exercise, we use this Diels-Alder reaction to determine the orbital symmetry requirements for a reaction to take place, and to show the effect of hybridisation and bond order on the length of C-C bonds. We also probe into the mechanism of the reaction, and determine if bond formation is synchronous or asynchronous.

The link to this completed exercise can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_states_(st4215):_Exercise_1 here].

=== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ===
The reaction of cyclohexadiene and 1,3-dioxole is also a Diels-Alder reaction, in which cyclohexadiene is the diene and 1,3-dioxole is the dienophile. However, unlike the simple Diels-Alder reaction between butadiene and ethylene, this reaction is slightly more complex - 1,3-dioxole can approach the diene at different orientations, leading to the formation of the endo- and exo- Diels-Alder products. This can be seen in the reaction scheme below:
(insert chemdraw diagram)

The endo- product is formed from a transition state where the substituents on the dienophile point towards the π system of the diene, while the exo- product is formed from a transition state where the substituents are pointing away.

In this exercise, we take a closer look at a different aspect of the Diels-Alder reaction - whether it is normal or inverse electron demand. We also consider the Diels-Alder reaction when an unsymmetrical diene is involved, and compare the endo- and exo- DA reactions in terms of which is more kinetically or thermodynamically favourable. In the process, we confirm that the orbital symmetry requirements as elucidated in Exercise 1 still apply, and illustrate that there are differences between the PM6 and B3LYP calculation methods, with one being more suitable than the other in this case.

The link to this completed exercise can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_states_(st4215):_Exercise_2 here].

=== Exercise 3: Diels-Alder vs Cheletropic ===
In this exercise, we examine the possible reactions between o-xylylene and SO<sub>2</sub> - the Diels-Alder reaction and the cheletropic reaction, as illustrated in the reaction scheme below.
(insert chemdraw diagram)

Again, in the Diels-Alder reaction, the dienophile SO<sub>2</sub> can approach the diene o-xylylene at different orientations, resulting in the endo- and exo- DA products. The cheletropic reaction, which is a pericyclic reaction in which the new bonds formed are made to the same atom, results in a single product.

In this exercise, we compare the three different reaction pathways - both Diels-Alder reactions and the cheletropic reaction - in terms of their reaction coordinates, as well as which is the most thermodynamically or kinetically favoured. We also investigate the possibility of a Diels-Alder reaction at a second site in xylylene.

The link to this completed exercise can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_states_(st4215):_Exercise_3 here].

Rep:Transition states (st4215)

2017-10-25T10:20:52Z

St4215:

== Introduction ==
In a chemical reaction, reactants can change into the products via a multitude of different configurations of atoms, each with a different energy. These energies corresponds to a energy profile (when there is 1 degree of freedom), or a Potential Energy Surface (PES) (when there are two degrees of freedom). An example of the PES for a reaction can be seen below.

[[File:st4215_Pes.jpeg|thumb|250px|right| A possible potential energy surface (PES) for a reaction. (Source: [http://www.kf.elf.stuba.sk/~ballo/piatok/prezentacia/hartree-fock/hf_2.html Department of Physics, Slovak University of Technology in Bratislava])]]

As illustrated in the PES, the reactants and products correspond to energy minima - where energy increases in all directions, meaning that the reactants and products sit in a well. At this point, the gradient of the PES curve is zero, and the second derivative yields a positive value, indicating it is a minimum.

The reaction coordinate is hence the minimum energy pathway that leads from the reactants to the products, where the maximum energy along this pathway corresponds to the transition state. In terms of the PES, this corresponds to a first-order saddle point - where energy increases in all directions but one. At this point, the gradient of the PES curve is also zero - it is both a maximum and a minimum. However, the second derivative leads a negative value, indicating that energy is a maximum in one direction but a minimum in all other directions. This value is a negative force constant which corresponds to the imaginary frequency in the vibration spectrum of the transition state. The normal mode corresponding to this imaginary frequency usually show the relevant atoms of the reactants moving towards each other to form the product.

Hence the presence of a negative imaginary frequency in the transition state calculation confirms that the structure at a saddle point and hence corresponds to the transition state. However, energy minima where reactants and products lie should not contain any imaginary frequencies, as the second derivative only yields positive force constant values. The lack of imaginary frequencies in a frequency calculation can confirm that the structures lie in energy minima, and correspond to either the reactants or products.

In this module, computational methods were used to locate and characterise transition states for various pericyclic reactions, including Diels-Alder and cheletropic reactions. An overview of the various methods that were used in the calculations are detailed [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial here].

== Exercises ==

=== Exercise 1: Reaction of Butadiene with Ethylene ===
The reaction between butadiene and ethylene is a [4+2] cycloaddition reaction, or more specifically, a Diels-Alder reaction - a reaction involving a conjugated diene in the s-cis conformation, and a dienophile containing a double bond. In this simple Diels-Alder reaction, butadiene is the diene and ethylene is the dienophile. The reaction scheme for this reaction is shown below:
(insert chemdraw diagram)

In this exercise, we use this Diels-Alder reaction to determine the orbital symmetry requirements for a reaction to take place, and to show the effect of hybridisation and bond order on the length of C-C bonds. We also probe into the mechanism of the reaction, and determine if bond formation is synchronous or asynchronous.

The link to this completed exercise can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_states_(st4215):_Exercise_1 here].

=== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ===
The reaction of cyclohexadiene and 1,3-dioxole is also a Diels-Alder reaction, in which cyclohexadiene is the diene and 1,3-dioxole is the dienophile. However, unlike the simple Diels-Alder reaction between butadiene and ethylene, this reaction is slightly more complex - 1,3-dioxole can approach the diene at different orientations, leading to the formation of the endo- and exo- Diels-Alder products. This can be seen in the reaction scheme below:
(insert chemdraw diagram)

The endo- product is formed from a transition state where the substituents on the dienophile point towards the π system of the diene, while the exo- product is formed from a transition state where the substituents are pointing away.

In this exercise, we take a closer look at a different aspect of the Diels-Alder reaction - whether it is normal or inverse electron demand. We also consider the Diels-Alder reaction when an unsymmetrical diene is involved, and compare the endo- and exo- DA reactions in terms of which is more kinetically or thermodynamically favourable. In the process, we confirm that the orbital symmetry requirements as elucidated in Exercise 1 still apply, and illustrate that there are differences between the PM6 and B3LYP calculation methods, with one being more suitable than the other in this case.

The link to this completed exercise can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_states_(st4215):_Exercise_2 here].

=== Exercise 3: Diels-Alder vs Cheletropic ===
In this exercise, we examine the possible reactions between o-xylylene and SO<sub>2</sub> - the Diels-Alder reaction and the cheletropic reaction, as illustrated in the reaction scheme below.
(insert chemdraw diagram)

Again, in the Diels-Alder reaction, the dienophile SO<sub>2</sub> can approach the diene o-xylylene at different orientations, resulting in the endo- and exo- DA products. The cheletropic reaction, which is a pericyclic reaction in which the new bonds formed are made to the same atom, results in a single product.

In this exercise, we compare the three different reaction pathways - both Diels-Alder reactions and the cheletropic reaction - in terms of their reaction coordinates, as well as which is the most thermodynamically or kinetically favoured. We also investigate the possibility of a Diels-Alder reaction at a second site in xylylene.

The link to this completed exercise can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_states_(st4215):_Exercise_3 here].

Rep:Transition states (st4215): Exercise 3

2017-10-25T10:17:37Z

St4215: /* Thermodynamic and kinetic products */

== Exercise 3: Diels-Alder vs Cheletropic ==
In this exercise, we examine the possible reactions between o-xylylene and SO<sub>2</sub> - the Diels-Alder reaction and the cheletropic reaction, as illustrated in the reaction scheme below.
(insert chemdraw diagram)

Again, in the Diels-Alder reaction, the dienophile SO<sub>2</sub> can approach the diene o-xylylene at different orientations, resulting in the endo- and exo- DA products. The cheletropic reaction, which is a pericyclic reaction in which the new bonds formed are made to the same atom, results in a single product.

In this exercise, we compare the three different reaction pathways - both Diels-Alder reactions and the cheletropic reaction - in terms of their reaction coordinates, as well as which is the most thermodynamically or kinetically favoured. We also investigate the possibility of a Diels-Alder reaction at a second site in xylylene.

=== Calculations ===
Calculations were performed at the PM6 level. Method 3 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial#Method_3 tutorial]) was used to locate the transition state.

The optimised molecules can be seen here:

{| class="wikitable"
! colspan="2" | Reactants
|-
| style="text-align: center;" | o-xylylene
| style="text-align: center;" | SO<sub>2</sub>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16</script>
<uploadedFileContents>st4215_XYLYLENE_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16</script>
<uploadedFileContents>st4215_SO2_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo || style="text-align: center;" | Exo
|-
| style="text-align: center;" | Transition state
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>St4215_ex3_ENDO_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_ex3_ENDO_TS_IRC2_PM6.LOG | IRC file]]
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>st4215_ex3_Exo_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_ex3_Exo_TS_IRC_PM6.LOG | IRC file]]
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>st4215_ex3_CHEL_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_ex3_CHEL_TS_IRC_PM6.LOG | IRC file]]
|-
| style="text-align: center;" | Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>St4215_ex3_ENDO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>st4215_ex3_EXO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>st4215_ex3_CHEL_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Reaction coordinate ===
<small><i>Visualise the reaction coordinate with an IRC calculation for each path. Include a .gif file in the wiki of these IRCs.</i></small>

The formation of the products for each of the endo- and exo- Diels-Alder reactions, as well as the cheletropic reaction, can be visualised below.

{| class="wikitable"
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
|-
| [[File:st4215_ENDO_TS_IRCmovie.gif]]
| [[File:st4215_Exo_TS_IRCmovie.gif]]
| [[File:st4215_Chel_TS_IRCmovie.gif]]
|}

We can see that SO<sub>2</sub> approaches xylylene at a different orientation and angle for each of these reactions. This difference in approach trajectories hence lead to the formation of different products.

It can also be observed that in each of the reactions, as the product is formed, the 6-membered ring in xylylene becomes aromatic. This means that there is a strong driving force for the formation of the products. In contrast, the reactant xylylene is highly unstable as it is non-aromatic, and as can be seen in these reactions, can readily react with unsaturated bonds to form a more stable aromatic product.

=== Energy analysis ===
<small><i>Calculate the activation and reaction energies (converting to kJ/mol) for each step as in Exercise 2 to determine which route is preferred. Using Excel or Chemdraw, draw a reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels-Alder reactions and the cheletropic reaction. You can set the 0 energy level to the reactants at infinite separation.</i></small>

==== Free energies ====
The free energies of the reactants, transition states and products for each of the 3 reactions are tabulated below. The reaction barriers and energies are also calculated.

{| class="wikitable"
! rowspan="2" scope="col" style="width: 150px;" |
! colspan="2" scope="col" style="width: 300px;" | Energy at 298 K (PM6)
|-
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
|-
| colspan="3" style="background: #B7C3D0" | <b>Reactants</b>
|-
| Xylylene || style="text-align: center;" | 0.17876 || style="text-align: center;" | 469.34
|-
| SO<sub>2</sub> || style="text-align: center;" | -0.11927 || style="text-align: center;" | -313.14
|-
| Total reactants || style="text-align: center;" | 0.059496 || style="text-align: center;" | 156.21
|-
| colspan="3" style="background: #B7C3D0" | <b>Endo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | 0.090560 || style="text-align: center;" | 237.77
|-
| Product || style="text-align: center;" | 0.021704 || style="text-align: center;" | 56.984
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0311 || style="text-align: center;" | 81.6
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0378 || style="text-align: center;" | -99.2
|-
| colspan="3" style="background: #B7C3D0" | <b>Exo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | 0.092078 || style="text-align: center;" | 241.75
|-
| Product || style="text-align: center;" | 0.021455 || style="text-align: center;" | 56.330
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0326 || style="text-align: center;" | 85.5
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0380 || style="text-align: center;" | -99.9
|-
| colspan="3" style="background: #B7C3D0" | <b>Cheletropic</b>
|-
| Transition state || style="text-align: center;" | 0.099058 || style="text-align: center;" | 260.08
|-
| Product || style="text-align: center;" | -0.000002 || style="text-align: center;" | -0.0052510
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0396 || style="text-align: center;" | 104
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0595 || style="text-align: center;" | -156
|}
<small><i>^Note that all values from the calculations are reported to 5 s.f. unless more decimal places are needed to differentiate between each reaction type. Derived quantities (reaction barrier and reaction energy) are reported to 3 s.f.</i></small>

==== Thermodynamic and kinetic products ====
From the values above, a combined reaction profile showing the reaction barriers and reaction energies can also be plotted as seen below.
[[File:st4215_ex3_Reaction_profile2.PNG|600px|thumb|center|Reaction profile diagram for the 3 Diels-Alder and cheletropic reactions, setting the energy of the reactants to zero]]

We can clearly see that the endo- Diels-Alder product is the kinetic product as it has the lowest reaction barrier of +81.6 kJmol<sup>-1</sup>, while the cheletropic product is the thermodynamic product as it is most stable as has the lowest energy of -156 kJmol<sup>-1</sup>. This is consistent with experimental and computational data.<ref name="chel_3"/><ref name="chel_1"/>

The high stability of the cheletropic product is likely due to its high symmetry, which minimises steric clash, as well as the preference of S to adopt a five-membered compared to 6-membered ring structure. This is in contrast to saturated carbon rings, where 6-membered cyclohexane is more stable than 5-membered cyclopentane due to deviation from tetrahedral bond angles of 109° in cyclopentane, resulting in angle strain. However, due to the larger size of the S atom, C-C<sub>tet</sub>-S bond angles in a 5-membered unsaturated sulfur ring (like in the cheletropic product) are much closer to the tetrahedral bond angle, at 105°. In comparison, the 6-membered heterocycle in the Diels-Alder products have C-C<sub>tet</sub>-S bond angles of around 114°, which are comparatively larger than 109°. This is illustrated below:

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
|-
| Products
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; measure 3 16 11</script>
<uploadedFileContents>St4215_ex3_ENDO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; rotate y 180; measure 3 16 11</script>
<uploadedFileContents>st4215_ex3_EXO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; measure 1 7 15</script>
<uploadedFileContents>st4215_ex3_CHEL_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

It is also expected that one of the Diels-Alder products (the endo- product) is the kinetic product instead of the cheletropic product.<ref name="chel_3"/> While the reaction barriers for both endo- and exo- Diels-Alder reactions are similar, the reaction barrier for the cheletropic reaction is much higher. Examining their transition states (see below) allows us to infer why.

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
|-
| Transition state HOMO
| style="text-align: center;" | [[File:st4215_ex3_Endo_TS_HOMO.PNG]]
| style="text-align: center;" | [[File:st4215_ex3_Exo_TS_HOMO.PNG]]
| style="text-align: center;" | [[File:st4215_ex3_Chel_TS_HOMO.PNG]]
|-
| Discussion
| colspan="2" | Some stabilising secondary orbital interactions can be seen in the HOMOs of the endo- and exo- transition states, hence lowering its energy and reducing the reaction barriers for these reactions.
| No stabilising secondary orbital interactions are present here - in fact, the HOMO of the transition state is highly antisymmetric with many nodes, and hence likely to be high in energy.
|}

Like most Diels-Alder reactions, the endo and not the exo- product is the kinetic product due to more or greater stabilising secondary orbital interactions in the transition state. However, in this reaction, both the endo- and exo- transition states seem to have an approximately equal but not significant amount of stabilising orbital interactions in the HOMO. This explains why the endo- and exo- transition states are relatively close in energy.

== Extra: Diels-Alder reaction at a different site ==
O-xylylene also contains a cis-butadiene fragment that can act as the diene in another Diels-Alder reaction. However, this reaction is very kinetically and thermodynamically favourable, as proven by computational methods.

=== Calculations ===
Calculations were performed at the PM6 level. Method 3 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial#Method_3 tutorial]) was used to locate the transition state.

The optimised molecules can be seen here. Optimised reactants (o-xylylene and SO<sub>2</sub>) from the earlier reaction were used.

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder (2)
|-
| style="text-align: center;" | Endo || style="text-align: center;" | Exo
|-
| style="text-align: center;" | Transition state
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>st4215_BAD_ENDO_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_BAD_ENDO_IRC_PM6.LOG | IRC file]]
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>st4215_BAD_EXO_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_BAD_EXO_IRC_PM6.LOG | IRC file]]
|-
| style="text-align: center;" | Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 64</script>
<uploadedFileContents>st4215_BAD_ENDO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_BAD_EXO_PDT_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Energy analysis ===
The free energies of the reactants, transition states and products for both the endo- and exo- Diels Alder reactions are tabulated below. The reaction barriers and energies are also calculated.

{| class="wikitable"
! rowspan="2" scope="col" style="width: 150px;" |
! colspan="2" scope="col" style="width: 300px;" | Energy at 298 K (PM6)
|-
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
|-
| colspan="3" style="background: #B7C3D0" | <b>Reactants</b>
|-
| Xylylene || style="text-align: center;" | 0.17876 || style="text-align: center;" | 469.34
|-
| SO<sub>2</sub> || style="text-align: center;" | -0.11927 || style="text-align: center;" | -313.14
|-
| Total reactants || style="text-align: center;" | 0.059496 || style="text-align: center;" | 156.21
|-
| colspan="3" style="background: #B7C3D0" | <b>Endo- Diels-Alder (2)</b>
|-
| Transition state || style="text-align: center;" | 0.10207 || style="text-align: center;" | 267.99
|-
| Product || style="text-align: center;" | 0.065613 || style="text-align: center;" | 172.27
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0426 || style="text-align: center;" | 112
|-
| Reaction energy (ΔG) || style="text-align: center;" | +0.00612 || style="text-align: center;" | +16.1
|-
| colspan="3" style="background: #B7C3D0" | <b>Exo- Diels-Alder (2)</b>
|-
| Transition state || style="text-align: center;" | 0.10505 || style="text-align: center;" | 275.82
|-
| Product || style="text-align: center;" | 0.067305 || style="text-align: center;" | 176.71
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0456 || style="text-align: center;" | 120
|-
| Reaction energy (ΔG) || style="text-align: center;" | +0.00781 || style="text-align: center;" | +20.5
|}
<small><i>^Note that all values from the calculations are reported to 5 s.f. unless more decimal places are needed to differentiate between each reaction type. Derived quantities (reaction barrier and reaction energy) are reported to 3 s.f.</i></small>

We can hence see that this reaction is both kinetically and thermodynamically unfavourable compared to the other Diels-Alder reaction (previously discussed) and the cheletropic reaction.

Comparing the reaction barriers, the activation energies of 112 kJmol<sup>-1</sup> (endo) and 120 kJmol<sup>-1</sup> (exo) are much higher than that of the other DA reaction, at 81.6 kJmol<sup>-1</sup> (endo) and 85.5 kJmol<sup>-1</sup> (exo), as well as the cheletropic reaction, at 104 kJmol<sup>-1</sup>. Hence this Diels-Alder reaction is the most kinetically unfavourable reaction.

Comparing the reaction energies, we can see that both the endo- and exo- reactions are endothermic - compared to the other two DA reactions as well as the cheletropic reaction, which are exothermic. This indicates that this Diels-Alder reaction is also highly thermodynamically unfavourable as ΔG<0 and it is not spontaneous.

=== Conclusion ===
While there are several possible reactions between o-xylylene and SO<sub>2</sub>, including a Diels-Alder reaction at two different sites and a cheletropic reaction, not all are comparable in terms of kinetic and thermodynamic favourability. Calculations show that the cheletropic reaction is the most thermodynamically favoured due to the higher stability of a 5-membered S ring, and the Diels-Alder reaction between the two terminal alkene carbons of xylylene is much more kinetically and thermodynamically favourable compared to the Diels-Alder reaction involving the cis-butadiene fragment in the aromatic 6-membered ring. This is because the aromaticity of the ring is not broken in the former reaction.

== References ==

<references>
<ref name="chel_1">F. Monnat, P. Vogel, J. A. Sordo. [http://onlinelibrary.wiley.com/doi/10.1002/1522-2675(200203)85:3%3C712::AID-HLCA712%3E3.0.CO;2-5/epdf <i>Hetero-Diels-Alder and Cheletropic Additions of Sulfur Dioxide to 1,2-Dimethylidenecycloalkanes. Determination of Thermochemical and Kinetics Parameters for Reactions in Solution and Comparison with Estimates From Quantum Calculations</i>] Helv. Chim. Acta. <b>85</b> (3), 712–732 (2002).</ref>
<ref name="chel_3">D. Suarez, T. L. Sordo, J. A. Sordo. [http://pubs.acs.org/doi/pdf/10.1021/jo00114a039 <i>A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls</i>] J. Org. Chem., <b>60</b> (9), 2848–2852 (1995).</ref>

</references>

Rep:Transition states (st4215): Exercise 3

2017-10-25T10:16:36Z

St4215: /* Extra: Diels-Alder reaction at a different site */

== Exercise 3: Diels-Alder vs Cheletropic ==
In this exercise, we examine the possible reactions between o-xylylene and SO<sub>2</sub> - the Diels-Alder reaction and the cheletropic reaction, as illustrated in the reaction scheme below.
(insert chemdraw diagram)

Again, in the Diels-Alder reaction, the dienophile SO<sub>2</sub> can approach the diene o-xylylene at different orientations, resulting in the endo- and exo- DA products. The cheletropic reaction, which is a pericyclic reaction in which the new bonds formed are made to the same atom, results in a single product.

In this exercise, we compare the three different reaction pathways - both Diels-Alder reactions and the cheletropic reaction - in terms of their reaction coordinates, as well as which is the most thermodynamically or kinetically favoured. We also investigate the possibility of a Diels-Alder reaction at a second site in xylylene.

=== Calculations ===
Calculations were performed at the PM6 level. Method 3 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial#Method_3 tutorial]) was used to locate the transition state.

The optimised molecules can be seen here:

{| class="wikitable"
! colspan="2" | Reactants
|-
| style="text-align: center;" | o-xylylene
| style="text-align: center;" | SO<sub>2</sub>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16</script>
<uploadedFileContents>st4215_XYLYLENE_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16</script>
<uploadedFileContents>st4215_SO2_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo || style="text-align: center;" | Exo
|-
| style="text-align: center;" | Transition state
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>St4215_ex3_ENDO_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_ex3_ENDO_TS_IRC2_PM6.LOG | IRC file]]
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>st4215_ex3_Exo_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_ex3_Exo_TS_IRC_PM6.LOG | IRC file]]
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>st4215_ex3_CHEL_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_ex3_CHEL_TS_IRC_PM6.LOG | IRC file]]
|-
| style="text-align: center;" | Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>St4215_ex3_ENDO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>st4215_ex3_EXO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>st4215_ex3_CHEL_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Reaction coordinate ===
<small><i>Visualise the reaction coordinate with an IRC calculation for each path. Include a .gif file in the wiki of these IRCs.</i></small>

The formation of the products for each of the endo- and exo- Diels-Alder reactions, as well as the cheletropic reaction, can be visualised below.

{| class="wikitable"
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
|-
| [[File:st4215_ENDO_TS_IRCmovie.gif]]
| [[File:st4215_Exo_TS_IRCmovie.gif]]
| [[File:st4215_Chel_TS_IRCmovie.gif]]
|}

We can see that SO<sub>2</sub> approaches xylylene at a different orientation and angle for each of these reactions. This difference in approach trajectories hence lead to the formation of different products.

It can also be observed that in each of the reactions, as the product is formed, the 6-membered ring in xylylene becomes aromatic. This means that there is a strong driving force for the formation of the products. In contrast, the reactant xylylene is highly unstable as it is non-aromatic, and as can be seen in these reactions, can readily react with unsaturated bonds to form a more stable aromatic product.

=== Energy analysis ===
<small><i>Calculate the activation and reaction energies (converting to kJ/mol) for each step as in Exercise 2 to determine which route is preferred. Using Excel or Chemdraw, draw a reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels-Alder reactions and the cheletropic reaction. You can set the 0 energy level to the reactants at infinite separation.</i></small>

==== Free energies ====
The free energies of the reactants, transition states and products for each of the 3 reactions are tabulated below. The reaction barriers and energies are also calculated.

{| class="wikitable"
! rowspan="2" scope="col" style="width: 150px;" |
! colspan="2" scope="col" style="width: 300px;" | Energy at 298 K (PM6)
|-
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
|-
| colspan="3" style="background: #B7C3D0" | <b>Reactants</b>
|-
| Xylylene || style="text-align: center;" | 0.17876 || style="text-align: center;" | 469.34
|-
| SO<sub>2</sub> || style="text-align: center;" | -0.11927 || style="text-align: center;" | -313.14
|-
| Total reactants || style="text-align: center;" | 0.059496 || style="text-align: center;" | 156.21
|-
| colspan="3" style="background: #B7C3D0" | <b>Endo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | 0.090560 || style="text-align: center;" | 237.77
|-
| Product || style="text-align: center;" | 0.021704 || style="text-align: center;" | 56.984
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0311 || style="text-align: center;" | 81.6
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0378 || style="text-align: center;" | -99.2
|-
| colspan="3" style="background: #B7C3D0" | <b>Exo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | 0.092078 || style="text-align: center;" | 241.75
|-
| Product || style="text-align: center;" | 0.021455 || style="text-align: center;" | 56.330
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0326 || style="text-align: center;" | 85.5
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0380 || style="text-align: center;" | -99.9
|-
| colspan="3" style="background: #B7C3D0" | <b>Cheletropic</b>
|-
| Transition state || style="text-align: center;" | 0.099058 || style="text-align: center;" | 260.08
|-
| Product || style="text-align: center;" | -0.000002 || style="text-align: center;" | -0.0052510
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0396 || style="text-align: center;" | 104
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0595 || style="text-align: center;" | -156
|}
<small><i>^Note that all values from the calculations are reported to 5 s.f. unless more decimal places are needed to differentiate between each reaction type. Derived quantities (reaction barrier and reaction energy) are reported to 3 s.f.</i></small>

==== Thermodynamic and kinetic products ====
From the values above, a combined reaction profile showing the reaction barriers and reaction energies can also be plotted as seen below.
[[File:st4215_ex3_Reaction_profile2.PNG|600px|thumb|center|Reaction profile diagram for the 3 Diels-Alder and cheletropic reactions, setting the energy of the reactants to zero]]

We can clearly see that the endo- Diels-Alder product is the kinetic product as it has the lowest reaction barrier of +81.6 kJmol<sup>-1</sup>, while the cheletropic product is the thermodynamic product as it is most stable as has the lowest energy of -156 kJmol<sup>-1</sup>. This is consistent with experimental and computational data.<ref name="chel_3"/><ref name="chel_1"/>

The high stability of the cheletropic product is likely due to the preference of S to adopt a five-membered compared to 6-membered ring structure. This is in contrast to saturated carbon rings, where 6-membered cyclohexane is more stable than 5-membered cyclopentane due to deviation from tetrahedral bond angles of 109° in cyclopentane, resulting in angle strain. However, due to the larger size of the S atom, C-C<sub>tet</sub>-S bond angles in a 5-membered unsaturated sulfur ring (like in the cheletropic product) are much closer to the tetrahedral bond angle, at 105°. In comparison, the 6-membered heterocycle in the Diels-Alder products have C-C<sub>tet</sub>-S bond angles of around 114°, which are comparatively larger than 109°. This is illustrated below:

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
|-
| Products
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; measure 3 16 11</script>
<uploadedFileContents>St4215_ex3_ENDO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; rotate y 180; measure 3 16 11</script>
<uploadedFileContents>st4215_ex3_EXO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; measure 1 7 15</script>
<uploadedFileContents>st4215_ex3_CHEL_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

It is also expected that one of the Diels-Alder products (the endo- product) is the kinetic product instead of the cheletropic product.<ref name="chel_3"/> While the reaction barriers for both endo- and exo- Diels-Alder reactions are similar, the reaction barrier for the cheletropic reaction is much higher. Examining their transition states (see below) allows us to infer why.

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
|-
| Transition state HOMO
| style="text-align: center;" | [[File:st4215_ex3_Endo_TS_HOMO.PNG]]
| style="text-align: center;" | [[File:st4215_ex3_Exo_TS_HOMO.PNG]]
| style="text-align: center;" | [[File:st4215_ex3_Chel_TS_HOMO.PNG]]
|-
| Discussion
| colspan="2" | Some stabilising secondary orbital interactions can be seen in the HOMOs of the endo- and exo- transition states, hence lowering its energy and reducing the reaction barriers for these reactions.
| No stabilising secondary orbital interactions are present here - in fact, the HOMO of the transition state is highly antisymmetric with many nodes, and hence likely to be high in energy.
|}

Like most Diels-Alder reactions, the endo and not the exo- product is the kinetic product due to more or greater stabilising secondary orbital interactions in the transition state. However, in this reaction, both the endo- and exo- transition states seem to have an approximately equal but not significant amount of stabilising orbital interactions in the HOMO. This explains why the endo- and exo- transition states are relatively close in energy.

== Extra: Diels-Alder reaction at a different site ==
O-xylylene also contains a cis-butadiene fragment that can act as the diene in another Diels-Alder reaction. However, this reaction is very kinetically and thermodynamically favourable, as proven by computational methods.

=== Calculations ===
Calculations were performed at the PM6 level. Method 3 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial#Method_3 tutorial]) was used to locate the transition state.

The optimised molecules can be seen here. Optimised reactants (o-xylylene and SO<sub>2</sub>) from the earlier reaction were used.

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder (2)
|-
| style="text-align: center;" | Endo || style="text-align: center;" | Exo
|-
| style="text-align: center;" | Transition state
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>st4215_BAD_ENDO_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_BAD_ENDO_IRC_PM6.LOG | IRC file]]
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>st4215_BAD_EXO_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_BAD_EXO_IRC_PM6.LOG | IRC file]]
|-
| style="text-align: center;" | Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 64</script>
<uploadedFileContents>st4215_BAD_ENDO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_BAD_EXO_PDT_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Energy analysis ===
The free energies of the reactants, transition states and products for both the endo- and exo- Diels Alder reactions are tabulated below. The reaction barriers and energies are also calculated.

{| class="wikitable"
! rowspan="2" scope="col" style="width: 150px;" |
! colspan="2" scope="col" style="width: 300px;" | Energy at 298 K (PM6)
|-
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
|-
| colspan="3" style="background: #B7C3D0" | <b>Reactants</b>
|-
| Xylylene || style="text-align: center;" | 0.17876 || style="text-align: center;" | 469.34
|-
| SO<sub>2</sub> || style="text-align: center;" | -0.11927 || style="text-align: center;" | -313.14
|-
| Total reactants || style="text-align: center;" | 0.059496 || style="text-align: center;" | 156.21
|-
| colspan="3" style="background: #B7C3D0" | <b>Endo- Diels-Alder (2)</b>
|-
| Transition state || style="text-align: center;" | 0.10207 || style="text-align: center;" | 267.99
|-
| Product || style="text-align: center;" | 0.065613 || style="text-align: center;" | 172.27
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0426 || style="text-align: center;" | 112
|-
| Reaction energy (ΔG) || style="text-align: center;" | +0.00612 || style="text-align: center;" | +16.1
|-
| colspan="3" style="background: #B7C3D0" | <b>Exo- Diels-Alder (2)</b>
|-
| Transition state || style="text-align: center;" | 0.10505 || style="text-align: center;" | 275.82
|-
| Product || style="text-align: center;" | 0.067305 || style="text-align: center;" | 176.71
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0456 || style="text-align: center;" | 120
|-
| Reaction energy (ΔG) || style="text-align: center;" | +0.00781 || style="text-align: center;" | +20.5
|}
<small><i>^Note that all values from the calculations are reported to 5 s.f. unless more decimal places are needed to differentiate between each reaction type. Derived quantities (reaction barrier and reaction energy) are reported to 3 s.f.</i></small>

We can hence see that this reaction is both kinetically and thermodynamically unfavourable compared to the other Diels-Alder reaction (previously discussed) and the cheletropic reaction.

Comparing the reaction barriers, the activation energies of 112 kJmol<sup>-1</sup> (endo) and 120 kJmol<sup>-1</sup> (exo) are much higher than that of the other DA reaction, at 81.6 kJmol<sup>-1</sup> (endo) and 85.5 kJmol<sup>-1</sup> (exo), as well as the cheletropic reaction, at 104 kJmol<sup>-1</sup>. Hence this Diels-Alder reaction is the most kinetically unfavourable reaction.

Comparing the reaction energies, we can see that both the endo- and exo- reactions are endothermic - compared to the other two DA reactions as well as the cheletropic reaction, which are exothermic. This indicates that this Diels-Alder reaction is also highly thermodynamically unfavourable as ΔG<0 and it is not spontaneous.

=== Conclusion ===
While there are several possible reactions between o-xylylene and SO<sub>2</sub>, including a Diels-Alder reaction at two different sites and a cheletropic reaction, not all are comparable in terms of kinetic and thermodynamic favourability. Calculations show that the cheletropic reaction is the most thermodynamically favoured due to the higher stability of a 5-membered S ring, and the Diels-Alder reaction between the two terminal alkene carbons of xylylene is much more kinetically and thermodynamically favourable compared to the Diels-Alder reaction involving the cis-butadiene fragment in the aromatic 6-membered ring. This is because the aromaticity of the ring is not broken in the former reaction.

== References ==

<references>
<ref name="chel_1">F. Monnat, P. Vogel, J. A. Sordo. [http://onlinelibrary.wiley.com/doi/10.1002/1522-2675(200203)85:3%3C712::AID-HLCA712%3E3.0.CO;2-5/epdf <i>Hetero-Diels-Alder and Cheletropic Additions of Sulfur Dioxide to 1,2-Dimethylidenecycloalkanes. Determination of Thermochemical and Kinetics Parameters for Reactions in Solution and Comparison with Estimates From Quantum Calculations</i>] Helv. Chim. Acta. <b>85</b> (3), 712–732 (2002).</ref>
<ref name="chel_3">D. Suarez, T. L. Sordo, J. A. Sordo. [http://pubs.acs.org/doi/pdf/10.1021/jo00114a039 <i>A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls</i>] J. Org. Chem., <b>60</b> (9), 2848–2852 (1995).</ref>

</references>

Rep:Transition states (st4215): Exercise 3

2017-10-25T10:06:31Z

St4215: /* Thermodynamic and kinetic products */

== Exercise 3: Diels-Alder vs Cheletropic ==
In this exercise, we examine the possible reactions between o-xylylene and SO<sub>2</sub> - the Diels-Alder reaction and the cheletropic reaction, as illustrated in the reaction scheme below.
(insert chemdraw diagram)

Again, in the Diels-Alder reaction, the dienophile SO<sub>2</sub> can approach the diene o-xylylene at different orientations, resulting in the endo- and exo- DA products. The cheletropic reaction, which is a pericyclic reaction in which the new bonds formed are made to the same atom, results in a single product.

In this exercise, we compare the three different reaction pathways - both Diels-Alder reactions and the cheletropic reaction - in terms of their reaction coordinates, as well as which is the most thermodynamically or kinetically favoured. We also investigate the possibility of a Diels-Alder reaction at a second site in xylylene.

=== Calculations ===
Calculations were performed at the PM6 level. Method 3 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial#Method_3 tutorial]) was used to locate the transition state.

The optimised molecules can be seen here:

{| class="wikitable"
! colspan="2" | Reactants
|-
| style="text-align: center;" | o-xylylene
| style="text-align: center;" | SO<sub>2</sub>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16</script>
<uploadedFileContents>st4215_XYLYLENE_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16</script>
<uploadedFileContents>st4215_SO2_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo || style="text-align: center;" | Exo
|-
| style="text-align: center;" | Transition state
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>St4215_ex3_ENDO_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_ex3_ENDO_TS_IRC2_PM6.LOG | IRC file]]
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>st4215_ex3_Exo_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_ex3_Exo_TS_IRC_PM6.LOG | IRC file]]
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>st4215_ex3_CHEL_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_ex3_CHEL_TS_IRC_PM6.LOG | IRC file]]
|-
| style="text-align: center;" | Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>St4215_ex3_ENDO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>st4215_ex3_EXO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>st4215_ex3_CHEL_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Reaction coordinate ===
<small><i>Visualise the reaction coordinate with an IRC calculation for each path. Include a .gif file in the wiki of these IRCs.</i></small>

The formation of the products for each of the endo- and exo- Diels-Alder reactions, as well as the cheletropic reaction, can be visualised below.

{| class="wikitable"
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
|-
| [[File:st4215_ENDO_TS_IRCmovie.gif]]
| [[File:st4215_Exo_TS_IRCmovie.gif]]
| [[File:st4215_Chel_TS_IRCmovie.gif]]
|}

We can see that SO<sub>2</sub> approaches xylylene at a different orientation and angle for each of these reactions. This difference in approach trajectories hence lead to the formation of different products.

It can also be observed that in each of the reactions, as the product is formed, the 6-membered ring in xylylene becomes aromatic. This means that there is a strong driving force for the formation of the products. In contrast, the reactant xylylene is highly unstable as it is non-aromatic, and as can be seen in these reactions, can readily react with unsaturated bonds to form a more stable aromatic product.

=== Energy analysis ===
<small><i>Calculate the activation and reaction energies (converting to kJ/mol) for each step as in Exercise 2 to determine which route is preferred. Using Excel or Chemdraw, draw a reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels-Alder reactions and the cheletropic reaction. You can set the 0 energy level to the reactants at infinite separation.</i></small>

==== Free energies ====
The free energies of the reactants, transition states and products for each of the 3 reactions are tabulated below. The reaction barriers and energies are also calculated.

{| class="wikitable"
! rowspan="2" scope="col" style="width: 150px;" |
! colspan="2" scope="col" style="width: 300px;" | Energy at 298 K (PM6)
|-
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
|-
| colspan="3" style="background: #B7C3D0" | <b>Reactants</b>
|-
| Xylylene || style="text-align: center;" | 0.17876 || style="text-align: center;" | 469.34
|-
| SO<sub>2</sub> || style="text-align: center;" | -0.11927 || style="text-align: center;" | -313.14
|-
| Total reactants || style="text-align: center;" | 0.059496 || style="text-align: center;" | 156.21
|-
| colspan="3" style="background: #B7C3D0" | <b>Endo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | 0.090560 || style="text-align: center;" | 237.77
|-
| Product || style="text-align: center;" | 0.021704 || style="text-align: center;" | 56.984
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0311 || style="text-align: center;" | 81.6
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0378 || style="text-align: center;" | -99.2
|-
| colspan="3" style="background: #B7C3D0" | <b>Exo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | 0.092078 || style="text-align: center;" | 241.75
|-
| Product || style="text-align: center;" | 0.021455 || style="text-align: center;" | 56.330
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0326 || style="text-align: center;" | 85.5
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0380 || style="text-align: center;" | -99.9
|-
| colspan="3" style="background: #B7C3D0" | <b>Cheletropic</b>
|-
| Transition state || style="text-align: center;" | 0.099058 || style="text-align: center;" | 260.08
|-
| Product || style="text-align: center;" | -0.000002 || style="text-align: center;" | -0.0052510
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0396 || style="text-align: center;" | 104
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0595 || style="text-align: center;" | -156
|}
<small><i>^Note that all values from the calculations are reported to 5 s.f. unless more decimal places are needed to differentiate between each reaction type. Derived quantities (reaction barrier and reaction energy) are reported to 3 s.f.</i></small>

==== Thermodynamic and kinetic products ====
From the values above, a combined reaction profile showing the reaction barriers and reaction energies can also be plotted as seen below.
[[File:st4215_ex3_Reaction_profile2.PNG|600px|thumb|center|Reaction profile diagram for the 3 Diels-Alder and cheletropic reactions, setting the energy of the reactants to zero]]

We can clearly see that the endo- Diels-Alder product is the kinetic product as it has the lowest reaction barrier of +81.6 kJmol<sup>-1</sup>, while the cheletropic product is the thermodynamic product as it is most stable as has the lowest energy of -156 kJmol<sup>-1</sup>. This is consistent with experimental and computational data.<ref name="chel_3"/><ref name="chel_1"/>

The high stability of the cheletropic product is likely due to the preference of S to adopt a five-membered compared to 6-membered ring structure. This is in contrast to saturated carbon rings, where 6-membered cyclohexane is more stable than 5-membered cyclopentane due to deviation from tetrahedral bond angles of 109° in cyclopentane, resulting in angle strain. However, due to the larger size of the S atom, C-C<sub>tet</sub>-S bond angles in a 5-membered unsaturated sulfur ring (like in the cheletropic product) are much closer to the tetrahedral bond angle, at 105°. In comparison, the 6-membered heterocycle in the Diels-Alder products have C-C<sub>tet</sub>-S bond angles of around 114°, which are comparatively larger than 109°. This is illustrated below:

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
|-
| Products
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; measure 3 16 11</script>
<uploadedFileContents>St4215_ex3_ENDO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; rotate y 180; measure 3 16 11</script>
<uploadedFileContents>st4215_ex3_EXO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; measure 1 7 15</script>
<uploadedFileContents>st4215_ex3_CHEL_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

It is also expected that one of the Diels-Alder products (the endo- product) is the kinetic product instead of the cheletropic product.<ref name="chel_3"/> While the reaction barriers for both endo- and exo- Diels-Alder reactions are similar, the reaction barrier for the cheletropic reaction is much higher. Examining their transition states (see below) allows us to infer why.

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
|-
| Transition state HOMO
| style="text-align: center;" | [[File:st4215_ex3_Endo_TS_HOMO.PNG]]
| style="text-align: center;" | [[File:st4215_ex3_Exo_TS_HOMO.PNG]]
| style="text-align: center;" | [[File:st4215_ex3_Chel_TS_HOMO.PNG]]
|-
| Discussion
| colspan="2" | Some stabilising secondary orbital interactions can be seen in the HOMOs of the endo- and exo- transition states, hence lowering its energy and reducing the reaction barriers for these reactions.
| No stabilising secondary orbital interactions are present here - in fact, the HOMO of the transition state is highly antisymmetric with many nodes, and hence likely to be high in energy.
|}

Like most Diels-Alder reactions, the endo and not the exo- product is the kinetic product due to more or greater stabilising secondary orbital interactions in the transition state. However, in this reaction, both the endo- and exo- transition states seem to have an approximately equal but not significant amount of stabilising orbital interactions in the HOMO. This explains why the endo- and exo- transition states are relatively close in energy.

== Extra: Diels-Alder reaction at a different site ==
O-xylylene also contains a cis-butadiene fragment that can act as the diene in another Diels-Alder reaction. However, this reaction is very kinetically and thermodynamically favourable.

=== Optimised molecules ===
The optimised molecules can be seen here. Optimised reactants (o-xylylene and SO<sub>2</sub>) from the earlier reaction were used.

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder (2)
|-
| style="text-align: center;" | Endo || style="text-align: center;" | Exo
|-
| style="text-align: center;" | Transition state
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>st4215_BAD_ENDO_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_BAD_ENDO_IRC_PM6.LOG | IRC file]]
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>st4215_BAD_EXO_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_BAD_EXO_IRC_PM6.LOG | IRC file]]
|-
| style="text-align: center;" | Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 64</script>
<uploadedFileContents>st4215_BAD_ENDO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_BAD_EXO_PDT_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Energy analysis ===
The free energies of the reactants, transition states and products for both the endo- and exo- Diels Alder reactions are tabulated below. The reaction barriers and energies are also calculated.

{| class="wikitable"
! rowspan="2" scope="col" style="width: 150px;" |
! colspan="2" scope="col" style="width: 300px;" | Energy at 298 K (PM6)
|-
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
|-
| colspan="3" style="background: #B7C3D0" | <b>Reactants</b>
|-
| Xylylene || style="text-align: center;" | 0.17876 || style="text-align: center;" | 469.34
|-
| SO<sub>2</sub> || style="text-align: center;" | -0.11927 || style="text-align: center;" | -313.14
|-
| Total reactants || style="text-align: center;" | 0.059496 || style="text-align: center;" | 156.21
|-
| colspan="3" style="background: #B7C3D0" | <b>Endo- Diels-Alder (2)</b>
|-
| Transition state || style="text-align: center;" | 0.10207 || style="text-align: center;" | 267.99
|-
| Product || style="text-align: center;" | 0.065613 || style="text-align: center;" | 172.27
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0426 || style="text-align: center;" | 112
|-
| Reaction energy (ΔG) || style="text-align: center;" | +0.00612 || style="text-align: center;" | +16.1
|-
| colspan="3" style="background: #B7C3D0" | <b>Exo- Diels-Alder (2)</b>
|-
| Transition state || style="text-align: center;" | 0.10505 || style="text-align: center;" | 275.82
|-
| Product || style="text-align: center;" | 0.067305 || style="text-align: center;" | 176.71
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0456 || style="text-align: center;" | 120
|-
| Reaction energy (ΔG) || style="text-align: center;" | +0.00781 || style="text-align: center;" | +20.5
|}
<small><i>^Note that all values from the calculations are reported to 5 s.f. unless more decimal places are needed to differentiate between each reaction type. Derived quantities (reaction barrier and reaction energy) are reported to 3 s.f.</i></small>

We can hence see that this reaction is both kinetically and thermodynamically unfavourable compared to the other Diels-Alder reaction (previously discussed) and the cheletropic reaction.

Comparing the reaction barriers, the activation energies of 112 kJmol<sup>-1</sup> (endo) and 120 kJmol<sup>-1</sup> (exo) are much higher than that of the other DA reaction, at 81.6 kJmol<sup>-1</sup> (endo) and 85.5 kJmol<sup>-1</sup> (exo), as well as the cheletropic reaction, at 104 kJmol<sup>-1</sup>. Hence this Diels-Alder reaction is the most kinetically unfavourable reaction possible.

Comparing the reaction energies, we can see that both the endo- and exo- reactions are endothermic - compared to the other two DA reactions as well as the cheletropic reaction, which are exothermic. This indicates that this Diels-Alder reaction is also highly thermodynamically unfavourable as ΔG<0 and it is not spontaneous.

== References ==

<references>
<ref name="chel_1">F. Monnat, P. Vogel, J. A. Sordo. [http://onlinelibrary.wiley.com/doi/10.1002/1522-2675(200203)85:3%3C712::AID-HLCA712%3E3.0.CO;2-5/epdf <i>Hetero-Diels-Alder and Cheletropic Additions of Sulfur Dioxide to 1,2-Dimethylidenecycloalkanes. Determination of Thermochemical and Kinetics Parameters for Reactions in Solution and Comparison with Estimates From Quantum Calculations</i>] Helv. Chim. Acta. <b>85</b> (3), 712–732 (2002).</ref>
<ref name="chel_3">D. Suarez, T. L. Sordo, J. A. Sordo. [http://pubs.acs.org/doi/pdf/10.1021/jo00114a039 <i>A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls</i>] J. Org. Chem., <b>60</b> (9), 2848–2852 (1995).</ref>

</references>

Rep:Transition states (st4215): Exercise 3

2017-10-25T10:05:55Z

St4215: /* Thermodynamic and kinetic products */

== Exercise 3: Diels-Alder vs Cheletropic ==
In this exercise, we examine the possible reactions between o-xylylene and SO<sub>2</sub> - the Diels-Alder reaction and the cheletropic reaction, as illustrated in the reaction scheme below.
(insert chemdraw diagram)

Again, in the Diels-Alder reaction, the dienophile SO<sub>2</sub> can approach the diene o-xylylene at different orientations, resulting in the endo- and exo- DA products. The cheletropic reaction, which is a pericyclic reaction in which the new bonds formed are made to the same atom, results in a single product.

In this exercise, we compare the three different reaction pathways - both Diels-Alder reactions and the cheletropic reaction - in terms of their reaction coordinates, as well as which is the most thermodynamically or kinetically favoured. We also investigate the possibility of a Diels-Alder reaction at a second site in xylylene.

=== Calculations ===
Calculations were performed at the PM6 level. Method 3 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial#Method_3 tutorial]) was used to locate the transition state.

The optimised molecules can be seen here:

{| class="wikitable"
! colspan="2" | Reactants
|-
| style="text-align: center;" | o-xylylene
| style="text-align: center;" | SO<sub>2</sub>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16</script>
<uploadedFileContents>st4215_XYLYLENE_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16</script>
<uploadedFileContents>st4215_SO2_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo || style="text-align: center;" | Exo
|-
| style="text-align: center;" | Transition state
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>St4215_ex3_ENDO_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_ex3_ENDO_TS_IRC2_PM6.LOG | IRC file]]
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>st4215_ex3_Exo_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_ex3_Exo_TS_IRC_PM6.LOG | IRC file]]
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>st4215_ex3_CHEL_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_ex3_CHEL_TS_IRC_PM6.LOG | IRC file]]
|-
| style="text-align: center;" | Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>St4215_ex3_ENDO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>st4215_ex3_EXO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>st4215_ex3_CHEL_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Reaction coordinate ===
<small><i>Visualise the reaction coordinate with an IRC calculation for each path. Include a .gif file in the wiki of these IRCs.</i></small>

The formation of the products for each of the endo- and exo- Diels-Alder reactions, as well as the cheletropic reaction, can be visualised below.

{| class="wikitable"
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
|-
| [[File:st4215_ENDO_TS_IRCmovie.gif]]
| [[File:st4215_Exo_TS_IRCmovie.gif]]
| [[File:st4215_Chel_TS_IRCmovie.gif]]
|}

We can see that SO<sub>2</sub> approaches xylylene at a different orientation and angle for each of these reactions. This difference in approach trajectories hence lead to the formation of different products.

It can also be observed that in each of the reactions, as the product is formed, the 6-membered ring in xylylene becomes aromatic. This means that there is a strong driving force for the formation of the products. In contrast, the reactant xylylene is highly unstable as it is non-aromatic, and as can be seen in these reactions, can readily react with unsaturated bonds to form a more stable aromatic product.

=== Energy analysis ===
<small><i>Calculate the activation and reaction energies (converting to kJ/mol) for each step as in Exercise 2 to determine which route is preferred. Using Excel or Chemdraw, draw a reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels-Alder reactions and the cheletropic reaction. You can set the 0 energy level to the reactants at infinite separation.</i></small>

==== Free energies ====
The free energies of the reactants, transition states and products for each of the 3 reactions are tabulated below. The reaction barriers and energies are also calculated.

{| class="wikitable"
! rowspan="2" scope="col" style="width: 150px;" |
! colspan="2" scope="col" style="width: 300px;" | Energy at 298 K (PM6)
|-
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
|-
| colspan="3" style="background: #B7C3D0" | <b>Reactants</b>
|-
| Xylylene || style="text-align: center;" | 0.17876 || style="text-align: center;" | 469.34
|-
| SO<sub>2</sub> || style="text-align: center;" | -0.11927 || style="text-align: center;" | -313.14
|-
| Total reactants || style="text-align: center;" | 0.059496 || style="text-align: center;" | 156.21
|-
| colspan="3" style="background: #B7C3D0" | <b>Endo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | 0.090560 || style="text-align: center;" | 237.77
|-
| Product || style="text-align: center;" | 0.021704 || style="text-align: center;" | 56.984
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0311 || style="text-align: center;" | 81.6
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0378 || style="text-align: center;" | -99.2
|-
| colspan="3" style="background: #B7C3D0" | <b>Exo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | 0.092078 || style="text-align: center;" | 241.75
|-
| Product || style="text-align: center;" | 0.021455 || style="text-align: center;" | 56.330
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0326 || style="text-align: center;" | 85.5
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0380 || style="text-align: center;" | -99.9
|-
| colspan="3" style="background: #B7C3D0" | <b>Cheletropic</b>
|-
| Transition state || style="text-align: center;" | 0.099058 || style="text-align: center;" | 260.08
|-
| Product || style="text-align: center;" | -0.000002 || style="text-align: center;" | -0.0052510
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0396 || style="text-align: center;" | 104
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0595 || style="text-align: center;" | -156
|}
<small><i>^Note that all values from the calculations are reported to 5 s.f. unless more decimal places are needed to differentiate between each reaction type. Derived quantities (reaction barrier and reaction energy) are reported to 3 s.f.</i></small>

==== Thermodynamic and kinetic products ====
From the values above, a combined reaction profile showing the reaction barriers and reaction energies can also be plotted as seen below.
[[File:st4215_ex3_Reaction_profile2.PNG|600px|thumb|center|Reaction profile diagram for the 3 Diels-Alder and cheletropic reactions, setting the energy of the reactants to zero]]

We can clearly see that the endo- Diels-Alder product is the kinetic product as it has the lowest reaction barrier of +81.6 kJmol<sup>-1</sup>, while the cheletropic product is the thermodynamic product as it is most stable as has the lowest energy of -156 kJmol<sup>-1</sup>. This is consistent with experimental and computational data.<ref name="chel_3"/><ref name="chel_1"/>

The high stability of the cheletropic product is likely due to the preference of S to adopt a five-membered compared to 6-membered ring structure. This is in contrast to saturated carbon rings, where 6-membered cyclohexane is more stable than 5-membered cyclopentane due to deviation from tetrahedral bond angles of 109° in cyclopentane, resulting in angle strain. However, due to the larger size of the S atom, C-C<sub>tet</sub>-S bond angles in a 5-membered unsaturated sulfur ring (like in the cheletropic product) are much closer to the tetrahedral bond angle, at 105°. In comparison, the 6-membered heterocycle in the Diels-Alder products have C-C<sub>tet</sub>-S bond angles of around 114°, which are comparatively larger than 109°. This is illustrated below:

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
|-
| Products
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; measure 3 16 11</script>
<uploadedFileContents>St4215_ex3_ENDO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; rotate y 180; measure 3 6 11</script>
<uploadedFileContents>st4215_ex3_EXO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; measure 1 7 15</script>
<uploadedFileContents>st4215_ex3_CHEL_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

It is also expected that one of the Diels-Alder products (the endo- product) is the kinetic product instead of the cheletropic product.<ref name="chel_3"/> While the reaction barriers for both endo- and exo- Diels-Alder reactions are similar, the reaction barrier for the cheletropic reaction is much higher. Examining their transition states (see below) allows us to infer why.

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
|-
| Transition state HOMO
| style="text-align: center;" | [[File:st4215_ex3_Endo_TS_HOMO.PNG]]
| style="text-align: center;" | [[File:st4215_ex3_Exo_TS_HOMO.PNG]]
| style="text-align: center;" | [[File:st4215_ex3_Chel_TS_HOMO.PNG]]
|-
| Discussion
| colspan="2" | Some stabilising secondary orbital interactions can be seen in the HOMOs of the endo- and exo- transition states, hence lowering its energy and reducing the reaction barriers for these reactions.
| No stabilising secondary orbital interactions are present here - in fact, the HOMO of the transition state is highly antisymmetric with many nodes, and hence likely to be high in energy.
|}

Like most Diels-Alder reactions, the endo and not the exo- product is the kinetic product due to more or greater stabilising secondary orbital interactions in the transition state. However, in this reaction, both the endo- and exo- transition states seem to have an approximately equal but not significant amount of stabilising orbital interactions in the HOMO. This explains why the endo- and exo- transition states are relatively close in energy.

== Extra: Diels-Alder reaction at a different site ==
O-xylylene also contains a cis-butadiene fragment that can act as the diene in another Diels-Alder reaction. However, this reaction is very kinetically and thermodynamically favourable.

=== Optimised molecules ===
The optimised molecules can be seen here. Optimised reactants (o-xylylene and SO<sub>2</sub>) from the earlier reaction were used.

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder (2)
|-
| style="text-align: center;" | Endo || style="text-align: center;" | Exo
|-
| style="text-align: center;" | Transition state
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>st4215_BAD_ENDO_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_BAD_ENDO_IRC_PM6.LOG | IRC file]]
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>st4215_BAD_EXO_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_BAD_EXO_IRC_PM6.LOG | IRC file]]
|-
| style="text-align: center;" | Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 64</script>
<uploadedFileContents>st4215_BAD_ENDO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_BAD_EXO_PDT_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Energy analysis ===
The free energies of the reactants, transition states and products for both the endo- and exo- Diels Alder reactions are tabulated below. The reaction barriers and energies are also calculated.

{| class="wikitable"
! rowspan="2" scope="col" style="width: 150px;" |
! colspan="2" scope="col" style="width: 300px;" | Energy at 298 K (PM6)
|-
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
|-
| colspan="3" style="background: #B7C3D0" | <b>Reactants</b>
|-
| Xylylene || style="text-align: center;" | 0.17876 || style="text-align: center;" | 469.34
|-
| SO<sub>2</sub> || style="text-align: center;" | -0.11927 || style="text-align: center;" | -313.14
|-
| Total reactants || style="text-align: center;" | 0.059496 || style="text-align: center;" | 156.21
|-
| colspan="3" style="background: #B7C3D0" | <b>Endo- Diels-Alder (2)</b>
|-
| Transition state || style="text-align: center;" | 0.10207 || style="text-align: center;" | 267.99
|-
| Product || style="text-align: center;" | 0.065613 || style="text-align: center;" | 172.27
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0426 || style="text-align: center;" | 112
|-
| Reaction energy (ΔG) || style="text-align: center;" | +0.00612 || style="text-align: center;" | +16.1
|-
| colspan="3" style="background: #B7C3D0" | <b>Exo- Diels-Alder (2)</b>
|-
| Transition state || style="text-align: center;" | 0.10505 || style="text-align: center;" | 275.82
|-
| Product || style="text-align: center;" | 0.067305 || style="text-align: center;" | 176.71
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0456 || style="text-align: center;" | 120
|-
| Reaction energy (ΔG) || style="text-align: center;" | +0.00781 || style="text-align: center;" | +20.5
|}
<small><i>^Note that all values from the calculations are reported to 5 s.f. unless more decimal places are needed to differentiate between each reaction type. Derived quantities (reaction barrier and reaction energy) are reported to 3 s.f.</i></small>

We can hence see that this reaction is both kinetically and thermodynamically unfavourable compared to the other Diels-Alder reaction (previously discussed) and the cheletropic reaction.

Comparing the reaction barriers, the activation energies of 112 kJmol<sup>-1</sup> (endo) and 120 kJmol<sup>-1</sup> (exo) are much higher than that of the other DA reaction, at 81.6 kJmol<sup>-1</sup> (endo) and 85.5 kJmol<sup>-1</sup> (exo), as well as the cheletropic reaction, at 104 kJmol<sup>-1</sup>. Hence this Diels-Alder reaction is the most kinetically unfavourable reaction possible.

Comparing the reaction energies, we can see that both the endo- and exo- reactions are endothermic - compared to the other two DA reactions as well as the cheletropic reaction, which are exothermic. This indicates that this Diels-Alder reaction is also highly thermodynamically unfavourable as ΔG<0 and it is not spontaneous.

== References ==

<references>
<ref name="chel_1">F. Monnat, P. Vogel, J. A. Sordo. [http://onlinelibrary.wiley.com/doi/10.1002/1522-2675(200203)85:3%3C712::AID-HLCA712%3E3.0.CO;2-5/epdf <i>Hetero-Diels-Alder and Cheletropic Additions of Sulfur Dioxide to 1,2-Dimethylidenecycloalkanes. Determination of Thermochemical and Kinetics Parameters for Reactions in Solution and Comparison with Estimates From Quantum Calculations</i>] Helv. Chim. Acta. <b>85</b> (3), 712–732 (2002).</ref>
<ref name="chel_3">D. Suarez, T. L. Sordo, J. A. Sordo. [http://pubs.acs.org/doi/pdf/10.1021/jo00114a039 <i>A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls</i>] J. Org. Chem., <b>60</b> (9), 2848–2852 (1995).</ref>

</references>

Rep:Transition states (st4215): Exercise 3

2017-10-25T10:01:12Z

St4215: /* Exercise 3: Diels-Alder vs Cheletropic */

== Exercise 3: Diels-Alder vs Cheletropic ==
In this exercise, we examine the possible reactions between o-xylylene and SO<sub>2</sub> - the Diels-Alder reaction and the cheletropic reaction, as illustrated in the reaction scheme below.
(insert chemdraw diagram)

Again, in the Diels-Alder reaction, the dienophile SO<sub>2</sub> can approach the diene o-xylylene at different orientations, resulting in the endo- and exo- DA products. The cheletropic reaction, which is a pericyclic reaction in which the new bonds formed are made to the same atom, results in a single product.

In this exercise, we compare the three different reaction pathways - both Diels-Alder reactions and the cheletropic reaction - in terms of their reaction coordinates, as well as which is the most thermodynamically or kinetically favoured. We also investigate the possibility of a Diels-Alder reaction at a second site in xylylene.

=== Calculations ===
Calculations were performed at the PM6 level. Method 3 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial#Method_3 tutorial]) was used to locate the transition state.

The optimised molecules can be seen here:

{| class="wikitable"
! colspan="2" | Reactants
|-
| style="text-align: center;" | o-xylylene
| style="text-align: center;" | SO<sub>2</sub>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16</script>
<uploadedFileContents>st4215_XYLYLENE_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16</script>
<uploadedFileContents>st4215_SO2_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo || style="text-align: center;" | Exo
|-
| style="text-align: center;" | Transition state
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>St4215_ex3_ENDO_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_ex3_ENDO_TS_IRC2_PM6.LOG | IRC file]]
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>st4215_ex3_Exo_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_ex3_Exo_TS_IRC_PM6.LOG | IRC file]]
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>st4215_ex3_CHEL_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_ex3_CHEL_TS_IRC_PM6.LOG | IRC file]]
|-
| style="text-align: center;" | Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>St4215_ex3_ENDO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>st4215_ex3_EXO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>st4215_ex3_CHEL_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Reaction coordinate ===
<small><i>Visualise the reaction coordinate with an IRC calculation for each path. Include a .gif file in the wiki of these IRCs.</i></small>

The formation of the products for each of the endo- and exo- Diels-Alder reactions, as well as the cheletropic reaction, can be visualised below.

{| class="wikitable"
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
|-
| [[File:st4215_ENDO_TS_IRCmovie.gif]]
| [[File:st4215_Exo_TS_IRCmovie.gif]]
| [[File:st4215_Chel_TS_IRCmovie.gif]]
|}

We can see that SO<sub>2</sub> approaches xylylene at a different orientation and angle for each of these reactions. This difference in approach trajectories hence lead to the formation of different products.

It can also be observed that in each of the reactions, as the product is formed, the 6-membered ring in xylylene becomes aromatic. This means that there is a strong driving force for the formation of the products. In contrast, the reactant xylylene is highly unstable as it is non-aromatic, and as can be seen in these reactions, can readily react with unsaturated bonds to form a more stable aromatic product.

=== Energy analysis ===
<small><i>Calculate the activation and reaction energies (converting to kJ/mol) for each step as in Exercise 2 to determine which route is preferred. Using Excel or Chemdraw, draw a reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels-Alder reactions and the cheletropic reaction. You can set the 0 energy level to the reactants at infinite separation.</i></small>

==== Free energies ====
The free energies of the reactants, transition states and products for each of the 3 reactions are tabulated below. The reaction barriers and energies are also calculated.

{| class="wikitable"
! rowspan="2" scope="col" style="width: 150px;" |
! colspan="2" scope="col" style="width: 300px;" | Energy at 298 K (PM6)
|-
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
|-
| colspan="3" style="background: #B7C3D0" | <b>Reactants</b>
|-
| Xylylene || style="text-align: center;" | 0.17876 || style="text-align: center;" | 469.34
|-
| SO<sub>2</sub> || style="text-align: center;" | -0.11927 || style="text-align: center;" | -313.14
|-
| Total reactants || style="text-align: center;" | 0.059496 || style="text-align: center;" | 156.21
|-
| colspan="3" style="background: #B7C3D0" | <b>Endo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | 0.090560 || style="text-align: center;" | 237.77
|-
| Product || style="text-align: center;" | 0.021704 || style="text-align: center;" | 56.984
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0311 || style="text-align: center;" | 81.6
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0378 || style="text-align: center;" | -99.2
|-
| colspan="3" style="background: #B7C3D0" | <b>Exo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | 0.092078 || style="text-align: center;" | 241.75
|-
| Product || style="text-align: center;" | 0.021455 || style="text-align: center;" | 56.330
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0326 || style="text-align: center;" | 85.5
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0380 || style="text-align: center;" | -99.9
|-
| colspan="3" style="background: #B7C3D0" | <b>Cheletropic</b>
|-
| Transition state || style="text-align: center;" | 0.099058 || style="text-align: center;" | 260.08
|-
| Product || style="text-align: center;" | -0.000002 || style="text-align: center;" | -0.0052510
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0396 || style="text-align: center;" | 104
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0595 || style="text-align: center;" | -156
|}
<small><i>^Note that all values from the calculations are reported to 5 s.f. unless more decimal places are needed to differentiate between each reaction type. Derived quantities (reaction barrier and reaction energy) are reported to 3 s.f.</i></small>

==== Thermodynamic and kinetic products ====
From the values above, a combined reaction profile showing the reaction barriers and reaction energies can also be plotted as seen below.
[[File:st4215_ex3_Reaction_profile2.PNG|600px|thumb|center|Reaction profile diagram for the 3 Diels-Alder and cheletropic reactions, setting the energy of the reactants to zero]]

We can clearly see that the endo- Diels-Alder product is the kinetic product as it has the lowest reaction barrier of +81.6 kJmol<sup>-1</sup>, while the cheletropic product is the thermodynamic product as it is most stable as has the lowest energy of -156 kJmol<sup>-1</sup>. This is consistent with experimental and computational data.<ref name="chel_3"/><ref name="chel_1"/>

The high stability of the cheletropic product is likely due to the preference of S to adopt a five-membered compared to 6-membered ring structure. This is in contrast to saturated carbon rings, where 6-membered cyclohexane is more stable than 5-membered cyclopentane due to deviation from tetrahedral bond angles of 109° in cyclopentane, resulting in angle strain. However, due to the larger size of the S atom, C-C<sub>tet</sub>-S bond angles in a 5-membered unsaturated sulfur ring (like in the cheletropic product) are much closer to the tetrahedral bond angle, at 105°. In comparison, the 6-membered heterocycle in the Diels-Alder products have C-C<sub>tet</sub>-S bond angles of around 114°, which are comparatively larger than 109°. This is illustrated below:

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
|-
| Products
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; measure 3 16 11</script>
<uploadedFileContents>St4215_ex3_ENDO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; rotate y 180; measure 3 16 11</script>
<uploadedFileContents>st4215_ex3_EXO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; measure 1 7 15</script>
<uploadedFileContents>st4215_ex3_CHEL_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

It is also expected that one of the Diels-Alder products (the endo- product) is the kinetic product instead of the cheletropic product.<ref name="chel_3"/> While the reaction barriers for both endo- and exo- Diels-Alder reactions are similar, the reaction barrier for the cheletropic reaction is much higher. Examining their transition states (see below) allows us to infer why.

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
|-
| Transition state HOMO
| style="text-align: center;" | [[File:st4215_ex3_Endo_TS_HOMO.PNG]]
| style="text-align: center;" | [[File:st4215_ex3_Exo_TS_HOMO.PNG]]
| style="text-align: center;" | [[File:st4215_ex3_Chel_TS_HOMO.PNG]]
|-
| Discussion
| colspan="2" | Some stabilising secondary orbital interactions can be seen in the HOMOs of the endo- and exo- transition states, hence lowering its energy and reducing the reaction barriers for these reactions.
| No stabilising secondary orbital interactions are present here - in fact, the HOMO of the transition state is highly antisymmetric with many nodes, and hence likely to be high in energy.
|}

Like most Diels-Alder reactions, the endo and not the exo- product is the kinetic product due to more or greater stabilising secondary orbital interactions in the transition state. However, in this reaction, both the endo- and exo- transition states seem to have an approximately equal but not significant amount of stabilising orbital interactions in the HOMO. This explains why the endo- and exo- transition states are relatively close in energy.

== Extra: Diels-Alder reaction at a different site ==
O-xylylene also contains a cis-butadiene fragment that can act as the diene in another Diels-Alder reaction. However, this reaction is very kinetically and thermodynamically favourable.

=== Optimised molecules ===
The optimised molecules can be seen here. Optimised reactants (o-xylylene and SO<sub>2</sub>) from the earlier reaction were used.

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder (2)
|-
| style="text-align: center;" | Endo || style="text-align: center;" | Exo
|-
| style="text-align: center;" | Transition state
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>st4215_BAD_ENDO_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_BAD_ENDO_IRC_PM6.LOG | IRC file]]
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>st4215_BAD_EXO_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_BAD_EXO_IRC_PM6.LOG | IRC file]]
|-
| style="text-align: center;" | Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 64</script>
<uploadedFileContents>st4215_BAD_ENDO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_BAD_EXO_PDT_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Energy analysis ===
The free energies of the reactants, transition states and products for both the endo- and exo- Diels Alder reactions are tabulated below. The reaction barriers and energies are also calculated.

{| class="wikitable"
! rowspan="2" scope="col" style="width: 150px;" |
! colspan="2" scope="col" style="width: 300px;" | Energy at 298 K (PM6)
|-
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
|-
| colspan="3" style="background: #B7C3D0" | <b>Reactants</b>
|-
| Xylylene || style="text-align: center;" | 0.17876 || style="text-align: center;" | 469.34
|-
| SO<sub>2</sub> || style="text-align: center;" | -0.11927 || style="text-align: center;" | -313.14
|-
| Total reactants || style="text-align: center;" | 0.059496 || style="text-align: center;" | 156.21
|-
| colspan="3" style="background: #B7C3D0" | <b>Endo- Diels-Alder (2)</b>
|-
| Transition state || style="text-align: center;" | 0.10207 || style="text-align: center;" | 267.99
|-
| Product || style="text-align: center;" | 0.065613 || style="text-align: center;" | 172.27
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0426 || style="text-align: center;" | 112
|-
| Reaction energy (ΔG) || style="text-align: center;" | +0.00612 || style="text-align: center;" | +16.1
|-
| colspan="3" style="background: #B7C3D0" | <b>Exo- Diels-Alder (2)</b>
|-
| Transition state || style="text-align: center;" | 0.10505 || style="text-align: center;" | 275.82
|-
| Product || style="text-align: center;" | 0.067305 || style="text-align: center;" | 176.71
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0456 || style="text-align: center;" | 120
|-
| Reaction energy (ΔG) || style="text-align: center;" | +0.00781 || style="text-align: center;" | +20.5
|}
<small><i>^Note that all values from the calculations are reported to 5 s.f. unless more decimal places are needed to differentiate between each reaction type. Derived quantities (reaction barrier and reaction energy) are reported to 3 s.f.</i></small>

We can hence see that this reaction is both kinetically and thermodynamically unfavourable compared to the other Diels-Alder reaction (previously discussed) and the cheletropic reaction.

Comparing the reaction barriers, the activation energies of 112 kJmol<sup>-1</sup> (endo) and 120 kJmol<sup>-1</sup> (exo) are much higher than that of the other DA reaction, at 81.6 kJmol<sup>-1</sup> (endo) and 85.5 kJmol<sup>-1</sup> (exo), as well as the cheletropic reaction, at 104 kJmol<sup>-1</sup>. Hence this Diels-Alder reaction is the most kinetically unfavourable reaction possible.

Comparing the reaction energies, we can see that both the endo- and exo- reactions are endothermic - compared to the other two DA reactions as well as the cheletropic reaction, which are exothermic. This indicates that this Diels-Alder reaction is also highly thermodynamically unfavourable as ΔG<0 and it is not spontaneous.

== References ==

<references>
<ref name="chel_1">F. Monnat, P. Vogel, J. A. Sordo. [http://onlinelibrary.wiley.com/doi/10.1002/1522-2675(200203)85:3%3C712::AID-HLCA712%3E3.0.CO;2-5/epdf <i>Hetero-Diels-Alder and Cheletropic Additions of Sulfur Dioxide to 1,2-Dimethylidenecycloalkanes. Determination of Thermochemical and Kinetics Parameters for Reactions in Solution and Comparison with Estimates From Quantum Calculations</i>] Helv. Chim. Acta. <b>85</b> (3), 712–732 (2002).</ref>
<ref name="chel_3">D. Suarez, T. L. Sordo, J. A. Sordo. [http://pubs.acs.org/doi/pdf/10.1021/jo00114a039 <i>A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls</i>] J. Org. Chem., <b>60</b> (9), 2848–2852 (1995).</ref>

</references>

Rep:Transition states (st4215): Exercise 2

2017-10-25T09:55:24Z

St4215: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
The reaction of cyclohexadiene and 1,3-dioxole is also a Diels-Alder reaction, in which cyclohexadiene is the diene and 1,3-dioxole is the dienophile. However, unlike the simple Diels-Alder reaction between butadiene and ethylene, this reaction is slightly more complex - 1,3-dioxole can approach the diene at different orientations, leading to the formation of the endo- and exo- Diels-Alder products. This can be seen in the reaction scheme below:
(insert chemdraw diagram)

The endo- product is formed from a transition state where the substituents on the dienophile point towards the π system of the diene, while the exo- product is formed from a transition state where the substituents are pointing away.

In this exercise, we take a closer look at a different aspect of the Diels-Alder reaction - whether it is normal or inverse electron demand. We also consider the Diels-Alder reaction when an unsymmetrical diene is involved, and compare the endo- and exo- DA reactions in terms of which is more kinetically or thermodynamically favourable. In the process, we confirm that the orbital symmetry requirements as elucidated in Exercise 1 still apply, and illustrate that there are differences between the PM6 and B3LYP calculation methods, with one being more suitable than the other in this case.

=== Calculations ===
Calculations were performed at both the PM6 and B3LYP/6-31G(d) level. Method 2 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial#Method_2 tutorial]) was used to locate the transition state.

The optimised molecules can be seen here:

{| class="wikitable"
! rowspan="2" | Calculation method
! colspan="2" | Reactants
! colspan="2" | Endo
! colspan="2" | Exo
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-dioxole
| style="text-align: center;" | Transition state
| style="text-align: center;" | Product
| style="text-align: center;" | Transition state
| style="text-align: center;" | Product
|-
| style="text-align: center;" | B3LYP
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18</script>
<uploadedFileContents>st4215_CYCLOHEXADIENE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26</script>
<uploadedFileContents>st4215_DIOXOLE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18</script>
<uploadedFileContents>st4215_ENDO_PDT_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>st4215_EXO_PDT_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" | PM6
| style="text-align: center;" | [[Media:st4215_CYCLOHEXADIENE_OPTFREQ_PM6.LOG| Cyclohexadiene (PM6)]]
| style="text-align: center;" | [[Media:st4215_DIOXOLE_OPTFREQ_PM6.LOG| 1,3-dioxole (PM6)]]
| style="text-align: center;" | [[Media:st4215_ENDO_TS_OPTFREQ_PM6.LOG| Endo-TS (PM6)]] <br> [[Media:st4215_ENDO_TS_IRC2_PM6ONPM6.LOG| IRC file]]
| style="text-align: center;" | [[Media:st4215_ENDO_PDT_OPTFREQ_PM6.LOG| Endo-product (PM6)]]
| style="text-align: center;" | [[Media:st4215_EXO_TS_OPTFREQ_PM6.LOG| Exo-TS (PM6)]] <br> [[Media:st4215_EXO_TS_IRC_PM6ONPM6.LOG| IRC file]]
| style="text-align: center;" | [[Media:st4215_EXO_PDT_OPTFREQ_PM6.LOG| Exo-product(PM6)]]

|}

=== Molecular orbitals ===

==== Computed MOs ====
<small><i>Using your MO diagram for the Diels-Alder reaction, locate the occupied and unoccupied orbitals associated with the DA reaction for both TSs by symmetry. Find the relevant MOs and add them to your wiki (at an appropriate angle to show symmetry).</i></small>

The MOs involved in this reaction - the HOMOs and LUMOs for the reactants (cyclohexadiene and 1,3-dioxole), as well as the 4 MOs that these produce in each of the endo and exo transition states - are shown below. As determined in Exercise 1, which is also a Diels-Alder reaction, only orbitals of the same symmetry are able to interact. This is illustrated in the table below, where the symmetry or antisymmetry of each orbital can be clearly seen.

{| class="wikitable"
! rowspan="2"| Symmetry
! colspan="2" | Reactants
! colspan="2" rowspan="2"| Transition state (Endo)
! colspan="2" rowspan="2"| Transition state (Exo)
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
|-
| Antisymmmetric
| <b>MO 22</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXADIENE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 20</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26; mo 20; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_DIOXOLE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 40</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 40; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 43</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 43; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 40</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 43</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Symmetric
| <b>MO 23</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXADIENE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 19</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26; mo 19; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_DIOXOLE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 41</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 41; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 42</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 42; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 41</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 42</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

It is important to note that these MOs were generated from the B3LYP and not the PM6 calculation. While both calculation methods were used, the B3LYP calculation proved to be a better choice in visualising the MOs as it allowed us to see the symmetry of the orbitals more clearly, and corresponded more closely to the graphical representation of the orbitals in the MO diagram (see next section).

==== MO diagrams ====
<i><small>Construct a new MO diagram using these new orbitals, adjusting energy levels as necessary. Is this a normal or inverse demand DA reaction?</small></i>

MO diagrams for both the endo- and exo- Diels-Alder reactions were constructed as shown below. Energy levels of the MOs have been adjusted to reflect their actual values, as calculated in the B3LYP calculation.

{| class="wikitable"
! Endo- Diels-Alder
! Exo- Diels-Alder
|-
| [[File:st4215_Endo_MO_diagram.PNG|500px]]
| [[File:st4215_Exo_MO_diagram.PNG|500px]]
|}

From the MO diagrams above, we can conclude that both the endo- and exo- reactions are inverse demand DA reactions. In contrast to a normal electron demand DA reaction, where the diene is electron rich with a high LUMO and the dienophile is electron poor with a low HOMO, cyclohexadiene (the diene) is electron poor with a low HOMO and 1,3-dioxole (the dienophile) is electron rich with a high LUMO. Hence we can classify these reactions as inverse demand.

This is likely due to the nature of the dienophile, 1-3-dioxole, which has an electron-donating O atom. The lone pairs on the two adjacent O atoms are able to donate electron density into the double bond, making the dienophile more electron rich and raising the energy of its MOs, including its LUMO. In contrast, cyclohexadiene does not have any electron-donating substituents and is relatively electron poor. Hence, considering the Frontier Molecular Orbitals (FMOs), the LUMO<sub>dienophile</sub> is relatively high-energy and closer in energy to the low-energy HOMO<sub>diene</sub>, as compared to HOMO<sub>dienophile</sub> and LUMO<sub>diene</sub>. Thus the interaction between the LUMO<sub>dienophile</sub> and HOMO<sub>diene</sub> is the strongest and dominates in this reaction, causing it to be inverse demand.<ref name="inverse"/>

=== Energy analysis ===
<small><i>Tabulate the energies and determine the reaction barriers and reaction energies (in kJ/mol) at room temperature (the corrected energies are labelled "Sum of electronic and thermal Free Energies", corresponding to the Gibbs free energy). Which are the kinetically and thermodynamically favourable products? Look at the HOMO of the TSs. Are there any secondary orbital interactions or sterics that might affect the reaction barrier energy?</i></small>

==== Free energies ====
The free energy of the reactants as well as the endo- and exo- Diels-Alder transition states and products are tabulated below. The reaction barriers and energies are also calculated.

{| class="wikitable"
! rowspan="3" scope="col" style="width: 150px;" |
! colspan="4" scope="col" style="width: 500px;" | Energy at 298 K
|-
| colspan="2" style="text-align: center;" | B3LYP
| colspan="2" style="text-align: center;" | PM6
|-
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
|-
| colspan="5" style="background: #B7C3D0" | <b>Reactants</b>
|-
| Cyclohexadiene || style="text-align: center;" | -233.32 || style="text-align: center;" | -6.1259 x 10<sup>5</sup> || style="text-align: center;" | 0.11688 || style="text-align: center;" | 306.86
|-
| 1,3-dioxole || style="text-align: center;" | -267.07 || style="text-align: center;" | -7.0119 x 10<sup>5</sup> || style="text-align: center;" | -0.052279 || style="text-align: center;" | -137.26
|-
| Total reactants || style="text-align: center;" | -500.39 || style="text-align: center;" | -1.3138 x 10<sup>6</sup> || style="text-align: center;" | 0.064598 || style="text-align: center;" | 169.60
|-
| colspan="5" style="background: #B7C3D0" | <b>Endo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | -500.332 || style="text-align: center;" | -1.3136 x 10<sup>6</sup> || style="text-align: center;" | 0.13794 ||style="text-align: center;" | 362.17
|-
| Product || style="text-align: center;" | -500.419 || style="text-align: center;" | -1.3138 x 10<sup>6</sup> || style="text-align: center;" | 0.037807 || style="text-align: center;" | 99.26
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0609 || style="text-align: center;" | 160 || style="text-align: center;" | 0.0733 || style="text-align: center;" | 193
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0257 || style="text-align: center;" | -67.4 || style="text-align: center;" | -0.0268 || style="text-align: center;" | -70.3
|-
| colspan="5" style="background: #B7C3D0" | <b>Exo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | -500.329 || style="text-align: center;" | -1.3136 x 10<sup>6</sup> || style="text-align: center;" | 0.13890 || style="text-align: center;" | 364.68
|-
| Product || style="text-align: center;" | -500.417 || style="text-align: center;" | -1.3138 x 10<sup>6</sup> || style="text-align: center;" | 0.037977 || style="text-align: center;" | 99.71
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0639 || style="text-align: center;" | 168 || style="text-align: center;" | 0.0743 || style="text-align: center;" | 195
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0243 || style="text-align: center;" | -63.8 || style="text-align: center;" | -0.0266 || style="text-align: center;" | -69.9
|}
<small><i>^Note that all values from the calculations are reported to 5 s.f. unless more decimal places are needed to differentiate between endo- and exo- geometries. Derived quantities (reaction barrier and reaction energy) are reported to 3 s.f.</i></small>

==== Thermodynamic and kinetic products ====
From the table above, we can conclude that the endo- product is both the kinetic and thermodynamic product. This is because it has a lower reaction barrier, meaning that less activation energy is required for the reaction, making it the kinetic product. The endo- product also has a lower reaction energy (ΔG), meaning that the endo- product is lower in energy and more stable than the exo- product, hence making it the thermodynamic product.

This is in contrast to most Diels-Alder reactions, in which the exo- product is the thermodynamic product as it is less sterically hindered and more stable, while the endo- product is the kinetic product due to stabilising orbital interactions in the transition state.<ref name="fmo"/> However, the difference for this reaction can be explained.

As seen in the jmols below, the endo- TS indeed has stabilising secondary orbital interactions between the p orbitals of O in 1,3-dioxole and the p orbitals of C in cyclohexadiene, which are absent in the exo- TS. The presence of these interactions lower the energy of the transition state, hence lowering the reaction barrier and making the endo-product the kinetic product.

Comparing the endo- and exo- products, we can also see that these stabilising orbital interactions are also in present in the endo- product. Additionally, the endo- product is less sterically hindered compared to the exo-product, in which there is steric clash between the hydrogens which are pointing towards each other. These two factors cause the energy of the endo- product to be lower than that of the exo- product, hence lowering the reaction energy and making the endo- product the thermodynamic product as well.

{| class="wikitable"
!
! Endo
! Exo
|-
| Transition state
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 41; rotate x 90; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; rotate x 90; rotate y 180; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 41; rotate x 90; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>st4215_ENDO_PDT_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 41; rotate x 90; rotate y 180; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>st4215_EXO_PDT_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Conclusion ===
As per Exercise 1, MO calculations and visualisation for this Diels-Alder reaction prove that only orbitals with the same symmetry can overlap and interact, hence showing that this is not unique to a singular reaction. A closer examination of the MO diagram also allows us to determine that this reaction is an inverse electron demand DA reaction, due to the presence of electron-donating groups on the dienophile (1,3-dioxole) which raises the energy of its LUMO. Analysing the energy levels of the reactants, TSs and products also reveal that the endo- product is both the kinetic and thermodynamic product, due to greater stability of the transition state (due to stabilising secondary orbital interactions) and the final product (due to lesser steric clash).

== References ==
<references>
<ref name="inverse">D. Boger. <i>Progress in heterocyclic chemistry. (1st ed.).</i> (1989).</ref>
<ref name="fmo">I. Fleming. <i>Frontier Orbitals and Organic Chemical Reactions.</i> (1976).</ref>
</references>

Rep:Transition states (st4215): Exercise 1

2017-10-25T09:36:44Z

St4215: /* Exercise 1: Reaction of Butadiene with Ethylene */

== Exercise 1: Reaction of Butadiene with Ethylene ==
The reaction between butadiene and ethylene is a [4+2] cycloaddition reaction, or more specifically, a Diels-Alder reaction - a reaction involving a conjugated diene in the s-cis conformation, and a dienophile containing a double bond. In this simple Diels-Alder reaction, butadiene is the diene and ethylene is the dienophile. The reaction scheme for this reaction is shown below:
(insert chemdraw diagram)

In this exercise, we use this Diels-Alder reaction to determine the orbital symmetry requirements for a reaction to take place, and to show the effect of hybridisation and bond order on the length of C-C bonds. We also probe into the mechanism of the reaction, and determine if bond formation is synchronous or asynchronous.

=== Calculations ===
Calculations were performed at the PM6 level. Method 1 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial#Method_1 tutorial]) was used to locate the transition state.

The optimised molecules can be seen here:

{| class="wikitable"
! colspan="2" | Reactants
! Transition state
! Product
|-
|<jmol>
<jmolApplet>
<title>Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_CYCLOHEXENE_TS_IRC3_PM6.LOG | IRC file]]
| <jmol>
<jmolApplet>
<title>Cyclohexene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_CYCLOHEXENE_PDT_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Molecular orbitals ===

==== MO diagram ====
<small><i>Construct an MO diagram for the formation of the butadiene/ethene TS, including basic symmetry labels (symmetric/antisymmetric or s/a).</i></small><br>

The MO diagram for this cycloaddition reaction was constructed as shown below. We first assume based on prior knowledge that only orbitals of the same symmetry can combine; however, this is proven in a later section.

The MOs have been labelled accordingly with their numbers according to the calculations, and can be visualised in the section below.<br>
[[File:st4215_ex1_MO_diagram.PNG]]

Considering the actual energy levels of the MOs computed from the calculations, a more accurate MO diagram can be constructed, as seen [[Media:st4215_ex1_MO_diagram_actual.PNG|here]]. However, this does not affect the relative energy levels of the MOs (within each molecule) or the interactions between these MOs.

==== Computed MOs ====
<small><i>Include images (or Jmol objects) for each of the HOMO and LUMO of butadiene and ethene, and the four MOs these produce for the TS. Correlate these MOs with the ones in your MO diagram to show which orbitals interact.</i></small><br>

The HOMOs and LUMOs for each reactant, butadiene and ethylene, as well as the 4 MOs that these produce for the TS, were calculated and can be visualised below. The MO numbers correspond to that labelled on the MO diagram, allowing us to see which orbitals interact. We can also observe that these computed MOs bear physical resemblance to that drawn in the MO diagram, in terms of the bonding and antibonding phases in each MO.

{| class="wikitable"
! rowspan="2" | Symmetry
! colspan="2" | Reactants
! rowspan="2" colspan="2"| Transition state
|-
| style="text-align: center;" | Butadiene
| style="text-align: center;" | Ethylene
|-
| Antisymmetric
| <b>MO 11</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 7</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 16</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 19</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Symmetric
| <b>MO 12</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 6</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 17</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 18</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Symmetry requirements ====
<small><i>What can you conclude about the requirements for symmetry for a reaction (when is a reaction 'allowed' and when is it 'forbidden')? Write whether the orbital overlap integral is zero or non-zero for the case of a symmetric-antisymmetric interaction, a symmetric-symmetric interaction and an antisymmetric-antisymmetric interaction.</i></small><br>

From the table above as well as the MO diagram, we can see that the HOMO/LUMO of butadiene interact with the corresponding LUMO/HOMO in ethylene respectively. These interactions can occur as each pair of orbitals share the same symmetry. The HOMO of butadiene (MO 11) and the LUMO of ethylene (MO 7) are both antisymmetric, and interact to give two antisymmetric MOs in the TS (MOs 16 and 19). Similarly, the LUMO of ethylene (MO 12) and the HOMO of butadiene (MO 6) are both symmetric, and interact to give two symmetric MOs in the TS (MOs 17 and 18). Hence we can conclude that a reaction is only allowed when the relevant orbitals share the same symmetry, as this would allow orbitals to overlap and thus interact. This is illustrated in the following table:

{| class="wikitable"
! Symmetry of interaction
! Orbital overlap integral
|-
| style="text-align: center;" | Symmetric-antisymmetric
| style="text-align: center;" | Zero
|-
| style="text-align: center;" | Symmetric-symmetric
| style="text-align: center;" | Non-zero
|-
| style="text-align: center;" | Antisymmetric-antisymmetric
| style="text-align: center;" | Non-zero
|}

=== C-C bond lengths ===
<small><i>Include measurements of the 4 C-C bond lengths of the reactants and the 6 C-C bond lengths of the TS and products. How do the bond lengths change as the reaction progresses? What are typical sp3 and sp2 C-C bond lengths? What is the Van der Waals radius of the C atom? How does this compare with the length of the partly formed C-C bonds in the TS.</i></small>

The C-C bond lengths in the reactants, TS and products are tabulated below.

{| class="wikitable"
! rowspan="2" colspan="2" |
! colspan="2" | Reactants
! rowspan="2" | Transition state
! rowspan="2" | Product
|-
| style="text-align: center;" | Butadiene
| style="text-align: center;" | Ethylene
|-
| colspan="2" style="text-align: center;"| Labelled C atoms
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7; label display</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4; label display</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>st4215_CYCLOHEXENE_PDT_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| rowspan="6" style="text-align: center;" | C-C bond<br> length / Å
| style="width: 50px;" | Bond A || <center> C1-C4: 1.34 </center>|| || <center> C1-C4: 1.38 </center> || <center> C1-C4: 1.50 </center>
|-
| Bond B || <center> C4-C6: 1.47 </center> || || <center> C4-C6: 1.41 </center> || <center> C4-C6: 1.34 </center>
|-
| Bond C || <center> C6-C7: 1.34 </center> || || <center> C6-C7: 1.38 </center> || <center> C6-C7: 1.50 </center>
|-
| Bond D || || <center> C1-C4: 1.33 </center> || <center> C11-C14: 1.38 </center> || <center> C11-C14: 1.54 </center>
|-
| Bond E || || || <center> C7-C14: 2.11 </center> || <center> C7-C14: 1.54 </center>
|-
| Bond F || || || <center> C1-C11: 2.11 </center> || <center> C1-C11: 1.54 </center>
|}

From the values above, we can observe the following changes in bond length as the reaction progresses.

{| class="wikitable" style="width: 750px;"
! Bond
! Trend in bond length as reaction progresses
! Graph
|-
| A || As the reaction progresses, the length of Bond A increases. This is because Bond A is initially a C=C double bond in butadiene, which becomes a sp<sup>2</sup>-sp<sup>3</sup> C-C single bond in cyclohexene. These lengths are similar to typical values of 1.34 Å for alkenes and 1.50 Å sp<sup>2</sup>-sp<sup>3</sup> C-C bonds.<ref name="bondlength"/>
| [[File:st4215_BondA.JPG|200px]]
|-
| B || As the reaction progresses, the length of Bond B decreases. This is because Bond B is initially an sp<sup>2</sup>-sp<sup>2</sup> C-C single bond in butadiene, which becomes a C=C double bond in cyclohexene. These lengths are similar to typical values of 1.47 Å for sp<sup>2</sup>-sp<sup>2</sup> C-C bonds and 1.34 Å for alkenes.<ref name="bondlength"/>
| [[File:st4215_BondB.JPG|200px]]
|-
| C || Similar to Bond A, as the reaction progresses, the length of Bond C increases. This is due to the same reason as explained for Bond A.
| [[File:st4215_BondC.JPG|200px]]
|-
| D || As the reaction progresses, the length of Bond D increases. This is because Bond B is initially an C=C single bond in ethylene, which becomes a sp<sup>3</sup>-sp<sup>3</sup> C-C single bond in cyclohexene. These lengths are similar to typical values of 1.34 Å for alkenes and 1.54 Å for sp<sup>3</sup>-sp<sup>3</sup> C-C bonds.<ref name="bondlength"/>
| [[File:st4215_BondD.JPG|200px]]
|-
| E || Bond E is formed in this reaction. Hence as the reaction progresses from the transition state to the product, the length of Bond E increases. The length of the fully formed Bond E in the product, an sp<sup>3</sup>-sp<sup>3</sup> C-C single bond, corresponds to the typical value of 1.54 Å.<ref name="bondlength"/> The distance between the C atoms in the TS (2.11 Å) falls between twice the van der Waal radius of C (2 x 1.70 Å<ref name="vdw_c"/> = 3.40 Å) and the length of the fully formed Bond E, indicating that the atoms are approaching each other.
| [[File:st4215_BondE.JPG|200px]]
|-
| F || Like Bond E, Bond F is also formed in this reaction. Hence as the reaction progresses from the transition state to the product, the length of Bond F increases, due to the same reasons as explained above.
| [[File:st4215_BondF.JPG|200px]]
|}

We can hence conclude that bond lengths in the reactants and product do not deviate from typical values. Additionally, we can also show that an increase in bond order from 1 to 2 indeed shortens the C-C bond, while an increase in hybridisation from sp<sup>2</sup> to sp<sup>3</sup> does lengthen the C-C bond, as seen in the comparison of theoretical values.

=== Transition state ===
<i><small>Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous?</small></i>
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 7; rotate x -40; select atomno=1, atomno=7, atomno=11, atomno=14; label display </script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
<name>cyclohexeneTS</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>cyclohexeneTS</target>
</jmolbutton>
<jmolbutton>
<script>measure 1 11; measure 7 14</script>
<text>C-C Distances</text>
<target>cyclohexeneTS</target>
</jmolbutton>
</jmol>
<br><br>
As illustrated above, the formation of the two bonds are synchronous as the relevant pairs of atoms (C1/C11 and C7/C14) are moving towards each other at the same time, with the distance between the two atoms being approximately equal in both pairs. This is to be expected as evidence shows that the Diels-Alder reaction can proceed via a concerted, synchronous mechanism.<ref name="DA_1"/> However, it is important to note that this may also be the result of the calculation method used, as studies with other calculation methods (DFT/B3LYP) have also shown that other mechanisms are feasible.<ref name="DA_2"/>

=== Conclusion ===
By examining this simple Diels-Alder reaction between butadiene and ethylene, we can conclude from computational data that only orbitals need to share the same symmetry to be able to overlap and hence interact. This knowledge will be useful in Exercise 2, where we again construct a MO diagram for a another Diels-Alder reaction. By following the change in C-C bond lengths over the course of the reaction, it can also be concluded that as per theoretical data, bond lengths shorten when bond order increases and hybridisation decreases. Lastly, based on this calculation, we can conclude that the Diels-Alder reaction between butadiene and ethylene proceeds via synchronous bond formation in the transition state.

== References ==
<references>
<ref name="bondlength">M. A. Fox, J. K. Whitesell, E. Buchholz. <i>Organische Chemie: Grundlagen, Mechanismen, bioorganische Anwendungen</i> (1995).</ref>
<ref name="vdw_c">A. Bondi. [http://pubs.acs.org/doi/pdf/10.1021/j100785a001 <i>van der Waals Volumes and Radii </i>] J. Phys. Chem. <b>68</b>(3), 441–451 (1996).</ref>
<ref name="DA_1">K. N. Houk, Y. T Lin & F. K. Brown. [http://pubs.acs.org/doi/pdf/10.1021/ja00263a059 <i>Evidence for the Concerted Mechanism of the Diels-Alder Reaction of Butadiene with Ethylene.</i>] J. Am. Chem. SOC. <b>108</b>, 554-556 (1986).</ref>
<ref name="DA_2">E. Goldstein, B. Beno & K. N. Houk. [http://pubs.acs.org/doi/pdf/10.1021/ja9601494 <i>Density Functional Theory Prediction of the Relative Energies and Isotope Effects for the Concerted and Stepwise Mechanisms of the Diels-Alder Reaction of Butadiene and Ethylene</i>] J. Am. Chem. Soc. <b>118</b>, 6036-6043 (1996).
</ref>
</references>

Rep:Transition states (st4215): Exercise 1

2017-10-25T09:25:57Z

St4215:

== Exercise 1: Reaction of Butadiene with Ethylene ==
The reaction between butadiene and ethylene is a [4+2] cycloaddition reaction, or more specifically, a Diels-Alder reaction - a reaction involving a conjugated diene in the s-cis conformation, and a dienophile containing a double bond. In this simple Diels-Alder reaction, butadiene is the diene and ethylene is the dienophile. The reaction scheme for this reaction is shown below:
(insert chemdraw diagram)

In this exercise, we use this Diels-Alder reaction to determine the orbital symmetry requirements for a reaction to take place, and to show the effect of hybridisation and bond order on the length of C-C bonds. We also probe into the mechanism of the reaction, and determine if bond formation is synchronous or asynchronous.

=== Calculations ===
Calculations were performed at the PM6 level. Method 1 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial#Method_1 tutorial]) was used to locate the transition state.

The optimised molecules can be seen here:

{| class="wikitable"
! colspan="2" | Reactants
! Transition state
! Product
|-
|<jmol>
<jmolApplet>
<title>Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_CYCLOHEXENE_TS_IRC3_PM6.LOG | IRC file]]
| <jmol>
<jmolApplet>
<title>Cyclohexene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_CYCLOHEXENE_PDT_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Molecular orbitals ===

==== MO diagram ====
<small><i>Construct an MO diagram for the formation of the butadiene/ethene TS, including basic symmetry labels (symmetric/antisymmetric or s/a).</i></small><br>

The MO diagram for this cycloaddition reaction was constructed as shown below. We first assume based on prior knowledge that only orbitals of the same symmetry can combine; however, this is proven in a later section.

The MOs have been labelled accordingly with their numbers according to the calculations, and can be visualised in the section below.<br>
[[File:st4215_ex1_MO_diagram.PNG]]

Considering the actual energy levels of the MOs computed from the calculations, a more accurate MO diagram can be constructed, as seen [[Media:st4215_ex1_MO_diagram_actual.PNG|here]]. However, this does not affect the relative energy levels of the MOs (within each molecule) or the interactions between these MOs.

==== Computed MOs ====
<small><i>Include images (or Jmol objects) for each of the HOMO and LUMO of butadiene and ethene, and the four MOs these produce for the TS. Correlate these MOs with the ones in your MO diagram to show which orbitals interact.</i></small><br>

The HOMOs and LUMOs for each reactant, butadiene and ethylene, as well as the 4 MOs that these produce for the TS, were calculated and can be visualised below. The MO numbers correspond to that labelled on the MO diagram, allowing us to see which orbitals interact. We can also observe that these computed MOs bear physical resemblance to that drawn in the MO diagram, in terms of the bonding and antibonding phases in each MO.

{| class="wikitable"
! rowspan="2" | Symmetry
! colspan="2" | Reactants
! rowspan="2" colspan="2"| Transition state
|-
| style="text-align: center;" | Butadiene
| style="text-align: center;" | Ethylene
|-
| Antisymmetric
| <b>MO 11</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 7</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 16</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 19</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Symmetric
| <b>MO 12</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 6</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 17</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 18</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Symmetry requirements ====
<small><i>What can you conclude about the requirements for symmetry for a reaction (when is a reaction 'allowed' and when is it 'forbidden')? Write whether the orbital overlap integral is zero or non-zero for the case of a symmetric-antisymmetric interaction, a symmetric-symmetric interaction and an antisymmetric-antisymmetric interaction.</i></small><br>

From the table above as well as the MO diagram, we can see that the HOMO/LUMO of butadiene interact with the corresponding LUMO/HOMO in ethylene respectively. These interactions can occur as each pair of orbitals share the same symmetry. The HOMO of butadiene (MO 11) and the LUMO of ethylene (MO 7) are both antisymmetric, and interact to give two antisymmetric MOs in the TS (MOs 16 and 19). Similarly, the LUMO of ethylene (MO 12) and the HOMO of butadiene (MO 6) are both symmetric, and interact to give two symmetric MOs in the TS (MOs 17 and 18). Hence we can conclude that a reaction is only allowed when the relevant orbitals share the same symmetry, as this would allow orbitals to overlap. This is illustrated in the following table:

{| class="wikitable"
! Symmetry of interaction
! Orbital overlap integral
|-
| style="text-align: center;" | Symmetric-antisymmetric
| style="text-align: center;" | Zero
|-
| style="text-align: center;" | Symmetric-symmetric
| style="text-align: center;" | Non-zero
|-
| style="text-align: center;" | Antisymmetric-antisymmetric
| style="text-align: center;" | Non-zero
|}

=== C-C bond lengths ===
<small><i>Include measurements of the 4 C-C bond lengths of the reactants and the 6 C-C bond lengths of the TS and products. How do the bond lengths change as the reaction progresses? What are typical sp3 and sp2 C-C bond lengths? What is the Van der Waals radius of the C atom? How does this compare with the length of the partly formed C-C bonds in the TS.</i></small>

The C-C bond lengths in the reactants, TS and products are tabulated below.

{| class="wikitable"
! rowspan="2" colspan="2" |
! colspan="2" | Reactants
! rowspan="2" | Transition state
! rowspan="2" | Product
|-
| style="text-align: center;" | Butadiene
| style="text-align: center;" | Ethylene
|-
| colspan="2" style="text-align: center;"| Labelled C atoms
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7; label display</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4; label display</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>st4215_CYCLOHEXENE_PDT_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| rowspan="6" style="text-align: center;" | C-C bond<br> length / Å
| style="width: 50px;" | Bond A || <center> C1-C4: 1.34 </center>|| || <center> C1-C4: 1.38 </center> || <center> C1-C4: 1.50 </center>
|-
| Bond B || <center> C4-C6: 1.47 </center> || || <center> C4-C6: 1.41 </center> || <center> C4-C6: 1.34 </center>
|-
| Bond C || <center> C6-C7: 1.34 </center> || || <center> C6-C7: 1.38 </center> || <center> C6-C7: 1.50 </center>
|-
| Bond D || || <center> C1-C4: 1.33 </center> || <center> C11-C14: 1.38 </center> || <center> C11-C14: 1.54 </center>
|-
| Bond E || || || <center> C7-C14: 2.11 </center> || <center> C7-C14: 1.54 </center>
|-
| Bond F || || || <center> C1-C11: 2.11 </center> || <center> C1-C11: 1.54 </center>
|}

From the values above, we can observe the following changes in bond length as the reaction progresses.

{| class="wikitable" style="width: 750px;"
! Bond
! Trend in bond length as reaction progresses
! Graph
|-
| A || As the reaction progresses, the length of Bond A increases. This is because Bond A is initially a C=C double bond in butadiene, which becomes a sp<sup>2</sup>-sp<sup>3</sup> C-C single bond in cyclohexene. These lengths are similar to typical values of 1.34 Å for alkenes and 1.50 Å sp<sup>2</sup>-sp<sup>3</sup> C-C bonds.<ref name="bondlength"/>
| [[File:st4215_BondA.JPG|200px]]
|-
| B || As the reaction progresses, the length of Bond B decreases. This is because Bond B is initially an sp<sup>2</sup>-sp<sup>2</sup> C-C single bond in butadiene, which becomes a C=C double bond in cyclohexene. These lengths are similar to typical values of 1.47 Å for sp<sup>2</sup>-sp<sup>2</sup> C-C bonds and 1.34 Å for alkenes.<ref name="bondlength"/>
| [[File:st4215_BondB.JPG|200px]]
|-
| C || Similar to Bond A, as the reaction progresses, the length of Bond C increases. This is due to the same reason as explained for Bond A.
| [[File:st4215_BondC.JPG|200px]]
|-
| D || As the reaction progresses, the length of Bond D increases. This is because Bond B is initially an C=C single bond in ethylene, which becomes a sp<sup>3</sup>-sp<sup>3</sup> C-C single bond in cyclohexene. These lengths are similar to typical values of 1.34 Å for alkenes and 1.54 Å for sp<sup>3</sup>-sp<sup>3</sup> C-C bonds.<ref name="bondlength"/>
| [[File:st4215_BondD.JPG|200px]]
|-
| E || Bond E is formed in this reaction. Hence as the reaction progresses from the transition state to the product, the length of Bond E increases. The length of the fully formed Bond E in the product, an sp<sup>3</sup>-sp<sup>3</sup> C-C single bond, corresponds to the typical value of 1.54 Å.<ref name="bondlength"/> The distance between the C atoms in the TS (2.11 Å) falls between twice the van der Waal radius of C (2 x 1.70 Å<ref name="vdw_c"/> = 3.40 Å) and the length of the fully formed Bond E, indicating that the atoms are approaching each other.
| [[File:st4215_BondE.JPG|200px]]
|-
| F || Like Bond E, Bond F is also formed in this reaction. Hence as the reaction progresses from the transition state to the product, the length of Bond F increases, due to the same reasons as explained above.
| [[File:st4215_BondF.JPG|200px]]
|}

We can hence conclude that bond lengths in the reactants and product do not deviate from typical values. Additionally, we can also show that an increase in bond order from 1 to 2 indeed shortens the C-C bond, while an increase in hybridisation from sp<sup>2</sup> to sp<sup>3</sup> does lengthen the C-C bond, as seen in the comparison of theoretical values.

=== Transition state ===
<i><small>Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous?</small></i>
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 7; rotate x -40; select atomno=1, atomno=7, atomno=11, atomno=14; label display </script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
<name>cyclohexeneTS</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>cyclohexeneTS</target>
</jmolbutton>
<jmolbutton>
<script>measure 1 11; measure 7 14</script>
<text>C-C Distances</text>
<target>cyclohexeneTS</target>
</jmolbutton>
</jmol>
<br><br>
As illustrated above, the formation of the two bonds are synchronous as the relevant pairs of atoms (C1/C11 and C7/C14) are moving towards each other at the same time, with the distance between the two atoms being approximately equal in both pairs. This is to be expected as evidence shows that the Diels-Alder reaction can proceed via a concerted, synchronous mechanism.<ref name="DA_1"/> However, it is important to note that this may also be the result of the calculation method used, as studies with other calculation methods (DFT/B3LYP) have also shown that other mechanisms are feasible.<ref name="DA_2"/>

== References ==
<references>
<ref name="bondlength">M. A. Fox, J. K. Whitesell, E. Buchholz. <i>Organische Chemie: Grundlagen, Mechanismen, bioorganische Anwendungen</i> (1995).</ref>
<ref name="vdw_c">A. Bondi. [http://pubs.acs.org/doi/pdf/10.1021/j100785a001 <i>van der Waals Volumes and Radii </i>] J. Phys. Chem. <b>68</b>(3), 441–451 (1996).</ref>
<ref name="DA_1">K. N. Houk, Y. T Lin & F. K. Brown. [http://pubs.acs.org/doi/pdf/10.1021/ja00263a059 <i>Evidence for the Concerted Mechanism of the Diels-Alder Reaction of Butadiene with Ethylene.</i>] J. Am. Chem. SOC. <b>108</b>, 554-556 (1986).</ref>
<ref name="DA_2">E. Goldstein, B. Beno & K. N. Houk. [http://pubs.acs.org/doi/pdf/10.1021/ja9601494 <i>Density Functional Theory Prediction of the Relative Energies and Isotope Effects for the Concerted and Stepwise Mechanisms of the Diels-Alder Reaction of Butadiene and Ethylene</i>] J. Am. Chem. Soc. <b>118</b>, 6036-6043 (1996).
</ref>
</references>

Rep:Transition states (st4215): Exercise 1

2017-10-25T09:19:50Z

St4215: /* Exercise 1: Reaction of Butadiene with Ethylene */

== Exercise 1: Reaction of Butadiene with Ethylene ==
The reaction between butadiene and ethylene is a [4+2] cycloaddition reaction, or more specifically, a Diels-Alder reaction - a reaction involving a conjugated diene in the s-cis conformation, and a dienophile containing a double bond. In this simple Diels-Alder reaction, butadiene is the diene and ethylene is the dienophile. The reaction scheme for this reaction is shown below:
(insert chemdraw diagram)

In this exercise, we use this Diels-Alder reaction to determine the orbital symmetry requirements for a reaction to take place, and to show the effect of hybridisation and bond order on the length of C-C bonds. We also probe into the mechanism of the reaction, and determine if bond formation is synchronous or asynchronous.

=== Calculations ===
Calculations were performed at the PM6 level. Method 1 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial#Method_1 tutorial]) was used to locate the transition state.

The optimised molecules can be seen here:

{| class="wikitable"
! colspan="2" | Reactants
! Transition state
! Product
|-
|<jmol>
<jmolApplet>
<title>Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_CYCLOHEXENE_TS_IRC3_PM6.LOG | IRC file]]
| <jmol>
<jmolApplet>
<title>Cyclohexene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_CYCLOHEXENE_PDT_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Molecular orbitals ===

==== MO diagram ====
<small><i>Construct an MO diagram for the formation of the butadiene/ethene TS, including basic symmetry labels (symmetric/antisymmetric or s/a).</i></small><br>

The MO diagram for this cycloaddition reaction was constructed as shown below. We first assume based on prior knowledge that only orbitals of the same symmetry can combine; however, this is proven in a later section.

The MOs have been labelled accordingly with their numbers according to the calculations, and can be visualised in the section below.<br>
[[File:st4215_ex1_MO_diagram.PNG]]

Considering the actual energy levels of the MOs computed from the calculations, a more accurate MO diagram can be constructed, as seen [[Media:st4215_ex1_MO_diagram_actual.PNG|here]]. However, this does not affect the relative energy levels of the MOs (within each molecule) or the interactions between these MOs.

==== Computed MOs ====
<small><i>Include images (or Jmol objects) for each of the HOMO and LUMO of butadiene and ethene, and the four MOs these produce for the TS. Correlate these MOs with the ones in your MO diagram to show which orbitals interact.</i></small><br>

The HOMOs and LUMOs for each reactant, butadiene and ethylene, as well as the 4 MOs that these produce for the TS, were calculated and can be visualised below. The MO numbers correspond to that labelled on the MO diagram, allowing us to see which orbitals interact. We can also observe that these computed MOs bear physical resemblance to that drawn in the MO diagram, in terms of the bonding and antibonding phases in each MO.

{| class="wikitable"
! rowspan="2" | Symmetry
! colspan="2" | Reactants
! rowspan="2" colspan="2"| Transition state
|-
| style="text-align: center;" | Butadiene
| style="text-align: center;" | Ethylene
|-
| Antisymmetric
| <b>MO 11</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 7</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 16</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 19</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Symmetric
| <b>MO 12</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 6</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 17</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 18</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Symmetry requirements ====
<small><i>What can you conclude about the requirements for symmetry for a reaction (when is a reaction 'allowed' and when is it 'forbidden')? Write whether the orbital overlap integral is zero or non-zero for the case of a symmetric-antisymmetric interaction, a symmetric-symmetric interaction and an antisymmetric-antisymmetric interaction.</i></small><br>

From the table above as well as the MO diagram, we can see that the HOMO/LUMO of butadiene interact with the corresponding LUMO/HOMO in ethylene respectively. These interactions can occur as each pair of orbitals share the same symmetry. The HOMO of butadiene (MO 11) and the LUMO of ethylene (MO 7) are both antisymmetric, and interact to give two antisymmetric MOs in the TS (MOs 16 and 19). Similarly, the LUMO of ethylene (MO 12) and the HOMO of butadiene (MO 6) are both symmetric, and interact to give two symmetric MOs in the TS (MOs 17 and 18). Hence we can conclude that a reaction is only allowed when the relevant orbitals share the same symmetry, as this would allow orbitals to overlap. This is illustrated in the following table:

{| class="wikitable"
! Symmetry of interaction
! Orbital overlap integral
|-
| style="text-align: center;" | Symmetric-antisymmetric
| style="text-align: center;" | Zero
|-
| style="text-align: center;" | Symmetric-symmetric
| style="text-align: center;" | Non-zero
|-
| style="text-align: center;" | Antisymmetric-antisymmetric
| style="text-align: center;" | Non-zero
|}

=== C-C bond lengths ===
<small><i>Include measurements of the 4 C-C bond lengths of the reactants and the 6 C-C bond lengths of the TS and products. How do the bond lengths change as the reaction progresses? What are typical sp3 and sp2 C-C bond lengths? What is the Van der Waals radius of the C atom? How does this compare with the length of the partly formed C-C bonds in the TS.</i></small>

The C-C bond lengths in the reactants, TS and products are tabulated below.

{| class="wikitable"
! rowspan="2" colspan="2" |
! colspan="2" | Reactants
! rowspan="2" | Transition state
! rowspan="2" | Product
|-
| style="text-align: center;" | Butadiene
| style="text-align: center;" | Ethylene
|-
| colspan="2" style="text-align: center;"| Labelled C atoms
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7; label display</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4; label display</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>st4215_CYCLOHEXENE_PDT_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| rowspan="6" style="text-align: center;" | C-C bond<br> length / Å
| style="width: 50px;" | Bond A || <center> C1-C4: 1.34 </center>|| || <center> C1-C4: 1.38 </center> || <center> C1-C4: 1.50 </center>
|-
| Bond B || <center> C4-C6: 1.47 </center> || || <center> C4-C6: 1.41 </center> || <center> C4-C6: 1.34 </center>
|-
| Bond C || <center> C6-C7: 1.34 </center> || || <center> C6-C7: 1.38 </center> || <center> C6-C7: 1.50 </center>
|-
| Bond D || || <center> C1-C4: 1.33 </center> || <center> C11-C14: 1.38 </center> || <center> C11-C14: 1.54 </center>
|-
| Bond E || || || <center> C7-C14: 2.11 </center> || <center> C7-C14: 1.54 </center>
|-
| Bond F || || || <center> C1-C11: 2.11 </center> || <center> C1-C11: 1.54 </center>
|}

From the values above, we can observe the following changes in bond length as the reaction progresses.

{| class="wikitable" style="width: 750px;"
! Bond
! Trend in bond length as reaction progresses
! Graph
|-
| A || As the reaction progresses, the length of Bond A increases. This is because Bond A is initially a C=C double bond in butadiene, which becomes a sp<sup>2</sup>-sp<sup>3</sup> C-C single bond in cyclohexene. These lengths are similar to typical values of 1.34 Å for alkenes and 1.50 Å sp<sup>2</sup>-sp<sup>3</sup> C-C bonds.<ref name="bondlength"/>
| [[File:st4215_BondA.JPG|200px]]
|-
| B || As the reaction progresses, the length of Bond B decreases. This is because Bond B is initially an sp<sup>2</sup>-sp<sup>2</sup> C-C single bond in butadiene, which becomes a C=C double bond in cyclohexene. These lengths are similar to typical values of 1.47 Å for sp<sup>2</sup>-sp<sup>2</sup> C-C bonds and 1.34 Å for alkenes.<ref name="bondlength"/>
| [[File:st4215_BondB.JPG|200px]]
|-
| C || Similar to Bond A, as the reaction progresses, the length of Bond C increases. This is due to the same reason as explained for Bond A.
| [[File:st4215_BondC.JPG|200px]]
|-
| D || As the reaction progresses, the length of Bond D increases. This is because Bond B is initially an C=C single bond in ethylene, which becomes a sp<sup>3</sup>-sp<sup>3</sup> C-C single bond in cyclohexene. These lengths are similar to typical values of 1.34 Å for alkenes and 1.54 Å for sp<sup>3</sup>-sp<sup>3</sup> C-C bonds.<ref name="bondlength"/>
| [[File:st4215_BondD.JPG|200px]]
|-
| E || Bond E is formed in this reaction. Hence as the reaction progresses from the transition state to the product, the length of Bond E increases. The length of the fully formed Bond E in the product, an sp<sup>3</sup>-sp<sup>3</sup> C-C single bond, corresponds to the typical value of 1.54 Å.<ref name="bondlength"/> The distance between the C atoms in the TS (2.11 Å) falls between twice the van der Waal radius of C (2 x 1.70 Å<ref name="vdw_c"/> = 3.40 Å) and the length of the fully formed Bond E, indicating that the atoms are approaching each other.
| [[File:st4215_BondE.JPG|200px]]
|-
| F || Like Bond E, Bond F is also formed in this reaction. Hence as the reaction progresses from the transition state to the product, the length of Bond F increases, due to the same reasons as explained above.
| [[File:st4215_BondF.JPG|200px]]
|}

=== Transition state ===
<i><small>Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous?</small></i>
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 7; rotate x -40; select atomno=1, atomno=7, atomno=11, atomno=14; label display </script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
<name>cyclohexeneTS</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>cyclohexeneTS</target>
</jmolbutton>
<jmolbutton>
<script>measure 1 11; measure 7 14</script>
<text>C-C Distances</text>
<target>cyclohexeneTS</target>
</jmolbutton>
</jmol>
<br><br>
As illustrated above, the formation of the two bonds are synchronous as the relevant pairs of atoms (C1/C11 and C7/C14) are moving towards each other at the same time, with the distance between the two atoms being approximately equal in both pairs. This is to be expected as evidence shows that the Diels-Alder reaction can proceed via a concerted, synchronous mechanism.<ref name="DA_1"/> However, it is important to note that this may also be the result of the calculation method used, as studies with other calculation methods (DFT/B3LYP) have also shown that other mechanisms are feasible.<ref name="DA_2"/>

== References ==
<references>
<ref name="bondlength">M. A. Fox, J. K. Whitesell, E. Buchholz. <i>Organische Chemie: Grundlagen, Mechanismen, bioorganische Anwendungen</i> (1995).</ref>
<ref name="vdw_c">A. Bondi. [http://pubs.acs.org/doi/pdf/10.1021/j100785a001 <i>van der Waals Volumes and Radii </i>] J. Phys. Chem. <b>68</b>(3), 441–451 (1996).</ref>
<ref name="DA_1">K. N. Houk, Y. T Lin & F. K. Brown. [http://pubs.acs.org/doi/pdf/10.1021/ja00263a059 <i>Evidence for the Concerted Mechanism of the Diels-Alder Reaction of Butadiene with Ethylene.</i>] J. Am. Chem. SOC. <b>108</b>, 554-556 (1986).</ref>
<ref name="DA_2">E. Goldstein, B. Beno & K. N. Houk. [http://pubs.acs.org/doi/pdf/10.1021/ja9601494 <i>Density Functional Theory Prediction of the Relative Energies and Isotope Effects for the Concerted and Stepwise Mechanisms of the Diels-Alder Reaction of Butadiene and Ethylene</i>] J. Am. Chem. Soc. <b>118</b>, 6036-6043 (1996).
</ref>
</references>

Rep:Transition states (st4215): Exercise 1

2017-10-25T09:16:57Z

St4215: /* Symmetry requirements */

== Exercise 1: Reaction of Butadiene with Ethylene ==
The reaction between butadiene and ethylene is a [4+2] cycloaddition reaction, or more specifically, a Diels-Alder reaction - a reaction involving a conjugated diene in the s-cis conformation, and a dienophile containing a double bond. In this simple Diels-Alder reaction, butadiene is the diene and ethylene is the dienophile. The reaction scheme for this reaction is shown below:
(insert chemdraw diagram)

In this exercise, we use this Diels-Alder reaction to determine the orbital symmetry requirements for a reaction to take place, and to show the effect of hybridisation and bond order on the length of C-C bonds.

=== Calculations ===
Calculations were performed at the PM6 level. Method 1 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial#Method_1 tutorial]) was used to locate the transition state.

The optimised molecules can be seen here:

{| class="wikitable"
! colspan="2" | Reactants
! Transition state
! Product
|-
|<jmol>
<jmolApplet>
<title>Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_CYCLOHEXENE_TS_IRC3_PM6.LOG | IRC file]]
| <jmol>
<jmolApplet>
<title>Cyclohexene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_CYCLOHEXENE_PDT_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Molecular orbitals ===

==== MO diagram ====
<small><i>Construct an MO diagram for the formation of the butadiene/ethene TS, including basic symmetry labels (symmetric/antisymmetric or s/a).</i></small><br>

The MO diagram for this cycloaddition reaction was constructed as shown below. We first assume based on prior knowledge that only orbitals of the same symmetry can combine; however, this is proven in a later section.

The MOs have been labelled accordingly with their numbers according to the calculations, and can be visualised in the section below.<br>
[[File:st4215_ex1_MO_diagram.PNG]]

Considering the actual energy levels of the MOs computed from the calculations, a more accurate MO diagram can be constructed, as seen [[Media:st4215_ex1_MO_diagram_actual.PNG|here]]. However, this does not affect the relative energy levels of the MOs (within each molecule) or the interactions between these MOs.

==== Computed MOs ====
<small><i>Include images (or Jmol objects) for each of the HOMO and LUMO of butadiene and ethene, and the four MOs these produce for the TS. Correlate these MOs with the ones in your MO diagram to show which orbitals interact.</i></small><br>

The HOMOs and LUMOs for each reactant, butadiene and ethylene, as well as the 4 MOs that these produce for the TS, were calculated and can be visualised below. The MO numbers correspond to that labelled on the MO diagram, allowing us to see which orbitals interact. We can also observe that these computed MOs bear physical resemblance to that drawn in the MO diagram, in terms of the bonding and antibonding phases in each MO.

{| class="wikitable"
! rowspan="2" | Symmetry
! colspan="2" | Reactants
! rowspan="2" colspan="2"| Transition state
|-
| style="text-align: center;" | Butadiene
| style="text-align: center;" | Ethylene
|-
| Antisymmetric
| <b>MO 11</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 7</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 16</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 19</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Symmetric
| <b>MO 12</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 6</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 17</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 18</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Symmetry requirements ====
<small><i>What can you conclude about the requirements for symmetry for a reaction (when is a reaction 'allowed' and when is it 'forbidden')? Write whether the orbital overlap integral is zero or non-zero for the case of a symmetric-antisymmetric interaction, a symmetric-symmetric interaction and an antisymmetric-antisymmetric interaction.</i></small><br>

From the table above as well as the MO diagram, we can see that the HOMO/LUMO of butadiene interact with the corresponding LUMO/HOMO in ethylene respectively. These interactions can occur as each pair of orbitals share the same symmetry. The HOMO of butadiene (MO 11) and the LUMO of ethylene (MO 7) are both antisymmetric, and interact to give two antisymmetric MOs in the TS (MOs 16 and 19). Similarly, the LUMO of ethylene (MO 12) and the HOMO of butadiene (MO 6) are both symmetric, and interact to give two symmetric MOs in the TS (MOs 17 and 18). Hence we can conclude that a reaction is only allowed when the relevant orbitals share the same symmetry, as this would allow orbitals to overlap. This is illustrated in the following table:

{| class="wikitable"
! Symmetry of interaction
! Orbital overlap integral
|-
| style="text-align: center;" | Symmetric-antisymmetric
| style="text-align: center;" | Zero
|-
| style="text-align: center;" | Symmetric-symmetric
| style="text-align: center;" | Non-zero
|-
| style="text-align: center;" | Antisymmetric-antisymmetric
| style="text-align: center;" | Non-zero
|}

=== C-C bond lengths ===
<small><i>Include measurements of the 4 C-C bond lengths of the reactants and the 6 C-C bond lengths of the TS and products. How do the bond lengths change as the reaction progresses? What are typical sp3 and sp2 C-C bond lengths? What is the Van der Waals radius of the C atom? How does this compare with the length of the partly formed C-C bonds in the TS.</i></small>

The C-C bond lengths in the reactants, TS and products are tabulated below.

{| class="wikitable"
! rowspan="2" colspan="2" |
! colspan="2" | Reactants
! rowspan="2" | Transition state
! rowspan="2" | Product
|-
| style="text-align: center;" | Butadiene
| style="text-align: center;" | Ethylene
|-
| colspan="2" style="text-align: center;"| Labelled C atoms
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7; label display</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4; label display</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>st4215_CYCLOHEXENE_PDT_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| rowspan="6" style="text-align: center;" | C-C bond<br> length / Å
| style="width: 50px;" | Bond A || <center> C1-C4: 1.34 </center>|| || <center> C1-C4: 1.38 </center> || <center> C1-C4: 1.50 </center>
|-
| Bond B || <center> C4-C6: 1.47 </center> || || <center> C4-C6: 1.41 </center> || <center> C4-C6: 1.34 </center>
|-
| Bond C || <center> C6-C7: 1.34 </center> || || <center> C6-C7: 1.38 </center> || <center> C6-C7: 1.50 </center>
|-
| Bond D || || <center> C1-C4: 1.33 </center> || <center> C11-C14: 1.38 </center> || <center> C11-C14: 1.54 </center>
|-
| Bond E || || || <center> C7-C14: 2.11 </center> || <center> C7-C14: 1.54 </center>
|-
| Bond F || || || <center> C1-C11: 2.11 </center> || <center> C1-C11: 1.54 </center>
|}

From the values above, we can observe the following changes in bond length as the reaction progresses.

{| class="wikitable" style="width: 750px;"
! Bond
! Trend in bond length as reaction progresses
! Graph
|-
| A || As the reaction progresses, the length of Bond A increases. This is because Bond A is initially a C=C double bond in butadiene, which becomes a sp<sup>2</sup>-sp<sup>3</sup> C-C single bond in cyclohexene. These lengths are similar to typical values of 1.34 Å for alkenes and 1.50 Å sp<sup>2</sup>-sp<sup>3</sup> C-C bonds.<ref name="bondlength"/>
| [[File:st4215_BondA.JPG|200px]]
|-
| B || As the reaction progresses, the length of Bond B decreases. This is because Bond B is initially an sp<sup>2</sup>-sp<sup>2</sup> C-C single bond in butadiene, which becomes a C=C double bond in cyclohexene. These lengths are similar to typical values of 1.47 Å for sp<sup>2</sup>-sp<sup>2</sup> C-C bonds and 1.34 Å for alkenes.<ref name="bondlength"/>
| [[File:st4215_BondB.JPG|200px]]
|-
| C || Similar to Bond A, as the reaction progresses, the length of Bond C increases. This is due to the same reason as explained for Bond A.
| [[File:st4215_BondC.JPG|200px]]
|-
| D || As the reaction progresses, the length of Bond D increases. This is because Bond B is initially an C=C single bond in ethylene, which becomes a sp<sup>3</sup>-sp<sup>3</sup> C-C single bond in cyclohexene. These lengths are similar to typical values of 1.34 Å for alkenes and 1.54 Å for sp<sup>3</sup>-sp<sup>3</sup> C-C bonds.<ref name="bondlength"/>
| [[File:st4215_BondD.JPG|200px]]
|-
| E || Bond E is formed in this reaction. Hence as the reaction progresses from the transition state to the product, the length of Bond E increases. The length of the fully formed Bond E in the product, an sp<sup>3</sup>-sp<sup>3</sup> C-C single bond, corresponds to the typical value of 1.54 Å.<ref name="bondlength"/> The distance between the C atoms in the TS (2.11 Å) falls between twice the van der Waal radius of C (2 x 1.70 Å<ref name="vdw_c"/> = 3.40 Å) and the length of the fully formed Bond E, indicating that the atoms are approaching each other.
| [[File:st4215_BondE.JPG|200px]]
|-
| F || Like Bond E, Bond F is also formed in this reaction. Hence as the reaction progresses from the transition state to the product, the length of Bond F increases, due to the same reasons as explained above.
| [[File:st4215_BondF.JPG|200px]]
|}

=== Transition state ===
<i><small>Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous?</small></i>
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 7; rotate x -40; select atomno=1, atomno=7, atomno=11, atomno=14; label display </script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
<name>cyclohexeneTS</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>cyclohexeneTS</target>
</jmolbutton>
<jmolbutton>
<script>measure 1 11; measure 7 14</script>
<text>C-C Distances</text>
<target>cyclohexeneTS</target>
</jmolbutton>
</jmol>
<br><br>
As illustrated above, the formation of the two bonds are synchronous as the relevant pairs of atoms (C1/C11 and C7/C14) are moving towards each other at the same time, with the distance between the two atoms being approximately equal in both pairs. This is to be expected as evidence shows that the Diels-Alder reaction can proceed via a concerted, synchronous mechanism.<ref name="DA_1"/> However, it is important to note that this may also be the result of the calculation method used, as studies with other calculation methods (DFT/B3LYP) have also shown that other mechanisms are feasible.<ref name="DA_2"/>

== References ==
<references>
<ref name="bondlength">M. A. Fox, J. K. Whitesell, E. Buchholz. <i>Organische Chemie: Grundlagen, Mechanismen, bioorganische Anwendungen</i> (1995).</ref>
<ref name="vdw_c">A. Bondi. [http://pubs.acs.org/doi/pdf/10.1021/j100785a001 <i>van der Waals Volumes and Radii </i>] J. Phys. Chem. <b>68</b>(3), 441–451 (1996).</ref>
<ref name="DA_1">K. N. Houk, Y. T Lin & F. K. Brown. [http://pubs.acs.org/doi/pdf/10.1021/ja00263a059 <i>Evidence for the Concerted Mechanism of the Diels-Alder Reaction of Butadiene with Ethylene.</i>] J. Am. Chem. SOC. <b>108</b>, 554-556 (1986).</ref>
<ref name="DA_2">E. Goldstein, B. Beno & K. N. Houk. [http://pubs.acs.org/doi/pdf/10.1021/ja9601494 <i>Density Functional Theory Prediction of the Relative Energies and Isotope Effects for the Concerted and Stepwise Mechanisms of the Diels-Alder Reaction of Butadiene and Ethylene</i>] J. Am. Chem. Soc. <b>118</b>, 6036-6043 (1996).
</ref>
</references>

Rep:Transition states (st4215): Exercise 1

2017-10-25T09:14:02Z

St4215: /* MO diagram */

== Exercise 1: Reaction of Butadiene with Ethylene ==
The reaction between butadiene and ethylene is a [4+2] cycloaddition reaction, or more specifically, a Diels-Alder reaction - a reaction involving a conjugated diene in the s-cis conformation, and a dienophile containing a double bond. In this simple Diels-Alder reaction, butadiene is the diene and ethylene is the dienophile. The reaction scheme for this reaction is shown below:
(insert chemdraw diagram)

In this exercise, we use this Diels-Alder reaction to determine the orbital symmetry requirements for a reaction to take place, and to show the effect of hybridisation and bond order on the length of C-C bonds.

=== Calculations ===
Calculations were performed at the PM6 level. Method 1 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial#Method_1 tutorial]) was used to locate the transition state.

The optimised molecules can be seen here:

{| class="wikitable"
! colspan="2" | Reactants
! Transition state
! Product
|-
|<jmol>
<jmolApplet>
<title>Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_CYCLOHEXENE_TS_IRC3_PM6.LOG | IRC file]]
| <jmol>
<jmolApplet>
<title>Cyclohexene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_CYCLOHEXENE_PDT_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Molecular orbitals ===

==== MO diagram ====
<small><i>Construct an MO diagram for the formation of the butadiene/ethene TS, including basic symmetry labels (symmetric/antisymmetric or s/a).</i></small><br>

The MO diagram for this cycloaddition reaction was constructed as shown below. We first assume based on prior knowledge that only orbitals of the same symmetry can combine; however, this is proven in a later section.

The MOs have been labelled accordingly with their numbers according to the calculations, and can be visualised in the section below.<br>
[[File:st4215_ex1_MO_diagram.PNG]]

Considering the actual energy levels of the MOs computed from the calculations, a more accurate MO diagram can be constructed, as seen [[Media:st4215_ex1_MO_diagram_actual.PNG|here]]. However, this does not affect the relative energy levels of the MOs (within each molecule) or the interactions between these MOs.

==== Computed MOs ====
<small><i>Include images (or Jmol objects) for each of the HOMO and LUMO of butadiene and ethene, and the four MOs these produce for the TS. Correlate these MOs with the ones in your MO diagram to show which orbitals interact.</i></small><br>

The HOMOs and LUMOs for each reactant, butadiene and ethylene, as well as the 4 MOs that these produce for the TS, were calculated and can be visualised below. The MO numbers correspond to that labelled on the MO diagram, allowing us to see which orbitals interact. We can also observe that these computed MOs bear physical resemblance to that drawn in the MO diagram, in terms of the bonding and antibonding phases in each MO.

{| class="wikitable"
! rowspan="2" | Symmetry
! colspan="2" | Reactants
! rowspan="2" colspan="2"| Transition state
|-
| style="text-align: center;" | Butadiene
| style="text-align: center;" | Ethylene
|-
| Antisymmetric
| <b>MO 11</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 7</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 16</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 19</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Symmetric
| <b>MO 12</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 6</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 17</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 18</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Symmetry requirements ====
<small><i>What can you conclude about the requirements for symmetry for a reaction (when is a reaction 'allowed' and when is it 'forbidden')? Write whether the orbital overlap integral is zero or non-zero for the case of a symmetric-antisymmetric interaction, a symmetric-symmetric interaction and an antisymmetric-antisymmetric interaction.</i></small><br>

From the table above as well as the MO diagram, we can see that the HOMO/LUMO of butadiene interact with the corresponding LUMO/HOMO in ethylene respectively. These interactions can occur as each pair of orbitals share the same symmetry. The HOMO of butadiene (MO 11) and the LUMO of ethylene (MO 7) are both antisymmetric, and interact to give two antisymmetric MOs in the TS (MOs 16 and 19). Similarly, the LUMO of ethylene (MO 12) and the HOMO of butadiene (MO 6) are both symmetric, and interact to give two symmetric MOs in the TS (MOs 17 and 18). Hence we can conclude that a reaction is only allowed when the relevant orbitals share the same symmetry, as this would allow orbitals to overlap. (QUANTUM EXPLANATION?????) This is illustrated in the following table:

{| class="wikitable"
! Symmetry of interaction
! Orbital overlap integral
|-
| style="text-align: center;" | Symmetric-antisymmetric
| style="text-align: center;" | Zero
|-
| style="text-align: center;" | Symmetric-symmetric
| style="text-align: center;" | Non-zero
|-
| style="text-align: center;" | Antisymmetric-antisymmetric
| style="text-align: center;" | Non-zero
|}

=== C-C bond lengths ===
<small><i>Include measurements of the 4 C-C bond lengths of the reactants and the 6 C-C bond lengths of the TS and products. How do the bond lengths change as the reaction progresses? What are typical sp3 and sp2 C-C bond lengths? What is the Van der Waals radius of the C atom? How does this compare with the length of the partly formed C-C bonds in the TS.</i></small>

The C-C bond lengths in the reactants, TS and products are tabulated below.

{| class="wikitable"
! rowspan="2" colspan="2" |
! colspan="2" | Reactants
! rowspan="2" | Transition state
! rowspan="2" | Product
|-
| style="text-align: center;" | Butadiene
| style="text-align: center;" | Ethylene
|-
| colspan="2" style="text-align: center;"| Labelled C atoms
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7; label display</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4; label display</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>st4215_CYCLOHEXENE_PDT_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| rowspan="6" style="text-align: center;" | C-C bond<br> length / Å
| style="width: 50px;" | Bond A || <center> C1-C4: 1.34 </center>|| || <center> C1-C4: 1.38 </center> || <center> C1-C4: 1.50 </center>
|-
| Bond B || <center> C4-C6: 1.47 </center> || || <center> C4-C6: 1.41 </center> || <center> C4-C6: 1.34 </center>
|-
| Bond C || <center> C6-C7: 1.34 </center> || || <center> C6-C7: 1.38 </center> || <center> C6-C7: 1.50 </center>
|-
| Bond D || || <center> C1-C4: 1.33 </center> || <center> C11-C14: 1.38 </center> || <center> C11-C14: 1.54 </center>
|-
| Bond E || || || <center> C7-C14: 2.11 </center> || <center> C7-C14: 1.54 </center>
|-
| Bond F || || || <center> C1-C11: 2.11 </center> || <center> C1-C11: 1.54 </center>
|}

From the values above, we can observe the following changes in bond length as the reaction progresses.

{| class="wikitable" style="width: 750px;"
! Bond
! Trend in bond length as reaction progresses
! Graph
|-
| A || As the reaction progresses, the length of Bond A increases. This is because Bond A is initially a C=C double bond in butadiene, which becomes a sp<sup>2</sup>-sp<sup>3</sup> C-C single bond in cyclohexene. These lengths are similar to typical values of 1.34 Å for alkenes and 1.50 Å sp<sup>2</sup>-sp<sup>3</sup> C-C bonds.<ref name="bondlength"/>
| [[File:st4215_BondA.JPG|200px]]
|-
| B || As the reaction progresses, the length of Bond B decreases. This is because Bond B is initially an sp<sup>2</sup>-sp<sup>2</sup> C-C single bond in butadiene, which becomes a C=C double bond in cyclohexene. These lengths are similar to typical values of 1.47 Å for sp<sup>2</sup>-sp<sup>2</sup> C-C bonds and 1.34 Å for alkenes.<ref name="bondlength"/>
| [[File:st4215_BondB.JPG|200px]]
|-
| C || Similar to Bond A, as the reaction progresses, the length of Bond C increases. This is due to the same reason as explained for Bond A.
| [[File:st4215_BondC.JPG|200px]]
|-
| D || As the reaction progresses, the length of Bond D increases. This is because Bond B is initially an C=C single bond in ethylene, which becomes a sp<sup>3</sup>-sp<sup>3</sup> C-C single bond in cyclohexene. These lengths are similar to typical values of 1.34 Å for alkenes and 1.54 Å for sp<sup>3</sup>-sp<sup>3</sup> C-C bonds.<ref name="bondlength"/>
| [[File:st4215_BondD.JPG|200px]]
|-
| E || Bond E is formed in this reaction. Hence as the reaction progresses from the transition state to the product, the length of Bond E increases. The length of the fully formed Bond E in the product, an sp<sup>3</sup>-sp<sup>3</sup> C-C single bond, corresponds to the typical value of 1.54 Å.<ref name="bondlength"/> The distance between the C atoms in the TS (2.11 Å) falls between twice the van der Waal radius of C (2 x 1.70 Å<ref name="vdw_c"/> = 3.40 Å) and the length of the fully formed Bond E, indicating that the atoms are approaching each other.
| [[File:st4215_BondE.JPG|200px]]
|-
| F || Like Bond E, Bond F is also formed in this reaction. Hence as the reaction progresses from the transition state to the product, the length of Bond F increases, due to the same reasons as explained above.
| [[File:st4215_BondF.JPG|200px]]
|}

=== Transition state ===
<i><small>Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous?</small></i>
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 7; rotate x -40; select atomno=1, atomno=7, atomno=11, atomno=14; label display </script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
<name>cyclohexeneTS</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>cyclohexeneTS</target>
</jmolbutton>
<jmolbutton>
<script>measure 1 11; measure 7 14</script>
<text>C-C Distances</text>
<target>cyclohexeneTS</target>
</jmolbutton>
</jmol>
<br><br>
As illustrated above, the formation of the two bonds are synchronous as the relevant pairs of atoms (C1/C11 and C7/C14) are moving towards each other at the same time, with the distance between the two atoms being approximately equal in both pairs. This is to be expected as evidence shows that the Diels-Alder reaction can proceed via a concerted, synchronous mechanism.<ref name="DA_1"/> However, it is important to note that this may also be the result of the calculation method used, as studies with other calculation methods (DFT/B3LYP) have also shown that other mechanisms are feasible.<ref name="DA_2"/>

== References ==
<references>
<ref name="bondlength">M. A. Fox, J. K. Whitesell, E. Buchholz. <i>Organische Chemie: Grundlagen, Mechanismen, bioorganische Anwendungen</i> (1995).</ref>
<ref name="vdw_c">A. Bondi. [http://pubs.acs.org/doi/pdf/10.1021/j100785a001 <i>van der Waals Volumes and Radii </i>] J. Phys. Chem. <b>68</b>(3), 441–451 (1996).</ref>
<ref name="DA_1">K. N. Houk, Y. T Lin & F. K. Brown. [http://pubs.acs.org/doi/pdf/10.1021/ja00263a059 <i>Evidence for the Concerted Mechanism of the Diels-Alder Reaction of Butadiene with Ethylene.</i>] J. Am. Chem. SOC. <b>108</b>, 554-556 (1986).</ref>
<ref name="DA_2">E. Goldstein, B. Beno & K. N. Houk. [http://pubs.acs.org/doi/pdf/10.1021/ja9601494 <i>Density Functional Theory Prediction of the Relative Energies and Isotope Effects for the Concerted and Stepwise Mechanisms of the Diels-Alder Reaction of Butadiene and Ethylene</i>] J. Am. Chem. Soc. <b>118</b>, 6036-6043 (1996).
</ref>
</references>

Rep:Transition states (st4215)

2017-10-25T09:06:29Z

St4215:

Rep:Transition states (st4215)

2017-10-25T09:05:22Z

St4215:

test

Rep:Transition states (st4215)

2017-10-25T09:04:53Z

St4215: Blanked the page

Rep:Transition states (st4215)

2017-10-25T09:04:32Z

St4215:

Rep:Transition states (st4215)

2017-10-25T09:04:00Z

St4215:

Rep:Transition states (st4215)

2017-10-25T09:03:14Z

St4215: /* Introduction */

Rep:Transition states (st4215)

2017-10-25T08:54:43Z

St4215: /* Exercise 1: Reaction of Butadiene with Ethylene */

File:St4215 Pes.jpeg

2017-10-25T04:12:42Z

St4215:

Rep:Transition states (st4215): Exercise 3

2017-10-25T03:50:33Z

St4215: /* Calculations */

== Exercise 3: Diels-Alder vs Cheletropic ==
In this exercise, we examine the possible reactions between o-xylylene and SO<sub>2</sub> - the Diels-Alder reaction and the cheletropic reaction, as illustrated in the reaction scheme below.
(insert chemdraw diagram)

Again, in the Diels-Alder reaction, the dienophile SO<sub>2</sub> can approach the diene o-xylylene at different orientations, resulting in the endo- and exo- DA products. The cheletropic reaction, which is a pericyclic reaction in which the new bonds formed are made to the same atom, results in a single product.

In this exercise, we compare the three different reaction pathways - both Diels-Alder reactions and the cheletropic reaction - in terms of their reaction coordinates, as well as which is the most thermodynamically or kinetically favoured. We also investigate the possibility of a Diels-Alder reaction at a second site in xylylene.

=== Calculations ===
Calculations were performed at the PM6 level. Method 3 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial#Method_3 tutorial]) was used to locate the transition state.

The optimised molecules can be seen here:

{| class="wikitable"
! colspan="2" | Reactants
|-
| style="text-align: center;" | o-xylylene
| style="text-align: center;" | SO<sub>2</sub>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16</script>
<uploadedFileContents>st4215_XYLYLENE_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16</script>
<uploadedFileContents>st4215_SO2_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo || style="text-align: center;" | Exo
|-
| style="text-align: center;" | Transition state
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>St4215_ex3_ENDO_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_ex3_ENDO_TS_IRC2_PM6.LOG | IRC file]]
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>st4215_ex3_Exo_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_ex3_Exo_TS_IRC_PM6.LOG | IRC file]]
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>st4215_ex3_CHEL_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_ex3_CHEL_TS_IRC_PM6.LOG | IRC file]]
|-
| style="text-align: center;" | Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>St4215_ex3_ENDO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>st4215_ex3_EXO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>st4215_ex3_CHEL_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Reaction coordinate ===
<small><i>Visualise the reaction coordinate with an IRC calculation for each path. Include a .gif file in the wiki of these IRCs.</i></small>

The formation of the products for each of the endo- and exo- Diels-Alder reactions, as well as the cheletropic reaction, can be visualised below.

{| class="wikitable"
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
|-
| [[File:st4215_ENDO_TS_IRCmovie.gif]]
| [[File:st4215_Exo_TS_IRCmovie.gif]]
| [[File:st4215_Chel_TS_IRCmovie.gif]]
|}

We can see that SO<sub>2</sub> approaches xylylene at a different orientation and angle for each of these reactions. This difference in approach trajectories hence lead to the formation of different products.

It can also be observed that in each of the reactions, as the product is formed, the 6-membered ring in xylylene becomes aromatic. This means that there is a strong driving force for the formation of the products. In contrast, the reactant xylylene is highly unstable as it is non-aromatic, and as can be seen in these reactions, can readily react with unsaturated bonds to form a aromatic product.

=== Energy analysis ===
<small><i>Calculate the activation and reaction energies (converting to kJ/mol) for each step as in Exercise 2 to determine which route is preferred. Using Excel or Chemdraw, draw a reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels-Alder reactions and the cheletropic reaction. You can set the 0 energy level to the reactants at infinite separation.</i></small>

==== Free energies ====
The free energies of the reactants, transition states and products for each of the 3 reactions are tabulated below. The reaction barriers and energies are also calculated.

{| class="wikitable"
! rowspan="2" scope="col" style="width: 150px;" |
! colspan="2" scope="col" style="width: 300px;" | Energy at 298 K (PM6)
|-
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
|-
| colspan="3" style="background: #B7C3D0" | <b>Reactants</b>
|-
| Xylylene || style="text-align: center;" | 0.17876 || style="text-align: center;" | 469.34
|-
| SO<sub>2</sub> || style="text-align: center;" | -0.11927 || style="text-align: center;" | -313.14
|-
| Total reactants || style="text-align: center;" | 0.059496 || style="text-align: center;" | 156.21
|-
| colspan="3" style="background: #B7C3D0" | <b>Endo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | 0.090560 || style="text-align: center;" | 237.77
|-
| Product || style="text-align: center;" | 0.021704 || style="text-align: center;" | 56.984
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0311 || style="text-align: center;" | 81.6
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0378 || style="text-align: center;" | -99.2
|-
| colspan="3" style="background: #B7C3D0" | <b>Exo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | 0.092078 || style="text-align: center;" | 241.75
|-
| Product || style="text-align: center;" | 0.021455 || style="text-align: center;" | 56.330
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0326 || style="text-align: center;" | 85.5
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0380 || style="text-align: center;" | -99.9
|-
| colspan="3" style="background: #B7C3D0" | <b>Cheletropic</b>
|-
| Transition state || style="text-align: center;" | 0.099058 || style="text-align: center;" | 260.08
|-
| Product || style="text-align: center;" | -0.000002 || style="text-align: center;" | -0.0052510
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0396 || style="text-align: center;" | 104
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0595 || style="text-align: center;" | -156
|}
<small><i>^Note that all values from the calculations are reported to 5 s.f. unless more decimal places are needed to differentiate between each reaction type. Derived quantities (reaction barrier and reaction energy) are reported to 3 s.f.</i></small>

==== Thermodynamic and kinetic products ====
From the values above, a combined reaction profile showing the reaction barriers and reaction energies can also be plotted as seen below.
[[File:st4215_ex3_Reaction_profile2.PNG|600px|thumb|center|Reaction profile diagram for the 3 Diels-Alder and cheletropic reactions, setting the energy of the reactants to zero]]

We can clearly see that the endo- Diels-Alder product is the kinetic product as it has the lowest reaction barrier of +81.6 kJmol<sup>-1</sup>, while the cheletropic product is the thermodynamic product as it is most stable as has the lowest energy of -156 kJmol<sup>-1</sup>. This is consistent with experimental and computational data.<ref name="chel_3"/><ref name="chel_1"/>

The high stability of the cheletropic product is likely due to the preference of S to adopt a five-membered compared to 6-membered ring structure. This is in contrast to saturated carbon rings, where 6-membered cyclohexane is more stable than 5-membered cyclopentane due to deviation from tetrahedral bond angles of 109° in cyclopentane, resulting in angle strain. However, due to the larger size of the S atom, C-C<sub>tet</sub>-S bond angles in a 5-membered unsaturated sulfur ring (like in the cheletropic product) are much closer to the tetrahedral bond angle, at 105°. In comparison, the 6-membered heterocycle in the Diels-Alder products have C-C<sub>tet</sub>-S bond angles of around 114°, which are comparatively much larger than 109°. This is illustrated below:

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
|-
| Products
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; measure 3 16 11</script>
<uploadedFileContents>St4215_ex3_ENDO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; rotate y 180; measure 3 16 11</script>
<uploadedFileContents>st4215_ex3_EXO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; measure 1 7 15</script>
<uploadedFileContents>st4215_ex3_CHEL_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

It is also expected that one of the Diels-Alder products (the endo- product) is the kinetic product instead of the cheletropic product.<ref name="chel_3"/> While the reaction barriers for both endo- and exo- Diels-Alder reactions are similar, the reaction barrier for the cheletropic reaction is much higher. Examining their transition states (see below) allows us to infer why.

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
|-
| Transition state HOMO
| style="text-align: center;" | [[File:st4215_ex3_Endo_TS_HOMO.PNG]]
| style="text-align: center;" | [[File:st4215_ex3_Exo_TS_HOMO.PNG]]
| style="text-align: center;" | [[File:st4215_ex3_Chel_TS_HOMO.PNG]]
|-
| Discussion
| colspan="2" | Some stabilising secondary orbital interactions can be seen in the HOMOs of the endo- and exo- transition states, hence lowering its energy and reducing the reaction barriers for these reactions.
| No stabilising secondary orbital interactions are present here - in fact, the HOMO of the transition state is highly antisymmetric with many nodes, and hence likely to be high in energy.
|}

Like most Diels-Alder reactions, the endo and not the exo- product is the kinetic product due to more or greater stabilising secondary orbital interactions in the transition state. However, in this reaction, both the endo- and exo- transition states seem to have an approximately equal but not significant amount of stabilising orbital interactions in the HOMO. This explains why the endo- and exo- transition states are relatively close in energy.

== Extra: Diels-Alder reaction at a different site ==
O-xylylene also contains a cis-butadiene fragment that can act as the diene in another Diels-Alder reaction. However, this reaction is very kinetically and thermodynamically favourable.

=== Optimised molecules ===
The optimised molecules can be seen here. Optimised reactants (o-xylylene and SO<sub>2</sub>) from the earlier reaction were used.

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder (2)
|-
| style="text-align: center;" | Endo || style="text-align: center;" | Exo
|-
| style="text-align: center;" | Transition state
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>st4215_BAD_ENDO_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_BAD_ENDO_IRC_PM6.LOG | IRC file]]
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>st4215_BAD_EXO_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_BAD_EXO_IRC_PM6.LOG | IRC file]]
|-
| style="text-align: center;" | Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 64</script>
<uploadedFileContents>st4215_BAD_ENDO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_BAD_EXO_PDT_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Energy analysis ===
The free energies of the reactants, transition states and products for both the endo- and exo- Diels Alder reactions are tabulated below. The reaction barriers and energies are also calculated.

{| class="wikitable"
! rowspan="2" scope="col" style="width: 150px;" |
! colspan="2" scope="col" style="width: 300px;" | Energy at 298 K (PM6)
|-
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
|-
| colspan="3" style="background: #B7C3D0" | <b>Reactants</b>
|-
| Xylylene || style="text-align: center;" | 0.17876 || style="text-align: center;" | 469.34
|-
| SO<sub>2</sub> || style="text-align: center;" | -0.11927 || style="text-align: center;" | -313.14
|-
| Total reactants || style="text-align: center;" | 0.059496 || style="text-align: center;" | 156.21
|-
| colspan="3" style="background: #B7C3D0" | <b>Endo- Diels-Alder (2)</b>
|-
| Transition state || style="text-align: center;" | 0.10207 || style="text-align: center;" | 267.99
|-
| Product || style="text-align: center;" | 0.065613 || style="text-align: center;" | 172.27
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0426 || style="text-align: center;" | 112
|-
| Reaction energy (ΔG) || style="text-align: center;" | +0.00612 || style="text-align: center;" | +16.1
|-
| colspan="3" style="background: #B7C3D0" | <b>Exo- Diels-Alder (2)</b>
|-
| Transition state || style="text-align: center;" | 0.10505 || style="text-align: center;" | 275.82
|-
| Product || style="text-align: center;" | 0.067305 || style="text-align: center;" | 176.71
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0456 || style="text-align: center;" | 120
|-
| Reaction energy (ΔG) || style="text-align: center;" | +0.00781 || style="text-align: center;" | +20.5
|}
<small><i>^Note that all values from the calculations are reported to 5 s.f. unless more decimal places are needed to differentiate between each reaction type. Derived quantities (reaction barrier and reaction energy) are reported to 3 s.f.</i></small>

We can hence see that this reaction is both kinetically and thermodynamically unfavourable compared to the other Diels-Alder reaction (previously discussed) and the cheletropic reaction.

Comparing the reaction barriers, the activation energies of 112 kJmol<sup>-1</sup> (endo) and 120 kJmol<sup>-1</sup> (exo) are much higher than that of the other DA reaction, at 81.6 kJmol<sup>-1</sup> (endo) and 85.5 kJmol<sup>-1</sup> (exo), as well as the cheletropic reaction, at 104 kJmol<sup>-1</sup>. Hence this Diels-Alder reaction is the most kinetically unfavourable reaction possible.

Comparing the reaction energies, we can see that both the endo- and exo- reactions are endothermic - compared to the other two DA reactions as well as the cheletropic reaction, which are exothermic. This indicates that this Diels-Alder reaction is also highly thermodynamically unfavourable as ΔG<0 and it is not spontaneous.

== References ==

<references>
<ref name="chel_1">F. Monnat, P. Vogel, J. A. Sordo. [http://onlinelibrary.wiley.com/doi/10.1002/1522-2675(200203)85:3%3C712::AID-HLCA712%3E3.0.CO;2-5/epdf <i>Hetero-Diels-Alder and Cheletropic Additions of Sulfur Dioxide to 1,2-Dimethylidenecycloalkanes. Determination of Thermochemical and Kinetics Parameters for Reactions in Solution and Comparison with Estimates From Quantum Calculations</i>] Helv. Chim. Acta. <b>85</b> (3), 712–732 (2002).</ref>
<ref name="chel_3">D. Suarez, T. L. Sordo, J. A. Sordo. [http://pubs.acs.org/doi/pdf/10.1021/jo00114a039 <i>A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls</i>] J. Org. Chem., <b>60</b> (9), 2848–2852 (1995).</ref>

</references>

Rep:Transition states (st4215): Exercise 2

2017-10-25T03:50:26Z

St4215: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
The reaction of cyclohexadiene and 1,3-dioxole is also a Diels-Alder reaction, in which cyclohexadiene is the diene and 1,3-dioxole is the dienophile. However, unlike the simple Diels-Alder reaction between butadiene and ethylene, this reaction is slightly more complex - 1,3-dioxole can approach the diene at different orientations, leading to the formation of the endo- and exo- Diels-Alder products. This can be seen in the reaction scheme below:
(insert chemdraw diagram)

The endo- product is formed from a transition state where the substituents on the dienophile point towards the π system of the diene, while the exo- product is formed from a transition state where the substituents are pointing away.

In this exercise, we take a closer look at a different aspect of the Diels-Alder reaction - whether it is normal or inverse electron demand. We also consider the Diels-Alder reaction when an unsymmetrical diene is involved, and compare the endo- and exo- DA reactions in terms of which is more kinetically or thermodynamically favourable. In the process, we confirm that the orbital symmetry requirements as elucidated in Exercise 1 still apply, and illustrate that there are differences between the PM6 and B3LYP calculation methods, with one being more suitable than the other in this case.

=== Calculations ===
Calculations were performed at both the PM6 and B3LYP/6-31G(d) level. Method 2 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial#Method_2 tutorial]) was used to locate the transition state.

The optimised molecules can be seen here:

{| class="wikitable"
! rowspan="2" | Calculation method
! colspan="2" | Reactants
! colspan="2" | Endo
! colspan="2" | Exo
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-dioxole
| style="text-align: center;" | Transition state
| style="text-align: center;" | Product
| style="text-align: center;" | Transition state
| style="text-align: center;" | Product
|-
| style="text-align: center;" | B3LYP
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18</script>
<uploadedFileContents>st4215_CYCLOHEXADIENE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26</script>
<uploadedFileContents>st4215_DIOXOLE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18</script>
<uploadedFileContents>st4215_ENDO_PDT_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>st4215_EXO_PDT_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" | PM6
| style="text-align: center;" | [[Media:st4215_CYCLOHEXADIENE_OPTFREQ_PM6.LOG| Cyclohexadiene (PM6)]]
| style="text-align: center;" | [[Media:st4215_DIOXOLE_OPTFREQ_PM6.LOG| 1,3-dioxole (PM6)]]
| style="text-align: center;" | [[Media:st4215_ENDO_TS_OPTFREQ_PM6.LOG| Endo-TS (PM6)]] <br> [[Media:st4215_ENDO_TS_IRC2_PM6ONPM6.LOG| IRC file]]
| style="text-align: center;" | [[Media:st4215_ENDO_PDT_OPTFREQ_PM6.LOG| Endo-product (PM6)]]
| style="text-align: center;" | [[Media:st4215_EXO_TS_OPTFREQ_PM6.LOG| Exo-TS(PM6)]] <br> [[Media:st4215_EXO_TS_IRC_PM6ONPM6.LOG| IRC file]]
| style="text-align: center;" | [[Media:st4215_EXO_PDT_OPTFREQ_PM6.LOG| Exo-product(PM6)]]

|}

=== Molecular orbitals ===

==== Computed MOs ====
<small><i>Using your MO diagram for the Diels-Alder reaction, locate the occupied and unoccupied orbitals associated with the DA reaction for both TSs by symmetry. Find the relevant MOs and add them to your wiki (at an appropriate angle to show symmetry).</i></small>

The MOs involved in this reaction - the HOMOs and LUMOs for the reactants (cyclohexadiene and 1,3-dioxole), as well as the 4 MOs that these produce in each of the endo and exo transition states - are shown below. As explained in Exercise 1, which is also a Diels-Alder reaction, only orbitals of the same symmetry are able to interact. This is illustrated in the table below, where the symmetry or antisymmetry of each orbital can be clearly seen.

{| class="wikitable"
! rowspan="2"| Symmetry
! colspan="2" | Reactants
! colspan="2" rowspan="2"| Transition state (Endo)
! colspan="2" rowspan="2"| Transition state (Exo)
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
|-
| Antisymmmetric
| <b>MO 22</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXADIENE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 20</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26; mo 20; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_DIOXOLE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 40</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 40; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 43</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 43; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 40</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 43</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Symmetric
| <b>MO 23</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXADIENE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 19</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26; mo 19; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_DIOXOLE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 41</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 41; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 42</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 42; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 41</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 42</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

It is important to note that these MOs were generated from the B3LYP and not the PM6 calculation. While both calculation methods were used, the B3LYP calculation proved to be a better choice in visualising the MOs as it allowed us to see the symmetry of the orbitals more clearly, and corresponded more closely to the graphical representation of the orbitals in the MO diagram (see next section).

==== MO diagrams ====
<i><small>Construct a new MO diagram using these new orbitals, adjusting energy levels as necessary. Is this a normal or inverse demand DA reaction?</small></i>

MO diagrams for both the endo- and exo- Diels-Alder reactions were constructed as shown below. Energy levels of the MOs have been adjusted to reflect their actual values, as calculated in the B3LYP calculation.

{| class="wikitable"
! Endo geometry
! Exo geometry
|-
| [[File:st4215_Endo_MO_diagram.PNG|500px]]
| [[File:st4215_Exo_MO_diagram.PNG|500px]]
|}

From the MO diagrams above, we can conclude that both the endo- and exo- reactions are inverse demand DA reactions. In contrast to a normal electron demand DA reaction, where the diene is electron rich with a high LUMO and the dienophile is electron poor with a low HOMO, cyclohexadiene is electron poor with a low HOMO and 1,3-dioxole is electron rich with a high LUMO. Hence we can classify these reactions as inverse demand.

This is likely due to the nature of the dienophile, 1-3-dioxole, which has an electron-donating O atom. The lone pairs on the two adjacent O atoms are able to donate electron density into the double bond, making the dienophile more electron rich and raising the energy of its MOs, including its LUMO. In contrast, cyclohexadiene does not have any electron-donating substituents and is relatively electron poor. Hence, considering the Frontier Molecular Orbitals (FMOs), the LUMO<sub>dienophile</sub> is relatively high-energy and closer in energy to the low-energy HOMO<sub>diene</sub>, compared to HOMO<sub>dienophile</sub> and LUMO<sub>diene</sub>. Thus the interaction between the LUMO<sub>dienophile</sub> and HOMO<sub>diene</sub> is the strongest and dominates in this reaction, causing it to be inverse demand.<ref name="inverse"/>

=== Energy analysis ===
<small><i>Tabulate the energies and determine the reaction barriers and reaction energies (in kJ/mol) at room temperature (the corrected energies are labelled "Sum of electronic and thermal Free Energies", corresponding to the Gibbs free energy). Which are the kinetically and thermodynamically favourable products? Look at the HOMO of the TSs. Are there any secondary orbital interactions or sterics that might affect the reaction barrier energy?</i></small>

==== Free energies ====
The free energy of the reactants as well as the endo- and exo- Diels-Alder transition states and products are tabulated below. The reaction barriers and energies are also calculated.

{| class="wikitable"
! rowspan="3" scope="col" style="width: 150px;" |
! colspan="4" scope="col" style="width: 500px;" | Energy at 298 K
|-
| colspan="2" style="text-align: center;" | B3LYP
| colspan="2" style="text-align: center;" | PM6
|-
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
|-
| colspan="5" style="background: #B7C3D0" | <b>Reactants</b>
|-
| Cyclohexadiene || style="text-align: center;" | -233.32 || style="text-align: center;" | -6.1259 x 10<sup>5</sup> || style="text-align: center;" | 0.11688 || style="text-align: center;" | 306.86
|-
| 1,3-dioxole || style="text-align: center;" | -267.07 || style="text-align: center;" | -7.0119 x 10<sup>5</sup> || style="text-align: center;" | -0.052279 || style="text-align: center;" | -137.26
|-
| Total reactants || style="text-align: center;" | -500.39 || style="text-align: center;" | -1.3138 x 10<sup>6</sup> || style="text-align: center;" | 0.064598 || style="text-align: center;" | 169.60
|-
| colspan="5" style="background: #B7C3D0" | <b>Endo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | -500.332 || style="text-align: center;" | -1.3136 x 10<sup>6</sup> || style="text-align: center;" | 0.13794 ||style="text-align: center;" | 362.17
|-
| Product || style="text-align: center;" | -500.419 || style="text-align: center;" | -1.3138 x 10<sup>6</sup> || style="text-align: center;" | 0.037807 || style="text-align: center;" | 99.26
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0609 || style="text-align: center;" | 160 || style="text-align: center;" | 0.0733 || style="text-align: center;" | 193
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0257 || style="text-align: center;" | -67.4 || style="text-align: center;" | -0.0268 || style="text-align: center;" | -70.3
|-
| colspan="5" style="background: #B7C3D0" | <b>Exo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | -500.329 || style="text-align: center;" | -1.3136 x 10<sup>6</sup> || style="text-align: center;" | 0.13890 || style="text-align: center;" | 364.68
|-
| Product || style="text-align: center;" | -500.417 || style="text-align: center;" | -1.3138 x 10<sup>6</sup> || style="text-align: center;" | 0.037977 || style="text-align: center;" | 99.71
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0639 || style="text-align: center;" | 168 || style="text-align: center;" | 0.0743 || style="text-align: center;" | 195
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0243 || style="text-align: center;" | -63.8 || style="text-align: center;" | -0.0266 || style="text-align: center;" | -69.9
|}
<small><i>^Note that all values from the calculations are reported to 5 s.f. unless more decimal places are needed to differentiate between endo- and exo- geometries. Derived quantities (reaction barrier and reaction energy) are reported to 3 s.f.</i></small>

==== Thermodynamic and kinetic products ====
From the table above, we can conclude that the endo- product is both the kinetic and thermodynamic product. This is because it has a lower reaction barrier, meaning that less activation energy is required for the reaction, making it the kinetic product. The endo- product also has a lower reaction energy (ΔG), meaning that the endo- product is lower in energy and more stable than the exo- product, making it the thermodynamic product.

This is in contrast to most Diels-Alder reactions, in which the exo- product is the thermodynamic product as it is less sterically hindered and more stable, while the endo- product is the kinetic product due to stabilising orbital interactions in the transition state.<ref name="fmo"/> However, the difference for this reaction can be explained.

As seen in the jmols below, the endo- TS indeed has stabilising secondary orbital interactions between the p orbitals of O in 1,3-dioxole and the p orbitals of C in cyclohexadiene, which are absent in the exo- TS. The presence of these interactions lower the energy of the transition state, hence lowering the reaction barrier and making the endo-product the kinetic product.

Comparing the endo- and exo- products, we can also see that these stabilising orbital interactions are also in present in the endo- product. Additionally, the endo- product is less sterically hindered compared to the exo-product, in which there is steric clash between the hydrogens which are pointing towards each other. These two factors cause the energy of the endo- product to be lower than that of the exo- product, hence lowering the reaction energy and making the endo- product the thermodynamic product as well.

{| class="wikitable"
!
! Endo
! Exo
|-
| Transition state
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 41; rotate x 90; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; rotate x 90; rotate y 180; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 41; rotate x 90; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>st4215_ENDO_PDT_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 41; rotate x 90; rotate y 180; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>st4215_EXO_PDT_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== References ==
<references>
<ref name="inverse">D. Boger. <i>Progress in heterocyclic chemistry. (1st ed.).</i> (1989).</ref>
<ref name="fmo">I. Fleming. <i>Frontier Orbitals and Organic Chemical Reactions.</i> (1976).</ref>
</references>

Rep:Transition states (st4215): Exercise 3

2017-10-25T03:49:33Z

St4215: /* Calculations */

== Exercise 3: Diels-Alder vs Cheletropic ==
In this exercise, we examine the possible reactions between o-xylylene and SO<sub>2</sub> - the Diels-Alder reaction and the cheletropic reaction, as illustrated in the reaction scheme below.
(insert chemdraw diagram)

Again, in the Diels-Alder reaction, the dienophile SO<sub>2</sub> can approach the diene o-xylylene at different orientations, resulting in the endo- and exo- DA products. The cheletropic reaction, which is a pericyclic reaction in which the new bonds formed are made to the same atom, results in a single product.

In this exercise, we compare the three different reaction pathways - both Diels-Alder reactions and the cheletropic reaction - in terms of their reaction coordinates, as well as which is the most thermodynamically or kinetically favoured. We also investigate the possibility of a Diels-Alder reaction at a second site in xylylene.

=== Calculations ===
Calculations were performed at both the PM6 level. Method 3 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial#Method_3 tutorial]) was used to locate the transition state.

The optimised molecules can be seen here:

{| class="wikitable"
! colspan="2" | Reactants
|-
| style="text-align: center;" | o-xylylene
| style="text-align: center;" | SO<sub>2</sub>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16</script>
<uploadedFileContents>st4215_XYLYLENE_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16</script>
<uploadedFileContents>st4215_SO2_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo || style="text-align: center;" | Exo
|-
| style="text-align: center;" | Transition state
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>St4215_ex3_ENDO_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_ex3_ENDO_TS_IRC2_PM6.LOG | IRC file]]
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>st4215_ex3_Exo_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_ex3_Exo_TS_IRC_PM6.LOG | IRC file]]
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>st4215_ex3_CHEL_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_ex3_CHEL_TS_IRC_PM6.LOG | IRC file]]
|-
| style="text-align: center;" | Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>St4215_ex3_ENDO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>st4215_ex3_EXO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>st4215_ex3_CHEL_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Reaction coordinate ===
<small><i>Visualise the reaction coordinate with an IRC calculation for each path. Include a .gif file in the wiki of these IRCs.</i></small>

The formation of the products for each of the endo- and exo- Diels-Alder reactions, as well as the cheletropic reaction, can be visualised below.

{| class="wikitable"
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
|-
| [[File:st4215_ENDO_TS_IRCmovie.gif]]
| [[File:st4215_Exo_TS_IRCmovie.gif]]
| [[File:st4215_Chel_TS_IRCmovie.gif]]
|}

We can see that SO<sub>2</sub> approaches xylylene at a different orientation and angle for each of these reactions. This difference in approach trajectories hence lead to the formation of different products.

It can also be observed that in each of the reactions, as the product is formed, the 6-membered ring in xylylene becomes aromatic. This means that there is a strong driving force for the formation of the products. In contrast, the reactant xylylene is highly unstable as it is non-aromatic, and as can be seen in these reactions, can readily react with unsaturated bonds to form a aromatic product.

=== Energy analysis ===
<small><i>Calculate the activation and reaction energies (converting to kJ/mol) for each step as in Exercise 2 to determine which route is preferred. Using Excel or Chemdraw, draw a reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels-Alder reactions and the cheletropic reaction. You can set the 0 energy level to the reactants at infinite separation.</i></small>

==== Free energies ====
The free energies of the reactants, transition states and products for each of the 3 reactions are tabulated below. The reaction barriers and energies are also calculated.

{| class="wikitable"
! rowspan="2" scope="col" style="width: 150px;" |
! colspan="2" scope="col" style="width: 300px;" | Energy at 298 K (PM6)
|-
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
|-
| colspan="3" style="background: #B7C3D0" | <b>Reactants</b>
|-
| Xylylene || style="text-align: center;" | 0.17876 || style="text-align: center;" | 469.34
|-
| SO<sub>2</sub> || style="text-align: center;" | -0.11927 || style="text-align: center;" | -313.14
|-
| Total reactants || style="text-align: center;" | 0.059496 || style="text-align: center;" | 156.21
|-
| colspan="3" style="background: #B7C3D0" | <b>Endo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | 0.090560 || style="text-align: center;" | 237.77
|-
| Product || style="text-align: center;" | 0.021704 || style="text-align: center;" | 56.984
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0311 || style="text-align: center;" | 81.6
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0378 || style="text-align: center;" | -99.2
|-
| colspan="3" style="background: #B7C3D0" | <b>Exo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | 0.092078 || style="text-align: center;" | 241.75
|-
| Product || style="text-align: center;" | 0.021455 || style="text-align: center;" | 56.330
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0326 || style="text-align: center;" | 85.5
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0380 || style="text-align: center;" | -99.9
|-
| colspan="3" style="background: #B7C3D0" | <b>Cheletropic</b>
|-
| Transition state || style="text-align: center;" | 0.099058 || style="text-align: center;" | 260.08
|-
| Product || style="text-align: center;" | -0.000002 || style="text-align: center;" | -0.0052510
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0396 || style="text-align: center;" | 104
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0595 || style="text-align: center;" | -156
|}
<small><i>^Note that all values from the calculations are reported to 5 s.f. unless more decimal places are needed to differentiate between each reaction type. Derived quantities (reaction barrier and reaction energy) are reported to 3 s.f.</i></small>

==== Thermodynamic and kinetic products ====
From the values above, a combined reaction profile showing the reaction barriers and reaction energies can also be plotted as seen below.
[[File:st4215_ex3_Reaction_profile2.PNG|600px|thumb|center|Reaction profile diagram for the 3 Diels-Alder and cheletropic reactions, setting the energy of the reactants to zero]]

We can clearly see that the endo- Diels-Alder product is the kinetic product as it has the lowest reaction barrier of +81.6 kJmol<sup>-1</sup>, while the cheletropic product is the thermodynamic product as it is most stable as has the lowest energy of -156 kJmol<sup>-1</sup>. This is consistent with experimental and computational data.<ref name="chel_3"/><ref name="chel_1"/>

The high stability of the cheletropic product is likely due to the preference of S to adopt a five-membered compared to 6-membered ring structure. This is in contrast to saturated carbon rings, where 6-membered cyclohexane is more stable than 5-membered cyclopentane due to deviation from tetrahedral bond angles of 109° in cyclopentane, resulting in angle strain. However, due to the larger size of the S atom, C-C<sub>tet</sub>-S bond angles in a 5-membered unsaturated sulfur ring (like in the cheletropic product) are much closer to the tetrahedral bond angle, at 105°. In comparison, the 6-membered heterocycle in the Diels-Alder products have C-C<sub>tet</sub>-S bond angles of around 114°, which are comparatively much larger than 109°. This is illustrated below:

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
|-
| Products
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; measure 3 16 11</script>
<uploadedFileContents>St4215_ex3_ENDO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; rotate y 180; measure 3 16 11</script>
<uploadedFileContents>st4215_ex3_EXO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; measure 1 7 15</script>
<uploadedFileContents>st4215_ex3_CHEL_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

It is also expected that one of the Diels-Alder products (the endo- product) is the kinetic product instead of the cheletropic product.<ref name="chel_3"/> While the reaction barriers for both endo- and exo- Diels-Alder reactions are similar, the reaction barrier for the cheletropic reaction is much higher. Examining their transition states (see below) allows us to infer why.

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
|-
| Transition state HOMO
| style="text-align: center;" | [[File:st4215_ex3_Endo_TS_HOMO.PNG]]
| style="text-align: center;" | [[File:st4215_ex3_Exo_TS_HOMO.PNG]]
| style="text-align: center;" | [[File:st4215_ex3_Chel_TS_HOMO.PNG]]
|-
| Discussion
| colspan="2" | Some stabilising secondary orbital interactions can be seen in the HOMOs of the endo- and exo- transition states, hence lowering its energy and reducing the reaction barriers for these reactions.
| No stabilising secondary orbital interactions are present here - in fact, the HOMO of the transition state is highly antisymmetric with many nodes, and hence likely to be high in energy.
|}

Like most Diels-Alder reactions, the endo and not the exo- product is the kinetic product due to more or greater stabilising secondary orbital interactions in the transition state. However, in this reaction, both the endo- and exo- transition states seem to have an approximately equal but not significant amount of stabilising orbital interactions in the HOMO. This explains why the endo- and exo- transition states are relatively close in energy.

== Extra: Diels-Alder reaction at a different site ==
O-xylylene also contains a cis-butadiene fragment that can act as the diene in another Diels-Alder reaction. However, this reaction is very kinetically and thermodynamically favourable.

=== Optimised molecules ===
The optimised molecules can be seen here. Optimised reactants (o-xylylene and SO<sub>2</sub>) from the earlier reaction were used.

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder (2)
|-
| style="text-align: center;" | Endo || style="text-align: center;" | Exo
|-
| style="text-align: center;" | Transition state
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>st4215_BAD_ENDO_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_BAD_ENDO_IRC_PM6.LOG | IRC file]]
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>st4215_BAD_EXO_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_BAD_EXO_IRC_PM6.LOG | IRC file]]
|-
| style="text-align: center;" | Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 64</script>
<uploadedFileContents>st4215_BAD_ENDO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_BAD_EXO_PDT_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Energy analysis ===
The free energies of the reactants, transition states and products for both the endo- and exo- Diels Alder reactions are tabulated below. The reaction barriers and energies are also calculated.

{| class="wikitable"
! rowspan="2" scope="col" style="width: 150px;" |
! colspan="2" scope="col" style="width: 300px;" | Energy at 298 K (PM6)
|-
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
|-
| colspan="3" style="background: #B7C3D0" | <b>Reactants</b>
|-
| Xylylene || style="text-align: center;" | 0.17876 || style="text-align: center;" | 469.34
|-
| SO<sub>2</sub> || style="text-align: center;" | -0.11927 || style="text-align: center;" | -313.14
|-
| Total reactants || style="text-align: center;" | 0.059496 || style="text-align: center;" | 156.21
|-
| colspan="3" style="background: #B7C3D0" | <b>Endo- Diels-Alder (2)</b>
|-
| Transition state || style="text-align: center;" | 0.10207 || style="text-align: center;" | 267.99
|-
| Product || style="text-align: center;" | 0.065613 || style="text-align: center;" | 172.27
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0426 || style="text-align: center;" | 112
|-
| Reaction energy (ΔG) || style="text-align: center;" | +0.00612 || style="text-align: center;" | +16.1
|-
| colspan="3" style="background: #B7C3D0" | <b>Exo- Diels-Alder (2)</b>
|-
| Transition state || style="text-align: center;" | 0.10505 || style="text-align: center;" | 275.82
|-
| Product || style="text-align: center;" | 0.067305 || style="text-align: center;" | 176.71
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0456 || style="text-align: center;" | 120
|-
| Reaction energy (ΔG) || style="text-align: center;" | +0.00781 || style="text-align: center;" | +20.5
|}
<small><i>^Note that all values from the calculations are reported to 5 s.f. unless more decimal places are needed to differentiate between each reaction type. Derived quantities (reaction barrier and reaction energy) are reported to 3 s.f.</i></small>

We can hence see that this reaction is both kinetically and thermodynamically unfavourable compared to the other Diels-Alder reaction (previously discussed) and the cheletropic reaction.

Comparing the reaction barriers, the activation energies of 112 kJmol<sup>-1</sup> (endo) and 120 kJmol<sup>-1</sup> (exo) are much higher than that of the other DA reaction, at 81.6 kJmol<sup>-1</sup> (endo) and 85.5 kJmol<sup>-1</sup> (exo), as well as the cheletropic reaction, at 104 kJmol<sup>-1</sup>. Hence this Diels-Alder reaction is the most kinetically unfavourable reaction possible.

Comparing the reaction energies, we can see that both the endo- and exo- reactions are endothermic - compared to the other two DA reactions as well as the cheletropic reaction, which are exothermic. This indicates that this Diels-Alder reaction is also highly thermodynamically unfavourable as ΔG<0 and it is not spontaneous.

== References ==

<references>
<ref name="chel_1">F. Monnat, P. Vogel, J. A. Sordo. [http://onlinelibrary.wiley.com/doi/10.1002/1522-2675(200203)85:3%3C712::AID-HLCA712%3E3.0.CO;2-5/epdf <i>Hetero-Diels-Alder and Cheletropic Additions of Sulfur Dioxide to 1,2-Dimethylidenecycloalkanes. Determination of Thermochemical and Kinetics Parameters for Reactions in Solution and Comparison with Estimates From Quantum Calculations</i>] Helv. Chim. Acta. <b>85</b> (3), 712–732 (2002).</ref>
<ref name="chel_3">D. Suarez, T. L. Sordo, J. A. Sordo. [http://pubs.acs.org/doi/pdf/10.1021/jo00114a039 <i>A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls</i>] J. Org. Chem., <b>60</b> (9), 2848–2852 (1995).</ref>

</references>

Rep:Transition states (st4215): Exercise 3

2017-10-25T03:47:10Z

St4215: /* Exercise 3: Diels-Alder vs Cheletropic */

== Exercise 3: Diels-Alder vs Cheletropic ==
In this exercise, we examine the possible reactions between o-xylylene and SO<sub>2</sub> - the Diels-Alder reaction and the cheletropic reaction, as illustrated in the reaction scheme below.
(insert chemdraw diagram)

Again, in the Diels-Alder reaction, the dienophile SO<sub>2</sub> can approach the diene o-xylylene at different orientations, resulting in the endo- and exo- DA products. The cheletropic reaction, which is a pericyclic reaction in which the new bonds formed are made to the same atom, results in a single product.

In this exercise, we compare the three different reaction pathways - both Diels-Alder reactions and the cheletropic reaction - in terms of their reaction coordinates, as well as which is the most thermodynamically or kinetically favoured. We also investigate the possibility of a Diels-Alder reaction at a second site in xylylene.

=== Calculations ===
Calculations were performed at both the PM6 level. Method 3 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial#Method_3 tutorial) was used to locate the transition state.

The optimised molecules can be seen here:

{| class="wikitable"
! colspan="2" | Reactants
|-
| style="text-align: center;" | o-xylylene
| style="text-align: center;" | SO<sub>2</sub>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16</script>
<uploadedFileContents>st4215_XYLYLENE_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16</script>
<uploadedFileContents>st4215_SO2_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo || style="text-align: center;" | Exo
|-
| style="text-align: center;" | Transition state
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>St4215_ex3_ENDO_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_ex3_ENDO_TS_IRC2_PM6.LOG | IRC file]]
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>st4215_ex3_Exo_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_ex3_Exo_TS_IRC_PM6.LOG | IRC file]]
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>st4215_ex3_CHEL_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_ex3_CHEL_TS_IRC_PM6.LOG | IRC file]]
|-
| style="text-align: center;" | Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>St4215_ex3_ENDO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>st4215_ex3_EXO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>st4215_ex3_CHEL_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Reaction coordinate ===
<small><i>Visualise the reaction coordinate with an IRC calculation for each path. Include a .gif file in the wiki of these IRCs.</i></small>

The formation of the products for each of the endo- and exo- Diels-Alder reactions, as well as the cheletropic reaction, can be visualised below.

{| class="wikitable"
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
|-
| [[File:st4215_ENDO_TS_IRCmovie.gif]]
| [[File:st4215_Exo_TS_IRCmovie.gif]]
| [[File:st4215_Chel_TS_IRCmovie.gif]]
|}

We can see that SO<sub>2</sub> approaches xylylene at a different orientation and angle for each of these reactions. This difference in approach trajectories hence lead to the formation of different products.

It can also be observed that in each of the reactions, as the product is formed, the 6-membered ring in xylylene becomes aromatic. This means that there is a strong driving force for the formation of the products. In contrast, the reactant xylylene is highly unstable as it is non-aromatic, and as can be seen in these reactions, can readily react with unsaturated bonds to form a aromatic product.

=== Energy analysis ===
<small><i>Calculate the activation and reaction energies (converting to kJ/mol) for each step as in Exercise 2 to determine which route is preferred. Using Excel or Chemdraw, draw a reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels-Alder reactions and the cheletropic reaction. You can set the 0 energy level to the reactants at infinite separation.</i></small>

==== Free energies ====
The free energies of the reactants, transition states and products for each of the 3 reactions are tabulated below. The reaction barriers and energies are also calculated.

{| class="wikitable"
! rowspan="2" scope="col" style="width: 150px;" |
! colspan="2" scope="col" style="width: 300px;" | Energy at 298 K (PM6)
|-
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
|-
| colspan="3" style="background: #B7C3D0" | <b>Reactants</b>
|-
| Xylylene || style="text-align: center;" | 0.17876 || style="text-align: center;" | 469.34
|-
| SO<sub>2</sub> || style="text-align: center;" | -0.11927 || style="text-align: center;" | -313.14
|-
| Total reactants || style="text-align: center;" | 0.059496 || style="text-align: center;" | 156.21
|-
| colspan="3" style="background: #B7C3D0" | <b>Endo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | 0.090560 || style="text-align: center;" | 237.77
|-
| Product || style="text-align: center;" | 0.021704 || style="text-align: center;" | 56.984
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0311 || style="text-align: center;" | 81.6
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0378 || style="text-align: center;" | -99.2
|-
| colspan="3" style="background: #B7C3D0" | <b>Exo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | 0.092078 || style="text-align: center;" | 241.75
|-
| Product || style="text-align: center;" | 0.021455 || style="text-align: center;" | 56.330
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0326 || style="text-align: center;" | 85.5
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0380 || style="text-align: center;" | -99.9
|-
| colspan="3" style="background: #B7C3D0" | <b>Cheletropic</b>
|-
| Transition state || style="text-align: center;" | 0.099058 || style="text-align: center;" | 260.08
|-
| Product || style="text-align: center;" | -0.000002 || style="text-align: center;" | -0.0052510
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0396 || style="text-align: center;" | 104
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0595 || style="text-align: center;" | -156
|}
<small><i>^Note that all values from the calculations are reported to 5 s.f. unless more decimal places are needed to differentiate between each reaction type. Derived quantities (reaction barrier and reaction energy) are reported to 3 s.f.</i></small>

==== Thermodynamic and kinetic products ====
From the values above, a combined reaction profile showing the reaction barriers and reaction energies can also be plotted as seen below.
[[File:st4215_ex3_Reaction_profile2.PNG|600px|thumb|center|Reaction profile diagram for the 3 Diels-Alder and cheletropic reactions, setting the energy of the reactants to zero]]

We can clearly see that the endo- Diels-Alder product is the kinetic product as it has the lowest reaction barrier of +81.6 kJmol<sup>-1</sup>, while the cheletropic product is the thermodynamic product as it is most stable as has the lowest energy of -156 kJmol<sup>-1</sup>. This is consistent with experimental and computational data.<ref name="chel_3"/><ref name="chel_1"/>

The high stability of the cheletropic product is likely due to the preference of S to adopt a five-membered compared to 6-membered ring structure. This is in contrast to saturated carbon rings, where 6-membered cyclohexane is more stable than 5-membered cyclopentane due to deviation from tetrahedral bond angles of 109° in cyclopentane, resulting in angle strain. However, due to the larger size of the S atom, C-C<sub>tet</sub>-S bond angles in a 5-membered unsaturated sulfur ring (like in the cheletropic product) are much closer to the tetrahedral bond angle, at 105°. In comparison, the 6-membered heterocycle in the Diels-Alder products have C-C<sub>tet</sub>-S bond angles of around 114°, which are comparatively much larger than 109°. This is illustrated below:

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
|-
| Products
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; measure 3 16 11</script>
<uploadedFileContents>St4215_ex3_ENDO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; rotate y 180; measure 3 16 11</script>
<uploadedFileContents>st4215_ex3_EXO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; measure 1 7 15</script>
<uploadedFileContents>st4215_ex3_CHEL_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

It is also expected that one of the Diels-Alder products (the endo- product) is the kinetic product instead of the cheletropic product.<ref name="chel_3"/> While the reaction barriers for both endo- and exo- Diels-Alder reactions are similar, the reaction barrier for the cheletropic reaction is much higher. Examining their transition states (see below) allows us to infer why.

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
|-
| Transition state HOMO
| style="text-align: center;" | [[File:st4215_ex3_Endo_TS_HOMO.PNG]]
| style="text-align: center;" | [[File:st4215_ex3_Exo_TS_HOMO.PNG]]
| style="text-align: center;" | [[File:st4215_ex3_Chel_TS_HOMO.PNG]]
|-
| Discussion
| colspan="2" | Some stabilising secondary orbital interactions can be seen in the HOMOs of the endo- and exo- transition states, hence lowering its energy and reducing the reaction barriers for these reactions.
| No stabilising secondary orbital interactions are present here - in fact, the HOMO of the transition state is highly antisymmetric with many nodes, and hence likely to be high in energy.
|}

Like most Diels-Alder reactions, the endo and not the exo- product is the kinetic product due to more or greater stabilising secondary orbital interactions in the transition state. However, in this reaction, both the endo- and exo- transition states seem to have an approximately equal but not significant amount of stabilising orbital interactions in the HOMO. This explains why the endo- and exo- transition states are relatively close in energy.

== Extra: Diels-Alder reaction at a different site ==
O-xylylene also contains a cis-butadiene fragment that can act as the diene in another Diels-Alder reaction. However, this reaction is very kinetically and thermodynamically favourable.

=== Optimised molecules ===
The optimised molecules can be seen here. Optimised reactants (o-xylylene and SO<sub>2</sub>) from the earlier reaction were used.

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder (2)
|-
| style="text-align: center;" | Endo || style="text-align: center;" | Exo
|-
| style="text-align: center;" | Transition state
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>st4215_BAD_ENDO_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_BAD_ENDO_IRC_PM6.LOG | IRC file]]
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>st4215_BAD_EXO_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_BAD_EXO_IRC_PM6.LOG | IRC file]]
|-
| style="text-align: center;" | Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 64</script>
<uploadedFileContents>st4215_BAD_ENDO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_BAD_EXO_PDT_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Energy analysis ===
The free energies of the reactants, transition states and products for both the endo- and exo- Diels Alder reactions are tabulated below. The reaction barriers and energies are also calculated.

{| class="wikitable"
! rowspan="2" scope="col" style="width: 150px;" |
! colspan="2" scope="col" style="width: 300px;" | Energy at 298 K (PM6)
|-
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
|-
| colspan="3" style="background: #B7C3D0" | <b>Reactants</b>
|-
| Xylylene || style="text-align: center;" | 0.17876 || style="text-align: center;" | 469.34
|-
| SO<sub>2</sub> || style="text-align: center;" | -0.11927 || style="text-align: center;" | -313.14
|-
| Total reactants || style="text-align: center;" | 0.059496 || style="text-align: center;" | 156.21
|-
| colspan="3" style="background: #B7C3D0" | <b>Endo- Diels-Alder (2)</b>
|-
| Transition state || style="text-align: center;" | 0.10207 || style="text-align: center;" | 267.99
|-
| Product || style="text-align: center;" | 0.065613 || style="text-align: center;" | 172.27
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0426 || style="text-align: center;" | 112
|-
| Reaction energy (ΔG) || style="text-align: center;" | +0.00612 || style="text-align: center;" | +16.1
|-
| colspan="3" style="background: #B7C3D0" | <b>Exo- Diels-Alder (2)</b>
|-
| Transition state || style="text-align: center;" | 0.10505 || style="text-align: center;" | 275.82
|-
| Product || style="text-align: center;" | 0.067305 || style="text-align: center;" | 176.71
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0456 || style="text-align: center;" | 120
|-
| Reaction energy (ΔG) || style="text-align: center;" | +0.00781 || style="text-align: center;" | +20.5
|}
<small><i>^Note that all values from the calculations are reported to 5 s.f. unless more decimal places are needed to differentiate between each reaction type. Derived quantities (reaction barrier and reaction energy) are reported to 3 s.f.</i></small>

We can hence see that this reaction is both kinetically and thermodynamically unfavourable compared to the other Diels-Alder reaction (previously discussed) and the cheletropic reaction.

Comparing the reaction barriers, the activation energies of 112 kJmol<sup>-1</sup> (endo) and 120 kJmol<sup>-1</sup> (exo) are much higher than that of the other DA reaction, at 81.6 kJmol<sup>-1</sup> (endo) and 85.5 kJmol<sup>-1</sup> (exo), as well as the cheletropic reaction, at 104 kJmol<sup>-1</sup>. Hence this Diels-Alder reaction is the most kinetically unfavourable reaction possible.

Comparing the reaction energies, we can see that both the endo- and exo- reactions are endothermic - compared to the other two DA reactions as well as the cheletropic reaction, which are exothermic. This indicates that this Diels-Alder reaction is also highly thermodynamically unfavourable as ΔG<0 and it is not spontaneous.

== References ==

<references>
<ref name="chel_1">F. Monnat, P. Vogel, J. A. Sordo. [http://onlinelibrary.wiley.com/doi/10.1002/1522-2675(200203)85:3%3C712::AID-HLCA712%3E3.0.CO;2-5/epdf <i>Hetero-Diels-Alder and Cheletropic Additions of Sulfur Dioxide to 1,2-Dimethylidenecycloalkanes. Determination of Thermochemical and Kinetics Parameters for Reactions in Solution and Comparison with Estimates From Quantum Calculations</i>] Helv. Chim. Acta. <b>85</b> (3), 712–732 (2002).</ref>
<ref name="chel_3">D. Suarez, T. L. Sordo, J. A. Sordo. [http://pubs.acs.org/doi/pdf/10.1021/jo00114a039 <i>A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls</i>] J. Org. Chem., <b>60</b> (9), 2848–2852 (1995).</ref>

</references>

Rep:Transition states (st4215): Exercise 2

2017-10-25T03:47:02Z

St4215: /* Calculations */

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
The reaction of cyclohexadiene and 1,3-dioxole is also a Diels-Alder reaction, in which cyclohexadiene is the diene and 1,3-dioxole is the dienophile. However, unlike the simple Diels-Alder reaction between butadiene and ethylene, this reaction is slightly more complex - 1,3-dioxole can approach the diene at different orientations, leading to the formation of the endo- and exo- Diels-Alder products. This can be seen in the reaction scheme below:
(insert chemdraw diagram)

The endo- product is formed from a transition state where the substituents on the dienophile point towards the π system of the diene, while the exo- product is formed from a transition state where the substituents are pointing away.

In this exercise, we take a closer look at a different aspect of the Diels-Alder reaction - whether it is normal or inverse electron demand. We also consider the Diels-Alder reaction when an unsymmetrical diene is involved, and compare the endo- and exo- DA reactions in terms of which is more kinetically or thermodynamically favourable. In the process, we confirm that the orbital symmetry requirements as elucidated in Exercise 1 still apply, and illustrate that there are differences between the PM6 and B3LYP calculation methods, with one being more suitable than the other in this case.

=== Calculations ===
Calculations were performed at both the PM6 and B3LYP/6-31G(d) level. Method 2 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial#Method_2 tutorial) was used to locate the transition state.

The optimised molecules can be seen here:

{| class="wikitable"
! rowspan="2" | Calculation method
! colspan="2" | Reactants
! colspan="2" | Endo
! colspan="2" | Exo
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-dioxole
| style="text-align: center;" | Transition state
| style="text-align: center;" | Product
| style="text-align: center;" | Transition state
| style="text-align: center;" | Product
|-
| style="text-align: center;" | B3LYP
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18</script>
<uploadedFileContents>st4215_CYCLOHEXADIENE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26</script>
<uploadedFileContents>st4215_DIOXOLE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18</script>
<uploadedFileContents>st4215_ENDO_PDT_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>st4215_EXO_PDT_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" | PM6
| style="text-align: center;" | [[Media:st4215_CYCLOHEXADIENE_OPTFREQ_PM6.LOG| Cyclohexadiene (PM6)]]
| style="text-align: center;" | [[Media:st4215_DIOXOLE_OPTFREQ_PM6.LOG| 1,3-dioxole (PM6)]]
| style="text-align: center;" | [[Media:st4215_ENDO_TS_OPTFREQ_PM6.LOG| Endo-TS (PM6)]] <br> [[Media:st4215_ENDO_TS_IRC2_PM6ONPM6.LOG| IRC file]]
| style="text-align: center;" | [[Media:st4215_ENDO_PDT_OPTFREQ_PM6.LOG| Endo-product (PM6)]]
| style="text-align: center;" | [[Media:st4215_EXO_TS_OPTFREQ_PM6.LOG| Exo-TS(PM6)]] <br> [[Media:st4215_EXO_TS_IRC_PM6ONPM6.LOG| IRC file]]
| style="text-align: center;" | [[Media:st4215_EXO_PDT_OPTFREQ_PM6.LOG| Exo-product(PM6)]]

|}

=== Molecular orbitals ===

==== Computed MOs ====
<small><i>Using your MO diagram for the Diels-Alder reaction, locate the occupied and unoccupied orbitals associated with the DA reaction for both TSs by symmetry. Find the relevant MOs and add them to your wiki (at an appropriate angle to show symmetry).</i></small>

The MOs involved in this reaction - the HOMOs and LUMOs for the reactants (cyclohexadiene and 1,3-dioxole), as well as the 4 MOs that these produce in each of the endo and exo transition states - are shown below. As explained in Exercise 1, which is also a Diels-Alder reaction, only orbitals of the same symmetry are able to interact. This is illustrated in the table below, where the symmetry or antisymmetry of each orbital can be clearly seen.

{| class="wikitable"
! rowspan="2"| Symmetry
! colspan="2" | Reactants
! colspan="2" rowspan="2"| Transition state (Endo)
! colspan="2" rowspan="2"| Transition state (Exo)
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
|-
| Antisymmmetric
| <b>MO 22</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXADIENE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 20</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26; mo 20; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_DIOXOLE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 40</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 40; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 43</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 43; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 40</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 43</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Symmetric
| <b>MO 23</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXADIENE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 19</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26; mo 19; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_DIOXOLE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 41</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 41; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 42</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 42; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 41</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 42</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

It is important to note that these MOs were generated from the B3LYP and not the PM6 calculation. While both calculation methods were used, the B3LYP calculation proved to be a better choice in visualising the MOs as it allowed us to see the symmetry of the orbitals more clearly, and corresponded more closely to the graphical representation of the orbitals in the MO diagram (see next section).

==== MO diagrams ====
<i><small>Construct a new MO diagram using these new orbitals, adjusting energy levels as necessary. Is this a normal or inverse demand DA reaction?</small></i>

MO diagrams for both the endo- and exo- Diels-Alder reactions were constructed as shown below. Energy levels of the MOs have been adjusted to reflect their actual values, as calculated in the B3LYP calculation.

{| class="wikitable"
! Endo geometry
! Exo geometry
|-
| [[File:st4215_Endo_MO_diagram.PNG|500px]]
| [[File:st4215_Exo_MO_diagram.PNG|500px]]
|}

From the MO diagrams above, we can conclude that both the endo- and exo- reactions are inverse demand DA reactions. In contrast to a normal electron demand DA reaction, where the diene is electron rich with a high LUMO and the dienophile is electron poor with a low HOMO, cyclohexadiene is electron poor with a low HOMO and 1,3-dioxole is electron rich with a high LUMO. Hence we can classify these reactions as inverse demand.

This is likely due to the nature of the dienophile, 1-3-dioxole, which has an electron-donating O atom. The lone pairs on the two adjacent O atoms are able to donate electron density into the double bond, making the dienophile more electron rich and raising the energy of its MOs, including its LUMO. In contrast, cyclohexadiene does not have any electron-donating substituents and is relatively electron poor. Hence, considering the Frontier Molecular Orbitals (FMOs), the LUMO<sub>dienophile</sub> is relatively high-energy and closer in energy to the low-energy HOMO<sub>diene</sub>, compared to HOMO<sub>dienophile</sub> and LUMO<sub>diene</sub>. Thus the interaction between the LUMO<sub>dienophile</sub> and HOMO<sub>diene</sub> is the strongest and dominates in this reaction, causing it to be inverse demand.<ref name="inverse"/>

=== Energy analysis ===
<small><i>Tabulate the energies and determine the reaction barriers and reaction energies (in kJ/mol) at room temperature (the corrected energies are labelled "Sum of electronic and thermal Free Energies", corresponding to the Gibbs free energy). Which are the kinetically and thermodynamically favourable products? Look at the HOMO of the TSs. Are there any secondary orbital interactions or sterics that might affect the reaction barrier energy?</i></small>

==== Free energies ====
The free energy of the reactants as well as the endo- and exo- Diels-Alder transition states and products are tabulated below. The reaction barriers and energies are also calculated.

{| class="wikitable"
! rowspan="3" scope="col" style="width: 150px;" |
! colspan="4" scope="col" style="width: 500px;" | Energy at 298 K
|-
| colspan="2" style="text-align: center;" | B3LYP
| colspan="2" style="text-align: center;" | PM6
|-
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
|-
| colspan="5" style="background: #B7C3D0" | <b>Reactants</b>
|-
| Cyclohexadiene || style="text-align: center;" | -233.32 || style="text-align: center;" | -6.1259 x 10<sup>5</sup> || style="text-align: center;" | 0.11688 || style="text-align: center;" | 306.86
|-
| 1,3-dioxole || style="text-align: center;" | -267.07 || style="text-align: center;" | -7.0119 x 10<sup>5</sup> || style="text-align: center;" | -0.052279 || style="text-align: center;" | -137.26
|-
| Total reactants || style="text-align: center;" | -500.39 || style="text-align: center;" | -1.3138 x 10<sup>6</sup> || style="text-align: center;" | 0.064598 || style="text-align: center;" | 169.60
|-
| colspan="5" style="background: #B7C3D0" | <b>Endo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | -500.332 || style="text-align: center;" | -1.3136 x 10<sup>6</sup> || style="text-align: center;" | 0.13794 ||style="text-align: center;" | 362.17
|-
| Product || style="text-align: center;" | -500.419 || style="text-align: center;" | -1.3138 x 10<sup>6</sup> || style="text-align: center;" | 0.037807 || style="text-align: center;" | 99.26
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0609 || style="text-align: center;" | 160 || style="text-align: center;" | 0.0733 || style="text-align: center;" | 193
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0257 || style="text-align: center;" | -67.4 || style="text-align: center;" | -0.0268 || style="text-align: center;" | -70.3
|-
| colspan="5" style="background: #B7C3D0" | <b>Exo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | -500.329 || style="text-align: center;" | -1.3136 x 10<sup>6</sup> || style="text-align: center;" | 0.13890 || style="text-align: center;" | 364.68
|-
| Product || style="text-align: center;" | -500.417 || style="text-align: center;" | -1.3138 x 10<sup>6</sup> || style="text-align: center;" | 0.037977 || style="text-align: center;" | 99.71
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0639 || style="text-align: center;" | 168 || style="text-align: center;" | 0.0743 || style="text-align: center;" | 195
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0243 || style="text-align: center;" | -63.8 || style="text-align: center;" | -0.0266 || style="text-align: center;" | -69.9
|}
<small><i>^Note that all values from the calculations are reported to 5 s.f. unless more decimal places are needed to differentiate between endo- and exo- geometries. Derived quantities (reaction barrier and reaction energy) are reported to 3 s.f.</i></small>

==== Thermodynamic and kinetic products ====
From the table above, we can conclude that the endo- product is both the kinetic and thermodynamic product. This is because it has a lower reaction barrier, meaning that less activation energy is required for the reaction, making it the kinetic product. The endo- product also has a lower reaction energy (ΔG), meaning that the endo- product is lower in energy and more stable than the exo- product, making it the thermodynamic product.

This is in contrast to most Diels-Alder reactions, in which the exo- product is the thermodynamic product as it is less sterically hindered and more stable, while the endo- product is the kinetic product due to stabilising orbital interactions in the transition state.<ref name="fmo"/> However, the difference for this reaction can be explained.

As seen in the jmols below, the endo- TS indeed has stabilising secondary orbital interactions between the p orbitals of O in 1,3-dioxole and the p orbitals of C in cyclohexadiene, which are absent in the exo- TS. The presence of these interactions lower the energy of the transition state, hence lowering the reaction barrier and making the endo-product the kinetic product.

Comparing the endo- and exo- products, we can also see that these stabilising orbital interactions are also in present in the endo- product. Additionally, the endo- product is less sterically hindered compared to the exo-product, in which there is steric clash between the hydrogens which are pointing towards each other. These two factors cause the energy of the endo- product to be lower than that of the exo- product, hence lowering the reaction energy and making the endo- product the thermodynamic product as well.

{| class="wikitable"
!
! Endo
! Exo
|-
| Transition state
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 41; rotate x 90; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; rotate x 90; rotate y 180; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 41; rotate x 90; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>st4215_ENDO_PDT_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 41; rotate x 90; rotate y 180; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>st4215_EXO_PDT_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== References ==
<references>
<ref name="inverse">D. Boger. <i>Progress in heterocyclic chemistry. (1st ed.).</i> (1989).</ref>
<ref name="fmo">I. Fleming. <i>Frontier Orbitals and Organic Chemical Reactions.</i> (1976).</ref>
</references>

Rep:Transition states (st4215): Exercise 2

2017-10-25T02:59:27Z

St4215: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
The reaction of cyclohexadiene and 1,3-dioxole is also a Diels-Alder reaction, in which cyclohexadiene is the diene and 1,3-dioxole is the dienophile. However, unlike the simple Diels-Alder reaction between butadiene and ethylene, this reaction is slightly more complex - 1,3-dioxole can approach the diene at different orientations, leading to the formation of the endo- and exo- Diels-Alder products. This can be seen in the reaction scheme below:
(insert chemdraw diagram)

The endo- product is formed from a transition state where the substituents on the dienophile point towards the π system of the diene, while the exo- product is formed from a transition state where the substituents are pointing away.

In this exercise, we take a closer look at a different aspect of the Diels-Alder reaction - whether it is normal or inverse electron demand. We also consider the Diels-Alder reaction when an unsymmetrical diene is involved, and compare the endo- and exo- DA reactions in terms of which is more kinetically or thermodynamically favourable. In the process, we confirm that the orbital symmetry requirements as elucidated in Exercise 1 still apply, and illustrate that there are differences between the PM6 and B3LYP calculation methods, with one being more suitable than the other in this case.

=== Calculations ===
Calculations were performed at both the PM6 and B3LYP/6-31G(d) level. Method 2 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial tutorial#Method_2) was used to locate the transition state.

The optimised molecules can be seen here:

{| class="wikitable"
! rowspan="2" | Calculation method
! colspan="2" | Reactants
! colspan="2" | Endo
! colspan="2" | Exo
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-dioxole
| style="text-align: center;" | Transition state
| style="text-align: center;" | Product
| style="text-align: center;" | Transition state
| style="text-align: center;" | Product
|-
| style="text-align: center;" | B3LYP
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18</script>
<uploadedFileContents>st4215_CYCLOHEXADIENE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26</script>
<uploadedFileContents>st4215_DIOXOLE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18</script>
<uploadedFileContents>st4215_ENDO_PDT_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>st4215_EXO_PDT_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" | PM6
| style="text-align: center;" | [[Media:st4215_CYCLOHEXADIENE_OPTFREQ_PM6.LOG| Cyclohexadiene (PM6)]]
| style="text-align: center;" | [[Media:st4215_DIOXOLE_OPTFREQ_PM6.LOG| 1,3-dioxole (PM6)]]
| style="text-align: center;" | [[Media:st4215_ENDO_TS_OPTFREQ_PM6.LOG| Endo-TS (PM6)]] <br> [[Media:st4215_ENDO_TS_IRC2_PM6ONPM6.LOG| IRC file]]
| style="text-align: center;" | [[Media:st4215_ENDO_PDT_OPTFREQ_PM6.LOG| Endo-product (PM6)]]
| style="text-align: center;" | [[Media:st4215_EXO_TS_OPTFREQ_PM6.LOG| Exo-TS(PM6)]] <br> [[Media:st4215_EXO_TS_IRC_PM6ONPM6.LOG| IRC file]]
| style="text-align: center;" | [[Media:st4215_EXO_PDT_OPTFREQ_PM6.LOG| Exo-product(PM6)]]

|}

=== Molecular orbitals ===

==== Computed MOs ====
<small><i>Using your MO diagram for the Diels-Alder reaction, locate the occupied and unoccupied orbitals associated with the DA reaction for both TSs by symmetry. Find the relevant MOs and add them to your wiki (at an appropriate angle to show symmetry).</i></small>

The MOs involved in this reaction - the HOMOs and LUMOs for the reactants (cyclohexadiene and 1,3-dioxole), as well as the 4 MOs that these produce in each of the endo and exo transition states - are shown below. As explained in Exercise 1, which is also a Diels-Alder reaction, only orbitals of the same symmetry are able to interact. This is illustrated in the table below, where the symmetry or antisymmetry of each orbital can be clearly seen.

{| class="wikitable"
! rowspan="2"| Symmetry
! colspan="2" | Reactants
! colspan="2" rowspan="2"| Transition state (Endo)
! colspan="2" rowspan="2"| Transition state (Exo)
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
|-
| Antisymmmetric
| <b>MO 22</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXADIENE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 20</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26; mo 20; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_DIOXOLE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 40</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 40; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 43</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 43; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 40</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 43</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Symmetric
| <b>MO 23</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXADIENE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 19</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26; mo 19; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_DIOXOLE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 41</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 41; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 42</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 42; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 41</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 42</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

It is important to note that these MOs were generated from the B3LYP and not the PM6 calculation. While both calculation methods were used, the B3LYP calculation proved to be a better choice in visualising the MOs as it allowed us to see the symmetry of the orbitals more clearly, and corresponded more closely to the graphical representation of the orbitals in the MO diagram (see next section).

==== MO diagrams ====
<i><small>Construct a new MO diagram using these new orbitals, adjusting energy levels as necessary. Is this a normal or inverse demand DA reaction?</small></i>

MO diagrams for both the endo- and exo- Diels-Alder reactions were constructed as shown below. Energy levels of the MOs have been adjusted to reflect their actual values, as calculated in the B3LYP calculation.

{| class="wikitable"
! Endo geometry
! Exo geometry
|-
| [[File:st4215_Endo_MO_diagram.PNG|500px]]
| [[File:st4215_Exo_MO_diagram.PNG|500px]]
|}

From the MO diagrams above, we can conclude that both the endo- and exo- reactions are inverse demand DA reactions. In contrast to a normal electron demand DA reaction, where the diene is electron rich with a high LUMO and the dienophile is electron poor with a low HOMO, cyclohexadiene is electron poor with a low HOMO and 1,3-dioxole is electron rich with a high LUMO. Hence we can classify these reactions as inverse demand.

This is likely due to the nature of the dienophile, 1-3-dioxole, which has an electron-donating O atom. The lone pairs on the two adjacent O atoms are able to donate electron density into the double bond, making the dienophile more electron rich and raising the energy of its MOs, including its LUMO. In contrast, cyclohexadiene does not have any electron-donating substituents and is relatively electron poor. Hence, considering the Frontier Molecular Orbitals (FMOs), the LUMO<sub>dienophile</sub> is relatively high-energy and closer in energy to the low-energy HOMO<sub>diene</sub>, compared to HOMO<sub>dienophile</sub> and LUMO<sub>diene</sub>. Thus the interaction between the LUMO<sub>dienophile</sub> and HOMO<sub>diene</sub> is the strongest and dominates in this reaction, causing it to be inverse demand.<ref name="inverse"/>

=== Energy analysis ===
<small><i>Tabulate the energies and determine the reaction barriers and reaction energies (in kJ/mol) at room temperature (the corrected energies are labelled "Sum of electronic and thermal Free Energies", corresponding to the Gibbs free energy). Which are the kinetically and thermodynamically favourable products? Look at the HOMO of the TSs. Are there any secondary orbital interactions or sterics that might affect the reaction barrier energy?</i></small>

==== Free energies ====
The free energy of the reactants as well as the endo- and exo- Diels-Alder transition states and products are tabulated below. The reaction barriers and energies are also calculated.

{| class="wikitable"
! rowspan="3" scope="col" style="width: 150px;" |
! colspan="4" scope="col" style="width: 500px;" | Energy at 298 K
|-
| colspan="2" style="text-align: center;" | B3LYP
| colspan="2" style="text-align: center;" | PM6
|-
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
|-
| colspan="5" style="background: #B7C3D0" | <b>Reactants</b>
|-
| Cyclohexadiene || style="text-align: center;" | -233.32 || style="text-align: center;" | -6.1259 x 10<sup>5</sup> || style="text-align: center;" | 0.11688 || style="text-align: center;" | 306.86
|-
| 1,3-dioxole || style="text-align: center;" | -267.07 || style="text-align: center;" | -7.0119 x 10<sup>5</sup> || style="text-align: center;" | -0.052279 || style="text-align: center;" | -137.26
|-
| Total reactants || style="text-align: center;" | -500.39 || style="text-align: center;" | -1.3138 x 10<sup>6</sup> || style="text-align: center;" | 0.064598 || style="text-align: center;" | 169.60
|-
| colspan="5" style="background: #B7C3D0" | <b>Endo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | -500.332 || style="text-align: center;" | -1.3136 x 10<sup>6</sup> || style="text-align: center;" | 0.13794 ||style="text-align: center;" | 362.17
|-
| Product || style="text-align: center;" | -500.419 || style="text-align: center;" | -1.3138 x 10<sup>6</sup> || style="text-align: center;" | 0.037807 || style="text-align: center;" | 99.26
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0609 || style="text-align: center;" | 160 || style="text-align: center;" | 0.0733 || style="text-align: center;" | 193
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0257 || style="text-align: center;" | -67.4 || style="text-align: center;" | -0.0268 || style="text-align: center;" | -70.3
|-
| colspan="5" style="background: #B7C3D0" | <b>Exo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | -500.329 || style="text-align: center;" | -1.3136 x 10<sup>6</sup> || style="text-align: center;" | 0.13890 || style="text-align: center;" | 364.68
|-
| Product || style="text-align: center;" | -500.417 || style="text-align: center;" | -1.3138 x 10<sup>6</sup> || style="text-align: center;" | 0.037977 || style="text-align: center;" | 99.71
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0639 || style="text-align: center;" | 168 || style="text-align: center;" | 0.0743 || style="text-align: center;" | 195
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0243 || style="text-align: center;" | -63.8 || style="text-align: center;" | -0.0266 || style="text-align: center;" | -69.9
|}
<small><i>^Note that all values from the calculations are reported to 5 s.f. unless more decimal places are needed to differentiate between endo- and exo- geometries. Derived quantities (reaction barrier and reaction energy) are reported to 3 s.f.</i></small>

==== Thermodynamic and kinetic products ====
From the table above, we can conclude that the endo- product is both the kinetic and thermodynamic product. This is because it has a lower reaction barrier, meaning that less activation energy is required for the reaction, making it the kinetic product. The endo- product also has a lower reaction energy (ΔG), meaning that the endo- product is lower in energy and more stable than the exo- product, making it the thermodynamic product.

This is in contrast to most Diels-Alder reactions, in which the exo- product is the thermodynamic product as it is less sterically hindered and more stable, while the endo- product is the kinetic product due to stabilising orbital interactions in the transition state.<ref name="fmo"/> However, the difference for this reaction can be explained.

As seen in the jmols below, the endo- TS indeed has stabilising secondary orbital interactions between the p orbitals of O in 1,3-dioxole and the p orbitals of C in cyclohexadiene, which are absent in the exo- TS. The presence of these interactions lower the energy of the transition state, hence lowering the reaction barrier and making the endo-product the kinetic product.

Comparing the endo- and exo- products, we can also see that these stabilising orbital interactions are also in present in the endo- product. Additionally, the endo- product is less sterically hindered compared to the exo-product, in which there is steric clash between the hydrogens which are pointing towards each other. These two factors cause the energy of the endo- product to be lower than that of the exo- product, hence lowering the reaction energy and making the endo- product the thermodynamic product as well.

{| class="wikitable"
!
! Endo
! Exo
|-
| Transition state
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 41; rotate x 90; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; rotate x 90; rotate y 180; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 41; rotate x 90; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>st4215_ENDO_PDT_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 41; rotate x 90; rotate y 180; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>st4215_EXO_PDT_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== References ==
<references>
<ref name="inverse">D. Boger. <i>Progress in heterocyclic chemistry. (1st ed.).</i> (1989).</ref>
<ref name="fmo">I. Fleming. <i>Frontier Orbitals and Organic Chemical Reactions.</i> (1976).</ref>
</references>

Rep:Transition states (st4215): Exercise 2

2017-10-25T02:49:44Z

St4215: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
The reaction of cyclohexadiene and 1,3-dioxole is also a Diels-Alder reaction, in which cyclohexadiene is the diene and 1,3-dioxole is the dienophile. However, unlike the simple Diels-Alder reaction between butadiene and ethylene, this reaction is slightly more complex - 1,3-dioxole is an unsymmetrical diene and can approach the diene at different orientations, leading to the formation of the endo- and exo- Diels-Alder products. This can be seen in the reaction scheme below:
(insert chemdraw diagram)

The endo- product is formed from a transition state where the substituents on the dienophile point towards the π system of the diene, while the exo- product is formed from a transition state where the substituents are pointing away.

In this exercise, we take a closer look at a different aspect of the Diels-Alder reaction - whether it is normal or inverse electron demand. We also consider the Diels-Alder reaction when an unsymmetrical diene is involved, and compare the endo- and exo- DA reactions in terms of which is more kinetically or thermodynamically favourable. In the process, we confirm that the orbital symmetry requirements as elucidated in Exercise 1 still apply, and illustrate that there are differences between the PM6 and B3LYP calculation methods, with one being more suitable than the other in this case.

=== Calculations ===
Calculations were performed at both the PM6 and B3LYP/6-31G(d) level. Method 2 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial tutorial#Method_2) was used to locate the transition state.

The optimised molecules can be seen here:

{| class="wikitable"
! rowspan="2" | Calculation method
! colspan="2" | Reactants
! colspan="2" | Endo
! colspan="2" | Exo
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-dioxole
| style="text-align: center;" | Transition state
| style="text-align: center;" | Product
| style="text-align: center;" | Transition state
| style="text-align: center;" | Product
|-
| style="text-align: center;" | B3LYP
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18</script>
<uploadedFileContents>st4215_CYCLOHEXADIENE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26</script>
<uploadedFileContents>st4215_DIOXOLE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18</script>
<uploadedFileContents>st4215_ENDO_PDT_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>st4215_EXO_PDT_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" | PM6
| style="text-align: center;" | [[Media:st4215_CYCLOHEXADIENE_OPTFREQ_PM6.LOG| Cyclohexadiene (PM6)]]
| style="text-align: center;" | [[Media:st4215_DIOXOLE_OPTFREQ_PM6.LOG| 1,3-dioxole (PM6)]]
| style="text-align: center;" | [[Media:st4215_ENDO_TS_OPTFREQ_PM6.LOG| Endo-TS (PM6)]] <br> [[Media:st4215_ENDO_TS_IRC2_PM6ONPM6.LOG| IRC file]]
| style="text-align: center;" | [[Media:st4215_ENDO_PDT_OPTFREQ_PM6.LOG| Endo-product (PM6)]]
| style="text-align: center;" | [[Media:st4215_EXO_TS_OPTFREQ_PM6.LOG| Exo-TS(PM6)]] <br> [[Media:st4215_EXO_TS_IRC_PM6ONPM6.LOG| IRC file]]
| style="text-align: center;" | [[Media:st4215_EXO_PDT_OPTFREQ_PM6.LOG| Exo-product(PM6)]]

|}

=== Molecular orbitals ===

==== Computed MOs ====
<small><i>Using your MO diagram for the Diels-Alder reaction, locate the occupied and unoccupied orbitals associated with the DA reaction for both TSs by symmetry. Find the relevant MOs and add them to your wiki (at an appropriate angle to show symmetry).</i></small>

The MOs involved in this reaction - the HOMOs and LUMOs for the reactants (cyclohexadiene and 1,3-dioxole), as well as the 4 MOs that these produce in each of the endo and exo transition states - are shown below. As explained in Exercise 1, which is also a Diels-Alder reaction, only orbitals of the same symmetry are able to interact. This is illustrated in the table below, where the symmetry or antisymmetry of each orbital can be clearly seen.

{| class="wikitable"
! rowspan="2"| Symmetry
! colspan="2" | Reactants
! colspan="2" rowspan="2"| Transition state (Endo)
! colspan="2" rowspan="2"| Transition state (Exo)
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
|-
| Antisymmmetric
| <b>MO 22</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXADIENE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 20</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26; mo 20; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_DIOXOLE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 40</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 40; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 43</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 43; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 40</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 43</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Symmetric
| <b>MO 23</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXADIENE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 19</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26; mo 19; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_DIOXOLE_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 41</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 41; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 42</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 42; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 41</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 42</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; rotate x 90; rotate y 90; rotate z -20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

It is important to note that these MOs were generated from the B3LYP and not the PM6 calculation. While both calculation methods were used, the B3LYP calculation proved to be a better choice in visualising the MOs as it allowed us to see the symmetry of the orbitals more clearly, and corresponded more closely to the graphical representation of the orbitals in the MO diagram (see next section).

==== MO diagrams ====
<i><small>Construct a new MO diagram using these new orbitals, adjusting energy levels as necessary. Is this a normal or inverse demand DA reaction?</small></i>

MO diagrams for both the endo- and exo- Diels-Alder reactions were constructed as shown below. Energy levels of the MOs have been adjusted to reflect their actual values, as calculated in the B3LYP calculation.

{| class="wikitable"
! Endo geometry
! Exo geometry
|-
| [[File:st4215_Endo_MO_diagram.PNG|500px]]
| [[File:st4215_Exo_MO_diagram.PNG|500px]]
|}

From the MO diagrams above, we can conclude that both the endo- and exo- reactions are inverse demand DA reactions. In contrast to a normal electron demand DA reaction, where the diene is electron rich with a high LUMO and the dienophile is electron poor with a low HOMO, cyclohexadiene is electron poor with a low HOMO and 1,3-dioxole is electron rich with a high LUMO. Hence we can classify these reactions as inverse demand.

This is likely due to the nature of the dienophile, 1-3-dioxole, which has an electron-donating O atom. The lone pairs on the two adjacent O atoms are able to donate electron density into the double bond, making the dienophile more electron rich and raising the energy of its MOs, including its LUMO. In contrast, cyclohexadiene does not have any electron-donating substituents and is relatively electron poor. Hence, considering the Frontier Molecular Orbitals (FMOs), the LUMO<sub>dienophile</sub> is relatively high-energy and closer in energy to the low-energy HOMO<sub>diene</sub>, compared to HOMO<sub>dienophile</sub> and LUMO<sub>diene</sub>. Thus the interaction between the LUMO<sub>dienophile</sub> and HOMO<sub>diene</sub> is the strongest and dominates in this reaction, causing it to be inverse demand.<ref name="inverse"/>

=== Energy analysis ===
<small><i>Tabulate the energies and determine the reaction barriers and reaction energies (in kJ/mol) at room temperature (the corrected energies are labelled "Sum of electronic and thermal Free Energies", corresponding to the Gibbs free energy). Which are the kinetically and thermodynamically favourable products? Look at the HOMO of the TSs. Are there any secondary orbital interactions or sterics that might affect the reaction barrier energy?</i></small>

==== Free energies ====
The free energy of the reactants as well as the endo- and exo- Diels-Alder transition states and products are tabulated below. The reaction barriers and energies are also calculated.

{| class="wikitable"
! rowspan="3" scope="col" style="width: 150px;" |
! colspan="4" scope="col" style="width: 500px;" | Energy at 298 K
|-
| colspan="2" style="text-align: center;" | B3LYP
| colspan="2" style="text-align: center;" | PM6
|-
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
|-
| colspan="5" style="background: #B7C3D0" | <b>Reactants</b>
|-
| Cyclohexadiene || style="text-align: center;" | -233.32 || style="text-align: center;" | -6.1259 x 10<sup>5</sup> || style="text-align: center;" | 0.11688 || style="text-align: center;" | 306.86
|-
| 1,3-dioxole || style="text-align: center;" | -267.07 || style="text-align: center;" | -7.0119 x 10<sup>5</sup> || style="text-align: center;" | -0.052279 || style="text-align: center;" | -137.26
|-
| Total reactants || style="text-align: center;" | -500.39 || style="text-align: center;" | -1.3138 x 10<sup>6</sup> || style="text-align: center;" | 0.064598 || style="text-align: center;" | 169.60
|-
| colspan="5" style="background: #B7C3D0" | <b>Endo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | -500.332 || style="text-align: center;" | -1.3136 x 10<sup>6</sup> || style="text-align: center;" | 0.13794 ||style="text-align: center;" | 362.17
|-
| Product || style="text-align: center;" | -500.419 || style="text-align: center;" | -1.3138 x 10<sup>6</sup> || style="text-align: center;" | 0.037807 || style="text-align: center;" | 99.26
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0609 || style="text-align: center;" | 160 || style="text-align: center;" | 0.0733 || style="text-align: center;" | 193
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0257 || style="text-align: center;" | -67.4 || style="text-align: center;" | -0.0268 || style="text-align: center;" | -70.3
|-
| colspan="5" style="background: #B7C3D0" | <b>Exo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | -500.329 || style="text-align: center;" | -1.3136 x 10<sup>6</sup> || style="text-align: center;" | 0.13890 || style="text-align: center;" | 364.68
|-
| Product || style="text-align: center;" | -500.417 || style="text-align: center;" | -1.3138 x 10<sup>6</sup> || style="text-align: center;" | 0.037977 || style="text-align: center;" | 99.71
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0639 || style="text-align: center;" | 168 || style="text-align: center;" | 0.0743 || style="text-align: center;" | 195
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0243 || style="text-align: center;" | -63.8 || style="text-align: center;" | -0.0266 || style="text-align: center;" | -69.9
|}
<small><i>^Note that all values from the calculations are reported to 5 s.f. unless more decimal places are needed to differentiate between endo- and exo- geometries. Derived quantities (reaction barrier and reaction energy) are reported to 3 s.f.</i></small>

==== Thermodynamic and kinetic products ====
From the table above, we can conclude that the endo- product is both the kinetic and thermodynamic product. This is because it has a lower reaction barrier, meaning that less activation energy is required for the reaction, making it the kinetic product. The endo- product also has a lower reaction energy (ΔG), meaning that the endo- product is lower in energy and more stable than the exo- product, making it the thermodynamic product.

This is in contrast to most Diels-Alder reactions, in which the exo- product is the thermodynamic product as it is less sterically hindered and more stable, while the endo- product is the kinetic product due to stabilising orbital interactions in the transition state.<ref name="fmo"/> However, the difference for this reaction can be explained.

As seen in the jmols below, the endo- TS indeed has stabilising secondary orbital interactions between the p orbitals of O in 1,3-dioxole and the p orbitals of C in cyclohexadiene, which are absent in the exo- TS. The presence of these interactions lower the energy of the transition state, hence lowering the reaction barrier and making the endo-product the kinetic product.

Comparing the endo- and exo- products, we can also see that these stabilising orbital interactions are also in present in the endo- product. Additionally, the endo- product is less sterically hindered compared to the exo-product, in which there is steric clash between the hydrogens which are pointing towards each other. These two factors cause the energy of the endo- product to be lower than that of the exo- product, hence lowering the reaction energy and making the endo- product the thermodynamic product as well.

{| class="wikitable"
!
! Endo
! Exo
|-
| Transition state
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 41; rotate x 90; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>st4215_ENDO_TS_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; rotate x 90; rotate y 180; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>st4215_EXO_TS_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 41; rotate x 90; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>st4215_ENDO_PDT_OPTFREQ2_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 41; rotate x 90; rotate y 180; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>st4215_EXO_PDT_OPTFREQ_631G(D).LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== References ==
<references>
<ref name="inverse">D. Boger. <i>Progress in heterocyclic chemistry. (1st ed.).</i> (1989).</ref>
<ref name="fmo">I. Fleming. <i>Frontier Orbitals and Organic Chemical Reactions.</i> (1976).</ref>
</references>

Rep:Transition states (st4215): Exercise 1

2017-10-25T02:47:36Z

St4215: /* Calculations */

== Exercise 1: Reaction of Butadiene with Ethylene ==
The reaction between butadiene and ethylene is a [4+2] cycloaddition reaction, or more specifically, a Diels-Alder reaction - a reaction involving a conjugated diene in the s-cis conformation, and a dienophile containing a double bond. In this simple Diels-Alder reaction, butadiene is the diene and ethylene is the dienophile. The reaction scheme for this reaction is shown below:
(insert chemdraw diagram)

In this exercise, we use this Diels-Alder reaction to determine the orbital symmetry requirements for a reaction to take place, and to show the effect of hybridisation and bond order on the length of C-C bonds.

=== Calculations ===
Calculations were performed at the PM6 level. Method 1 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial#Method_1 tutorial]) was used to locate the transition state.

The optimised molecules can be seen here:

{| class="wikitable"
! colspan="2" | Reactants
! Transition state
! Product
|-
|<jmol>
<jmolApplet>
<title>Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_CYCLOHEXENE_TS_IRC3_PM6.LOG | IRC file]]
| <jmol>
<jmolApplet>
<title>Cyclohexene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_CYCLOHEXENE_PDT_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Molecular orbitals ===

==== MO diagram ====
<small><i>Construct an MO diagram for the formation of the butadiene/ethene TS, including basic symmetry labels (symmetric/antisymmetric or s/a).</i></small><br>

Keeping in mind that only orbitals of the same symmetry can combine, the MO diagram for this cycloaddition reaction was constructed as shown below. The MOs have been labelled accordingly with their numbers according to the calculations, and can be visualised in the section below.<br>
[[File:st4215_ex1_MO_diagram.PNG]]

Considering the actual energy levels of the MOs computed from the calculations, a more accurate MO diagram can be constructed, as seen [[Media:st4215_ex1_MO_diagram_actual.PNG|here]]. However, this does not affect the relative energy levels of the MOs (within each molecule) or the interactions between these MOs.

==== Computed MOs ====
<small><i>Include images (or Jmol objects) for each of the HOMO and LUMO of butadiene and ethene, and the four MOs these produce for the TS. Correlate these MOs with the ones in your MO diagram to show which orbitals interact.</i></small><br>

The HOMOs and LUMOs for each reactant, butadiene and ethylene, as well as the 4 MOs that these produce for the TS, were calculated and can be visualised below. The MO numbers correspond to that labelled on the MO diagram, allowing us to see which orbitals interact. We can also observe that these computed MOs bear physical resemblance to that drawn in the MO diagram, in terms of the bonding and antibonding phases in each MO.

{| class="wikitable"
! rowspan="2" | Symmetry
! colspan="2" | Reactants
! rowspan="2" colspan="2"| Transition state
|-
| style="text-align: center;" | Butadiene
| style="text-align: center;" | Ethylene
|-
| Antisymmetric
| <b>MO 11</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 7</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 16</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 19</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Symmetric
| <b>MO 12</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 6</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 17</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 18</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Symmetry requirements ====
<small><i>What can you conclude about the requirements for symmetry for a reaction (when is a reaction 'allowed' and when is it 'forbidden')? Write whether the orbital overlap integral is zero or non-zero for the case of a symmetric-antisymmetric interaction, a symmetric-symmetric interaction and an antisymmetric-antisymmetric interaction.</i></small><br>

From the table above as well as the MO diagram, we can see that the HOMO/LUMO of butadiene interact with the corresponding LUMO/HOMO in ethylene respectively. These interactions can occur as each pair of orbitals share the same symmetry. The HOMO of butadiene (MO 11) and the LUMO of ethylene (MO 7) are both antisymmetric, and interact to give two antisymmetric MOs in the TS (MOs 16 and 19). Similarly, the LUMO of ethylene (MO 12) and the HOMO of butadiene (MO 6) are both symmetric, and interact to give two symmetric MOs in the TS (MOs 17 and 18). Hence we can conclude that a reaction is only allowed when the relevant orbitals share the same symmetry, as this would allow orbitals to overlap. (QUANTUM EXPLANATION?????) This is illustrated in the following table:

{| class="wikitable"
! Symmetry of interaction
! Orbital overlap integral
|-
| style="text-align: center;" | Symmetric-antisymmetric
| style="text-align: center;" | Zero
|-
| style="text-align: center;" | Symmetric-symmetric
| style="text-align: center;" | Non-zero
|-
| style="text-align: center;" | Antisymmetric-antisymmetric
| style="text-align: center;" | Non-zero
|}

=== C-C bond lengths ===
<small><i>Include measurements of the 4 C-C bond lengths of the reactants and the 6 C-C bond lengths of the TS and products. How do the bond lengths change as the reaction progresses? What are typical sp3 and sp2 C-C bond lengths? What is the Van der Waals radius of the C atom? How does this compare with the length of the partly formed C-C bonds in the TS.</i></small>

The C-C bond lengths in the reactants, TS and products are tabulated below.

{| class="wikitable"
! rowspan="2" colspan="2" |
! colspan="2" | Reactants
! rowspan="2" | Transition state
! rowspan="2" | Product
|-
| style="text-align: center;" | Butadiene
| style="text-align: center;" | Ethylene
|-
| colspan="2" style="text-align: center;"| Labelled C atoms
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7; label display</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4; label display</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>st4215_CYCLOHEXENE_PDT_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| rowspan="6" style="text-align: center;" | C-C bond<br> length / Å
| style="width: 50px;" | Bond A || <center> C1-C4: 1.34 </center>|| || <center> C1-C4: 1.38 </center> || <center> C1-C4: 1.50 </center>
|-
| Bond B || <center> C4-C6: 1.47 </center> || || <center> C4-C6: 1.41 </center> || <center> C4-C6: 1.34 </center>
|-
| Bond C || <center> C6-C7: 1.34 </center> || || <center> C6-C7: 1.38 </center> || <center> C6-C7: 1.50 </center>
|-
| Bond D || || <center> C1-C4: 1.33 </center> || <center> C11-C14: 1.38 </center> || <center> C11-C14: 1.54 </center>
|-
| Bond E || || || <center> C7-C14: 2.11 </center> || <center> C7-C14: 1.54 </center>
|-
| Bond F || || || <center> C1-C11: 2.11 </center> || <center> C1-C11: 1.54 </center>
|}

From the values above, we can observe the following changes in bond length as the reaction progresses.

{| class="wikitable" style="width: 750px;"
! Bond
! Trend in bond length as reaction progresses
! Graph
|-
| A || As the reaction progresses, the length of Bond A increases. This is because Bond A is initially a C=C double bond in butadiene, which becomes a sp<sup>2</sup>-sp<sup>3</sup> C-C single bond in cyclohexene. These lengths are similar to typical values of 1.34 Å for alkenes and 1.50 Å sp<sup>2</sup>-sp<sup>3</sup> C-C bonds.<ref name="bondlength"/>
| [[File:st4215_BondA.JPG|200px]]
|-
| B || As the reaction progresses, the length of Bond B decreases. This is because Bond B is initially an sp<sup>2</sup>-sp<sup>2</sup> C-C single bond in butadiene, which becomes a C=C double bond in cyclohexene. These lengths are similar to typical values of 1.47 Å for sp<sup>2</sup>-sp<sup>2</sup> C-C bonds and 1.34 Å for alkenes.<ref name="bondlength"/>
| [[File:st4215_BondB.JPG|200px]]
|-
| C || Similar to Bond A, as the reaction progresses, the length of Bond C increases. This is due to the same reason as explained for Bond A.
| [[File:st4215_BondC.JPG|200px]]
|-
| D || As the reaction progresses, the length of Bond D increases. This is because Bond B is initially an C=C single bond in ethylene, which becomes a sp<sup>3</sup>-sp<sup>3</sup> C-C single bond in cyclohexene. These lengths are similar to typical values of 1.34 Å for alkenes and 1.54 Å for sp<sup>3</sup>-sp<sup>3</sup> C-C bonds.<ref name="bondlength"/>
| [[File:st4215_BondD.JPG|200px]]
|-
| E || Bond E is formed in this reaction. Hence as the reaction progresses from the transition state to the product, the length of Bond E increases. The length of the fully formed Bond E in the product, an sp<sup>3</sup>-sp<sup>3</sup> C-C single bond, corresponds to the typical value of 1.54 Å.<ref name="bondlength"/> The distance between the C atoms in the TS (2.11 Å) falls between twice the van der Waal radius of C (2 x 1.70 Å<ref name="vdw_c"/> = 3.40 Å) and the length of the fully formed Bond E, indicating that the atoms are approaching each other.
| [[File:st4215_BondE.JPG|200px]]
|-
| F || Like Bond E, Bond F is also formed in this reaction. Hence as the reaction progresses from the transition state to the product, the length of Bond F increases, due to the same reasons as explained above.
| [[File:st4215_BondF.JPG|200px]]
|}

=== Transition state ===
<i><small>Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous?</small></i>
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 7; rotate x -40; select atomno=1, atomno=7, atomno=11, atomno=14; label display </script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
<name>cyclohexeneTS</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>cyclohexeneTS</target>
</jmolbutton>
<jmolbutton>
<script>measure 1 11; measure 7 14</script>
<text>C-C Distances</text>
<target>cyclohexeneTS</target>
</jmolbutton>
</jmol>
<br><br>
As illustrated above, the formation of the two bonds are synchronous as the relevant pairs of atoms (C1/C11 and C7/C14) are moving towards each other at the same time, with the distance between the two atoms being approximately equal in both pairs. This is to be expected as evidence shows that the Diels-Alder reaction can proceed via a concerted, synchronous mechanism.<ref name="DA_1"/> However, it is important to note that this may also be the result of the calculation method used, as studies with other calculation methods (DFT/B3LYP) have also shown that other mechanisms are feasible.<ref name="DA_2"/>

== References ==
<references>
<ref name="bondlength">M. A. Fox, J. K. Whitesell, E. Buchholz. <i>Organische Chemie: Grundlagen, Mechanismen, bioorganische Anwendungen</i> (1995).</ref>
<ref name="vdw_c">A. Bondi. [http://pubs.acs.org/doi/pdf/10.1021/j100785a001 <i>van der Waals Volumes and Radii </i>] J. Phys. Chem. <b>68</b>(3), 441–451 (1996).</ref>
<ref name="DA_1">K. N. Houk, Y. T Lin & F. K. Brown. [http://pubs.acs.org/doi/pdf/10.1021/ja00263a059 <i>Evidence for the Concerted Mechanism of the Diels-Alder Reaction of Butadiene with Ethylene.</i>] J. Am. Chem. SOC. <b>108</b>, 554-556 (1986).</ref>
<ref name="DA_2">E. Goldstein, B. Beno & K. N. Houk. [http://pubs.acs.org/doi/pdf/10.1021/ja9601494 <i>Density Functional Theory Prediction of the Relative Energies and Isotope Effects for the Concerted and Stepwise Mechanisms of the Diels-Alder Reaction of Butadiene and Ethylene</i>] J. Am. Chem. Soc. <b>118</b>, 6036-6043 (1996).
</ref>
</references>

Rep:Transition states (st4215): Exercise 1

2017-10-25T02:19:58Z

St4215: /* Exercise 1: Reaction of Butadiene with Ethylene */

== Exercise 1: Reaction of Butadiene with Ethylene ==
The reaction between butadiene and ethylene is a [4+2] cycloaddition reaction, or more specifically, a Diels-Alder reaction - a reaction involving a conjugated diene in the s-cis conformation, and a dienophile containing a double bond. In this simple Diels-Alder reaction, butadiene is the diene and ethylene is the dienophile. The reaction scheme for this reaction is shown below:
(insert chemdraw diagram)

In this exercise, we use this Diels-Alder reaction to determine the orbital symmetry requirements for a reaction to take place, and to show the effect of hybridisation and bond order on the length of C-C bonds.

=== Calculations ===
Calculations were performed at the PM6 level. Method 1 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial tutorial]) was used to locate the transition state.

The optimised molecules can be seen here:

{| class="wikitable"
! colspan="2" | Reactants
! Transition state
! Product
|-
|<jmol>
<jmolApplet>
<title>Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_CYCLOHEXENE_TS_IRC3_PM6.LOG | IRC file]]
| <jmol>
<jmolApplet>
<title>Cyclohexene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_CYCLOHEXENE_PDT_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Molecular orbitals ===

==== MO diagram ====
<small><i>Construct an MO diagram for the formation of the butadiene/ethene TS, including basic symmetry labels (symmetric/antisymmetric or s/a).</i></small><br>

Keeping in mind that only orbitals of the same symmetry can combine, the MO diagram for this cycloaddition reaction was constructed as shown below. The MOs have been labelled accordingly with their numbers according to the calculations, and can be visualised in the section below.<br>
[[File:st4215_ex1_MO_diagram.PNG]]

Considering the actual energy levels of the MOs computed from the calculations, a more accurate MO diagram can be constructed, as seen [[Media:st4215_ex1_MO_diagram_actual.PNG|here]]. However, this does not affect the relative energy levels of the MOs (within each molecule) or the interactions between these MOs.

==== Computed MOs ====
<small><i>Include images (or Jmol objects) for each of the HOMO and LUMO of butadiene and ethene, and the four MOs these produce for the TS. Correlate these MOs with the ones in your MO diagram to show which orbitals interact.</i></small><br>

The HOMOs and LUMOs for each reactant, butadiene and ethylene, as well as the 4 MOs that these produce for the TS, were calculated and can be visualised below. The MO numbers correspond to that labelled on the MO diagram, allowing us to see which orbitals interact. We can also observe that these computed MOs bear physical resemblance to that drawn in the MO diagram, in terms of the bonding and antibonding phases in each MO.

{| class="wikitable"
! rowspan="2" | Symmetry
! colspan="2" | Reactants
! rowspan="2" colspan="2"| Transition state
|-
| style="text-align: center;" | Butadiene
| style="text-align: center;" | Ethylene
|-
| Antisymmetric
| <b>MO 11</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 7</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 16</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 19</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Symmetric
| <b>MO 12</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 6</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 17</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 18</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Symmetry requirements ====
<small><i>What can you conclude about the requirements for symmetry for a reaction (when is a reaction 'allowed' and when is it 'forbidden')? Write whether the orbital overlap integral is zero or non-zero for the case of a symmetric-antisymmetric interaction, a symmetric-symmetric interaction and an antisymmetric-antisymmetric interaction.</i></small><br>

From the table above as well as the MO diagram, we can see that the HOMO/LUMO of butadiene interact with the corresponding LUMO/HOMO in ethylene respectively. These interactions can occur as each pair of orbitals share the same symmetry. The HOMO of butadiene (MO 11) and the LUMO of ethylene (MO 7) are both antisymmetric, and interact to give two antisymmetric MOs in the TS (MOs 16 and 19). Similarly, the LUMO of ethylene (MO 12) and the HOMO of butadiene (MO 6) are both symmetric, and interact to give two symmetric MOs in the TS (MOs 17 and 18). Hence we can conclude that a reaction is only allowed when the relevant orbitals share the same symmetry, as this would allow orbitals to overlap. (QUANTUM EXPLANATION?????) This is illustrated in the following table:

{| class="wikitable"
! Symmetry of interaction
! Orbital overlap integral
|-
| style="text-align: center;" | Symmetric-antisymmetric
| style="text-align: center;" | Zero
|-
| style="text-align: center;" | Symmetric-symmetric
| style="text-align: center;" | Non-zero
|-
| style="text-align: center;" | Antisymmetric-antisymmetric
| style="text-align: center;" | Non-zero
|}

=== C-C bond lengths ===
<small><i>Include measurements of the 4 C-C bond lengths of the reactants and the 6 C-C bond lengths of the TS and products. How do the bond lengths change as the reaction progresses? What are typical sp3 and sp2 C-C bond lengths? What is the Van der Waals radius of the C atom? How does this compare with the length of the partly formed C-C bonds in the TS.</i></small>

The C-C bond lengths in the reactants, TS and products are tabulated below.

{| class="wikitable"
! rowspan="2" colspan="2" |
! colspan="2" | Reactants
! rowspan="2" | Transition state
! rowspan="2" | Product
|-
| style="text-align: center;" | Butadiene
| style="text-align: center;" | Ethylene
|-
| colspan="2" style="text-align: center;"| Labelled C atoms
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7; label display</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4; label display</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>st4215_CYCLOHEXENE_PDT_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| rowspan="6" style="text-align: center;" | C-C bond<br> length / Å
| style="width: 50px;" | Bond A || <center> C1-C4: 1.34 </center>|| || <center> C1-C4: 1.38 </center> || <center> C1-C4: 1.50 </center>
|-
| Bond B || <center> C4-C6: 1.47 </center> || || <center> C4-C6: 1.41 </center> || <center> C4-C6: 1.34 </center>
|-
| Bond C || <center> C6-C7: 1.34 </center> || || <center> C6-C7: 1.38 </center> || <center> C6-C7: 1.50 </center>
|-
| Bond D || || <center> C1-C4: 1.33 </center> || <center> C11-C14: 1.38 </center> || <center> C11-C14: 1.54 </center>
|-
| Bond E || || || <center> C7-C14: 2.11 </center> || <center> C7-C14: 1.54 </center>
|-
| Bond F || || || <center> C1-C11: 2.11 </center> || <center> C1-C11: 1.54 </center>
|}

From the values above, we can observe the following changes in bond length as the reaction progresses.

{| class="wikitable" style="width: 750px;"
! Bond
! Trend in bond length as reaction progresses
! Graph
|-
| A || As the reaction progresses, the length of Bond A increases. This is because Bond A is initially a C=C double bond in butadiene, which becomes a sp<sup>2</sup>-sp<sup>3</sup> C-C single bond in cyclohexene. These lengths are similar to typical values of 1.34 Å for alkenes and 1.50 Å sp<sup>2</sup>-sp<sup>3</sup> C-C bonds.<ref name="bondlength"/>
| [[File:st4215_BondA.JPG|200px]]
|-
| B || As the reaction progresses, the length of Bond B decreases. This is because Bond B is initially an sp<sup>2</sup>-sp<sup>2</sup> C-C single bond in butadiene, which becomes a C=C double bond in cyclohexene. These lengths are similar to typical values of 1.47 Å for sp<sup>2</sup>-sp<sup>2</sup> C-C bonds and 1.34 Å for alkenes.<ref name="bondlength"/>
| [[File:st4215_BondB.JPG|200px]]
|-
| C || Similar to Bond A, as the reaction progresses, the length of Bond C increases. This is due to the same reason as explained for Bond A.
| [[File:st4215_BondC.JPG|200px]]
|-
| D || As the reaction progresses, the length of Bond D increases. This is because Bond B is initially an C=C single bond in ethylene, which becomes a sp<sup>3</sup>-sp<sup>3</sup> C-C single bond in cyclohexene. These lengths are similar to typical values of 1.34 Å for alkenes and 1.54 Å for sp<sup>3</sup>-sp<sup>3</sup> C-C bonds.<ref name="bondlength"/>
| [[File:st4215_BondD.JPG|200px]]
|-
| E || Bond E is formed in this reaction. Hence as the reaction progresses from the transition state to the product, the length of Bond E increases. The length of the fully formed Bond E in the product, an sp<sup>3</sup>-sp<sup>3</sup> C-C single bond, corresponds to the typical value of 1.54 Å.<ref name="bondlength"/> The distance between the C atoms in the TS (2.11 Å) falls between twice the van der Waal radius of C (2 x 1.70 Å<ref name="vdw_c"/> = 3.40 Å) and the length of the fully formed Bond E, indicating that the atoms are approaching each other.
| [[File:st4215_BondE.JPG|200px]]
|-
| F || Like Bond E, Bond F is also formed in this reaction. Hence as the reaction progresses from the transition state to the product, the length of Bond F increases, due to the same reasons as explained above.
| [[File:st4215_BondF.JPG|200px]]
|}

=== Transition state ===
<i><small>Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous?</small></i>
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 7; rotate x -40; select atomno=1, atomno=7, atomno=11, atomno=14; label display </script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
<name>cyclohexeneTS</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>cyclohexeneTS</target>
</jmolbutton>
<jmolbutton>
<script>measure 1 11; measure 7 14</script>
<text>C-C Distances</text>
<target>cyclohexeneTS</target>
</jmolbutton>
</jmol>
<br><br>
As illustrated above, the formation of the two bonds are synchronous as the relevant pairs of atoms (C1/C11 and C7/C14) are moving towards each other at the same time, with the distance between the two atoms being approximately equal in both pairs. This is to be expected as evidence shows that the Diels-Alder reaction can proceed via a concerted, synchronous mechanism.<ref name="DA_1"/> However, it is important to note that this may also be the result of the calculation method used, as studies with other calculation methods (DFT/B3LYP) have also shown that other mechanisms are feasible.<ref name="DA_2"/>

== References ==
<references>
<ref name="bondlength">M. A. Fox, J. K. Whitesell, E. Buchholz. <i>Organische Chemie: Grundlagen, Mechanismen, bioorganische Anwendungen</i> (1995).</ref>
<ref name="vdw_c">A. Bondi. [http://pubs.acs.org/doi/pdf/10.1021/j100785a001 <i>van der Waals Volumes and Radii </i>] J. Phys. Chem. <b>68</b>(3), 441–451 (1996).</ref>
<ref name="DA_1">K. N. Houk, Y. T Lin & F. K. Brown. [http://pubs.acs.org/doi/pdf/10.1021/ja00263a059 <i>Evidence for the Concerted Mechanism of the Diels-Alder Reaction of Butadiene with Ethylene.</i>] J. Am. Chem. SOC. <b>108</b>, 554-556 (1986).</ref>
<ref name="DA_2">E. Goldstein, B. Beno & K. N. Houk. [http://pubs.acs.org/doi/pdf/10.1021/ja9601494 <i>Density Functional Theory Prediction of the Relative Energies and Isotope Effects for the Concerted and Stepwise Mechanisms of the Diels-Alder Reaction of Butadiene and Ethylene</i>] J. Am. Chem. Soc. <b>118</b>, 6036-6043 (1996).
</ref>
</references>

Rep:Transition states (st4215): Exercise 1

2017-10-25T00:36:59Z

St4215: /* Calculations */

== Exercise 1: Reaction of Butadiene with Ethylene ==
The reaction between butadiene and ethylene is a [4+2] cycloaddition reaction, or more specifically, a Diels-Alder reaction where butadiene is the diene and ethylene is the dienophile. The reaction scheme for this reaction is shown below:
(insert chemdraw diagram)

In this exercise, we use this simple Diels-Alder reaction to determine the orbital symmetry requirements for a reaction to take place, and to show the effect of hybridisation and bond order on the length of C-C bonds.

=== Calculations ===
Calculations were performed at the PM6 level. Method 1 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial tutorial]) was used to locate the transition state.

The optimised molecules can be seen here:

{| class="wikitable"
! colspan="2" | Reactants
! Transition state
! Product
|-
|<jmol>
<jmolApplet>
<title>Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_CYCLOHEXENE_TS_IRC3_PM6.LOG | IRC file]]
| <jmol>
<jmolApplet>
<title>Cyclohexene</title>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_CYCLOHEXENE_PDT_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Molecular orbitals ===

==== MO diagram ====
<small><i>Construct an MO diagram for the formation of the butadiene/ethene TS, including basic symmetry labels (symmetric/antisymmetric or s/a).</i></small><br>

Keeping in mind that only orbitals of the same symmetry can combine, the MO diagram for this cycloaddition reaction was constructed as shown below. The MOs have been labelled accordingly with their numbers according to the calculations, and can be visualised in the section below.<br>
[[File:st4215_ex1_MO_diagram.PNG]]

Considering the actual energy levels of the MOs computed from the calculations, a more accurate MO diagram can be constructed, as seen [[Media:st4215_ex1_MO_diagram_actual.PNG|here]]. However, this does not affect the relative energy levels of the MOs (within each molecule) or the interactions between these MOs.

==== Computed MOs ====
<small><i>Include images (or Jmol objects) for each of the HOMO and LUMO of butadiene and ethene, and the four MOs these produce for the TS. Correlate these MOs with the ones in your MO diagram to show which orbitals interact.</i></small><br>

The HOMOs and LUMOs for each reactant, butadiene and ethylene, as well as the 4 MOs that these produce for the TS, were calculated and can be visualised below. The MO numbers correspond to that labelled on the MO diagram, allowing us to see which orbitals interact. We can also observe that these computed MOs bear physical resemblance to that drawn in the MO diagram, in terms of the bonding and antibonding phases in each MO.

{| class="wikitable"
! rowspan="2" | Symmetry
! colspan="2" | Reactants
! rowspan="2" colspan="2"| Transition state
|-
| style="text-align: center;" | Butadiene
| style="text-align: center;" | Ethylene
|-
| Antisymmetric
| <b>MO 11</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 7</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 16</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 19</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Symmetric
| <b>MO 12</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 6</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 17</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 18</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Symmetry requirements ====
<small><i>What can you conclude about the requirements for symmetry for a reaction (when is a reaction 'allowed' and when is it 'forbidden')? Write whether the orbital overlap integral is zero or non-zero for the case of a symmetric-antisymmetric interaction, a symmetric-symmetric interaction and an antisymmetric-antisymmetric interaction.</i></small><br>

From the table above as well as the MO diagram, we can see that the HOMO/LUMO of butadiene interact with the corresponding LUMO/HOMO in ethylene respectively. These interactions can occur as each pair of orbitals share the same symmetry. The HOMO of butadiene (MO 11) and the LUMO of ethylene (MO 7) are both antisymmetric, and interact to give two antisymmetric MOs in the TS (MOs 16 and 19). Similarly, the LUMO of ethylene (MO 12) and the HOMO of butadiene (MO 6) are both symmetric, and interact to give two symmetric MOs in the TS (MOs 17 and 18). Hence we can conclude that a reaction is only allowed when the relevant orbitals share the same symmetry, as this would allow orbitals to overlap. (QUANTUM EXPLANATION?????) This is illustrated in the following table:

{| class="wikitable"
! Symmetry of interaction
! Orbital overlap integral
|-
| style="text-align: center;" | Symmetric-antisymmetric
| style="text-align: center;" | Zero
|-
| style="text-align: center;" | Symmetric-symmetric
| style="text-align: center;" | Non-zero
|-
| style="text-align: center;" | Antisymmetric-antisymmetric
| style="text-align: center;" | Non-zero
|}

=== C-C bond lengths ===
<small><i>Include measurements of the 4 C-C bond lengths of the reactants and the 6 C-C bond lengths of the TS and products. How do the bond lengths change as the reaction progresses? What are typical sp3 and sp2 C-C bond lengths? What is the Van der Waals radius of the C atom? How does this compare with the length of the partly formed C-C bonds in the TS.</i></small>

The C-C bond lengths in the reactants, TS and products are tabulated below.

{| class="wikitable"
! rowspan="2" colspan="2" |
! colspan="2" | Reactants
! rowspan="2" | Transition state
! rowspan="2" | Product
|-
| style="text-align: center;" | Butadiene
| style="text-align: center;" | Ethylene
|-
| colspan="2" style="text-align: center;"| Labelled C atoms
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7; label display</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4; label display</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>st4215_CYCLOHEXENE_PDT_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| rowspan="6" style="text-align: center;" | C-C bond<br> length / Å
| style="width: 50px;" | Bond A || <center> C1-C4: 1.34 </center>|| || <center> C1-C4: 1.38 </center> || <center> C1-C4: 1.50 </center>
|-
| Bond B || <center> C4-C6: 1.47 </center> || || <center> C4-C6: 1.41 </center> || <center> C4-C6: 1.34 </center>
|-
| Bond C || <center> C6-C7: 1.34 </center> || || <center> C6-C7: 1.38 </center> || <center> C6-C7: 1.50 </center>
|-
| Bond D || || <center> C1-C4: 1.33 </center> || <center> C11-C14: 1.38 </center> || <center> C11-C14: 1.54 </center>
|-
| Bond E || || || <center> C7-C14: 2.11 </center> || <center> C7-C14: 1.54 </center>
|-
| Bond F || || || <center> C1-C11: 2.11 </center> || <center> C1-C11: 1.54 </center>
|}

From the values above, we can observe the following changes in bond length as the reaction progresses.

{| class="wikitable" style="width: 750px;"
! Bond
! Trend in bond length as reaction progresses
! Graph
|-
| A || As the reaction progresses, the length of Bond A increases. This is because Bond A is initially a C=C double bond in butadiene, which becomes a sp<sup>2</sup>-sp<sup>3</sup> C-C single bond in cyclohexene. These lengths are similar to typical values of 1.34 Å for alkenes and 1.50 Å sp<sup>2</sup>-sp<sup>3</sup> C-C bonds.<ref name="bondlength"/>
| [[File:st4215_BondA.JPG|200px]]
|-
| B || As the reaction progresses, the length of Bond B decreases. This is because Bond B is initially an sp<sup>2</sup>-sp<sup>2</sup> C-C single bond in butadiene, which becomes a C=C double bond in cyclohexene. These lengths are similar to typical values of 1.47 Å for sp<sup>2</sup>-sp<sup>2</sup> C-C bonds and 1.34 Å for alkenes.<ref name="bondlength"/>
| [[File:st4215_BondB.JPG|200px]]
|-
| C || Similar to Bond A, as the reaction progresses, the length of Bond C increases. This is due to the same reason as explained for Bond A.
| [[File:st4215_BondC.JPG|200px]]
|-
| D || As the reaction progresses, the length of Bond D increases. This is because Bond B is initially an C=C single bond in ethylene, which becomes a sp<sup>3</sup>-sp<sup>3</sup> C-C single bond in cyclohexene. These lengths are similar to typical values of 1.34 Å for alkenes and 1.54 Å for sp<sup>3</sup>-sp<sup>3</sup> C-C bonds.<ref name="bondlength"/>
| [[File:st4215_BondD.JPG|200px]]
|-
| E || Bond E is formed in this reaction. Hence as the reaction progresses from the transition state to the product, the length of Bond E increases. The length of the fully formed Bond E in the product, an sp<sup>3</sup>-sp<sup>3</sup> C-C single bond, corresponds to the typical value of 1.54 Å.<ref name="bondlength"/> The distance between the C atoms in the TS (2.11 Å) falls between twice the van der Waal radius of C (2 x 1.70 Å<ref name="vdw_c"/> = 3.40 Å) and the length of the fully formed Bond E, indicating that the atoms are approaching each other.
| [[File:st4215_BondE.JPG|200px]]
|-
| F || Like Bond E, Bond F is also formed in this reaction. Hence as the reaction progresses from the transition state to the product, the length of Bond F increases, due to the same reasons as explained above.
| [[File:st4215_BondF.JPG|200px]]
|}

=== Transition state ===
<i><small>Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous?</small></i>
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 7; rotate x -40; select atomno=1, atomno=7, atomno=11, atomno=14; label display </script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
<name>cyclohexeneTS</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>cyclohexeneTS</target>
</jmolbutton>
<jmolbutton>
<script>measure 1 11; measure 7 14</script>
<text>C-C Distances</text>
<target>cyclohexeneTS</target>
</jmolbutton>
</jmol>
<br><br>
As illustrated above, the formation of the two bonds are synchronous as the relevant pairs of atoms (C1/C11 and C7/C14) are moving towards each other at the same time, with the distance between the two atoms being approximately equal in both pairs. This is to be expected as evidence shows that the Diels-Alder reaction can proceed via a concerted, synchronous mechanism.<ref name="DA_1"/> However, it is important to note that this may also be the result of the calculation method used, as studies with other calculation methods (DFT/B3LYP) have also shown that other mechanisms are feasible.<ref name="DA_2"/>

== References ==
<references>
<ref name="bondlength">M. A. Fox, J. K. Whitesell, E. Buchholz. <i>Organische Chemie: Grundlagen, Mechanismen, bioorganische Anwendungen</i> (1995).</ref>
<ref name="vdw_c">A. Bondi. [http://pubs.acs.org/doi/pdf/10.1021/j100785a001 <i>van der Waals Volumes and Radii </i>] J. Phys. Chem. <b>68</b>(3), 441–451 (1996).</ref>
<ref name="DA_1">K. N. Houk, Y. T Lin & F. K. Brown. [http://pubs.acs.org/doi/pdf/10.1021/ja00263a059 <i>Evidence for the Concerted Mechanism of the Diels-Alder Reaction of Butadiene with Ethylene.</i>] J. Am. Chem. SOC. <b>108</b>, 554-556 (1986).</ref>
<ref name="DA_2">E. Goldstein, B. Beno & K. N. Houk. [http://pubs.acs.org/doi/pdf/10.1021/ja9601494 <i>Density Functional Theory Prediction of the Relative Energies and Isotope Effects for the Concerted and Stepwise Mechanisms of the Diels-Alder Reaction of Butadiene and Ethylene</i>] J. Am. Chem. Soc. <b>118</b>, 6036-6043 (1996).
</ref>
</references>

Rep:Transition states (st4215): Exercise 1

2017-10-25T00:35:34Z

St4215: /* Exercise 1: Reaction of Butadiene with Ethylene */

== Exercise 1: Reaction of Butadiene with Ethylene ==
The reaction between butadiene and ethylene is a [4+2] cycloaddition reaction, or more specifically, a Diels-Alder reaction where butadiene is the diene and ethylene is the dienophile. The reaction scheme for this reaction is shown below:
(insert chemdraw diagram)

In this exercise, we use this simple Diels-Alder reaction to determine the orbital symmetry requirements for a reaction to take place, and to show the effect of hybridisation and bond order on the length of C-C bonds.

=== Calculations ===
Calculations were performed at the PM6 level. Method 1 (see [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_tutorial tutorial]) was used to locate the transition state.

The optimised molecules can be seen here:

{| class="wikitable"
! colspan="2" | Reactants
! Transition state
! Product
|-
|<jmol>
<jmolApplet>
<title>Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 6; rotate spin y 30</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 6; rotate spin y 30</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; rotate spin y 30</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_CYCLOHEXENE_TS_IRC3_PM6.LOG | IRC file]]
| <jmol>
<jmolApplet>
<title>Cyclohexene</title>
<color>white</color>
<size>200</size>
<script>frame 6; rotate spin y 30</script>
<uploadedFileContents>st4215_CYCLOHEXENE_PDT_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Molecular orbitals ===

==== MO diagram ====
<small><i>Construct an MO diagram for the formation of the butadiene/ethene TS, including basic symmetry labels (symmetric/antisymmetric or s/a).</i></small><br>

Keeping in mind that only orbitals of the same symmetry can combine, the MO diagram for this cycloaddition reaction was constructed as shown below. The MOs have been labelled accordingly with their numbers according to the calculations, and can be visualised in the section below.<br>
[[File:st4215_ex1_MO_diagram.PNG]]

Considering the actual energy levels of the MOs computed from the calculations, a more accurate MO diagram can be constructed, as seen [[Media:st4215_ex1_MO_diagram_actual.PNG|here]]. However, this does not affect the relative energy levels of the MOs (within each molecule) or the interactions between these MOs.

==== Computed MOs ====
<small><i>Include images (or Jmol objects) for each of the HOMO and LUMO of butadiene and ethene, and the four MOs these produce for the TS. Correlate these MOs with the ones in your MO diagram to show which orbitals interact.</i></small><br>

The HOMOs and LUMOs for each reactant, butadiene and ethylene, as well as the 4 MOs that these produce for the TS, were calculated and can be visualised below. The MO numbers correspond to that labelled on the MO diagram, allowing us to see which orbitals interact. We can also observe that these computed MOs bear physical resemblance to that drawn in the MO diagram, in terms of the bonding and antibonding phases in each MO.

{| class="wikitable"
! rowspan="2" | Symmetry
! colspan="2" | Reactants
! rowspan="2" colspan="2"| Transition state
|-
| style="text-align: center;" | Butadiene
| style="text-align: center;" | Ethylene
|-
| Antisymmetric
| <b>MO 11</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 7</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 16</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 19</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Symmetric
| <b>MO 12</b> (LUMO)<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 6</b> (HOMO) <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 17</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <b>MO 18</b><jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Symmetry requirements ====
<small><i>What can you conclude about the requirements for symmetry for a reaction (when is a reaction 'allowed' and when is it 'forbidden')? Write whether the orbital overlap integral is zero or non-zero for the case of a symmetric-antisymmetric interaction, a symmetric-symmetric interaction and an antisymmetric-antisymmetric interaction.</i></small><br>

From the table above as well as the MO diagram, we can see that the HOMO/LUMO of butadiene interact with the corresponding LUMO/HOMO in ethylene respectively. These interactions can occur as each pair of orbitals share the same symmetry. The HOMO of butadiene (MO 11) and the LUMO of ethylene (MO 7) are both antisymmetric, and interact to give two antisymmetric MOs in the TS (MOs 16 and 19). Similarly, the LUMO of ethylene (MO 12) and the HOMO of butadiene (MO 6) are both symmetric, and interact to give two symmetric MOs in the TS (MOs 17 and 18). Hence we can conclude that a reaction is only allowed when the relevant orbitals share the same symmetry, as this would allow orbitals to overlap. (QUANTUM EXPLANATION?????) This is illustrated in the following table:

{| class="wikitable"
! Symmetry of interaction
! Orbital overlap integral
|-
| style="text-align: center;" | Symmetric-antisymmetric
| style="text-align: center;" | Zero
|-
| style="text-align: center;" | Symmetric-symmetric
| style="text-align: center;" | Non-zero
|-
| style="text-align: center;" | Antisymmetric-antisymmetric
| style="text-align: center;" | Non-zero
|}

=== C-C bond lengths ===
<small><i>Include measurements of the 4 C-C bond lengths of the reactants and the 6 C-C bond lengths of the TS and products. How do the bond lengths change as the reaction progresses? What are typical sp3 and sp2 C-C bond lengths? What is the Van der Waals radius of the C atom? How does this compare with the length of the partly formed C-C bonds in the TS.</i></small>

The C-C bond lengths in the reactants, TS and products are tabulated below.

{| class="wikitable"
! rowspan="2" colspan="2" |
! colspan="2" | Reactants
! rowspan="2" | Transition state
! rowspan="2" | Product
|-
| style="text-align: center;" | Butadiene
| style="text-align: center;" | Ethylene
|-
| colspan="2" style="text-align: center;"| Labelled C atoms
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7; label display</script>
<uploadedFileContents>st4215_BUTADIENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4; label display</script>
<uploadedFileContents>st4215_ETHYLENE_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>st4215_CYCLOHEXENE_PDT_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| rowspan="6" style="text-align: center;" | C-C bond<br> length / Å
| style="width: 50px;" | Bond A || <center> C1-C4: 1.34 </center>|| || <center> C1-C4: 1.38 </center> || <center> C1-C4: 1.50 </center>
|-
| Bond B || <center> C4-C6: 1.47 </center> || || <center> C4-C6: 1.41 </center> || <center> C4-C6: 1.34 </center>
|-
| Bond C || <center> C6-C7: 1.34 </center> || || <center> C6-C7: 1.38 </center> || <center> C6-C7: 1.50 </center>
|-
| Bond D || || <center> C1-C4: 1.33 </center> || <center> C11-C14: 1.38 </center> || <center> C11-C14: 1.54 </center>
|-
| Bond E || || || <center> C7-C14: 2.11 </center> || <center> C7-C14: 1.54 </center>
|-
| Bond F || || || <center> C1-C11: 2.11 </center> || <center> C1-C11: 1.54 </center>
|}

From the values above, we can observe the following changes in bond length as the reaction progresses.

{| class="wikitable" style="width: 750px;"
! Bond
! Trend in bond length as reaction progresses
! Graph
|-
| A || As the reaction progresses, the length of Bond A increases. This is because Bond A is initially a C=C double bond in butadiene, which becomes a sp<sup>2</sup>-sp<sup>3</sup> C-C single bond in cyclohexene. These lengths are similar to typical values of 1.34 Å for alkenes and 1.50 Å sp<sup>2</sup>-sp<sup>3</sup> C-C bonds.<ref name="bondlength"/>
| [[File:st4215_BondA.JPG|200px]]
|-
| B || As the reaction progresses, the length of Bond B decreases. This is because Bond B is initially an sp<sup>2</sup>-sp<sup>2</sup> C-C single bond in butadiene, which becomes a C=C double bond in cyclohexene. These lengths are similar to typical values of 1.47 Å for sp<sup>2</sup>-sp<sup>2</sup> C-C bonds and 1.34 Å for alkenes.<ref name="bondlength"/>
| [[File:st4215_BondB.JPG|200px]]
|-
| C || Similar to Bond A, as the reaction progresses, the length of Bond C increases. This is due to the same reason as explained for Bond A.
| [[File:st4215_BondC.JPG|200px]]
|-
| D || As the reaction progresses, the length of Bond D increases. This is because Bond B is initially an C=C single bond in ethylene, which becomes a sp<sup>3</sup>-sp<sup>3</sup> C-C single bond in cyclohexene. These lengths are similar to typical values of 1.34 Å for alkenes and 1.54 Å for sp<sup>3</sup>-sp<sup>3</sup> C-C bonds.<ref name="bondlength"/>
| [[File:st4215_BondD.JPG|200px]]
|-
| E || Bond E is formed in this reaction. Hence as the reaction progresses from the transition state to the product, the length of Bond E increases. The length of the fully formed Bond E in the product, an sp<sup>3</sup>-sp<sup>3</sup> C-C single bond, corresponds to the typical value of 1.54 Å.<ref name="bondlength"/> The distance between the C atoms in the TS (2.11 Å) falls between twice the van der Waal radius of C (2 x 1.70 Å<ref name="vdw_c"/> = 3.40 Å) and the length of the fully formed Bond E, indicating that the atoms are approaching each other.
| [[File:st4215_BondE.JPG|200px]]
|-
| F || Like Bond E, Bond F is also formed in this reaction. Hence as the reaction progresses from the transition state to the product, the length of Bond F increases, due to the same reasons as explained above.
| [[File:st4215_BondF.JPG|200px]]
|}

=== Transition state ===
<i><small>Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous?</small></i>
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 7; rotate x -40; select atomno=1, atomno=7, atomno=11, atomno=14; label display </script>
<uploadedFileContents>st4215_CYCLOHEXENE_TS_OPTFREQ2_PM6.LOG</uploadedFileContents>
<name>cyclohexeneTS</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>cyclohexeneTS</target>
</jmolbutton>
<jmolbutton>
<script>measure 1 11; measure 7 14</script>
<text>C-C Distances</text>
<target>cyclohexeneTS</target>
</jmolbutton>
</jmol>
<br><br>
As illustrated above, the formation of the two bonds are synchronous as the relevant pairs of atoms (C1/C11 and C7/C14) are moving towards each other at the same time, with the distance between the two atoms being approximately equal in both pairs. This is to be expected as evidence shows that the Diels-Alder reaction can proceed via a concerted, synchronous mechanism.<ref name="DA_1"/> However, it is important to note that this may also be the result of the calculation method used, as studies with other calculation methods (DFT/B3LYP) have also shown that other mechanisms are feasible.<ref name="DA_2"/>

== References ==
<references>
<ref name="bondlength">M. A. Fox, J. K. Whitesell, E. Buchholz. <i>Organische Chemie: Grundlagen, Mechanismen, bioorganische Anwendungen</i> (1995).</ref>
<ref name="vdw_c">A. Bondi. [http://pubs.acs.org/doi/pdf/10.1021/j100785a001 <i>van der Waals Volumes and Radii </i>] J. Phys. Chem. <b>68</b>(3), 441–451 (1996).</ref>
<ref name="DA_1">K. N. Houk, Y. T Lin & F. K. Brown. [http://pubs.acs.org/doi/pdf/10.1021/ja00263a059 <i>Evidence for the Concerted Mechanism of the Diels-Alder Reaction of Butadiene with Ethylene.</i>] J. Am. Chem. SOC. <b>108</b>, 554-556 (1986).</ref>
<ref name="DA_2">E. Goldstein, B. Beno & K. N. Houk. [http://pubs.acs.org/doi/pdf/10.1021/ja9601494 <i>Density Functional Theory Prediction of the Relative Energies and Isotope Effects for the Concerted and Stepwise Mechanisms of the Diels-Alder Reaction of Butadiene and Ethylene</i>] J. Am. Chem. Soc. <b>118</b>, 6036-6043 (1996).
</ref>
</references>

Rep:Transition states (st4215): Exercise 3

2017-10-25T00:18:26Z

St4215: /* Energy analysis */

== Exercise 3: Diels-Alder vs Cheletropic ==
The reaction scheme for this reaction is shown below:
(insert chemdraw diagram)

=== Optimisation procedure ===

=== Optimised molecules ===
The optimised molecules can be seen here:

{| class="wikitable"
! colspan="2" | Reactants
|-
| style="text-align: center;" | o-xylylene
| style="text-align: center;" | SO<sub>2</sub>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16</script>
<uploadedFileContents>st4215_XYLYLENE_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16</script>
<uploadedFileContents>st4215_SO2_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo || style="text-align: center;" | Exo
|-
| style="text-align: center;" | Transition state
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>St4215_ex3_ENDO_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_ex3_ENDO_TS_IRC2_PM6.LOG | IRC file]]
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>st4215_ex3_Exo_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_ex3_Exo_TS_IRC_PM6.LOG | IRC file]]
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12</script>
<uploadedFileContents>st4215_ex3_CHEL_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_ex3_CHEL_TS_IRC_PM6.LOG | IRC file]]
|-
| style="text-align: center;" | Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>St4215_ex3_ENDO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>st4215_ex3_EXO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38</script>
<uploadedFileContents>st4215_ex3_CHEL_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Reaction coordinate ===
<small><i>Visualise the reaction coordinate with an IRC calculation for each path. Include a .gif file in the wiki of these IRCs.</i></small>

The formation of the products for each of the endo- and exo- Diels-Alder reactions, as well as the cheletropic reaction, can be visualised below.

{| class="wikitable"
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
|-
| [[File:st4215_ENDO_TS_IRCmovie.gif]]
| [[File:st4215_Exo_TS_IRCmovie.gif]]
| [[File:st4215_Chel_TS_IRCmovie.gif]]
|}

We can see that SO<sub>2</sub> approaches xylylene at a different orientation and angle for each of these reactions. This difference in approach trajectories hence lead to the formation of different products.

It can also be observed that in each of the reactions, as the product is formed, the 6-membered ring in xylylene becomes aromatic. This means that there is a strong driving force for the formation of the products. In contrast, the reactant xylylene is highly unstable as it is non-aromatic, and as can be seen in these reactions, can readily react with unsaturated bonds to form a aromatic product.

=== Energy analysis ===
<small><i>Calculate the activation and reaction energies (converting to kJ/mol) for each step as in Exercise 2 to determine which route is preferred. Using Excel or Chemdraw, draw a reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels-Alder reactions and the cheletropic reaction. You can set the 0 energy level to the reactants at infinite separation.</i></small>

==== Free energies ====
The free energies of the reactants, transition states and products for each of the 3 reactions are tabulated below. The reaction barriers and energies are also calculated.

{| class="wikitable"
! rowspan="2" scope="col" style="width: 150px;" |
! colspan="2" scope="col" style="width: 300px;" | Energy at 298 K (PM6)
|-
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
|-
| colspan="3" style="background: #B7C3D0" | <b>Reactants</b>
|-
| Xylylene || style="text-align: center;" | 0.17876 || style="text-align: center;" | 469.34
|-
| SO<sub>2</sub> || style="text-align: center;" | -0.11927 || style="text-align: center;" | -313.14
|-
| Total reactants || style="text-align: center;" | 0.059496 || style="text-align: center;" | 156.21
|-
| colspan="3" style="background: #B7C3D0" | <b>Endo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | 0.090560 || style="text-align: center;" | 237.77
|-
| Product || style="text-align: center;" | 0.021704 || style="text-align: center;" | 56.984
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0311 || style="text-align: center;" | 81.6
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0378 || style="text-align: center;" | -99.2
|-
| colspan="3" style="background: #B7C3D0" | <b>Exo- Diels-Alder</b>
|-
| Transition state || style="text-align: center;" | 0.092078 || style="text-align: center;" | 241.75
|-
| Product || style="text-align: center;" | 0.021455 || style="text-align: center;" | 56.330
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0326 || style="text-align: center;" | 85.5
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0380 || style="text-align: center;" | -99.9
|-
| colspan="3" style="background: #B7C3D0" | <b>Cheletropic</b>
|-
| Transition state || style="text-align: center;" | 0.099058 || style="text-align: center;" | 260.08
|-
| Product || style="text-align: center;" | -0.000002 || style="text-align: center;" | -0.0052510
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0396 || style="text-align: center;" | 104
|-
| Reaction energy (ΔG) || style="text-align: center;" | -0.0595 || style="text-align: center;" | -156
|}
<small><i>^Note that all values from the calculations are reported to 5 s.f. unless more decimal places are needed to differentiate between each reaction type. Derived quantities (reaction barrier and reaction energy) are reported to 3 s.f.</i></small>

==== Thermodynamic and kinetic products ====
From the values above, a combined reaction profile showing the reaction barriers and reaction energies can also be plotted as seen below.
[[File:st4215_ex3_Reaction_profile2.PNG|600px|thumb|center|Reaction profile diagram for the 3 Diels-Alder and cheletropic reactions, setting the energy of the reactants to zero]]

We can clearly see that the endo- Diels-Alder product is the kinetic product as it has the lowest reaction barrier of +81.6 kJmol<sup>-1</sup>, while the cheletropic product is the thermodynamic product as it is most stable as has the lowest energy of -156 kJmol<sup>-1</sup>. This is consistent with experimental and computational data.<ref name="chel_3"/><ref name="chel_1"/>

The high stability of the cheletropic product is likely due to the preference of S to adopt a five-membered compared to 6-membered ring structure. This is in contrast to saturated carbon rings, where 6-membered cyclohexane is more stable than 5-membered cyclopentane due to deviation from tetrahedral bond angles of 109° in cyclopentane, resulting in angle strain. However, due to the larger size of the S atom, C-C<sub>tet</sub>-S bond angles in a 5-membered unsaturated sulfur ring (like in the cheletropic product) are much closer to the tetrahedral bond angle, at 105°. In comparison, the 6-membered heterocycle in the Diels-Alder products have C-C<sub>tet</sub>-S bond angles of around 114°, which are comparatively much larger than 109°. This is illustrated below:

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
|-
| Products
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; measure 3 16 11</script>
<uploadedFileContents>St4215_ex3_ENDO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; rotate y 180; measure 3 16 11</script>
<uploadedFileContents>st4215_ex3_EXO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; measure 1 7 15</script>
<uploadedFileContents>st4215_ex3_CHEL_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

It is also expected that one of the Diels-Alder products (the endo- product) is the kinetic product instead of the cheletropic product.<ref name="chel_3"/> While the reaction barriers for both endo- and exo- Diels-Alder reactions are similar, the reaction barrier for the cheletropic reaction is much higher. Examining their transition states (see below) allows us to infer why.

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder
! rowspan="2" | Cheletropic
|-
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
|-
| Transition state HOMO
| style="text-align: center;" | [[File:st4215_ex3_Endo_TS_HOMO.PNG]]
| style="text-align: center;" | [[File:st4215_ex3_Exo_TS_HOMO.PNG]]
| style="text-align: center;" | [[File:st4215_ex3_Chel_TS_HOMO.PNG]]
|-
| Discussion
| colspan="2" | Some stabilising secondary orbital interactions can be seen in the HOMOs of the endo- and exo- transition states, hence lowering its energy and reducing the reaction barriers for these reactions.
| No stabilising secondary orbital interactions are present here - in fact, the HOMO of the transition state is highly antisymmetric with many nodes, and hence likely to be high in energy.
|}

Like most Diels-Alder reactions, the endo and not the exo- product is the kinetic product due to more or greater stabilising secondary orbital interactions in the transition state. However, in this reaction, both the endo- and exo- transition states seem to have an approximately equal but not significant amount of stabilising orbital interactions in the HOMO. This explains why the endo- and exo- transition states are relatively close in energy.

== Extra: Diels-Alder reaction at a different site ==
O-xylylene also contains a cis-butadiene fragment that can act as the diene in another Diels-Alder reaction. However, this reaction is very kinetically and thermodynamically favourable.

=== Optimised molecules ===
The optimised molecules can be seen here. Optimised reactants (o-xylylene and SO<sub>2</sub>) from the earlier reaction were used.

{| class="wikitable"
! rowspan="2" |
! colspan="2" | Diels-Alder (2)
|-
| style="text-align: center;" | Endo || style="text-align: center;" | Exo
|-
| style="text-align: center;" | Transition state
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20</script>
<uploadedFileContents>st4215_BAD_ENDO_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_BAD_ENDO_IRC_PM6.LOG | IRC file]]
| style="text-align: center;" | <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14</script>
<uploadedFileContents>st4215_BAD_EXO_TS_OPTFREQ_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
[[Media:st4215_BAD_EXO_IRC_PM6.LOG | IRC file]]
|-
| style="text-align: center;" | Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 64</script>
<uploadedFileContents>st4215_BAD_ENDO_PDT_OPTFREQ_PM6.LOG</uploadedFileContents>
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</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>st4215_BAD_EXO_PDT_OPTFREQ2_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Energy analysis ===
The free energies of the reactants, transition states and products for both the endo- and exo- Diels Alder reactions are tabulated below. The reaction barriers and energies are also calculated.

{| class="wikitable"
! rowspan="2" scope="col" style="width: 150px;" |
! colspan="2" scope="col" style="width: 300px;" | Energy at 298 K (PM6)
|-
| style="text-align: center;" | Hartree
| style="text-align: center;" | kJmol<sup>-1</sup>
|-
| colspan="3" style="background: #B7C3D0" | <b>Reactants</b>
|-
| Xylylene || style="text-align: center;" | 0.17876 || style="text-align: center;" | 469.34
|-
| SO<sub>2</sub> || style="text-align: center;" | -0.11927 || style="text-align: center;" | -313.14
|-
| Total reactants || style="text-align: center;" | 0.059496 || style="text-align: center;" | 156.21
|-
| colspan="3" style="background: #B7C3D0" | <b>Endo- Diels-Alder (2)</b>
|-
| Transition state || style="text-align: center;" | 0.10207 || style="text-align: center;" | 267.99
|-
| Product || style="text-align: center;" | 0.065613 || style="text-align: center;" | 172.27
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0426 || style="text-align: center;" | 112
|-
| Reaction energy (ΔG) || style="text-align: center;" | +0.00612 || style="text-align: center;" | +16.1
|-
| colspan="3" style="background: #B7C3D0" | <b>Exo- Diels-Alder (2)</b>
|-
| Transition state || style="text-align: center;" | 0.10505 || style="text-align: center;" | 275.82
|-
| Product || style="text-align: center;" | 0.067305 || style="text-align: center;" | 176.71
|-
| Reaction barrier (E<sub>a</sub>) || style="text-align: center;" | 0.0456 || style="text-align: center;" | 120
|-
| Reaction energy (ΔG) || style="text-align: center;" | +0.00781 || style="text-align: center;" | +20.5
|}
<small><i>^Note that all values from the calculations are reported to 5 s.f. unless more decimal places are needed to differentiate between each reaction type. Derived quantities (reaction barrier and reaction energy) are reported to 3 s.f.</i></small>

We can hence see that this reaction is both kinetically and thermodynamically unfavourable compared to the other Diels-Alder reaction (previously discussed) and the cheletropic reaction.

Comparing the reaction barriers, the activation energies of 112 kJmol<sup>-1</sup> (endo) and 120 kJmol<sup>-1</sup> (exo) are much higher than that of the other DA reaction, at 81.6 kJmol<sup>-1</sup> (endo) and 85.5 kJmol<sup>-1</sup> (exo), as well as the cheletropic reaction, at 104 kJmol<sup>-1</sup>. Hence this Diels-Alder reaction is the most kinetically unfavourable reaction possible.

Comparing the reaction energies, we can see that both the endo- and exo- reactions are endothermic - compared to the other two DA reactions as well as the cheletropic reaction, which are exothermic. This indicates that this Diels-Alder reaction is also highly thermodynamically unfavourable as ΔG<0 and it is not spontaneous.

== References ==

<references>
<ref name="chel_1">F. Monnat, P. Vogel, J. A. Sordo. [http://onlinelibrary.wiley.com/doi/10.1002/1522-2675(200203)85:3%3C712::AID-HLCA712%3E3.0.CO;2-5/epdf <i>Hetero-Diels-Alder and Cheletropic Additions of Sulfur Dioxide to 1,2-Dimethylidenecycloalkanes. Determination of Thermochemical and Kinetics Parameters for Reactions in Solution and Comparison with Estimates From Quantum Calculations</i>] Helv. Chim. Acta. <b>85</b> (3), 712–732 (2002).</ref>
<ref name="chel_3">D. Suarez, T. L. Sordo, J. A. Sordo. [http://pubs.acs.org/doi/pdf/10.1021/jo00114a039 <i>A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls</i>] J. Org. Chem., <b>60</b> (9), 2848–2852 (1995).</ref>

</references>