ChemWiki - User contributions [en]

Rep:MOD:tyl214

2017-03-24T00:44:26Z

Tyl214: /* Transition State Computational Lab */

Transition State Computational Lab

== Introduction ==

Whilst stereo-selectivity is one of the biggest challenges in synthetic chemistry, a better understanding of the transition state in a reaction would allow better synthetic routes. In this computational lab, GaussView 5.0 was used to perform simulations of different cycloaddition reactions. Both the semi-empirical/PM6 and B3LYP/6-31G(d) basis sets were used, where the PM6 method is based on experimental data and the 6-31G(d) originates from the Density Functional Theory (DFT)<ref name="Wiley" />.<br>
In a chemical reaction, there are always 3N-6 degree of freedoms<ref name="atkins" />. In order to extract information from the Potential Energy Surface (PES), we tend to fix all coordinate apart from one. In this computational lab, we are fixing all coordinates to a minimum apart from the reaction coordinate, where the transition state can be found at the maximum of the reaction coordinate. This is done by calculating the first and second derivatives of energy against the reaction coordinate. Note that since the maxima of a curve has a negative second derivative, therefore any transition state optimisations will give rise to a vibration at negative frequency, depicting an imaginary frequency.

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place<ref name="sue" />. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Analysis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. MOs throughout the reaction coordinate.
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_J_tyl214.LOG</uploadedFileContents>
<name>etheneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 7</script>
<text>LUMO</text>
<target>etheneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_J_tyl214.LOG</uploadedFileContents>
<name>butadieneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 11</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 11</script>
<text>HOMO</text>
<target>butadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 12</script>
<text>LUMO</text>
<target>butadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 36; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
<name>TSMOs</name>
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<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
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<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
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<jmolbutton>
<script>mo 17</script>
<text>HOMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 18</script>
<text>LUMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>LUMO+1</text>
<target>TSMOs</target>
</jmolbutton>
</jmol>
|}

From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Fig. 3: Vibration of reaction path.

|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 37; vibration 1;rotate x -20</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 4: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital Analysis===
[[File: Exe2 MO tyl214.png|thumb|right|x250px|500px|Fig. 5: Cyclohexadiene and 1,3-Dioxole reaction molecular orbital diagram.]]
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method. The outcome of the simulation suggested an inverse electron-demand Diels-Alder mechanism for this reaction, and the orbitals involved are shown both in the molecular diagram in <b>Figure 4</b> and in <b>Table 3</b> and <b>4</b>.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. MOs of the Exo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 26; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM 1 3DIOXO tyl214.LOG</uploadedFileContents>
<name>13DioxoleMOs</name>
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<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 48; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM CYCLOHEXENE tyl214.LOG</uploadedFileContents>
<name>CyclohexadieneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 exo TS J 631 tyl214.LOG</uploadedFileContents>
<name>exe2exoTSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
</jmol>
|}

====<u>Endo</u>====
In contrast, the transition state shown in <b>Table 4</b> indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 4. MOs of the Endo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 26; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM 1 3DIOXO tyl214.LOG</uploadedFileContents>
<name>13DioxoleMOs1</name>
</jmolApplet>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 48; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM CYCLOHEXENE tyl214.LOG</uploadedFileContents>
<name>CyclohexadieneMOs1</name>
</jmolApplet>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 endo TS J 631.LOG</uploadedFileContents>
<name>exe2endoTSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
</jmol>
|}

===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in <b>Table 5</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 5. Energies along the reaction path.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1313798.018
| -1313638.011
| -1313862.745
| 160.0071622
| -64.72748504

|-
! Exo
| -1313798.018
| -1313630.302
| -1313859.259
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: O-Xylylene-SO2 Cycloaddition==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 6: o-Xylylene-SO2 Cycloaddition reaction scheme.]]

===Reaction Coordinate===
After running the IRC simulation, the reaction pathway was recorded as an animation and is shown in <b>Table 6</b>. From this, we can observe that as the reaction coordinate reaches the transition state, aromaticity forms within the xylylene ring, which provides stabilisation to the molecule. Due to the instability of xylylene itself, the formation of the aromatic ring becomes the driving force of the reaction.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 6. Reaction pathways of the exo, endo and cheletropic product.

|-
!
! Animated IRC

|-
| Endo
| [[File: Endo movie tyl214.gif|200px × 200px|upright=0.01]]

|-
| Exo
| [[File: Exo movie1 tyl214.gif|200px × 200px]]

|-
| Cheletropic
| [[File: Che movie tyl214.gif|200px × 200px]]
|}

===Energy Calculations===
[[File: Exe3Reactionprofile tyl214.png|thumb|right|x250px|250px|Fig. 7: Reaction profile of the o-Xylylene-SO2 cycloaddition.]]
From <b>Table 7</b>, we can confirm that the endo transition state has the lowest energy barrier of activation, giving the kinetic product; whereas the cheletropic reaction has the lowest Gibbs free energy of reaction, hence giving the thermodynamic product of the reaction. An energy profile in <b>Figure 7</b> can be found in describing the different pathways of this reaction.

{| class="wikitable" style="text-align: centre; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 7. Relative energies of the three different reaction pathways.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| 154.422861
| 237.7594324
| 56.98507596
| 83.33657136
| -97.43778504

|-
! Exo
| 154.422861
| 241.7579705
| 56.32871711
| 87.33510951
| -98.0941439

|-
! Cheletropic
| 154.422861
| 260.0782589
| -0.005250871
| 105.6553979
| -154.4281119

|}

==Conclusion==
The semi-empirical/PM6 and B3LYP/6-31G(d) methods were used to run transition state simulations in GaussView5.0, where bond energies and transition state orbital interactions of three cycloaddition reactions were investigated. These calculations provides information about the reaction such as the electron demand mechanism, reaction and bond energies, and the visualisation of different molecular orbital involved in the reaction.

==Reference==
<references>
<ref name="atkins">Shriver, Atkins, Physical Chemistry, Oxford University Press, 10th Edition.</ref>
<ref name="Wiley">F. Jensen, Introduction to Computational Chemistry, Wiley, 2nd Edition., 2007</ref>
<ref name="sue">Sue Gibson, Pericyclic Reactions Lecture</ref>
<references/>

Rep:MOD:tyl214

2017-03-24T00:43:40Z

Tyl214:

=Transition State Computational Lab=

== Introduction ==

Whilst stereo-selectivity is one of the biggest challenges in synthetic chemistry, a better understanding of the transition state in a reaction would allow better synthetic routes. In this computational lab, GaussView 5.0 was used to perform simulations of different cycloaddition reactions. Both the semi-empirical/PM6 and B3LYP/6-31G(d) basis sets were used, where the PM6 method is based on experimental data and the 6-31G(d) originates from the Density Functional Theory (DFT)<ref name="Wiley" />.<br>
In a chemical reaction, there are always 3N-6 degree of freedoms<ref name="atkins" />. In order to extract information from the Potential Energy Surface (PES), we tend to fix all coordinate apart from one. In this computational lab, we are fixing all coordinates to a minimum apart from the reaction coordinate, where the transition state can be found at the maximum of the reaction coordinate. This is done by calculating the first and second derivatives of energy against the reaction coordinate. Note that since the maxima of a curve has a negative second derivative, therefore any transition state optimisations will give rise to a vibration at negative frequency, depicting an imaginary frequency.

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place<ref name="sue" />. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Analysis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. MOs throughout the reaction coordinate.
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
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<color>white</color>
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<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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<name>etheneMOs</name>
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<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
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<script>mo 6</script>
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<text>LUMO</text>
<target>etheneMOs</target>
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<script>mo 11</script>
<text>HOMO</text>
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<jmolbutton>
<script>mo 11</script>
<text>HOMO</text>
<target>butadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 12</script>
<text>LUMO</text>
<target>butadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
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<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
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<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
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<jmolbutton>
<script>mo 17</script>
<text>HOMO</text>
<target>TSMOs</target>
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<jmolbutton>
<script>mo 18</script>
<text>LUMO</text>
<target>TSMOs</target>
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<jmolbutton>
<script>mo 19</script>
<text>LUMO+1</text>
<target>TSMOs</target>
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From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Fig. 3: Vibration of reaction path.

|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 37; vibration 1;rotate x -20</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 4: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital Analysis===
[[File: Exe2 MO tyl214.png|thumb|right|x250px|500px|Fig. 5: Cyclohexadiene and 1,3-Dioxole reaction molecular orbital diagram.]]
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method. The outcome of the simulation suggested an inverse electron-demand Diels-Alder mechanism for this reaction, and the orbitals involved are shown both in the molecular diagram in <b>Figure 4</b> and in <b>Table 3</b> and <b>4</b>.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. MOs of the Exo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
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<script>mo 19</script>
<text>HOMO</text>
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</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
</jmol>

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<name>CyclohexadieneMOs</name>
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<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
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</jmolApplet>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
</jmol>
|}

====<u>Endo</u>====
In contrast, the transition state shown in <b>Table 4</b> indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 4. MOs of the Endo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
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<color>white</color>
<size>250</size>
<script>frame 26; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM 1 3DIOXO tyl214.LOG</uploadedFileContents>
<name>13DioxoleMOs1</name>
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<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 48; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM CYCLOHEXENE tyl214.LOG</uploadedFileContents>
<name>CyclohexadieneMOs1</name>
</jmolApplet>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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<name>exe2endoTSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
</jmol>
|}

===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in <b>Table 5</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 5. Energies along the reaction path.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1313798.018
| -1313638.011
| -1313862.745
| 160.0071622
| -64.72748504

|-
! Exo
| -1313798.018
| -1313630.302
| -1313859.259
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: O-Xylylene-SO2 Cycloaddition==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 6: o-Xylylene-SO2 Cycloaddition reaction scheme.]]

===Reaction Coordinate===
After running the IRC simulation, the reaction pathway was recorded as an animation and is shown in <b>Table 6</b>. From this, we can observe that as the reaction coordinate reaches the transition state, aromaticity forms within the xylylene ring, which provides stabilisation to the molecule. Due to the instability of xylylene itself, the formation of the aromatic ring becomes the driving force of the reaction.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 6. Reaction pathways of the exo, endo and cheletropic product.

|-
!
! Animated IRC

|-
| Endo
| [[File: Endo movie tyl214.gif|200px × 200px|upright=0.01]]

|-
| Exo
| [[File: Exo movie1 tyl214.gif|200px × 200px]]

|-
| Cheletropic
| [[File: Che movie tyl214.gif|200px × 200px]]
|}

===Energy Calculations===
[[File: Exe3Reactionprofile tyl214.png|thumb|right|x250px|250px|Fig. 7: Reaction profile of the o-Xylylene-SO2 cycloaddition.]]
From <b>Table 7</b>, we can confirm that the endo transition state has the lowest energy barrier of activation, giving the kinetic product; whereas the cheletropic reaction has the lowest Gibbs free energy of reaction, hence giving the thermodynamic product of the reaction. An energy profile in <b>Figure 7</b> can be found in describing the different pathways of this reaction.

{| class="wikitable" style="text-align: centre; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 7. Relative energies of the three different reaction pathways.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| 154.422861
| 237.7594324
| 56.98507596
| 83.33657136
| -97.43778504

|-
! Exo
| 154.422861
| 241.7579705
| 56.32871711
| 87.33510951
| -98.0941439

|-
! Cheletropic
| 154.422861
| 260.0782589
| -0.005250871
| 105.6553979
| -154.4281119

|}

==Conclusion==
The semi-empirical/PM6 and B3LYP/6-31G(d) methods were used to run transition state simulations in GaussView5.0, where bond energies and transition state orbital interactions of three cycloaddition reactions were investigated. These calculations provides information about the reaction such as the electron demand mechanism, reaction and bond energies, and the visualisation of different molecular orbital involved in the reaction.

==Reference==
<references>
<ref name="atkins">Shriver, Atkins, Physical Chemistry, Oxford University Press, 10th Edition.</ref>
<ref name="Wiley">F. Jensen, Introduction to Computational Chemistry, Wiley, 2nd Edition., 2007</ref>
<ref name="sue">Sue Gibson, Pericyclic Reactions Lecture</ref>
<references/>

Rep:MOD:tyl214

2017-03-24T00:40:13Z

Tyl214: /* Reference */

<b>Transition State Computational Lab</b>

== Introduction ==

Whilst stereo-selectivity is one of the biggest challenges in synthetic chemistry, a better understanding of the transition state in a reaction would allow better synthetic routes. In this computational lab, GaussView 5.0 was used to perform simulations of different cycloaddition reactions. Both the semi-empirical/PM6 and B3LYP/6-31G(d) basis sets were used, where the PM6 method is based on experimental data and the 6-31G(d) originates from the Density Functional Theory (DFT)<ref name="Wiley" />.<br>
In a chemical reaction, there are always 3N-6 degree of freedoms<ref name="atkins" />. In order to extract information from the Potential Energy Surface (PES), we tend to fix all coordinate apart from one. In this computational lab, we are fixing all coordinates to a minimum apart from the reaction coordinate, where the transition state can be found at the maximum of the reaction coordinate. This is done by calculating the first and second derivatives of energy against the reaction coordinate. Note that since the maxima of a curve has a negative second derivative, therefore any transition state optimisations will give rise to a vibration at negative frequency, depicting an imaginary frequency.

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place<ref name="sue" />. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Analysis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. MOs throughout the reaction coordinate.
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
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<script>mo 6</script>
<text>HOMO</text>
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<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
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<jmolbutton>
<script>mo 7</script>
<text>LUMO</text>
<target>etheneMOs</target>
</jmolbutton>
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<target>butadieneMOs</target>
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<jmolbutton>
<script>mo 12</script>
<text>LUMO</text>
<target>butadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
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<text>HOMO</text>
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<text>LUMO</text>
<target>TSMOs</target>
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<jmolbutton>
<script>mo 19</script>
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<target>TSMOs</target>
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From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Fig. 3: Vibration of reaction path.

|<jmol>
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<color>white</color>
<size>250</size>
<script>frame 37; vibration 1;rotate x -20</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
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</jmol>
|}
The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 4: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital Analysis===
[[File: Exe2 MO tyl214.png|thumb|right|x250px|500px|Fig. 5: Cyclohexadiene and 1,3-Dioxole reaction molecular orbital diagram.]]
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method. The outcome of the simulation suggested an inverse electron-demand Diels-Alder mechanism for this reaction, and the orbitals involved are shown both in the molecular diagram in <b>Figure 4</b> and in <b>Table 3</b> and <b>4</b>.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. MOs of the Exo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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<text>LUMO</text>
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<text>LUMO</text>
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====<u>Endo</u>====
In contrast, the transition state shown in <b>Table 4</b> indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 4. MOs of the Endo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in <b>Table 5</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 5. Energies along the reaction path.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1313798.018
| -1313638.011
| -1313862.745
| 160.0071622
| -64.72748504

|-
! Exo
| -1313798.018
| -1313630.302
| -1313859.259
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: O-Xylylene-SO2 Cycloaddition==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 6: o-Xylylene-SO2 Cycloaddition reaction scheme.]]

===Reaction Coordinate===
After running the IRC simulation, the reaction pathway was recorded as an animation and is shown in <b>Table 6</b>. From this, we can observe that as the reaction coordinate reaches the transition state, aromaticity forms within the xylylene ring, which provides stabilisation to the molecule. Due to the instability of xylylene itself, the formation of the aromatic ring becomes the driving force of the reaction.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 6. Reaction pathways of the exo, endo and cheletropic product.

|-
!
! Animated IRC

|-
| Endo
| [[File: Endo movie tyl214.gif|200px × 200px|upright=0.01]]

|-
| Exo
| [[File: Exo movie1 tyl214.gif|200px × 200px]]

|-
| Cheletropic
| [[File: Che movie tyl214.gif|200px × 200px]]
|}

===Energy Calculations===
[[File: Exe3Reactionprofile tyl214.png|thumb|right|x250px|250px|Fig. 7: Reaction profile of the o-Xylylene-SO2 cycloaddition.]]
From <b>Table 7</b>, we can confirm that the endo transition state has the lowest energy barrier of activation, giving the kinetic product; whereas the cheletropic reaction has the lowest Gibbs free energy of reaction, hence giving the thermodynamic product of the reaction. An energy profile in <b>Figure 7</b> can be found in describing the different pathways of this reaction.

{| class="wikitable" style="text-align: centre; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 7. Relative energies of the three different reaction pathways.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| 154.422861
| 237.7594324
| 56.98507596
| 83.33657136
| -97.43778504

|-
! Exo
| 154.422861
| 241.7579705
| 56.32871711
| 87.33510951
| -98.0941439

|-
! Cheletropic
| 154.422861
| 260.0782589
| -0.005250871
| 105.6553979
| -154.4281119

|}

==Conclusion==
The semi-empirical/PM6 and B3LYP/6-31G(d) methods were used to run transition state simulations in GaussView5.0, where bond energies and transition state orbital interactions of three cycloaddition reactions were investigated. These calculations provides information about the reaction such as the electron demand mechanism, reaction and bond energies, and the visualisation of different molecular orbital involved in the reaction.

==Reference==
<references>
<ref name="atkins">Shriver, Atkins, Physical Chemistry, Oxford University Press, 10th Edition.</ref>
<ref name="Wiley">F. Jensen, Introduction to Computational Chemistry, Wiley, 2nd Edition., 2007</ref>
<ref name="sue">Sue Gibson, Pericyclic Reactions Lecture</ref>
<references/>

Rep:MOD:tyl214

2017-03-24T00:38:17Z

Tyl214: /* Theory */

<b>Transition State Computational Lab</b>

== Introduction ==

Whilst stereo-selectivity is one of the biggest challenges in synthetic chemistry, a better understanding of the transition state in a reaction would allow better synthetic routes. In this computational lab, GaussView 5.0 was used to perform simulations of different cycloaddition reactions. Both the semi-empirical/PM6 and B3LYP/6-31G(d) basis sets were used, where the PM6 method is based on experimental data and the 6-31G(d) originates from the Density Functional Theory (DFT)<ref name="Wiley" />.<br>
In a chemical reaction, there are always 3N-6 degree of freedoms<ref name="atkins" />. In order to extract information from the Potential Energy Surface (PES), we tend to fix all coordinate apart from one. In this computational lab, we are fixing all coordinates to a minimum apart from the reaction coordinate, where the transition state can be found at the maximum of the reaction coordinate. This is done by calculating the first and second derivatives of energy against the reaction coordinate. Note that since the maxima of a curve has a negative second derivative, therefore any transition state optimisations will give rise to a vibration at negative frequency, depicting an imaginary frequency.

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place<ref name="sue" />. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Analysis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. MOs throughout the reaction coordinate.
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
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From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Fig. 3: Vibration of reaction path.

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The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 4: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital Analysis===
[[File: Exe2 MO tyl214.png|thumb|right|x250px|500px|Fig. 5: Cyclohexadiene and 1,3-Dioxole reaction molecular orbital diagram.]]
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method. The outcome of the simulation suggested an inverse electron-demand Diels-Alder mechanism for this reaction, and the orbitals involved are shown both in the molecular diagram in <b>Figure 4</b> and in <b>Table 3</b> and <b>4</b>.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
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! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
</jmol>
|}

====<u>Endo</u>====
In contrast, the transition state shown in <b>Table 4</b> indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 4. MOs of the Endo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
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<color>white</color>
<size>250</size>
<script>frame 26; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM 1 3DIOXO tyl214.LOG</uploadedFileContents>
<name>13DioxoleMOs1</name>
</jmolApplet>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 48; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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<name>CyclohexadieneMOs1</name>
</jmolApplet>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
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<name>exe2endoTSMOs</name>
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<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2endoTSMOs</target>
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<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
</jmol>
|}

===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in <b>Table 5</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 5. Energies along the reaction path.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1313798.018
| -1313638.011
| -1313862.745
| 160.0071622
| -64.72748504

|-
! Exo
| -1313798.018
| -1313630.302
| -1313859.259
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: O-Xylylene-SO2 Cycloaddition==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 6: o-Xylylene-SO2 Cycloaddition reaction scheme.]]

===Reaction Coordinate===
After running the IRC simulation, the reaction pathway was recorded as an animation and is shown in <b>Table 6</b>. From this, we can observe that as the reaction coordinate reaches the transition state, aromaticity forms within the xylylene ring, which provides stabilisation to the molecule. Due to the instability of xylylene itself, the formation of the aromatic ring becomes the driving force of the reaction.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 6. Reaction pathways of the exo, endo and cheletropic product.

|-
!
! Animated IRC

|-
| Endo
| [[File: Endo movie tyl214.gif|200px × 200px|upright=0.01]]

|-
| Exo
| [[File: Exo movie1 tyl214.gif|200px × 200px]]

|-
| Cheletropic
| [[File: Che movie tyl214.gif|200px × 200px]]
|}

===Energy Calculations===
[[File: Exe3Reactionprofile tyl214.png|thumb|right|x250px|250px|Fig. 7: Reaction profile of the o-Xylylene-SO2 cycloaddition.]]
From <b>Table 7</b>, we can confirm that the endo transition state has the lowest energy barrier of activation, giving the kinetic product; whereas the cheletropic reaction has the lowest Gibbs free energy of reaction, hence giving the thermodynamic product of the reaction. An energy profile in <b>Figure 7</b> can be found in describing the different pathways of this reaction.

{| class="wikitable" style="text-align: centre; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 7. Relative energies of the three different reaction pathways.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| 154.422861
| 237.7594324
| 56.98507596
| 83.33657136
| -97.43778504

|-
! Exo
| 154.422861
| 241.7579705
| 56.32871711
| 87.33510951
| -98.0941439

|-
! Cheletropic
| 154.422861
| 260.0782589
| -0.005250871
| 105.6553979
| -154.4281119

|}

==Conclusion==
The semi-empirical/PM6 and B3LYP/6-31G(d) methods were used to run transition state simulations in GaussView5.0, where bond energies and transition state orbital interactions of three cycloaddition reactions were investigated. These calculations provides information about the reaction such as the electron demand mechanism, reaction and bond energies, and the visualisation of different molecular orbital involved in the reaction.

==Reference==
<ref name="atkins">Shriver, Atkins, Physical Chemistry, Oxford University Press, 10th Edition.</ref>
<ref name="Wiley">F. Jensen, Introduction to Computational Chemistry, Wiley, 2nd Edition., 2007</ref>
<ref name="sue">Sue Gibson, Pericyclic Reactions Lecture</ref>

Rep:MOD:tyl214

2017-03-24T00:37:37Z

Tyl214: /* Reference */

<b>Transition State Computational Lab</b>

== Introduction ==

Whilst stereo-selectivity is one of the biggest challenges in synthetic chemistry, a better understanding of the transition state in a reaction would allow better synthetic routes. In this computational lab, GaussView 5.0 was used to perform simulations of different cycloaddition reactions. Both the semi-empirical/PM6 and B3LYP/6-31G(d) basis sets were used, where the PM6 method is based on experimental data and the 6-31G(d) originates from the Density Functional Theory (DFT)<ref name="Wiley" />.<br>
In a chemical reaction, there are always 3N-6 degree of freedoms<ref name="atkins" />. In order to extract information from the Potential Energy Surface (PES), we tend to fix all coordinate apart from one. In this computational lab, we are fixing all coordinates to a minimum apart from the reaction coordinate, where the transition state can be found at the maximum of the reaction coordinate. This is done by calculating the first and second derivatives of energy against the reaction coordinate. Note that since the maxima of a curve has a negative second derivative, therefore any transition state optimisations will give rise to a vibration at negative frequency, depicting an imaginary frequency.

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Analysis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. MOs throughout the reaction coordinate.
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_J_tyl214.LOG</uploadedFileContents>
<name>etheneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 7</script>
<text>LUMO</text>
<target>etheneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_J_tyl214.LOG</uploadedFileContents>
<name>butadieneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 11</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 11</script>
<text>HOMO</text>
<target>butadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 12</script>
<text>LUMO</text>
<target>butadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
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<name>TSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 17</script>
<text>HOMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 18</script>
<text>LUMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>LUMO+1</text>
<target>TSMOs</target>
</jmolbutton>
</jmol>
|}

From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Fig. 3: Vibration of reaction path.

|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 37; vibration 1;rotate x -20</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 4: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital Analysis===
[[File: Exe2 MO tyl214.png|thumb|right|x250px|500px|Fig. 5: Cyclohexadiene and 1,3-Dioxole reaction molecular orbital diagram.]]
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method. The outcome of the simulation suggested an inverse electron-demand Diels-Alder mechanism for this reaction, and the orbitals involved are shown both in the molecular diagram in <b>Figure 4</b> and in <b>Table 3</b> and <b>4</b>.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. MOs of the Exo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
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<script>mo 19</script>
<text>HOMO</text>
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<text>HOMO</text>
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<jmolbutton>
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<text>LUMO</text>
<target>13DioxoleMOs</target>
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<script>mo 22</script>
<text>HOMO</text>
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<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
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<text>HOMO-1</text>
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<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2exoTSMOs</target>
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<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2exoTSMOs</target>
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<jmolbutton>
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<text>LUMO+1</text>
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====<u>Endo</u>====
In contrast, the transition state shown in <b>Table 4</b> indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 4. MOs of the Endo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
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<script>mo 19</script>
<text>HOMO</text>
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<text>HOMO</text>
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<jmolbutton>
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<text>LUMO</text>
<target>13DioxoleMOs1</target>
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<text>HOMO</text>
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<jmolbutton>
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<text>LUMO</text>
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<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
</jmol>
|}

===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in <b>Table 5</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 5. Energies along the reaction path.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1313798.018
| -1313638.011
| -1313862.745
| 160.0071622
| -64.72748504

|-
! Exo
| -1313798.018
| -1313630.302
| -1313859.259
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: O-Xylylene-SO2 Cycloaddition==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 6: o-Xylylene-SO2 Cycloaddition reaction scheme.]]

===Reaction Coordinate===
After running the IRC simulation, the reaction pathway was recorded as an animation and is shown in <b>Table 6</b>. From this, we can observe that as the reaction coordinate reaches the transition state, aromaticity forms within the xylylene ring, which provides stabilisation to the molecule. Due to the instability of xylylene itself, the formation of the aromatic ring becomes the driving force of the reaction.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 6. Reaction pathways of the exo, endo and cheletropic product.

|-
!
! Animated IRC

|-
| Endo
| [[File: Endo movie tyl214.gif|200px × 200px|upright=0.01]]

|-
| Exo
| [[File: Exo movie1 tyl214.gif|200px × 200px]]

|-
| Cheletropic
| [[File: Che movie tyl214.gif|200px × 200px]]
|}

===Energy Calculations===
[[File: Exe3Reactionprofile tyl214.png|thumb|right|x250px|250px|Fig. 7: Reaction profile of the o-Xylylene-SO2 cycloaddition.]]
From <b>Table 7</b>, we can confirm that the endo transition state has the lowest energy barrier of activation, giving the kinetic product; whereas the cheletropic reaction has the lowest Gibbs free energy of reaction, hence giving the thermodynamic product of the reaction. An energy profile in <b>Figure 7</b> can be found in describing the different pathways of this reaction.

{| class="wikitable" style="text-align: centre; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 7. Relative energies of the three different reaction pathways.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| 154.422861
| 237.7594324
| 56.98507596
| 83.33657136
| -97.43778504

|-
! Exo
| 154.422861
| 241.7579705
| 56.32871711
| 87.33510951
| -98.0941439

|-
! Cheletropic
| 154.422861
| 260.0782589
| -0.005250871
| 105.6553979
| -154.4281119

|}

==Conclusion==
The semi-empirical/PM6 and B3LYP/6-31G(d) methods were used to run transition state simulations in GaussView5.0, where bond energies and transition state orbital interactions of three cycloaddition reactions were investigated. These calculations provides information about the reaction such as the electron demand mechanism, reaction and bond energies, and the visualisation of different molecular orbital involved in the reaction.

==Reference==
<ref name="atkins">Shriver, Atkins, Physical Chemistry, Oxford University Press, 10th Edition.</ref>
<ref name="Wiley">F. Jensen, Introduction to Computational Chemistry, Wiley, 2nd Edition., 2007</ref>
<ref name="sue">Sue Gibson, Pericyclic Reactions Lecture</ref>

Rep:MOD:tyl214

2017-03-24T00:33:59Z

Tyl214: /* Introduction */

<b>Transition State Computational Lab</b>

== Introduction ==

Whilst stereo-selectivity is one of the biggest challenges in synthetic chemistry, a better understanding of the transition state in a reaction would allow better synthetic routes. In this computational lab, GaussView 5.0 was used to perform simulations of different cycloaddition reactions. Both the semi-empirical/PM6 and B3LYP/6-31G(d) basis sets were used, where the PM6 method is based on experimental data and the 6-31G(d) originates from the Density Functional Theory (DFT)<ref name="Wiley" />.<br>
In a chemical reaction, there are always 3N-6 degree of freedoms<ref name="atkins" />. In order to extract information from the Potential Energy Surface (PES), we tend to fix all coordinate apart from one. In this computational lab, we are fixing all coordinates to a minimum apart from the reaction coordinate, where the transition state can be found at the maximum of the reaction coordinate. This is done by calculating the first and second derivatives of energy against the reaction coordinate. Note that since the maxima of a curve has a negative second derivative, therefore any transition state optimisations will give rise to a vibration at negative frequency, depicting an imaginary frequency.

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Analysis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. MOs throughout the reaction coordinate.
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_J_tyl214.LOG</uploadedFileContents>
<name>etheneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 7</script>
<text>LUMO</text>
<target>etheneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_J_tyl214.LOG</uploadedFileContents>
<name>butadieneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 11</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 11</script>
<text>HOMO</text>
<target>butadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 12</script>
<text>LUMO</text>
<target>butadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 36; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
<name>TSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 17</script>
<text>HOMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 18</script>
<text>LUMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>LUMO+1</text>
<target>TSMOs</target>
</jmolbutton>
</jmol>
|}

From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Fig. 3: Vibration of reaction path.

|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 37; vibration 1;rotate x -20</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 4: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital Analysis===
[[File: Exe2 MO tyl214.png|thumb|right|x250px|500px|Fig. 5: Cyclohexadiene and 1,3-Dioxole reaction molecular orbital diagram.]]
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method. The outcome of the simulation suggested an inverse electron-demand Diels-Alder mechanism for this reaction, and the orbitals involved are shown both in the molecular diagram in <b>Figure 4</b> and in <b>Table 3</b> and <b>4</b>.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. MOs of the Exo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 26; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM 1 3DIOXO tyl214.LOG</uploadedFileContents>
<name>13DioxoleMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 48; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM CYCLOHEXENE tyl214.LOG</uploadedFileContents>
<name>CyclohexadieneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 exo TS J 631 tyl214.LOG</uploadedFileContents>
<name>exe2exoTSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
</jmol>
|}

====<u>Endo</u>====
In contrast, the transition state shown in <b>Table 4</b> indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 4. MOs of the Endo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 26; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM 1 3DIOXO tyl214.LOG</uploadedFileContents>
<name>13DioxoleMOs1</name>
</jmolApplet>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 48; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM CYCLOHEXENE tyl214.LOG</uploadedFileContents>
<name>CyclohexadieneMOs1</name>
</jmolApplet>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 endo TS J 631.LOG</uploadedFileContents>
<name>exe2endoTSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
</jmol>
|}

===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in <b>Table 5</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 5. Energies along the reaction path.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1313798.018
| -1313638.011
| -1313862.745
| 160.0071622
| -64.72748504

|-
! Exo
| -1313798.018
| -1313630.302
| -1313859.259
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: O-Xylylene-SO2 Cycloaddition==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 6: o-Xylylene-SO2 Cycloaddition reaction scheme.]]

===Reaction Coordinate===
After running the IRC simulation, the reaction pathway was recorded as an animation and is shown in <b>Table 6</b>. From this, we can observe that as the reaction coordinate reaches the transition state, aromaticity forms within the xylylene ring, which provides stabilisation to the molecule. Due to the instability of xylylene itself, the formation of the aromatic ring becomes the driving force of the reaction.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 6. Reaction pathways of the exo, endo and cheletropic product.

|-
!
! Animated IRC

|-
| Endo
| [[File: Endo movie tyl214.gif|200px × 200px|upright=0.01]]

|-
| Exo
| [[File: Exo movie1 tyl214.gif|200px × 200px]]

|-
| Cheletropic
| [[File: Che movie tyl214.gif|200px × 200px]]
|}

===Energy Calculations===
[[File: Exe3Reactionprofile tyl214.png|thumb|right|x250px|250px|Fig. 7: Reaction profile of the o-Xylylene-SO2 cycloaddition.]]
From <b>Table 7</b>, we can confirm that the endo transition state has the lowest energy barrier of activation, giving the kinetic product; whereas the cheletropic reaction has the lowest Gibbs free energy of reaction, hence giving the thermodynamic product of the reaction. An energy profile in <b>Figure 7</b> can be found in describing the different pathways of this reaction.

{| class="wikitable" style="text-align: centre; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 7. Relative energies of the three different reaction pathways.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| 154.422861
| 237.7594324
| 56.98507596
| 83.33657136
| -97.43778504

|-
! Exo
| 154.422861
| 241.7579705
| 56.32871711
| 87.33510951
| -98.0941439

|-
! Cheletropic
| 154.422861
| 260.0782589
| -0.005250871
| 105.6553979
| -154.4281119

|}

==Conclusion==
The semi-empirical/PM6 and B3LYP/6-31G(d) methods were used to run transition state simulations in GaussView5.0, where bond energies and transition state orbital interactions of three cycloaddition reactions were investigated. These calculations provides information about the reaction such as the electron demand mechanism, reaction and bond energies, and the visualisation of different molecular orbital involved in the reaction.

==Reference==
<ref name="atkins">Atkins, Physical Chemistry, Oxford University Press, 10th Edition.</ref>
<ref name="Wiley">F. Jensen, Introduction to Computational Chemistry, Wiley, 2nd Edition., 2007</ref>

Rep:MOD:tyl214

2017-03-24T00:33:32Z

Tyl214: /* Reference */

<b>Transition State Computational Lab</b>

== Introduction ==

Whilst stereo-selectivity is one of the biggest challenges in synthetic chemistry, a better understanding of the transition state in a reaction would allow better synthetic routes. In this computational lab, GaussView 5.0 was used to perform simulations of different cycloaddition reactions. Both the semi-empirical/PM6 and B3LYP/6-31G(d) basis sets were used, where the PM6 method is based on experimental data and the 6-31G(d) originates from the Density Functional Theory (DFT).<br>
In a chemical reaction, there are always 3N-6 degree of freedoms<ref name="atkins" />. In order to extract information from the Potential Energy Surface (PES), we tend to fix all coordinate apart from one. In this computational lab, we are fixing all coordinates to a minimum apart from the reaction coordinate, where the transition state can be found at the maximum of the reaction coordinate. This is done by calculating the first and second derivatives of energy against the reaction coordinate. Note that since the maxima of a curve has a negative second derivative, therefore any transition state optimisations will give rise to a vibration at negative frequency, depicting an imaginary frequency.

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Analysis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. MOs throughout the reaction coordinate.
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_J_tyl214.LOG</uploadedFileContents>
<name>etheneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 7</script>
<text>LUMO</text>
<target>etheneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_J_tyl214.LOG</uploadedFileContents>
<name>butadieneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 11</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 11</script>
<text>HOMO</text>
<target>butadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 12</script>
<text>LUMO</text>
<target>butadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 36; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
<name>TSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
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<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 17</script>
<text>HOMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 18</script>
<text>LUMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>LUMO+1</text>
<target>TSMOs</target>
</jmolbutton>
</jmol>
|}

From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Fig. 3: Vibration of reaction path.

|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 37; vibration 1;rotate x -20</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 4: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital Analysis===
[[File: Exe2 MO tyl214.png|thumb|right|x250px|500px|Fig. 5: Cyclohexadiene and 1,3-Dioxole reaction molecular orbital diagram.]]
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method. The outcome of the simulation suggested an inverse electron-demand Diels-Alder mechanism for this reaction, and the orbitals involved are shown both in the molecular diagram in <b>Figure 4</b> and in <b>Table 3</b> and <b>4</b>.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. MOs of the Exo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
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<name>13DioxoleMOs</name>
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<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 48; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM CYCLOHEXENE tyl214.LOG</uploadedFileContents>
<name>CyclohexadieneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 exo TS J 631 tyl214.LOG</uploadedFileContents>
<name>exe2exoTSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
</jmol>
|}

====<u>Endo</u>====
In contrast, the transition state shown in <b>Table 4</b> indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 4. MOs of the Endo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 26; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM 1 3DIOXO tyl214.LOG</uploadedFileContents>
<name>13DioxoleMOs1</name>
</jmolApplet>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 48; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM CYCLOHEXENE tyl214.LOG</uploadedFileContents>
<name>CyclohexadieneMOs1</name>
</jmolApplet>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 endo TS J 631.LOG</uploadedFileContents>
<name>exe2endoTSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
</jmol>
|}

===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in <b>Table 5</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 5. Energies along the reaction path.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1313798.018
| -1313638.011
| -1313862.745
| 160.0071622
| -64.72748504

|-
! Exo
| -1313798.018
| -1313630.302
| -1313859.259
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: O-Xylylene-SO2 Cycloaddition==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 6: o-Xylylene-SO2 Cycloaddition reaction scheme.]]

===Reaction Coordinate===
After running the IRC simulation, the reaction pathway was recorded as an animation and is shown in <b>Table 6</b>. From this, we can observe that as the reaction coordinate reaches the transition state, aromaticity forms within the xylylene ring, which provides stabilisation to the molecule. Due to the instability of xylylene itself, the formation of the aromatic ring becomes the driving force of the reaction.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 6. Reaction pathways of the exo, endo and cheletropic product.

|-
!
! Animated IRC

|-
| Endo
| [[File: Endo movie tyl214.gif|200px × 200px|upright=0.01]]

|-
| Exo
| [[File: Exo movie1 tyl214.gif|200px × 200px]]

|-
| Cheletropic
| [[File: Che movie tyl214.gif|200px × 200px]]
|}

===Energy Calculations===
[[File: Exe3Reactionprofile tyl214.png|thumb|right|x250px|250px|Fig. 7: Reaction profile of the o-Xylylene-SO2 cycloaddition.]]
From <b>Table 7</b>, we can confirm that the endo transition state has the lowest energy barrier of activation, giving the kinetic product; whereas the cheletropic reaction has the lowest Gibbs free energy of reaction, hence giving the thermodynamic product of the reaction. An energy profile in <b>Figure 7</b> can be found in describing the different pathways of this reaction.

{| class="wikitable" style="text-align: centre; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 7. Relative energies of the three different reaction pathways.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| 154.422861
| 237.7594324
| 56.98507596
| 83.33657136
| -97.43778504

|-
! Exo
| 154.422861
| 241.7579705
| 56.32871711
| 87.33510951
| -98.0941439

|-
! Cheletropic
| 154.422861
| 260.0782589
| -0.005250871
| 105.6553979
| -154.4281119

|}

==Conclusion==
The semi-empirical/PM6 and B3LYP/6-31G(d) methods were used to run transition state simulations in GaussView5.0, where bond energies and transition state orbital interactions of three cycloaddition reactions were investigated. These calculations provides information about the reaction such as the electron demand mechanism, reaction and bond energies, and the visualisation of different molecular orbital involved in the reaction.

==Reference==
<ref name="atkins">Atkins, Physical Chemistry, Oxford University Press, 10th Edition.</ref>
<ref name="Wiley">F. Jensen, Introduction to Computational Chemistry, Wiley, 2nd Edition., 2007</ref>

Rep:MOD:tyl214

2017-03-24T00:32:50Z

Tyl214: /* Reference */

<b>Transition State Computational Lab</b>

== Introduction ==

Whilst stereo-selectivity is one of the biggest challenges in synthetic chemistry, a better understanding of the transition state in a reaction would allow better synthetic routes. In this computational lab, GaussView 5.0 was used to perform simulations of different cycloaddition reactions. Both the semi-empirical/PM6 and B3LYP/6-31G(d) basis sets were used, where the PM6 method is based on experimental data and the 6-31G(d) originates from the Density Functional Theory (DFT).<br>
In a chemical reaction, there are always 3N-6 degree of freedoms<ref name="atkins" />. In order to extract information from the Potential Energy Surface (PES), we tend to fix all coordinate apart from one. In this computational lab, we are fixing all coordinates to a minimum apart from the reaction coordinate, where the transition state can be found at the maximum of the reaction coordinate. This is done by calculating the first and second derivatives of energy against the reaction coordinate. Note that since the maxima of a curve has a negative second derivative, therefore any transition state optimisations will give rise to a vibration at negative frequency, depicting an imaginary frequency.

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Analysis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. MOs throughout the reaction coordinate.
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
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<script>mo 6</script>
<text>HOMO</text>
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<jmolbutton>
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<script>mo 11</script>
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<jmolbutton>
<script>mo 11</script>
<text>HOMO</text>
<target>butadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 12</script>
<text>LUMO</text>
<target>butadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
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<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
<name>TSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
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<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
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<jmolbutton>
<script>mo 17</script>
<text>HOMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 18</script>
<text>LUMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>LUMO+1</text>
<target>TSMOs</target>
</jmolbutton>
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|}

From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Fig. 3: Vibration of reaction path.

|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 37; vibration 1;rotate x -20</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 4: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital Analysis===
[[File: Exe2 MO tyl214.png|thumb|right|x250px|500px|Fig. 5: Cyclohexadiene and 1,3-Dioxole reaction molecular orbital diagram.]]
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method. The outcome of the simulation suggested an inverse electron-demand Diels-Alder mechanism for this reaction, and the orbitals involved are shown both in the molecular diagram in <b>Figure 4</b> and in <b>Table 3</b> and <b>4</b>.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. MOs of the Exo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
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<name>13DioxoleMOs</name>
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<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
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<name>CyclohexadieneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
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<name>exe2exoTSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
</jmol>
|}

====<u>Endo</u>====
In contrast, the transition state shown in <b>Table 4</b> indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 4. MOs of the Endo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 26; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM 1 3DIOXO tyl214.LOG</uploadedFileContents>
<name>13DioxoleMOs1</name>
</jmolApplet>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 48; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM CYCLOHEXENE tyl214.LOG</uploadedFileContents>
<name>CyclohexadieneMOs1</name>
</jmolApplet>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 endo TS J 631.LOG</uploadedFileContents>
<name>exe2endoTSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
</jmol>
|}

===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in <b>Table 5</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 5. Energies along the reaction path.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1313798.018
| -1313638.011
| -1313862.745
| 160.0071622
| -64.72748504

|-
! Exo
| -1313798.018
| -1313630.302
| -1313859.259
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: O-Xylylene-SO2 Cycloaddition==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 6: o-Xylylene-SO2 Cycloaddition reaction scheme.]]

===Reaction Coordinate===
After running the IRC simulation, the reaction pathway was recorded as an animation and is shown in <b>Table 6</b>. From this, we can observe that as the reaction coordinate reaches the transition state, aromaticity forms within the xylylene ring, which provides stabilisation to the molecule. Due to the instability of xylylene itself, the formation of the aromatic ring becomes the driving force of the reaction.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 6. Reaction pathways of the exo, endo and cheletropic product.

|-
!
! Animated IRC

|-
| Endo
| [[File: Endo movie tyl214.gif|200px × 200px|upright=0.01]]

|-
| Exo
| [[File: Exo movie1 tyl214.gif|200px × 200px]]

|-
| Cheletropic
| [[File: Che movie tyl214.gif|200px × 200px]]
|}

===Energy Calculations===
[[File: Exe3Reactionprofile tyl214.png|thumb|right|x250px|250px|Fig. 7: Reaction profile of the o-Xylylene-SO2 cycloaddition.]]
From <b>Table 7</b>, we can confirm that the endo transition state has the lowest energy barrier of activation, giving the kinetic product; whereas the cheletropic reaction has the lowest Gibbs free energy of reaction, hence giving the thermodynamic product of the reaction. An energy profile in <b>Figure 7</b> can be found in describing the different pathways of this reaction.

{| class="wikitable" style="text-align: centre; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 7. Relative energies of the three different reaction pathways.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| 154.422861
| 237.7594324
| 56.98507596
| 83.33657136
| -97.43778504

|-
! Exo
| 154.422861
| 241.7579705
| 56.32871711
| 87.33510951
| -98.0941439

|-
! Cheletropic
| 154.422861
| 260.0782589
| -0.005250871
| 105.6553979
| -154.4281119

|}

==Conclusion==
The semi-empirical/PM6 and B3LYP/6-31G(d) methods were used to run transition state simulations in GaussView5.0, where bond energies and transition state orbital interactions of three cycloaddition reactions were investigated. These calculations provides information about the reaction such as the electron demand mechanism, reaction and bond energies, and the visualisation of different molecular orbital involved in the reaction.

==Reference==
<ref name="atkins">Atkins, Physical Chemistry, Oxford University Press, 10th Edition.</ref>

Rep:MOD:tyl214

2017-03-24T00:32:04Z

Tyl214: /* Conclusion */

<b>Transition State Computational Lab</b>

== Introduction ==

Whilst stereo-selectivity is one of the biggest challenges in synthetic chemistry, a better understanding of the transition state in a reaction would allow better synthetic routes. In this computational lab, GaussView 5.0 was used to perform simulations of different cycloaddition reactions. Both the semi-empirical/PM6 and B3LYP/6-31G(d) basis sets were used, where the PM6 method is based on experimental data and the 6-31G(d) originates from the Density Functional Theory (DFT).<br>
In a chemical reaction, there are always 3N-6 degree of freedoms<ref name="atkins" />. In order to extract information from the Potential Energy Surface (PES), we tend to fix all coordinate apart from one. In this computational lab, we are fixing all coordinates to a minimum apart from the reaction coordinate, where the transition state can be found at the maximum of the reaction coordinate. This is done by calculating the first and second derivatives of energy against the reaction coordinate. Note that since the maxima of a curve has a negative second derivative, therefore any transition state optimisations will give rise to a vibration at negative frequency, depicting an imaginary frequency.

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Analysis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. MOs throughout the reaction coordinate.
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
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<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
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<jmolbutton>
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<text>HOMO</text>
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<jmolbutton>
<script>mo 7</script>
<text>LUMO</text>
<target>etheneMOs</target>
</jmolbutton>
</jmol>

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<script>mo 11</script>
<text>HOMO</text>
<target>butadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 12</script>
<text>LUMO</text>
<target>butadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
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<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
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<text>HOMO-1</text>
<target>TSMOs</target>
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<jmolbutton>
<script>mo 17</script>
<text>HOMO</text>
<target>TSMOs</target>
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<jmolbutton>
<script>mo 18</script>
<text>LUMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>LUMO+1</text>
<target>TSMOs</target>
</jmolbutton>
</jmol>
|}

From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Fig. 3: Vibration of reaction path.

|<jmol>
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<color>white</color>
<size>250</size>
<script>frame 37; vibration 1;rotate x -20</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
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|}
The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 4: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital Analysis===
[[File: Exe2 MO tyl214.png|thumb|right|x250px|500px|Fig. 5: Cyclohexadiene and 1,3-Dioxole reaction molecular orbital diagram.]]
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method. The outcome of the simulation suggested an inverse electron-demand Diels-Alder mechanism for this reaction, and the orbitals involved are shown both in the molecular diagram in <b>Figure 4</b> and in <b>Table 3</b> and <b>4</b>.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. MOs of the Exo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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<jmolbutton>
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<text>LUMO</text>
<target>13DioxoleMOs</target>
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<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
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<text>HOMO-1</text>
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<script>mo 41</script>
<text>HOMO</text>
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<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
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====<u>Endo</u>====
In contrast, the transition state shown in <b>Table 4</b> indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 4. MOs of the Endo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in <b>Table 5</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 5. Energies along the reaction path.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1313798.018
| -1313638.011
| -1313862.745
| 160.0071622
| -64.72748504

|-
! Exo
| -1313798.018
| -1313630.302
| -1313859.259
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: O-Xylylene-SO2 Cycloaddition==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 6: o-Xylylene-SO2 Cycloaddition reaction scheme.]]

===Reaction Coordinate===
After running the IRC simulation, the reaction pathway was recorded as an animation and is shown in <b>Table 6</b>. From this, we can observe that as the reaction coordinate reaches the transition state, aromaticity forms within the xylylene ring, which provides stabilisation to the molecule. Due to the instability of xylylene itself, the formation of the aromatic ring becomes the driving force of the reaction.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 6. Reaction pathways of the exo, endo and cheletropic product.

|-
!
! Animated IRC

|-
| Endo
| [[File: Endo movie tyl214.gif|200px × 200px|upright=0.01]]

|-
| Exo
| [[File: Exo movie1 tyl214.gif|200px × 200px]]

|-
| Cheletropic
| [[File: Che movie tyl214.gif|200px × 200px]]
|}

===Energy Calculations===
[[File: Exe3Reactionprofile tyl214.png|thumb|right|x250px|250px|Fig. 7: Reaction profile of the o-Xylylene-SO2 cycloaddition.]]
From <b>Table 7</b>, we can confirm that the endo transition state has the lowest energy barrier of activation, giving the kinetic product; whereas the cheletropic reaction has the lowest Gibbs free energy of reaction, hence giving the thermodynamic product of the reaction. An energy profile in <b>Figure 7</b> can be found in describing the different pathways of this reaction.

{| class="wikitable" style="text-align: centre; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 7. Relative energies of the three different reaction pathways.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| 154.422861
| 237.7594324
| 56.98507596
| 83.33657136
| -97.43778504

|-
! Exo
| 154.422861
| 241.7579705
| 56.32871711
| 87.33510951
| -98.0941439

|-
! Cheletropic
| 154.422861
| 260.0782589
| -0.005250871
| 105.6553979
| -154.4281119

|}

==Conclusion==
The semi-empirical/PM6 and B3LYP/6-31G(d) methods were used to run transition state simulations in GaussView5.0, where bond energies and transition state orbital interactions of three cycloaddition reactions were investigated. These calculations provides information about the reaction such as the electron demand mechanism, reaction and bond energies, and the visualisation of different molecular orbital involved in the reaction.

==Reference==
<ref name="atkins">Atkins, Physical Chemistry, Oxford University Press, 10th edn.</ref>

Rep:MOD:tyl214

2017-03-24T00:31:30Z

Tyl214: /* Introduction */

<b>Transition State Computational Lab</b>

== Introduction ==

Whilst stereo-selectivity is one of the biggest challenges in synthetic chemistry, a better understanding of the transition state in a reaction would allow better synthetic routes. In this computational lab, GaussView 5.0 was used to perform simulations of different cycloaddition reactions. Both the semi-empirical/PM6 and B3LYP/6-31G(d) basis sets were used, where the PM6 method is based on experimental data and the 6-31G(d) originates from the Density Functional Theory (DFT).<br>
In a chemical reaction, there are always 3N-6 degree of freedoms<ref name="atkins" />. In order to extract information from the Potential Energy Surface (PES), we tend to fix all coordinate apart from one. In this computational lab, we are fixing all coordinates to a minimum apart from the reaction coordinate, where the transition state can be found at the maximum of the reaction coordinate. This is done by calculating the first and second derivatives of energy against the reaction coordinate. Note that since the maxima of a curve has a negative second derivative, therefore any transition state optimisations will give rise to a vibration at negative frequency, depicting an imaginary frequency.

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Analysis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. MOs throughout the reaction coordinate.
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Fig. 3: Vibration of reaction path.

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The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 4: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital Analysis===
[[File: Exe2 MO tyl214.png|thumb|right|x250px|500px|Fig. 5: Cyclohexadiene and 1,3-Dioxole reaction molecular orbital diagram.]]
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method. The outcome of the simulation suggested an inverse electron-demand Diels-Alder mechanism for this reaction, and the orbitals involved are shown both in the molecular diagram in <b>Figure 4</b> and in <b>Table 3</b> and <b>4</b>.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
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! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
</jmol>
|}

====<u>Endo</u>====
In contrast, the transition state shown in <b>Table 4</b> indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 4. MOs of the Endo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 26; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM 1 3DIOXO tyl214.LOG</uploadedFileContents>
<name>13DioxoleMOs1</name>
</jmolApplet>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 48; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM CYCLOHEXENE tyl214.LOG</uploadedFileContents>
<name>CyclohexadieneMOs1</name>
</jmolApplet>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 endo TS J 631.LOG</uploadedFileContents>
<name>exe2endoTSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
</jmol>
|}

===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in <b>Table 5</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 5. Energies along the reaction path.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1313798.018
| -1313638.011
| -1313862.745
| 160.0071622
| -64.72748504

|-
! Exo
| -1313798.018
| -1313630.302
| -1313859.259
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: O-Xylylene-SO2 Cycloaddition==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 6: o-Xylylene-SO2 Cycloaddition reaction scheme.]]

===Reaction Coordinate===
After running the IRC simulation, the reaction pathway was recorded as an animation and is shown in <b>Table 6</b>. From this, we can observe that as the reaction coordinate reaches the transition state, aromaticity forms within the xylylene ring, which provides stabilisation to the molecule. Due to the instability of xylylene itself, the formation of the aromatic ring becomes the driving force of the reaction.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 6. Reaction pathways of the exo, endo and cheletropic product.

|-
!
! Animated IRC

|-
| Endo
| [[File: Endo movie tyl214.gif|200px × 200px|upright=0.01]]

|-
| Exo
| [[File: Exo movie1 tyl214.gif|200px × 200px]]

|-
| Cheletropic
| [[File: Che movie tyl214.gif|200px × 200px]]
|}

===Energy Calculations===
[[File: Exe3Reactionprofile tyl214.png|thumb|right|x250px|250px|Fig. 7: Reaction profile of the o-Xylylene-SO2 cycloaddition.]]
From <b>Table 7</b>, we can confirm that the endo transition state has the lowest energy barrier of activation, giving the kinetic product; whereas the cheletropic reaction has the lowest Gibbs free energy of reaction, hence giving the thermodynamic product of the reaction. An energy profile in <b>Figure 7</b> can be found in describing the different pathways of this reaction.

{| class="wikitable" style="text-align: centre; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 7. Relative energies of the three different reaction pathways.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| 154.422861
| 237.7594324
| 56.98507596
| 83.33657136
| -97.43778504

|-
! Exo
| 154.422861
| 241.7579705
| 56.32871711
| 87.33510951
| -98.0941439

|-
! Cheletropic
| 154.422861
| 260.0782589
| -0.005250871
| 105.6553979
| -154.4281119

|}

==Conclusion==
The semi-empirical/PM6 and B3LYP/6-31G(d) methods were used to run transition state simulations in GaussView5.0, where bond energies and transition state orbital interactions of three cycloaddition reactions were investigated. These calculations provides information about the reaction such as the electron demand mechanism, reaction and bond energies, and the visualisation of different molecular orbital involved in the reaction.

Rep:MOD:tyl214

2017-03-24T00:26:02Z

Tyl214: /* Orbital analysis */

<b>Transition State Computational Lab</b>

== Introduction ==

Whilst stereo-selectivity is one of the biggest challenges in synthetic chemistry, a better understanding of the transition state in a reaction would allow better synthetic routes. In this computational lab, GaussView 5.0 was used to perform simulations of different cycloaddition reactions. Both the semi-empirical/PM6 and B3LYP/6-31G(d) basis sets were used, where the PM6 method is based on experimental data and the 6-31G(d) originates from the Density Functional Theory (DFT).<br>
In a chemical reaction, there are always 3N-6 degree of freedoms. In order to extract information from the Potential Energy Surface (PES), we tend to fix all coordinate apart from one. In this computational lab, we are fixing all coordinates to a minimum apart from the reaction coordinate, where the transition state can be found at the maximum of the reaction coordinate. This is done by calculating the first and second derivatives of energy against the reaction coordinate. Note that since the maxima of a curve has a negative second derivative, therefore any transition state optimisations will give rise to a vibration at negative frequency, depicting an imaginary frequency.

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Analysis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. MOs throughout the reaction coordinate.
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_J_tyl214.LOG</uploadedFileContents>
<name>etheneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 7</script>
<text>LUMO</text>
<target>etheneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_J_tyl214.LOG</uploadedFileContents>
<name>butadieneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 11</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 11</script>
<text>HOMO</text>
<target>butadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 12</script>
<text>LUMO</text>
<target>butadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 36; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
<name>TSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 17</script>
<text>HOMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 18</script>
<text>LUMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>LUMO+1</text>
<target>TSMOs</target>
</jmolbutton>
</jmol>
|}

From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Fig. 3: Vibration of reaction path.

|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 37; vibration 1;rotate x -20</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 4: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital Analysis===
[[File: Exe2 MO tyl214.png|thumb|right|x250px|500px|Fig. 5: Cyclohexadiene and 1,3-Dioxole reaction molecular orbital diagram.]]
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method. The outcome of the simulation suggested an inverse electron-demand Diels-Alder mechanism for this reaction, and the orbitals involved are shown both in the molecular diagram in <b>Figure 4</b> and in <b>Table 3</b> and <b>4</b>.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. MOs of the Exo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 26; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM 1 3DIOXO tyl214.LOG</uploadedFileContents>
<name>13DioxoleMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 48; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM CYCLOHEXENE tyl214.LOG</uploadedFileContents>
<name>CyclohexadieneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 exo TS J 631 tyl214.LOG</uploadedFileContents>
<name>exe2exoTSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
</jmol>
|}

====<u>Endo</u>====
In contrast, the transition state shown in <b>Table 4</b> indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 4. MOs of the Endo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 26; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM 1 3DIOXO tyl214.LOG</uploadedFileContents>
<name>13DioxoleMOs1</name>
</jmolApplet>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 48; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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<name>CyclohexadieneMOs1</name>
</jmolApplet>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 endo TS J 631.LOG</uploadedFileContents>
<name>exe2endoTSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
</jmol>
|}

===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in <b>Table 5</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 5. Energies along the reaction path.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1313798.018
| -1313638.011
| -1313862.745
| 160.0071622
| -64.72748504

|-
! Exo
| -1313798.018
| -1313630.302
| -1313859.259
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: O-Xylylene-SO2 Cycloaddition==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 6: o-Xylylene-SO2 Cycloaddition reaction scheme.]]

===Reaction Coordinate===
After running the IRC simulation, the reaction pathway was recorded as an animation and is shown in <b>Table 6</b>. From this, we can observe that as the reaction coordinate reaches the transition state, aromaticity forms within the xylylene ring, which provides stabilisation to the molecule. Due to the instability of xylylene itself, the formation of the aromatic ring becomes the driving force of the reaction.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 6. Reaction pathways of the exo, endo and cheletropic product.

|-
!
! Animated IRC

|-
| Endo
| [[File: Endo movie tyl214.gif|200px × 200px|upright=0.01]]

|-
| Exo
| [[File: Exo movie1 tyl214.gif|200px × 200px]]

|-
| Cheletropic
| [[File: Che movie tyl214.gif|200px × 200px]]
|}

===Energy Calculations===
[[File: Exe3Reactionprofile tyl214.png|thumb|right|x250px|250px|Fig. 7: Reaction profile of the o-Xylylene-SO2 cycloaddition.]]
From <b>Table 7</b>, we can confirm that the endo transition state has the lowest energy barrier of activation, giving the kinetic product; whereas the cheletropic reaction has the lowest Gibbs free energy of reaction, hence giving the thermodynamic product of the reaction. An energy profile in <b>Figure 7</b> can be found in describing the different pathways of this reaction.

{| class="wikitable" style="text-align: centre; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 7. Relative energies of the three different reaction pathways.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| 154.422861
| 237.7594324
| 56.98507596
| 83.33657136
| -97.43778504

|-
! Exo
| 154.422861
| 241.7579705
| 56.32871711
| 87.33510951
| -98.0941439

|-
! Cheletropic
| 154.422861
| 260.0782589
| -0.005250871
| 105.6553979
| -154.4281119

|}

==Conclusion==
The semi-empirical/PM6 and B3LYP/6-31G(d) methods were used to run transition state simulations in GaussView5.0, where bond energies and transition state orbital interactions of three cycloaddition reactions were investigated. These calculations provides information about the reaction such as the electron demand mechanism, reaction and bond energies, and the visualisation of different molecular orbital involved in the reaction.

Rep:MOD:tyl214

2017-03-24T00:25:48Z

Tyl214: /* Orbital Anaylsis */

<b>Transition State Computational Lab</b>

== Introduction ==

Whilst stereo-selectivity is one of the biggest challenges in synthetic chemistry, a better understanding of the transition state in a reaction would allow better synthetic routes. In this computational lab, GaussView 5.0 was used to perform simulations of different cycloaddition reactions. Both the semi-empirical/PM6 and B3LYP/6-31G(d) basis sets were used, where the PM6 method is based on experimental data and the 6-31G(d) originates from the Density Functional Theory (DFT).<br>
In a chemical reaction, there are always 3N-6 degree of freedoms. In order to extract information from the Potential Energy Surface (PES), we tend to fix all coordinate apart from one. In this computational lab, we are fixing all coordinates to a minimum apart from the reaction coordinate, where the transition state can be found at the maximum of the reaction coordinate. This is done by calculating the first and second derivatives of energy against the reaction coordinate. Note that since the maxima of a curve has a negative second derivative, therefore any transition state optimisations will give rise to a vibration at negative frequency, depicting an imaginary frequency.

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Analysis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. MOs throughout the reaction coordinate.
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_J_tyl214.LOG</uploadedFileContents>
<name>etheneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 7</script>
<text>LUMO</text>
<target>etheneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_J_tyl214.LOG</uploadedFileContents>
<name>butadieneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 11</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 11</script>
<text>HOMO</text>
<target>butadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 12</script>
<text>LUMO</text>
<target>butadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 36; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
<name>TSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 17</script>
<text>HOMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 18</script>
<text>LUMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>LUMO+1</text>
<target>TSMOs</target>
</jmolbutton>
</jmol>
|}

From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Fig. 3: Vibration of reaction path.

|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 37; vibration 1;rotate x -20</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 4: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital analysis===
[[File: Exe2 MO tyl214.png|thumb|right|x250px|500px|Fig. 5: Cyclohexadiene and 1,3-Dioxole reaction molecular orbital diagram.]]
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method. The outcome of the simulation suggested an inverse electron-demand Diels-Alder mechanism for this reaction, and the orbitals involved are shown both in the molecular diagram in <b>Figure 4</b> and in <b>Table 3</b> and <b>4</b>.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. MOs of the Exo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 26; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM 1 3DIOXO tyl214.LOG</uploadedFileContents>
<name>13DioxoleMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 48; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM CYCLOHEXENE tyl214.LOG</uploadedFileContents>
<name>CyclohexadieneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 exo TS J 631 tyl214.LOG</uploadedFileContents>
<name>exe2exoTSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
</jmol>
|}

====<u>Endo</u>====
In contrast, the transition state shown in <b>Table 4</b> indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 4. MOs of the Endo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 26; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM 1 3DIOXO tyl214.LOG</uploadedFileContents>
<name>13DioxoleMOs1</name>
</jmolApplet>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 48; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM CYCLOHEXENE tyl214.LOG</uploadedFileContents>
<name>CyclohexadieneMOs1</name>
</jmolApplet>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 endo TS J 631.LOG</uploadedFileContents>
<name>exe2endoTSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
</jmol>
|}

===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in <b>Table 5</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 5. Energies along the reaction path.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1313798.018
| -1313638.011
| -1313862.745
| 160.0071622
| -64.72748504

|-
! Exo
| -1313798.018
| -1313630.302
| -1313859.259
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: O-Xylylene-SO2 Cycloaddition==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 6: o-Xylylene-SO2 Cycloaddition reaction scheme.]]

===Reaction Coordinate===
After running the IRC simulation, the reaction pathway was recorded as an animation and is shown in <b>Table 6</b>. From this, we can observe that as the reaction coordinate reaches the transition state, aromaticity forms within the xylylene ring, which provides stabilisation to the molecule. Due to the instability of xylylene itself, the formation of the aromatic ring becomes the driving force of the reaction.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 6. Reaction pathways of the exo, endo and cheletropic product.

|-
!
! Animated IRC

|-
| Endo
| [[File: Endo movie tyl214.gif|200px × 200px|upright=0.01]]

|-
| Exo
| [[File: Exo movie1 tyl214.gif|200px × 200px]]

|-
| Cheletropic
| [[File: Che movie tyl214.gif|200px × 200px]]
|}

===Energy Calculations===
[[File: Exe3Reactionprofile tyl214.png|thumb|right|x250px|250px|Fig. 7: Reaction profile of the o-Xylylene-SO2 cycloaddition.]]
From <b>Table 7</b>, we can confirm that the endo transition state has the lowest energy barrier of activation, giving the kinetic product; whereas the cheletropic reaction has the lowest Gibbs free energy of reaction, hence giving the thermodynamic product of the reaction. An energy profile in <b>Figure 7</b> can be found in describing the different pathways of this reaction.

{| class="wikitable" style="text-align: centre; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 7. Relative energies of the three different reaction pathways.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| 154.422861
| 237.7594324
| 56.98507596
| 83.33657136
| -97.43778504

|-
! Exo
| 154.422861
| 241.7579705
| 56.32871711
| 87.33510951
| -98.0941439

|-
! Cheletropic
| 154.422861
| 260.0782589
| -0.005250871
| 105.6553979
| -154.4281119

|}

==Conclusion==
The semi-empirical/PM6 and B3LYP/6-31G(d) methods were used to run transition state simulations in GaussView5.0, where bond energies and transition state orbital interactions of three cycloaddition reactions were investigated. These calculations provides information about the reaction such as the electron demand mechanism, reaction and bond energies, and the visualisation of different molecular orbital involved in the reaction.

Rep:MOD:tyl214

2017-03-23T23:48:42Z

Tyl214: /* Energy Calculations */

<b>Transition State Computational Lab</b>

== Introduction ==

Whilst stereo-selectivity is one of the biggest challenges in synthetic chemistry, a better understanding of the transition state in a reaction would allow better synthetic routes. In this computational lab, GaussView 5.0 was used to perform simulations of different cycloaddition reactions. Both the semi-empirical/PM6 and B3LYP/6-31G(d) basis sets were used, where the PM6 method is based on experimental data and the 6-31G(d) originates from the Density Functional Theory (DFT).<br>
In a chemical reaction, there are always 3N-6 degree of freedoms. In order to extract information from the Potential Energy Surface (PES), we tend to fix all coordinate apart from one. In this computational lab, we are fixing all coordinates to a minimum apart from the reaction coordinate, where the transition state can be found at the maximum of the reaction coordinate. This is done by calculating the first and second derivatives of energy against the reaction coordinate. Note that since the maxima of a curve has a negative second derivative, therefore any transition state optimisations will give rise to a vibration at negative frequency, depicting an imaginary frequency.

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Anaylsis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. MOs throughout the reaction coordinate.
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
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From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Fig. 3: Vibration of reaction path.

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The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 4: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital analysis===
[[File: Exe2 MO tyl214.png|thumb|right|x250px|500px|Fig. 5: Cyclohexadiene and 1,3-Dioxole reaction molecular orbital diagram.]]
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method. The outcome of the simulation suggested an inverse electron-demand Diels-Alder mechanism for this reaction, and the orbitals involved are shown both in the molecular diagram in <b>Figure 4</b> and in <b>Table 3</b> and <b>4</b>.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. MOs of the Exo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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====<u>Endo</u>====
In contrast, the transition state shown in <b>Table 4</b> indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 4. MOs of the Endo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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<text>HOMO</text>
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<text>HOMO</text>
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===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in <b>Table 5</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 5. Energies along the reaction path.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1313798.018
| -1313638.011
| -1313862.745
| 160.0071622
| -64.72748504

|-
! Exo
| -1313798.018
| -1313630.302
| -1313859.259
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: O-Xylylene-SO2 Cycloaddition==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 6: o-Xylylene-SO2 Cycloaddition reaction scheme.]]

===Reaction Coordinate===
After running the IRC simulation, the reaction pathway was recorded as an animation and is shown in <b>Table 6</b>. From this, we can observe that as the reaction coordinate reaches the transition state, aromaticity forms within the xylylene ring, which provides stabilisation to the molecule. Due to the instability of xylylene itself, the formation of the aromatic ring becomes the driving force of the reaction.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 6. Reaction pathways of the exo, endo and cheletropic product.

|-
!
! Animated IRC

|-
| Endo
| [[File: Endo movie tyl214.gif|200px × 200px|upright=0.01]]

|-
| Exo
| [[File: Exo movie1 tyl214.gif|200px × 200px]]

|-
| Cheletropic
| [[File: Che movie tyl214.gif|200px × 200px]]
|}

===Energy Calculations===
[[File: Exe3Reactionprofile tyl214.png|thumb|right|x250px|250px|Fig. 7: Reaction profile of the o-Xylylene-SO2 cycloaddition.]]
From <b>Table 7</b>, we can confirm that the endo transition state has the lowest energy barrier of activation, giving the kinetic product; whereas the cheletropic reaction has the lowest Gibbs free energy of reaction, hence giving the thermodynamic product of the reaction. An energy profile in <b>Figure 7</b> can be found in describing the different pathways of this reaction.

{| class="wikitable" style="text-align: centre; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 7. Relative energies of the three different reaction pathways.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| 154.422861
| 237.7594324
| 56.98507596
| 83.33657136
| -97.43778504

|-
! Exo
| 154.422861
| 241.7579705
| 56.32871711
| 87.33510951
| -98.0941439

|-
! Cheletropic
| 154.422861
| 260.0782589
| -0.005250871
| 105.6553979
| -154.4281119

|}

==Conclusion==
The semi-empirical/PM6 and B3LYP/6-31G(d) methods were used to run transition state simulations in GaussView5.0, where bond energies and transition state orbital interactions of three cycloaddition reactions were investigated. These calculations provides information about the reaction such as the electron demand mechanism, reaction and bond energies, and the visualisation of different molecular orbital involved in the reaction.

Rep:MOD:tyl214

2017-03-23T23:46:57Z

Tyl214: /* Conclusion */

<b>Transition State Computational Lab</b>

== Introduction ==

Whilst stereo-selectivity is one of the biggest challenges in synthetic chemistry, a better understanding of the transition state in a reaction would allow better synthetic routes. In this computational lab, GaussView 5.0 was used to perform simulations of different cycloaddition reactions. Both the semi-empirical/PM6 and B3LYP/6-31G(d) basis sets were used, where the PM6 method is based on experimental data and the 6-31G(d) originates from the Density Functional Theory (DFT).<br>
In a chemical reaction, there are always 3N-6 degree of freedoms. In order to extract information from the Potential Energy Surface (PES), we tend to fix all coordinate apart from one. In this computational lab, we are fixing all coordinates to a minimum apart from the reaction coordinate, where the transition state can be found at the maximum of the reaction coordinate. This is done by calculating the first and second derivatives of energy against the reaction coordinate. Note that since the maxima of a curve has a negative second derivative, therefore any transition state optimisations will give rise to a vibration at negative frequency, depicting an imaginary frequency.

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Anaylsis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. MOs throughout the reaction coordinate.
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
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<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
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<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
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<jmolbutton>
<script>mo 17</script>
<text>HOMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 18</script>
<text>LUMO</text>
<target>TSMOs</target>
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<jmolbutton>
<script>mo 19</script>
<text>LUMO+1</text>
<target>TSMOs</target>
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From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Fig. 3: Vibration of reaction path.

|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 37; vibration 1;rotate x -20</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
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|}
The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 4: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital analysis===
[[File: Exe2 MO tyl214.png|thumb|right|x250px|500px|Fig. 5: Cyclohexadiene and 1,3-Dioxole reaction molecular orbital diagram.]]
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method. The outcome of the simulation suggested an inverse electron-demand Diels-Alder mechanism for this reaction, and the orbitals involved are shown both in the molecular diagram in <b>Figure 4</b> and in <b>Table 3</b> and <b>4</b>.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. MOs of the Exo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
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<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
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||<jmol>
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<script>mo 22</script>
<text>HOMO</text>
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<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
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</jmolApplet>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
</jmol>
|}

====<u>Endo</u>====
In contrast, the transition state shown in <b>Table 4</b> indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 4. MOs of the Endo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
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<name>13DioxoleMOs1</name>
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<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
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<name>CyclohexadieneMOs1</name>
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<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
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<name>exe2endoTSMOs</name>
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<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2endoTSMOs</target>
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<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
</jmol>
|}

===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in <b>Table 5</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 5. Energies along the reaction path.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1313798.018
| -1313638.011
| -1313862.745
| 160.0071622
| -64.72748504

|-
! Exo
| -1313798.018
| -1313630.302
| -1313859.259
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: O-Xylylene-SO2 Cycloaddition==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 6: o-Xylylene-SO2 Cycloaddition reaction scheme.]]

===Reaction Coordinate===
After running the IRC simulation, the reaction pathway was recorded as an animation and is shown in <b>Table 6</b>. From this, we can observe that as the reaction coordinate reaches the transition state, aromaticity forms within the xylylene ring, which provides stabilisation to the molecule. Due to the instability of xylylene itself, the formation of the aromatic ring becomes the driving force of the reaction.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 6. Reaction pathways of the exo, endo and cheletropic product.

|-
!
! Animated IRC

|-
| Endo
| [[File: Endo movie tyl214.gif|200px × 200px|upright=0.01]]

|-
| Exo
| [[File: Exo movie1 tyl214.gif|200px × 200px]]

|-
| Cheletropic
| [[File: Che movie tyl214.gif|200px × 200px]]
|}

===Energy Calculations===
[[File: Exe3Reactionprofile tyl214.png|thumb|right|x250px|250px|Fig. 7: Reaction profile of the o-Xylylene-SO2 cycloaddition.]]
From <b>Table 7</b>, we can confirm that the endo transition state has the lowest energy barrier of activation, giving the kinetic product; whereas the cheletropic reaction has the lowest Gibbs free energy of reaction, hence giving the thermodynamic product of the reaction. An energy profile in Figure X can be found in describing the different pathways of this reaction.

{| class="wikitable" style="text-align: centre; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 7. Relative energies of the three different reaction pathways.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| 154.422861
| 237.7594324
| 56.98507596
| 83.33657136
| -97.43778504

|-
! Exo
| 154.422861
| 241.7579705
| 56.32871711
| 87.33510951
| -98.0941439

|-
! Cheletropic
| 154.422861
| 260.0782589
| -0.005250871
| 105.6553979
| -154.4281119

|}

==Conclusion==
The semi-empirical/PM6 and B3LYP/6-31G(d) methods were used to run transition state simulations in GaussView5.0, where bond energies and transition state orbital interactions of three cycloaddition reactions were investigated. These calculations provides information about the reaction such as the electron demand mechanism, reaction and bond energies, and the visualisation of different molecular orbital involved in the reaction.

Rep:MOD:tyl214

2017-03-23T23:46:35Z

Tyl214: /* Conclusion */

<b>Transition State Computational Lab</b>

== Introduction ==

Whilst stereo-selectivity is one of the biggest challenges in synthetic chemistry, a better understanding of the transition state in a reaction would allow better synthetic routes. In this computational lab, GaussView 5.0 was used to perform simulations of different cycloaddition reactions. Both the semi-empirical/PM6 and B3LYP/6-31G(d) basis sets were used, where the PM6 method is based on experimental data and the 6-31G(d) originates from the Density Functional Theory (DFT).<br>
In a chemical reaction, there are always 3N-6 degree of freedoms. In order to extract information from the Potential Energy Surface (PES), we tend to fix all coordinate apart from one. In this computational lab, we are fixing all coordinates to a minimum apart from the reaction coordinate, where the transition state can be found at the maximum of the reaction coordinate. This is done by calculating the first and second derivatives of energy against the reaction coordinate. Note that since the maxima of a curve has a negative second derivative, therefore any transition state optimisations will give rise to a vibration at negative frequency, depicting an imaginary frequency.

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Anaylsis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. MOs throughout the reaction coordinate.
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
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<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
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<script>mo 6</script>
<text>HOMO</text>
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<jmolbutton>
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<text>LUMO</text>
<target>etheneMOs</target>
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<jmolbutton>
<script>mo 12</script>
<text>LUMO</text>
<target>butadieneMOs</target>
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<jmolbutton>
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<target>TSMOs</target>
</jmolbutton>
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|}

From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Fig. 3: Vibration of reaction path.

|<jmol>
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<color>white</color>
<size>250</size>
<script>frame 37; vibration 1;rotate x -20</script>
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The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 4: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital analysis===
[[File: Exe2 MO tyl214.png|thumb|right|x250px|500px|Fig. 5: Cyclohexadiene and 1,3-Dioxole reaction molecular orbital diagram.]]
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method. The outcome of the simulation suggested an inverse electron-demand Diels-Alder mechanism for this reaction, and the orbitals involved are shown both in the molecular diagram in <b>Figure 4</b> and in <b>Table 3</b> and <b>4</b>.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. MOs of the Exo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
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<text>HOMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
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||<jmol>
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<text>HOMO</text>
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<text>HOMO</text>
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<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs</target>
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<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
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<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
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<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
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<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
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====<u>Endo</u>====
In contrast, the transition state shown in <b>Table 4</b> indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 4. MOs of the Endo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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<text>HOMO</text>
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<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
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<text>HOMO</text>
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<text>LUMO</text>
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<text>HOMO-1</text>
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<text>HOMO</text>
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<text>LUMO</text>
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<text>LUMO+1</text>
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===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in <b>Table 5</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 5. Energies along the reaction path.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1313798.018
| -1313638.011
| -1313862.745
| 160.0071622
| -64.72748504

|-
! Exo
| -1313798.018
| -1313630.302
| -1313859.259
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: O-Xylylene-SO2 Cycloaddition==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 6: o-Xylylene-SO2 Cycloaddition reaction scheme.]]

===Reaction Coordinate===
After running the IRC simulation, the reaction pathway was recorded as an animation and is shown in <b>Table 6</b>. From this, we can observe that as the reaction coordinate reaches the transition state, aromaticity forms within the xylylene ring, which provides stabilisation to the molecule. Due to the instability of xylylene itself, the formation of the aromatic ring becomes the driving force of the reaction.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 6. Reaction pathways of the exo, endo and cheletropic product.

|-
!
! Animated IRC

|-
| Endo
| [[File: Endo movie tyl214.gif|200px × 200px|upright=0.01]]

|-
| Exo
| [[File: Exo movie1 tyl214.gif|200px × 200px]]

|-
| Cheletropic
| [[File: Che movie tyl214.gif|200px × 200px]]
|}

===Energy Calculations===
[[File: Exe3Reactionprofile tyl214.png|thumb|right|x250px|250px|Fig. 7: Reaction profile of the o-Xylylene-SO2 cycloaddition.]]
From <b>Table 7</b>, we can confirm that the endo transition state has the lowest energy barrier of activation, giving the kinetic product; whereas the cheletropic reaction has the lowest Gibbs free energy of reaction, hence giving the thermodynamic product of the reaction. An energy profile in Figure X can be found in describing the different pathways of this reaction.

{| class="wikitable" style="text-align: centre; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 7. Relative energies of the three different reaction pathways.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| 154.422861
| 237.7594324
| 56.98507596
| 83.33657136
| -97.43778504

|-
! Exo
| 154.422861
| 241.7579705
| 56.32871711
| 87.33510951
| -98.0941439

|-
! Cheletropic
| 154.422861
| 260.0782589
| -0.005250871
| 105.6553979
| -154.4281119

|}

==Conclusion==
The semi-empirical/PM6 and B£LYP/6-31G(d) methods were used to run transition state simulations in GaussView5.0, where bond energies and transition state orbital interactions of three cycloaddition reactions were investigated. These calculations provides information about the reaction such as the electron demand mechanism, reaction and bond energies, and the visualisation of different molecular orbital involved in the reaction.

Rep:MOD:tyl214

2017-03-23T23:44:20Z

Tyl214: /* Energy Calculations */

<b>Transition State Computational Lab</b>

== Introduction ==

Whilst stereo-selectivity is one of the biggest challenges in synthetic chemistry, a better understanding of the transition state in a reaction would allow better synthetic routes. In this computational lab, GaussView 5.0 was used to perform simulations of different cycloaddition reactions. Both the semi-empirical/PM6 and B3LYP/6-31G(d) basis sets were used, where the PM6 method is based on experimental data and the 6-31G(d) originates from the Density Functional Theory (DFT).<br>
In a chemical reaction, there are always 3N-6 degree of freedoms. In order to extract information from the Potential Energy Surface (PES), we tend to fix all coordinate apart from one. In this computational lab, we are fixing all coordinates to a minimum apart from the reaction coordinate, where the transition state can be found at the maximum of the reaction coordinate. This is done by calculating the first and second derivatives of energy against the reaction coordinate. Note that since the maxima of a curve has a negative second derivative, therefore any transition state optimisations will give rise to a vibration at negative frequency, depicting an imaginary frequency.

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Anaylsis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. MOs throughout the reaction coordinate.
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
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<script>mo 6</script>
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|}

From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Fig. 3: Vibration of reaction path.

|<jmol>
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<script>frame 37; vibration 1;rotate x -20</script>
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The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 4: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital analysis===
[[File: Exe2 MO tyl214.png|thumb|right|x250px|500px|Fig. 5: Cyclohexadiene and 1,3-Dioxole reaction molecular orbital diagram.]]
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method. The outcome of the simulation suggested an inverse electron-demand Diels-Alder mechanism for this reaction, and the orbitals involved are shown both in the molecular diagram in <b>Figure 4</b> and in <b>Table 3</b> and <b>4</b>.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
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|+ style="text-align: left;"| Table 3. MOs of the Exo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
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|}

====<u>Endo</u>====
In contrast, the transition state shown in <b>Table 4</b> indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 4. MOs of the Endo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
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<name>13DioxoleMOs1</name>
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<script>mo 19</script>
<text>HOMO</text>
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<jmolbutton>
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<text>HOMO</text>
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<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs1</target>
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<text>HOMO</text>
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<text>HOMO</text>
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<jmolbutton>
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<text>LUMO</text>
<target>CyclohexadieneMOs1</target>
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<text>HOMO-1</text>
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<text>HOMO</text>
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<script>mo 42</script>
<text>LUMO</text>
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<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2endoTSMOs</target>
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|}

===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in <b>Table 5</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 5. Energies along the reaction path.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1313798.018
| -1313638.011
| -1313862.745
| 160.0071622
| -64.72748504

|-
! Exo
| -1313798.018
| -1313630.302
| -1313859.259
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: O-Xylylene-SO2 Cycloaddition==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 6: o-Xylylene-SO2 Cycloaddition reaction scheme.]]

===Reaction Coordinate===
After running the IRC simulation, the reaction pathway was recorded as an animation and is shown in <b>Table 6</b>. From this, we can observe that as the reaction coordinate reaches the transition state, aromaticity forms within the xylylene ring, which provides stabilisation to the molecule. Due to the instability of xylylene itself, the formation of the aromatic ring becomes the driving force of the reaction.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 6. Reaction pathways of the exo, endo and cheletropic product.

|-
!
! Animated IRC

|-
| Endo
| [[File: Endo movie tyl214.gif|200px × 200px|upright=0.01]]

|-
| Exo
| [[File: Exo movie1 tyl214.gif|200px × 200px]]

|-
| Cheletropic
| [[File: Che movie tyl214.gif|200px × 200px]]
|}

===Energy Calculations===
[[File: Exe3Reactionprofile tyl214.png|thumb|right|x250px|250px|Fig. 7: Reaction profile of the o-Xylylene-SO2 cycloaddition.]]
From <b>Table 7</b>, we can confirm that the endo transition state has the lowest energy barrier of activation, giving the kinetic product; whereas the cheletropic reaction has the lowest Gibbs free energy of reaction, hence giving the thermodynamic product of the reaction. An energy profile in Figure X can be found in describing the different pathways of this reaction.

{| class="wikitable" style="text-align: centre; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 7. Relative energies of the three different reaction pathways.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| 154.422861
| 237.7594324
| 56.98507596
| 83.33657136
| -97.43778504

|-
! Exo
| 154.422861
| 241.7579705
| 56.32871711
| 87.33510951
| -98.0941439

|-
! Cheletropic
| 154.422861
| 260.0782589
| -0.005250871
| 105.6553979
| -154.4281119

|}

==Conclusion==

Rep:MOD:tyl214

2017-03-23T23:43:41Z

Tyl214: /* Exercise 3: Diels-Alder vs Cheletropic */

<b>Transition State Computational Lab</b>

== Introduction ==

Whilst stereo-selectivity is one of the biggest challenges in synthetic chemistry, a better understanding of the transition state in a reaction would allow better synthetic routes. In this computational lab, GaussView 5.0 was used to perform simulations of different cycloaddition reactions. Both the semi-empirical/PM6 and B3LYP/6-31G(d) basis sets were used, where the PM6 method is based on experimental data and the 6-31G(d) originates from the Density Functional Theory (DFT).<br>
In a chemical reaction, there are always 3N-6 degree of freedoms. In order to extract information from the Potential Energy Surface (PES), we tend to fix all coordinate apart from one. In this computational lab, we are fixing all coordinates to a minimum apart from the reaction coordinate, where the transition state can be found at the maximum of the reaction coordinate. This is done by calculating the first and second derivatives of energy against the reaction coordinate. Note that since the maxima of a curve has a negative second derivative, therefore any transition state optimisations will give rise to a vibration at negative frequency, depicting an imaginary frequency.

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Anaylsis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. MOs throughout the reaction coordinate.
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
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<name>etheneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 7</script>
<text>LUMO</text>
<target>etheneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
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<color>white</color>
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<name>butadieneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 11</script>
<text>HOMO</text>
<target>etheneMOs</target>
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<jmolbutton>
<script>mo 11</script>
<text>HOMO</text>
<target>butadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 12</script>
<text>LUMO</text>
<target>butadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
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<text>HOMO-1</text>
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<script>mo 18</script>
<text>LUMO</text>
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<script>mo 19</script>
<text>LUMO+1</text>
<target>TSMOs</target>
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|}

From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Fig. 3: Vibration of reaction path.

|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 37; vibration 1;rotate x -20</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
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|}
The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 4: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital analysis===
[[File: Exe2 MO tyl214.png|thumb|right|x250px|500px|Fig. 5: Cyclohexadiene and 1,3-Dioxole reaction molecular orbital diagram.]]
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method. The outcome of the simulation suggested an inverse electron-demand Diels-Alder mechanism for this reaction, and the orbitals involved are shown both in the molecular diagram in <b>Figure 4</b> and in <b>Table 3</b> and <b>4</b>.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. MOs of the Exo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
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<text>HOMO</text>
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<jmolbutton>
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<text>HOMO</text>
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</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
</jmol>

||<jmol>
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<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
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<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
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<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
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<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2exoTSMOs</target>
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<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2exoTSMOs</target>
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====<u>Endo</u>====
In contrast, the transition state shown in <b>Table 4</b> indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 4. MOs of the Endo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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<text>HOMO</text>
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<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
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<jmolbutton>
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<text>LUMO</text>
<target>13DioxoleMOs1</target>
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<text>HOMO</text>
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<text>LUMO</text>
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<target>exe2endoTSMOs</target>
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===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in <b>Table 5</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 5. Energies along the reaction path.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1313798.018
| -1313638.011
| -1313862.745
| 160.0071622
| -64.72748504

|-
! Exo
| -1313798.018
| -1313630.302
| -1313859.259
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: O-Xylylene-SO2 Cycloaddition==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 6: o-Xylylene-SO2 Cycloaddition reaction scheme.]]

===Reaction Coordinate===
After running the IRC simulation, the reaction pathway was recorded as an animation and is shown in <b>Table 6</b>. From this, we can observe that as the reaction coordinate reaches the transition state, aromaticity forms within the xylylene ring, which provides stabilisation to the molecule. Due to the instability of xylylene itself, the formation of the aromatic ring becomes the driving force of the reaction.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 6. Reaction pathways of the exo, endo and cheletropic product.

|-
!
! Animated IRC

|-
| Endo
| [[File: Endo movie tyl214.gif|200px × 200px|upright=0.01]]

|-
| Exo
| [[File: Exo movie1 tyl214.gif|200px × 200px]]

|-
| Cheletropic
| [[File: Che movie tyl214.gif|200px × 200px]]
|}

===Energy Calculations===
[[File: Exe3Reactionprofile tyl214.png|thumb|right|x250px|250px|Fig. 7: Reaction profile of the o-Xylylene-SO2 cycloaddition.]]
From Table 5, we can confirm that the endo transition state has the lowest energy barrier of activation, giving the kinetic product; whereas the cheletropic reaction has the lowest Gibbs free energy of reaction, hence giving the thermodynamic product of the reaction. An energy profile in Figure X can be found in describing the different pathways of this reaction.

{| class="wikitable" style="text-align: centre; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 7. Relative energies of the three different reaction pathways.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| 154.422861
| 237.7594324
| 56.98507596
| 83.33657136
| -97.43778504

|-
! Exo
| 154.422861
| 241.7579705
| 56.32871711
| 87.33510951
| -98.0941439

|-
! Cheletropic
| 154.422861
| 260.0782589
| -0.005250871
| 105.6553979
| -154.4281119

|}

==Conclusion==

Rep:MOD:tyl214

2017-03-23T23:39:42Z

Tyl214: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

<b>Transition State Computational Lab</b>

== Introduction ==

Whilst stereo-selectivity is one of the biggest challenges in synthetic chemistry, a better understanding of the transition state in a reaction would allow better synthetic routes. In this computational lab, GaussView 5.0 was used to perform simulations of different cycloaddition reactions. Both the semi-empirical/PM6 and B3LYP/6-31G(d) basis sets were used, where the PM6 method is based on experimental data and the 6-31G(d) originates from the Density Functional Theory (DFT).<br>
In a chemical reaction, there are always 3N-6 degree of freedoms. In order to extract information from the Potential Energy Surface (PES), we tend to fix all coordinate apart from one. In this computational lab, we are fixing all coordinates to a minimum apart from the reaction coordinate, where the transition state can be found at the maximum of the reaction coordinate. This is done by calculating the first and second derivatives of energy against the reaction coordinate. Note that since the maxima of a curve has a negative second derivative, therefore any transition state optimisations will give rise to a vibration at negative frequency, depicting an imaginary frequency.

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Anaylsis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. MOs throughout the reaction coordinate.
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_J_tyl214.LOG</uploadedFileContents>
<name>etheneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 7</script>
<text>LUMO</text>
<target>etheneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_J_tyl214.LOG</uploadedFileContents>
<name>butadieneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 11</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 11</script>
<text>HOMO</text>
<target>butadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 12</script>
<text>LUMO</text>
<target>butadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 36; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
<name>TSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 17</script>
<text>HOMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 18</script>
<text>LUMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>LUMO+1</text>
<target>TSMOs</target>
</jmolbutton>
</jmol>
|}

From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Fig. 3: Vibration of reaction path.

|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 37; vibration 1;rotate x -20</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 4: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital analysis===
[[File: Exe2 MO tyl214.png|thumb|right|x250px|500px|Fig. 5: Cyclohexadiene and 1,3-Dioxole reaction molecular orbital diagram.]]
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method. The outcome of the simulation suggested an inverse electron-demand Diels-Alder mechanism for this reaction, and the orbitals involved are shown both in the molecular diagram in <b>Figure 4</b> and in <b>Table 3</b> and <b>4</b>.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. MOs of the Exo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 26; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM 1 3DIOXO tyl214.LOG</uploadedFileContents>
<name>13DioxoleMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 48; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM CYCLOHEXENE tyl214.LOG</uploadedFileContents>
<name>CyclohexadieneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 exo TS J 631 tyl214.LOG</uploadedFileContents>
<name>exe2exoTSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
</jmol>
|}

====<u>Endo</u>====
In contrast, the transition state shown in <b>Table 4</b> indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 4. MOs of the Endo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 26; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM 1 3DIOXO tyl214.LOG</uploadedFileContents>
<name>13DioxoleMOs1</name>
</jmolApplet>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 48; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM CYCLOHEXENE tyl214.LOG</uploadedFileContents>
<name>CyclohexadieneMOs1</name>
</jmolApplet>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 endo TS J 631.LOG</uploadedFileContents>
<name>exe2endoTSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
</jmol>
|}

===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in <b>Table 5</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 5. Energies along the reaction path.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1313798.018
| -1313638.011
| -1313862.745
| 160.0071622
| -64.72748504

|-
! Exo
| -1313798.018
| -1313630.302
| -1313859.259
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Reaction Coordinate===
After running the IRC simulation, the reaction pathway was recorded as an animation and is shown in Table 5. From this, we can observe that as the reaction coordinate reaches the transition state, aromaticity forms within the xylylene ring, which provides stabilisation to the molecule. Due to the instability of xylylene itself, the formation of the aromatic ring becomes the driving force of the reaction.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption

|-
!
! Animated IRC

|-
| Endo
| [[File: Endo movie tyl214.gif|200px × 200px|upright=0.01]]

|-
| Exo
| [[File: Exo movie1 tyl214.gif|200px × 200px]]

|-
| Cheletropic
| [[File: Che movie tyl214.gif|200px × 200px]]
|}

===Energy Calculations===
[[File: Exe3Reactionprofile tyl214.png|thumb|right|x250px|250px|Fig. 1: Butadiene and Ethene reaction scheme.]]
From Table 5, we can confirm that the endo transition state has the lowest energy barrier of activation, giving the kinetic product; whereas the cheletropic reaction has the lowest Gibbs free energy of reaction, hence giving the thermodynamic product of the reaction. An energy profile in Figure X can be found in describing the different pathways of this reaction.

{| class="wikitable" style="text-align: centre; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| 154.422861
| 237.7594324
| 56.98507596
| 83.33657136
| -97.43778504

|-
! Exo
| 154.422861
| 241.7579705
| 56.32871711
| 87.33510951
| -98.0941439

|-
! Cheletropic
| 154.422861
| 260.0782589
| -0.005250871
| 105.6553979
| -154.4281119

|}

==Conclusion==

Rep:MOD:tyl214

2017-03-23T23:38:20Z

Tyl214: /* Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene */

<b>Transition State Computational Lab</b>

== Introduction ==

Whilst stereo-selectivity is one of the biggest challenges in synthetic chemistry, a better understanding of the transition state in a reaction would allow better synthetic routes. In this computational lab, GaussView 5.0 was used to perform simulations of different cycloaddition reactions. Both the semi-empirical/PM6 and B3LYP/6-31G(d) basis sets were used, where the PM6 method is based on experimental data and the 6-31G(d) originates from the Density Functional Theory (DFT).<br>
In a chemical reaction, there are always 3N-6 degree of freedoms. In order to extract information from the Potential Energy Surface (PES), we tend to fix all coordinate apart from one. In this computational lab, we are fixing all coordinates to a minimum apart from the reaction coordinate, where the transition state can be found at the maximum of the reaction coordinate. This is done by calculating the first and second derivatives of energy against the reaction coordinate. Note that since the maxima of a curve has a negative second derivative, therefore any transition state optimisations will give rise to a vibration at negative frequency, depicting an imaginary frequency.

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Anaylsis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. MOs throughout the reaction coordinate.
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
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<name>etheneMOs</name>
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<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
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<target>etheneMOs</target>
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<jmolbutton>
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<text>LUMO</text>
<target>etheneMOs</target>
</jmolbutton>
</jmol>

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<text>LUMO</text>
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<text>HOMO</text>
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<script>mo 18</script>
<text>LUMO</text>
<target>TSMOs</target>
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<jmolbutton>
<script>mo 19</script>
<text>LUMO+1</text>
<target>TSMOs</target>
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From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Fig. 3: Vibration of reaction path.

|<jmol>
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<color>white</color>
<size>250</size>
<script>frame 37; vibration 1;rotate x -20</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
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The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 1: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital analysis===
[[File: Exe2 MO tyl214.png|thumb|right|x250px|500px|Fig. 5: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method. The outcome of the simulation suggested an inverse electron-demand Diels-Alder mechanism for this reaction, and the orbitals involved are shown both in the molecular diagram in <b>Figure 4</b> and in <b>Table 3</b> and <b>4</b>.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. MOs of the Exo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs</target>
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<text>HOMO</text>
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</jmolbutton>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
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</jmolApplet>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
</jmol>
|}

====<u>Endo</u>====
In contrast, the transition state shown in <b>Table 4</b> indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 4. MOs of the Endo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
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<name>13DioxoleMOs1</name>
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<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
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<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
</jmol>

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<name>CyclohexadieneMOs1</name>
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<script>mo 22</script>
<text>HOMO</text>
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<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs1</target>
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<text>HOMO-1</text>
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<text>HOMO</text>
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<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2endoTSMOs</target>
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<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2endoTSMOs</target>
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===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in <b>Table 5</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 5. Energies along the reaction path.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1313798.018
| -1313638.011
| -1313862.745
| 160.0071622
| -64.72748504

|-
! Exo
| -1313798.018
| -1313630.302
| -1313859.259
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Reaction Coordinate===
After running the IRC simulation, the reaction pathway was recorded as an animation and is shown in Table 5. From this, we can observe that as the reaction coordinate reaches the transition state, aromaticity forms within the xylylene ring, which provides stabilisation to the molecule. Due to the instability of xylylene itself, the formation of the aromatic ring becomes the driving force of the reaction.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption

|-
!
! Animated IRC

|-
| Endo
| [[File: Endo movie tyl214.gif|200px × 200px|upright=0.01]]

|-
| Exo
| [[File: Exo movie1 tyl214.gif|200px × 200px]]

|-
| Cheletropic
| [[File: Che movie tyl214.gif|200px × 200px]]
|}

===Energy Calculations===
[[File: Exe3Reactionprofile tyl214.png|thumb|right|x250px|250px|Fig. 1: Butadiene and Ethene reaction scheme.]]
From Table 5, we can confirm that the endo transition state has the lowest energy barrier of activation, giving the kinetic product; whereas the cheletropic reaction has the lowest Gibbs free energy of reaction, hence giving the thermodynamic product of the reaction. An energy profile in Figure X can be found in describing the different pathways of this reaction.

{| class="wikitable" style="text-align: centre; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| 154.422861
| 237.7594324
| 56.98507596
| 83.33657136
| -97.43778504

|-
! Exo
| 154.422861
| 241.7579705
| 56.32871711
| 87.33510951
| -98.0941439

|-
! Cheletropic
| 154.422861
| 260.0782589
| -0.005250871
| 105.6553979
| -154.4281119

|}

==Conclusion==

Rep:MOD:tyl214

2017-03-23T23:35:08Z

Tyl214: /* Energy Calculations */

<b>Transition State Computational Lab</b>

== Introduction ==

Whilst stereo-selectivity is one of the biggest challenges in synthetic chemistry, a better understanding of the transition state in a reaction would allow better synthetic routes. In this computational lab, GaussView 5.0 was used to perform simulations of different cycloaddition reactions. Both the semi-empirical/PM6 and B3LYP/6-31G(d) basis sets were used, where the PM6 method is based on experimental data and the 6-31G(d) originates from the Density Functional Theory (DFT).<br>
In a chemical reaction, there are always 3N-6 degree of freedoms. In order to extract information from the Potential Energy Surface (PES), we tend to fix all coordinate apart from one. In this computational lab, we are fixing all coordinates to a minimum apart from the reaction coordinate, where the transition state can be found at the maximum of the reaction coordinate. This is done by calculating the first and second derivatives of energy against the reaction coordinate. Note that since the maxima of a curve has a negative second derivative, therefore any transition state optimisations will give rise to a vibration at negative frequency, depicting an imaginary frequency.

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Anaylsis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. Caption
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
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From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Figure 3. Vibration of reaction path.

|<jmol>
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<script>frame 37; vibration 1;rotate x -20</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
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The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 1: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital analysis===
[[File: Exe2 MO tyl214.png|thumb|right|x250px|500px|Fig. 5: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method. The outcome of the simulation suggested an inverse electron-demand Diels-Alder mechanism for this reaction, and the orbitals involved are shown both in the molecular diagram in <b>Figure 4</b> and in <b>Table 3</b> and <b>4</b>.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. MOs of the Exo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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<text>LUMO</text>
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<text>HOMO-1</text>
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<text>HOMO</text>
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<text>LUMO</text>
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====<u>Endo</u>====
In contrast, the transition state shown in <b>Table 4</b> indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 4. MOs of the Endo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in <b>Table 5</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 5. Energies along the reaction path.
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1313798.018
| -1313638.011
| -1313862.745
| 160.0071622
| -64.72748504

|-
! Exo
| -1313798.018
| -1313630.302
| -1313859.259
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Reaction Coordinate===
After running the IRC simulation, the reaction pathway was recorded as an animation and is shown in Table 5. From this, we can observe that as the reaction coordinate reaches the transition state, aromaticity forms within the xylylene ring, which provides stabilisation to the molecule. Due to the instability of xylylene itself, the formation of the aromatic ring becomes the driving force of the reaction.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption

|-
!
! Animated IRC

|-
| Endo
| [[File: Endo movie tyl214.gif|200px × 200px|upright=0.01]]

|-
| Exo
| [[File: Exo movie1 tyl214.gif|200px × 200px]]

|-
| Cheletropic
| [[File: Che movie tyl214.gif|200px × 200px]]
|}

===Energy Calculations===
[[File: Exe3Reactionprofile tyl214.png|thumb|right|x250px|250px|Fig. 1: Butadiene and Ethene reaction scheme.]]
From Table 5, we can confirm that the endo transition state has the lowest energy barrier of activation, giving the kinetic product; whereas the cheletropic reaction has the lowest Gibbs free energy of reaction, hence giving the thermodynamic product of the reaction. An energy profile in Figure X can be found in describing the different pathways of this reaction.

{| class="wikitable" style="text-align: centre; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| 154.422861
| 237.7594324
| 56.98507596
| 83.33657136
| -97.43778504

|-
! Exo
| 154.422861
| 241.7579705
| 56.32871711
| 87.33510951
| -98.0941439

|-
! Cheletropic
| 154.422861
| 260.0782589
| -0.005250871
| 105.6553979
| -154.4281119

|}

==Conclusion==

Rep:MOD:tyl214

2017-03-23T23:34:00Z

Tyl214: /* Orbital analysis */

<b>Transition State Computational Lab</b>

== Introduction ==

Whilst stereo-selectivity is one of the biggest challenges in synthetic chemistry, a better understanding of the transition state in a reaction would allow better synthetic routes. In this computational lab, GaussView 5.0 was used to perform simulations of different cycloaddition reactions. Both the semi-empirical/PM6 and B3LYP/6-31G(d) basis sets were used, where the PM6 method is based on experimental data and the 6-31G(d) originates from the Density Functional Theory (DFT).<br>
In a chemical reaction, there are always 3N-6 degree of freedoms. In order to extract information from the Potential Energy Surface (PES), we tend to fix all coordinate apart from one. In this computational lab, we are fixing all coordinates to a minimum apart from the reaction coordinate, where the transition state can be found at the maximum of the reaction coordinate. This is done by calculating the first and second derivatives of energy against the reaction coordinate. Note that since the maxima of a curve has a negative second derivative, therefore any transition state optimisations will give rise to a vibration at negative frequency, depicting an imaginary frequency.

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Anaylsis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. Caption
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
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From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Figure 3. Vibration of reaction path.

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The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 1: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital analysis===
[[File: Exe2 MO tyl214.png|thumb|right|x250px|500px|Fig. 5: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method. The outcome of the simulation suggested an inverse electron-demand Diels-Alder mechanism for this reaction, and the orbitals involved are shown both in the molecular diagram in <b>Figure 4</b> and in <b>Table 3</b> and <b>4</b>.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
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! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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||<jmol>
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<name>exe2exoTSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
</jmol>
|}

====<u>Endo</u>====
In contrast, the transition state shown in <b>Table 4</b> indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 4. MOs of the Endo reaction.
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
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<name>13DioxoleMOs1</name>
</jmolApplet>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
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</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
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<name>CyclohexadieneMOs1</name>
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<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
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<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
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<script>mo 40</script>
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<script>mo 40</script>
<text>HOMO-1</text>
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<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
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</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
</jmol>
|}

===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in Table 5.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1313798.018
| -1313638.011
| -1313862.745
| 160.0071622
| -64.72748504

|-
! Exo
| -1313798.018
| -1313630.302
| -1313859.259
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Reaction Coordinate===
After running the IRC simulation, the reaction pathway was recorded as an animation and is shown in Table 5. From this, we can observe that as the reaction coordinate reaches the transition state, aromaticity forms within the xylylene ring, which provides stabilisation to the molecule. Due to the instability of xylylene itself, the formation of the aromatic ring becomes the driving force of the reaction.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption

|-
!
! Animated IRC

|-
| Endo
| [[File: Endo movie tyl214.gif|200px × 200px|upright=0.01]]

|-
| Exo
| [[File: Exo movie1 tyl214.gif|200px × 200px]]

|-
| Cheletropic
| [[File: Che movie tyl214.gif|200px × 200px]]
|}

===Energy Calculations===
[[File: Exe3Reactionprofile tyl214.png|thumb|right|x250px|250px|Fig. 1: Butadiene and Ethene reaction scheme.]]
From Table 5, we can confirm that the endo transition state has the lowest energy barrier of activation, giving the kinetic product; whereas the cheletropic reaction has the lowest Gibbs free energy of reaction, hence giving the thermodynamic product of the reaction. An energy profile in Figure X can be found in describing the different pathways of this reaction.

{| class="wikitable" style="text-align: centre; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| 154.422861
| 237.7594324
| 56.98507596
| 83.33657136
| -97.43778504

|-
! Exo
| 154.422861
| 241.7579705
| 56.32871711
| 87.33510951
| -98.0941439

|-
! Cheletropic
| 154.422861
| 260.0782589
| -0.005250871
| 105.6553979
| -154.4281119

|}

==Conclusion==

Rep:MOD:tyl214

2017-03-23T23:22:29Z

Tyl214: /* Energy Calculations */

<b>Transition State Computational Lab</b>

== Introduction ==

Whilst stereo-selectivity is one of the biggest challenges in synthetic chemistry, a better understanding of the transition state in a reaction would allow better synthetic routes. In this computational lab, GaussView 5.0 was used to perform simulations of different cycloaddition reactions. Both the semi-empirical/PM6 and B3LYP/6-31G(d) basis sets were used, where the PM6 method is based on experimental data and the 6-31G(d) originates from the Density Functional Theory (DFT).<br>
In a chemical reaction, there are always 3N-6 degree of freedoms. In order to extract information from the Potential Energy Surface (PES), we tend to fix all coordinate apart from one. In this computational lab, we are fixing all coordinates to a minimum apart from the reaction coordinate, where the transition state can be found at the maximum of the reaction coordinate. This is done by calculating the first and second derivatives of energy against the reaction coordinate. Note that since the maxima of a curve has a negative second derivative, therefore any transition state optimisations will give rise to a vibration at negative frequency, depicting an imaginary frequency.

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Anaylsis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. Caption
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
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<color>white</color>
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<uploadedFileContents>ETHENE_J_tyl214.LOG</uploadedFileContents>
<name>etheneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 7</script>
<text>LUMO</text>
<target>etheneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
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<color>white</color>
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<uploadedFileContents>BUTADIENE_J_tyl214.LOG</uploadedFileContents>
<name>butadieneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 11</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 11</script>
<text>HOMO</text>
<target>butadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 12</script>
<text>LUMO</text>
<target>butadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
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<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
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<script>mo 16</script>
<text>HOMO-1</text>
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<jmolbutton>
<script>mo 17</script>
<text>HOMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 18</script>
<text>LUMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>LUMO+1</text>
<target>TSMOs</target>
</jmolbutton>
</jmol>
|}

From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Figure 3. Vibration of reaction path.

|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 37; vibration 1;rotate x -20</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
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The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 1: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital analysis===
[[File: Exe2 MO tyl214.png|thumb|right|x250px|500px|Fig. 1: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. Caption
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
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<text>HOMO</text>
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<text>HOMO</text>
<target>13DioxoleMOs</target>
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<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs</target>
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</jmol>

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<script>mo 22</script>
<text>HOMO</text>
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<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs</target>
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<script>mo 40</script>
<text>HOMO-1</text>
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<script>mo 41</script>
<text>HOMO</text>
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<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2exoTSMOs</target>
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<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2exoTSMOs</target>
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|}

====<u>Endo</u>====
In contrast, the transition state shown in Table 4 indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. Caption
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
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<text>HOMO</text>
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<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
</jmol>

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<text>HOMO</text>
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<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
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<jmolbutton>
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<text>LUMO</text>
<target>CyclohexadieneMOs1</target>
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<text>HOMO</text>
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<text>LUMO</text>
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<jmolbutton>
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<text>LUMO+1</text>
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===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in Table 5.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1313798.018
| -1313638.011
| -1313862.745
| 160.0071622
| -64.72748504

|-
! Exo
| -1313798.018
| -1313630.302
| -1313859.259
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Reaction Coordinate===
After running the IRC simulation, the reaction pathway was recorded as an animation and is shown in Table 5. From this, we can observe that as the reaction coordinate reaches the transition state, aromaticity forms within the xylylene ring, which provides stabilisation to the molecule. Due to the instability of xylylene itself, the formation of the aromatic ring becomes the driving force of the reaction.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption

|-
!
! Animated IRC

|-
| Endo
| [[File: Endo movie tyl214.gif|200px × 200px|upright=0.01]]

|-
| Exo
| [[File: Exo movie1 tyl214.gif|200px × 200px]]

|-
| Cheletropic
| [[File: Che movie tyl214.gif|200px × 200px]]
|}

===Energy Calculations===
[[File: Exe3Reactionprofile tyl214.png|thumb|right|x250px|250px|Fig. 1: Butadiene and Ethene reaction scheme.]]
From Table 5, we can confirm that the endo transition state has the lowest energy barrier of activation, giving the kinetic product; whereas the cheletropic reaction has the lowest Gibbs free energy of reaction, hence giving the thermodynamic product of the reaction. An energy profile in Figure X can be found in describing the different pathways of this reaction.

{| class="wikitable" style="text-align: centre; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| 154.422861
| 237.7594324
| 56.98507596
| 83.33657136
| -97.43778504

|-
! Exo
| 154.422861
| 241.7579705
| 56.32871711
| 87.33510951
| -98.0941439

|-
! Cheletropic
| 154.422861
| 260.0782589
| -0.005250871
| 105.6553979
| -154.4281119

|}

==Conclusion==

Rep:MOD:tyl214

2017-03-23T23:20:57Z

Tyl214: /* Introduction */

<b>Transition State Computational Lab</b>

== Introduction ==

Whilst stereo-selectivity is one of the biggest challenges in synthetic chemistry, a better understanding of the transition state in a reaction would allow better synthetic routes. In this computational lab, GaussView 5.0 was used to perform simulations of different cycloaddition reactions. Both the semi-empirical/PM6 and B3LYP/6-31G(d) basis sets were used, where the PM6 method is based on experimental data and the 6-31G(d) originates from the Density Functional Theory (DFT).<br>
In a chemical reaction, there are always 3N-6 degree of freedoms. In order to extract information from the Potential Energy Surface (PES), we tend to fix all coordinate apart from one. In this computational lab, we are fixing all coordinates to a minimum apart from the reaction coordinate, where the transition state can be found at the maximum of the reaction coordinate. This is done by calculating the first and second derivatives of energy against the reaction coordinate. Note that since the maxima of a curve has a negative second derivative, therefore any transition state optimisations will give rise to a vibration at negative frequency, depicting an imaginary frequency.

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Anaylsis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. Caption
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_J_tyl214.LOG</uploadedFileContents>
<name>etheneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 7</script>
<text>LUMO</text>
<target>etheneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_J_tyl214.LOG</uploadedFileContents>
<name>butadieneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 11</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 11</script>
<text>HOMO</text>
<target>butadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 12</script>
<text>LUMO</text>
<target>butadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 36; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
<name>TSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
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<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 17</script>
<text>HOMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 18</script>
<text>LUMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>LUMO+1</text>
<target>TSMOs</target>
</jmolbutton>
</jmol>
|}

From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Figure 3. Vibration of reaction path.

|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 37; vibration 1;rotate x -20</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 1: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital analysis===
[[File: Exe2 MO tyl214.png|thumb|right|x250px|500px|Fig. 1: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. Caption
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 26; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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<name>13DioxoleMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 48; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM CYCLOHEXENE tyl214.LOG</uploadedFileContents>
<name>CyclohexadieneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 exo TS J 631 tyl214.LOG</uploadedFileContents>
<name>exe2exoTSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
</jmol>
|}

====<u>Endo</u>====
In contrast, the transition state shown in Table 4 indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. Caption
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
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<name>13DioxoleMOs1</name>
</jmolApplet>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 48; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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<name>CyclohexadieneMOs1</name>
</jmolApplet>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
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<name>exe2endoTSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
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<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2endoTSMOs</target>
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<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2endoTSMOs</target>
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<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2endoTSMOs</target>
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<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
</jmol>
|}

===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in Table 5.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1313798.018
| -1313638.011
| -1313862.745
| 160.0071622
| -64.72748504

|-
! Exo
| -1313798.018
| -1313630.302
| -1313859.259
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Reaction Coordinate===
After running the IRC simulation, the reaction pathway was recorded as an animation and is shown in Table 5. From this, we can observe that as the reaction coordinate reaches the transition state, aromaticity forms within the xylylene ring, which provides stabilisation to the molecule. Due to the instability of xylylene itself, the formation of the aromatic ring becomes the driving force of the reaction.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption

|-
!
! Animated IRC

|-
| Endo
| [[File: Endo movie tyl214.gif|200px × 200px|upright=0.01]]

|-
| Exo
| [[File: Exo movie1 tyl214.gif|200px × 200px]]

|-
| Cheletropic
| [[File: Che movie tyl214.gif|200px × 200px]]
|}

===Energy Calculations===
[[File: Exe3Reactionprofile tyl214.png|thumb|right|x250px|250px|Fig. 1: Butadiene and Ethene reaction scheme.]]
From Table 5, we can confirm that the endo transition state has the lowest energy barrier of activation, giving the kinetic product; whereas the cheletropic reaction has the lowest Gibbs free energy of reaction, hence giving the thermodynamic product of the reaction. An energy profile in Figure X can be found in describing the different pathways of this reaction.

{| class="wikitable" style="text-align: centre; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| 154.422861
| 237.7594324
| 56.98507596
| 83.33657136
| -97.43778504

|-
! Exo
| 154.422861
| 241.7579705
| 56.32871711
| 87.33510951
| -98.0941439

|-
! Cheletropic
| 154.422861
| 260.0782589
| -0.005250871
| 105.6553979
| -154.4281119

|}

Rep:MOD:tyl214

2017-03-23T23:20:33Z

Tyl214: /* Introduction */

<b>Transition State Computational Lab</b>

== Introduction ==

Whilst stereo-selectivity is one of the biggest challenges in synthetic chemistry, a better understanding of the transition state in a reaction would allow better synthetic routes. In this computational lab, GaussView 5.0 was used to perform simulations of different cycloaddition reactions. Both the semi-empirical/PM6 and B3LYP/6-31G(d) basis sets were used, where the PM6 method is based on experimental data and the 6-31G(d) originates from the Density Functional Theory (DFT).
In a chemical reaction, there are always 3N-6 degree of freedoms. In order to extract information from the Potential Energy Surface (PES), we tend to fix all coordinate apart from one. In this computational lab, we are fixing all coordinates to a minimum apart from the reaction coordinate, where the transition state can be found at the maximum of the reaction coordinate. This is done by calculating the first and second derivatives of energy against the reaction coordinate. Note that since the maxima of a curve has a negative second derivative, therefore any transition state optimisations will give rise to a vibration at negative frequency, depicting an imaginary frequency.

==== <u>1. PES minimum and TS</u> ====

==== Gradient and curvature relating to these points ====

==== Frequency calculation confirming structures ====

==== Methods used ====

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Anaylsis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. Caption
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_J_tyl214.LOG</uploadedFileContents>
<name>etheneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 7</script>
<text>LUMO</text>
<target>etheneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_J_tyl214.LOG</uploadedFileContents>
<name>butadieneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 11</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 11</script>
<text>HOMO</text>
<target>butadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 12</script>
<text>LUMO</text>
<target>butadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 36; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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<name>TSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
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<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 17</script>
<text>HOMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 18</script>
<text>LUMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>LUMO+1</text>
<target>TSMOs</target>
</jmolbutton>
</jmol>
|}

From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Figure 3. Vibration of reaction path.

|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 37; vibration 1;rotate x -20</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 1: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital analysis===
[[File: Exe2 MO tyl214.png|thumb|right|x250px|500px|Fig. 1: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. Caption
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 26; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM 1 3DIOXO tyl214.LOG</uploadedFileContents>
<name>13DioxoleMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 48; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM CYCLOHEXENE tyl214.LOG</uploadedFileContents>
<name>CyclohexadieneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 exo TS J 631 tyl214.LOG</uploadedFileContents>
<name>exe2exoTSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
</jmol>
|}

====<u>Endo</u>====
In contrast, the transition state shown in Table 4 indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. Caption
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 26; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM 1 3DIOXO tyl214.LOG</uploadedFileContents>
<name>13DioxoleMOs1</name>
</jmolApplet>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 48; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM CYCLOHEXENE tyl214.LOG</uploadedFileContents>
<name>CyclohexadieneMOs1</name>
</jmolApplet>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 endo TS J 631.LOG</uploadedFileContents>
<name>exe2endoTSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
</jmol>
|}

===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in Table 5.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1313798.018
| -1313638.011
| -1313862.745
| 160.0071622
| -64.72748504

|-
! Exo
| -1313798.018
| -1313630.302
| -1313859.259
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Reaction Coordinate===
After running the IRC simulation, the reaction pathway was recorded as an animation and is shown in Table 5. From this, we can observe that as the reaction coordinate reaches the transition state, aromaticity forms within the xylylene ring, which provides stabilisation to the molecule. Due to the instability of xylylene itself, the formation of the aromatic ring becomes the driving force of the reaction.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption

|-
!
! Animated IRC

|-
| Endo
| [[File: Endo movie tyl214.gif|200px × 200px|upright=0.01]]

|-
| Exo
| [[File: Exo movie1 tyl214.gif|200px × 200px]]

|-
| Cheletropic
| [[File: Che movie tyl214.gif|200px × 200px]]
|}

===Energy Calculations===
[[File: Exe3Reactionprofile tyl214.png|thumb|right|x250px|250px|Fig. 1: Butadiene and Ethene reaction scheme.]]
From Table 5, we can confirm that the endo transition state has the lowest energy barrier of activation, giving the kinetic product; whereas the cheletropic reaction has the lowest Gibbs free energy of reaction, hence giving the thermodynamic product of the reaction. An energy profile in Figure X can be found in describing the different pathways of this reaction.

{| class="wikitable" style="text-align: centre; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| 154.422861
| 237.7594324
| 56.98507596
| 83.33657136
| -97.43778504

|-
! Exo
| 154.422861
| 241.7579705
| 56.32871711
| 87.33510951
| -98.0941439

|-
! Cheletropic
| 154.422861
| 260.0782589
| -0.005250871
| 105.6553979
| -154.4281119

|}

Rep:MOD:tyl214

2017-03-23T22:58:35Z

Tyl214: /* Orbital analysis */

<b>Transition State Computational Lab</b>

== Introduction ==

Stereoselectivity is of extreme importance in the pharmaceutical industry, and a better understanding of the transition state in a reaction would a

Computational methods have become increasingly popular in synthetic designs due to its ability to predict possible reaction pathways

==== <u>1. PES minimum and TS</u> ====

==== Gradient and curvature relating to these points ====

==== Frequency calculation confirming structures ====

==== Methods used ====

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Anaylsis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. Caption
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_J_tyl214.LOG</uploadedFileContents>
<name>etheneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 7</script>
<text>LUMO</text>
<target>etheneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
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<jmolbutton>
<script>mo 11</script>
<text>HOMO</text>
<target>etheneMOs</target>
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<jmolbutton>
<script>mo 11</script>
<text>HOMO</text>
<target>butadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 12</script>
<text>LUMO</text>
<target>butadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
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</jmolApplet>
<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
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<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 17</script>
<text>HOMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 18</script>
<text>LUMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>LUMO+1</text>
<target>TSMOs</target>
</jmolbutton>
</jmol>
|}

From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Figure 3. Vibration of reaction path.

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The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 1: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital analysis===
[[File: Exe2 MO tyl214.png|thumb|right|x250px|500px|Fig. 1: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
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|+ style="text-align: left;"| Table 3. Caption
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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====<u>Endo</u>====
In contrast, the transition state shown in Table 4 indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
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! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in Table 5.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1313798.018
| -1313638.011
| -1313862.745
| 160.0071622
| -64.72748504

|-
! Exo
| -1313798.018
| -1313630.302
| -1313859.259
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Reaction Coordinate===
After running the IRC simulation, the reaction pathway was recorded as an animation and is shown in Table 5. From this, we can observe that as the reaction coordinate reaches the transition state, aromaticity forms within the xylylene ring, which provides stabilisation to the molecule. Due to the instability of xylylene itself, the formation of the aromatic ring becomes the driving force of the reaction.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption

|-
!
! Animated IRC

|-
| Endo
| [[File: Endo movie tyl214.gif|200px × 200px|upright=0.01]]

|-
| Exo
| [[File: Exo movie1 tyl214.gif|200px × 200px]]

|-
| Cheletropic
| [[File: Che movie tyl214.gif|200px × 200px]]
|}

===Energy Calculations===
[[File: Exe3Reactionprofile tyl214.png|thumb|right|x250px|250px|Fig. 1: Butadiene and Ethene reaction scheme.]]
From Table 5, we can confirm that the endo transition state has the lowest energy barrier of activation, giving the kinetic product; whereas the cheletropic reaction has the lowest Gibbs free energy of reaction, hence giving the thermodynamic product of the reaction. An energy profile in Figure X can be found in describing the different pathways of this reaction.

{| class="wikitable" style="text-align: centre; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| 154.422861
| 237.7594324
| 56.98507596
| 83.33657136
| -97.43778504

|-
! Exo
| 154.422861
| 241.7579705
| 56.32871711
| 87.33510951
| -98.0941439

|-
! Cheletropic
| 154.422861
| 260.0782589
| -0.005250871
| 105.6553979
| -154.4281119

|}

File:Exe2 MO tyl214.png

2017-03-23T22:56:40Z

Tyl214:

Rep:MOD:tyl214

2017-03-23T22:53:12Z

Tyl214: /* Energy Calculations */

<b>Transition State Computational Lab</b>

== Introduction ==

Stereoselectivity is of extreme importance in the pharmaceutical industry, and a better understanding of the transition state in a reaction would a

Computational methods have become increasingly popular in synthetic designs due to its ability to predict possible reaction pathways

==== <u>1. PES minimum and TS</u> ====

==== Gradient and curvature relating to these points ====

==== Frequency calculation confirming structures ====

==== Methods used ====

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Anaylsis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. Caption
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
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From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Figure 3. Vibration of reaction path.

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The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 1: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital analysis===
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
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! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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====<u>Endo</u>====
In contrast, the transition state shown in Table 4 indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. Caption
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
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<text>LUMO</text>
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<text>LUMO</text>
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<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2endoTSMOs</target>
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===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in Table 5.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1313798.018
| -1313638.011
| -1313862.745
| 160.0071622
| -64.72748504

|-
! Exo
| -1313798.018
| -1313630.302
| -1313859.259
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Reaction Coordinate===
After running the IRC simulation, the reaction pathway was recorded as an animation and is shown in Table 5. From this, we can observe that as the reaction coordinate reaches the transition state, aromaticity forms within the xylylene ring, which provides stabilisation to the molecule. Due to the instability of xylylene itself, the formation of the aromatic ring becomes the driving force of the reaction.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption

|-
!
! Animated IRC

|-
| Endo
| [[File: Endo movie tyl214.gif|200px × 200px|upright=0.01]]

|-
| Exo
| [[File: Exo movie1 tyl214.gif|200px × 200px]]

|-
| Cheletropic
| [[File: Che movie tyl214.gif|200px × 200px]]
|}

===Energy Calculations===
[[File: Exe3Reactionprofile tyl214.png|thumb|right|x250px|250px|Fig. 1: Butadiene and Ethene reaction scheme.]]
From Table 5, we can confirm that the endo transition state has the lowest energy barrier of activation, giving the kinetic product; whereas the cheletropic reaction has the lowest Gibbs free energy of reaction, hence giving the thermodynamic product of the reaction. An energy profile in Figure X can be found in describing the different pathways of this reaction.

{| class="wikitable" style="text-align: centre; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| 154.422861
| 237.7594324
| 56.98507596
| 83.33657136
| -97.43778504

|-
! Exo
| 154.422861
| 241.7579705
| 56.32871711
| 87.33510951
| -98.0941439

|-
! Cheletropic
| 154.422861
| 260.0782589
| -0.005250871
| 105.6553979
| -154.4281119

|}

File:Exe3Reactionprofile tyl214.png

2017-03-23T22:49:15Z

Tyl214:

Rep:MOD:tyl214

2017-03-23T22:34:09Z

Tyl214: /* Energy Calculations */

<b>Transition State Computational Lab</b>

== Introduction ==

Stereoselectivity is of extreme importance in the pharmaceutical industry, and a better understanding of the transition state in a reaction would a

Computational methods have become increasingly popular in synthetic designs due to its ability to predict possible reaction pathways

==== <u>1. PES minimum and TS</u> ====

==== Gradient and curvature relating to these points ====

==== Frequency calculation confirming structures ====

==== Methods used ====

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Anaylsis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. Caption
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
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<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
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<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 7</script>
<text>LUMO</text>
<target>etheneMOs</target>
</jmolbutton>
</jmol>

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<target>butadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 12</script>
<text>LUMO</text>
<target>butadieneMOs</target>
</jmolbutton>
</jmol>

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<text>HOMO</text>
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<text>LUMO</text>
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From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Figure 3. Vibration of reaction path.

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The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 1: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital analysis===
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. Caption
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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====<u>Endo</u>====
In contrast, the transition state shown in Table 4 indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. Caption
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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<jmolbutton>
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===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in Table 5.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1313798.018
| -1313638.011
| -1313862.745
| 160.0071622
| -64.72748504

|-
! Exo
| -1313798.018
| -1313630.302
| -1313859.259
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Reaction Coordinate===
After running the IRC simulation, the reaction pathway was recorded as an animation and is shown in Table 5. From this, we can observe that as the reaction coordinate reaches the transition state, aromaticity forms within the xylylene ring, which provides stabilisation to the molecule. Due to the instability of xylylene itself, the formation of the aromatic ring becomes the driving force of the reaction.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption

|-
!
! Animated IRC

|-
| Endo
| [[File: Endo movie tyl214.gif|200px × 200px|upright=0.01]]

|-
| Exo
| [[File: Exo movie1 tyl214.gif|200px × 200px]]

|-
| Cheletropic
| [[File: Che movie tyl214.gif|200px × 200px]]
|}

===Energy Calculations===
From Table 5, we can confirm that the endo transition state has the lowest energy barrier of activation, giving the kinetic product; whereas the cheletropic reaction has the lowest Gibbs free energy of reaction, hence giving the thermodynamic product of the reaction. An energy profile in Figure X can be found in describing the different pathways of this reaction.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| 154.422861
| 237.7594324
| 56.98507596
| 83.33657136
| -97.43778504

|-
! Exo
| 154.422861
| 241.7579705
| 56.32871711
| 87.33510951
| -98.0941439

|-
! Cheletropic
| 154.422861
| 260.0782589
| -0.005250871
| 105.6553979
| -154.4281119

|}

Rep:MOD:tyl214

2017-03-23T22:26:53Z

Tyl214: /* Energy Calculations */

<b>Transition State Computational Lab</b>

== Introduction ==

Stereoselectivity is of extreme importance in the pharmaceutical industry, and a better understanding of the transition state in a reaction would a

Computational methods have become increasingly popular in synthetic designs due to its ability to predict possible reaction pathways

==== <u>1. PES minimum and TS</u> ====

==== Gradient and curvature relating to these points ====

==== Frequency calculation confirming structures ====

==== Methods used ====

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Anaylsis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. Caption
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_J_tyl214.LOG</uploadedFileContents>
<name>etheneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 7</script>
<text>LUMO</text>
<target>etheneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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<name>butadieneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 11</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 11</script>
<text>HOMO</text>
<target>butadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 12</script>
<text>LUMO</text>
<target>butadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 36; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
<name>TSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 17</script>
<text>HOMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 18</script>
<text>LUMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>LUMO+1</text>
<target>TSMOs</target>
</jmolbutton>
</jmol>
|}

From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Figure 3. Vibration of reaction path.

|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 37; vibration 1;rotate x -20</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 1: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital analysis===
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. Caption
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 26; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM 1 3DIOXO tyl214.LOG</uploadedFileContents>
<name>13DioxoleMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 48; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM CYCLOHEXENE tyl214.LOG</uploadedFileContents>
<name>CyclohexadieneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 exo TS J 631 tyl214.LOG</uploadedFileContents>
<name>exe2exoTSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
</jmol>
|}

====<u>Endo</u>====
In contrast, the transition state shown in Table 4 indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. Caption
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 26; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM 1 3DIOXO tyl214.LOG</uploadedFileContents>
<name>13DioxoleMOs1</name>
</jmolApplet>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 48; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 IRCREOPT SM CYCLOHEXENE tyl214.LOG</uploadedFileContents>
<name>CyclohexadieneMOs1</name>
</jmolApplet>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 endo TS J 631.LOG</uploadedFileContents>
<name>exe2endoTSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
</jmol>
|}

===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in Table 5.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1313798.018
| -1313638.011
| -1313862.745
| 160.0071622
| -64.72748504

|-
! Exo
| -1313798.018
| -1313630.302
| -1313859.259
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Reaction Coordinate===
After running the IRC simulation, the reaction pathway was recorded as an animation and is shown in Table 5. From this, we can observe that as the reaction coordinate reaches the transition state, aromaticity forms within the xylylene ring, which provides stabilisation to the molecule. Due to the instability of xylylene itself, the formation of the aromatic ring becomes the driving force of the reaction.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption

|-
!
! Animated IRC

|-
| Endo
| [[File: Endo movie tyl214.gif|200px × 200px|upright=0.01]]

|-
| Exo
| [[File: Exo movie1 tyl214.gif|200px × 200px]]

|-
| Cheletropic
| [[File: Che movie tyl214.gif|200px × 200px]]
|}

===Energy Calculations===
reaction profile
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| 154.422861
| 237.7594324
| 56.98507596
| 83.33657136
| -97.43778504

|-
! Exo
| 154.422861
| 241.7579705
| 56.32871711
| 87.33510951
| -98.0941439

|-
! Cheletropic
| 154.422861
| 260.0782589
| -0.005250871
| 105.6553979
| -154.4281119

|}

Rep:Mod:tyl214

2017-03-23T22:26:43Z

Tyl214: /* Exercise 1 */

===MOs with Jmol===

MOs can be displayed using Jmol. This section covers a procedure to achieve this.

<jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>j1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>j1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<color>white</color>

<size>500</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>j1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>j1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

===Exercise 1===

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| 154.422861
| 237.7594324
| 56.98507596
| 83.33657136
| -97.43778504

|-
! Exo
| 154.422861
| 241.7579705
| 56.32871711
| 87.33510951
| -98.0941439

|-
! Cheletropic
| 154.422861
| 260.0782589
| -0.005250871
| 105.6553979
| -154.4281119

|}

Rep:MOD:tyl214

2017-03-23T22:21:22Z

Tyl214: /* Energy Calculations */

<b>Transition State Computational Lab</b>

== Introduction ==

Stereoselectivity is of extreme importance in the pharmaceutical industry, and a better understanding of the transition state in a reaction would a

Computational methods have become increasingly popular in synthetic designs due to its ability to predict possible reaction pathways

==== <u>1. PES minimum and TS</u> ====

==== Gradient and curvature relating to these points ====

==== Frequency calculation confirming structures ====

==== Methods used ====

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Anaylsis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. Caption
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_J_tyl214.LOG</uploadedFileContents>
<name>etheneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
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From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Figure 3. Vibration of reaction path.

|<jmol>
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<color>white</color>
<size>250</size>
<script>frame 37; vibration 1;rotate x -20</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
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The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 1: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital analysis===
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
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|+ style="text-align: left;"| Table 3. Caption
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! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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====<u>Endo</u>====
In contrast, the transition state shown in Table 4 indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. Caption
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! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in Table 5.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1313798.018
| -1313638.011
| -1313862.745
| 160.0071622
| -64.72748504

|-
! Exo
| -1313798.018
| -1313630.302
| -1313859.259
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Reaction Coordinate===
After running the IRC simulation, the reaction pathway was recorded as an animation and is shown in Table 5. From this, we can observe that as the reaction coordinate reaches the transition state, aromaticity forms within the xylylene ring, which provides stabilisation to the molecule. Due to the instability of xylylene itself, the formation of the aromatic ring becomes the driving force of the reaction.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption

|-
!
! Animated IRC

|-
| Endo
| [[File: Endo movie tyl214.gif|200px × 200px|upright=0.01]]

|-
| Exo
| [[File: Exo movie1 tyl214.gif|200px × 200px]]

|-
| Cheletropic
| [[File: Che movie tyl214.gif|200px × 200px]]
|}

===Energy Calculations===
reaction profile

Rep:MOD:tyl214

2017-03-23T22:07:56Z

Tyl214: /* Reaction Coordinate */

<b>Transition State Computational Lab</b>

== Introduction ==

Stereoselectivity is of extreme importance in the pharmaceutical industry, and a better understanding of the transition state in a reaction would a

Computational methods have become increasingly popular in synthetic designs due to its ability to predict possible reaction pathways

==== <u>1. PES minimum and TS</u> ====

==== Gradient and curvature relating to these points ====

==== Frequency calculation confirming structures ====

==== Methods used ====

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Anaylsis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. Caption
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
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From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Figure 3. Vibration of reaction path.

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The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 1: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital analysis===
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
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! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs</target>
</jmolbutton>
</jmol>

||<jmol>
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<name>CyclohexadieneMOs</name>
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<script>mo 22</script>
<text>HOMO</text>
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<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
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</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs</target>
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</jmol>

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<script>mo 40</script>
<text>HOMO-1</text>
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<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
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<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
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<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
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<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2exoTSMOs</target>
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====<u>Endo</u>====
In contrast, the transition state shown in Table 4 indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. Caption
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
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<text>HOMO</text>
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<text>HOMO</text>
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<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs1</target>
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<text>HOMO</text>
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<text>HOMO</text>
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<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs1</target>
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<script>mo 40</script>
<text>HOMO-1</text>
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<script>mo 40</script>
<text>HOMO-1</text>
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<script>mo 41</script>
<text>HOMO</text>
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<script>mo 42</script>
<text>LUMO</text>
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<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2endoTSMOs</target>
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</jmol>
|}

===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in Table 5.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1.90597E+13
| -1.90574E+13
| -1.90606E+13
| 160.0071622
| -64.72748504

|-
! Exo
| -1.90597E+13
| -1.90572E+13
| -1.90606E+13
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Reaction Coordinate===
After running the IRC simulation, the reaction pathway was recorded as an animation and is shown in Table 5. From this, we can observe that as the reaction coordinate reaches the transition state, aromaticity forms within the xylylene ring, which provides stabilisation to the molecule. Due to the instability of xylylene itself, the formation of the aromatic ring becomes the driving force of the reaction.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption

|-
!
! Animated IRC

|-
| Endo
| [[File: Endo movie tyl214.gif|200px × 200px|upright=0.01]]

|-
| Exo
| [[File: Exo movie1 tyl214.gif|200px × 200px]]

|-
| Cheletropic
| [[File: Che movie tyl214.gif|200px × 200px]]
|}

===Energy Calculations===
reaction profile

Rep:MOD:tyl214

2017-03-23T22:03:27Z

Tyl214: /* Reaction Coordinate */

<b>Transition State Computational Lab</b>

== Introduction ==

Stereoselectivity is of extreme importance in the pharmaceutical industry, and a better understanding of the transition state in a reaction would a

Computational methods have become increasingly popular in synthetic designs due to its ability to predict possible reaction pathways

==== <u>1. PES minimum and TS</u> ====

==== Gradient and curvature relating to these points ====

==== Frequency calculation confirming structures ====

==== Methods used ====

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Anaylsis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. Caption
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
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<name>etheneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
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<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 7</script>
<text>LUMO</text>
<target>etheneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
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<color>white</color>
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<name>butadieneMOs</name>
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<script>mo 11</script>
<text>HOMO</text>
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<jmolbutton>
<script>mo 11</script>
<text>HOMO</text>
<target>butadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 12</script>
<text>LUMO</text>
<target>butadieneMOs</target>
</jmolbutton>
</jmol>

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<text>HOMO-1</text>
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<jmolbutton>
<script>mo 17</script>
<text>HOMO</text>
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<script>mo 18</script>
<text>LUMO</text>
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<script>mo 19</script>
<text>LUMO+1</text>
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From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Figure 3. Vibration of reaction path.

|<jmol>
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<script>frame 37; vibration 1;rotate x -20</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
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The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 1: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital analysis===
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. Caption
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
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<jmolbutton>
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<text>HOMO</text>
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<jmolbutton>
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====<u>Endo</u>====
In contrast, the transition state shown in Table 4 indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. Caption
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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<jmolbutton>
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<text>LUMO</text>
<target>13DioxoleMOs1</target>
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===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in Table 5.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1.90597E+13
| -1.90574E+13
| -1.90606E+13
| 160.0071622
| -64.72748504

|-
! Exo
| -1.90597E+13
| -1.90572E+13
| -1.90606E+13
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Reaction Coordinate===
Formation of Aromaticity

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption

|-
!
! Animated IRC

|-
| Endo
| [[File: Endo movie tyl214.gif|200px × 200px|upright=0.01]]

|-
| Exo
| [[File: Exo movie1 tyl214.gif|200px × 200px]]

|-
| Cheletropic
| [[File: Che movie tyl214.gif|200px × 200px]]
|}

===Energy Calculations===
reaction profile

Rep:MOD:tyl214

2017-03-23T21:42:36Z

Tyl214: /* Reaction Coordinate */

<b>Transition State Computational Lab</b>

== Introduction ==

Stereoselectivity is of extreme importance in the pharmaceutical industry, and a better understanding of the transition state in a reaction would a

Computational methods have become increasingly popular in synthetic designs due to its ability to predict possible reaction pathways

==== <u>1. PES minimum and TS</u> ====

==== Gradient and curvature relating to these points ====

==== Frequency calculation confirming structures ====

==== Methods used ====

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Anaylsis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. Caption
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
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<script>mo 6</script>
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<target>etheneMOs</target>
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<text>LUMO</text>
<target>etheneMOs</target>
</jmolbutton>
</jmol>

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<text>LUMO</text>
<target>butadieneMOs</target>
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<text>LUMO</text>
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<text>LUMO+1</text>
<target>TSMOs</target>
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From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Figure 3. Vibration of reaction path.

|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 37; vibration 1;rotate x -20</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
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</jmol>
|}
The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 1: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital analysis===
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. Caption
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
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<text>HOMO</text>
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<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
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<script>mo 40</script>
<text>HOMO-1</text>
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<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
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<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
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<text>LUMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
</jmol>
|}

====<u>Endo</u>====
In contrast, the transition state shown in Table 4 indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. Caption
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
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<text>HOMO</text>
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<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
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<text>HOMO</text>
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<script>mo 22</script>
<text>HOMO</text>
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<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs1</target>
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<text>HOMO-1</text>
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<text>HOMO</text>
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<text>LUMO</text>
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===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in Table 5.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1.90597E+13
| -1.90574E+13
| -1.90606E+13
| 160.0071622
| -64.72748504

|-
! Exo
| -1.90597E+13
| -1.90572E+13
| -1.90606E+13
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Reaction Coordinate===
Formation of Aromaticity

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption

|-
! Endo product
! Exo product
! Cheletropic product

|-
| [[File: Endo movie tyl214.gif|250px]]
| [[File: Exo movie1 tyl214.gif|250px]]
| [[File: Che movie tyl214.gif|250px]]

|}
<br />
<br />
IRC For ENDO Cycloaddition
[[File: Endo movie tyl214.gif|600x200px]]
<br />
<br />
IRC For EXO Cycloaddition
[[File: Exo movie1 tyl214.gif|600x200px]]

===Energy Calculations===
reaction profile

Rep:MOD:tyl214

2017-03-23T21:39:59Z

Tyl214: /* Reaction Coordinate */

<b>Transition State Computational Lab</b>

== Introduction ==

Stereoselectivity is of extreme importance in the pharmaceutical industry, and a better understanding of the transition state in a reaction would a

Computational methods have become increasingly popular in synthetic designs due to its ability to predict possible reaction pathways

==== <u>1. PES minimum and TS</u> ====

==== Gradient and curvature relating to these points ====

==== Frequency calculation confirming structures ====

==== Methods used ====

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Anaylsis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. Caption
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
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From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Figure 3. Vibration of reaction path.

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<color>white</color>
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<script>frame 37; vibration 1;rotate x -20</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
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The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 1: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital analysis===
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. Caption
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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====<u>Endo</u>====
In contrast, the transition state shown in Table 4 indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. Caption
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in Table 5.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1.90597E+13
| -1.90574E+13
| -1.90606E+13
| 160.0071622
| -64.72748504

|-
! Exo
| -1.90597E+13
| -1.90572E+13
| -1.90606E+13
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Reaction Coordinate===
Formation of Aromaticity

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption

|-
! Endo product
! Exo product
! Cheletropic product

|-
| [[File: Endo movie tyl214.gif|250px]]
| [[File: Exo movie1 tyl214.gif|250px]]
| [[File: Che movie tyl214.gif|250px]]

|}

===Energy Calculations===
reaction profile

File:Exo movie1 tyl214.gif

2017-03-23T21:37:26Z

Tyl214:

File:Endo movie tyl214.gif

2017-03-23T21:37:06Z

Tyl214:

File:Che movie tyl214.gif

2017-03-23T21:36:49Z

Tyl214:

Rep:MOD:tyl214

2017-03-23T21:34:56Z

Tyl214: /* Reaction Coordinate */

<b>Transition State Computational Lab</b>

== Introduction ==

Stereoselectivity is of extreme importance in the pharmaceutical industry, and a better understanding of the transition state in a reaction would a

Computational methods have become increasingly popular in synthetic designs due to its ability to predict possible reaction pathways

==== <u>1. PES minimum and TS</u> ====

==== Gradient and curvature relating to these points ====

==== Frequency calculation confirming structures ====

==== Methods used ====

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Anaylsis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. Caption
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
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From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Figure 3. Vibration of reaction path.

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The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 1: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital analysis===
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
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! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
</jmol>
|}

====<u>Endo</u>====
In contrast, the transition state shown in Table 4 indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. Caption
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
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<jmolbutton>
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<text>LUMO</text>
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||<jmol>
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<text>LUMO</text>
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<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2endoTSMOs</target>
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|}

===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in Table 5.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1.90597E+13
| -1.90574E+13
| -1.90606E+13
| 160.0071622
| -64.72748504

|-
! Exo
| -1.90597E+13
| -1.90572E+13
| -1.90606E+13
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Reaction Coordinate===
Formation of Aromaticity

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption

|-
! Endo product
! Exo product
! Cheletropic product

|-
| -1.90597E+13
| -1.90574E+13
| -1.90606E+13

|}

===Energy Calculations===
reaction profile

Rep:MOD:tyl214

2017-03-23T21:27:54Z

Tyl214: /* Energy Calculations */

<b>Transition State Computational Lab</b>

== Introduction ==

Stereoselectivity is of extreme importance in the pharmaceutical industry, and a better understanding of the transition state in a reaction would a

Computational methods have become increasingly popular in synthetic designs due to its ability to predict possible reaction pathways

==== <u>1. PES minimum and TS</u> ====

==== Gradient and curvature relating to these points ====

==== Frequency calculation confirming structures ====

==== Methods used ====

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Anaylsis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. Caption
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
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<name>etheneMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 6</script>
<text>HOMO</text>
<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 7</script>
<text>LUMO</text>
<target>etheneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
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<jmolbutton>
<script>mo 11</script>
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<jmolbutton>
<script>mo 11</script>
<text>HOMO</text>
<target>butadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 12</script>
<text>LUMO</text>
<target>butadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
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<script>mo 16</script>
<text>HOMO-1</text>
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<jmolbutton>
<script>mo 17</script>
<text>HOMO</text>
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<jmolbutton>
<script>mo 18</script>
<text>LUMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>LUMO+1</text>
<target>TSMOs</target>
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|}

From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Figure 3. Vibration of reaction path.

|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 37; vibration 1;rotate x -20</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 1: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital analysis===
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. Caption
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
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<text>HOMO</text>
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<text>HOMO</text>
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<jmolbutton>
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<text>LUMO</text>
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||<jmol>
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<text>HOMO</text>
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<script>mo 22</script>
<text>HOMO</text>
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</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
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<script>mo 40</script>
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<text>LUMO</text>
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<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
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|}

====<u>Endo</u>====
In contrast, the transition state shown in Table 4 indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. Caption
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
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<text>HOMO</text>
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<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs1</target>
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</jmol>

||<jmol>
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<script>mo 22</script>
<text>HOMO</text>
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<jmolbutton>
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<text>LUMO</text>
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||<jmol>
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===Energy Calculations===
After running IRC calculations, the Gibbs free energy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in Table 5.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1.90597E+13
| -1.90574E+13
| -1.90606E+13
| 160.0071622
| -64.72748504

|-
! Exo
| -1.90597E+13
| -1.90572E+13
| -1.90606E+13
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Reaction Coordinate===
Formation of Aromaticity
===Energy Calculations===
reaction profile

Rep:MOD:tyl214

2017-03-23T21:21:57Z

Tyl214: /* Reaction Scheme */

<b>Transition State Computational Lab</b>

== Introduction ==

Stereoselectivity is of extreme importance in the pharmaceutical industry, and a better understanding of the transition state in a reaction would a

Computational methods have become increasingly popular in synthetic designs due to its ability to predict possible reaction pathways

==== <u>1. PES minimum and TS</u> ====

==== Gradient and curvature relating to these points ====

==== Frequency calculation confirming structures ====

==== Methods used ====

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Anaylsis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. Caption
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
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From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Figure 3. Vibration of reaction path.

|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 37; vibration 1;rotate x -20</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
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The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 1: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital analysis===
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. Caption
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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<text>HOMO</text>
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====<u>Endo</u>====
In contrast, the transition state shown in Table 4 indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. Caption
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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<jmolbutton>
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<text>LUMO</text>
<target>13DioxoleMOs1</target>
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<text>HOMO</text>
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<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
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===Energy Calculations===
After running IRC calculations, the enthalpy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in Table 5.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1.90597E+13
| -1.90574E+13
| -1.90606E+13
| 160.0071622
| -64.72748504

|-
! Exo
| -1.90597E+13
| -1.90572E+13
| -1.90606E+13
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===

[[File: Exe3Reactionschemenew tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Reaction Coordinate===
Formation of Aromaticity
===Energy Calculations===
reaction profile

File:Exe3Reactionschemenew tyl214.png

2017-03-23T21:20:42Z

Tyl214:

Rep:MOD:tyl214

2017-03-23T21:17:19Z

Tyl214: /* Reaction Scheme */

<b>Transition State Computational Lab</b>

== Introduction ==

Stereoselectivity is of extreme importance in the pharmaceutical industry, and a better understanding of the transition state in a reaction would a

Computational methods have become increasingly popular in synthetic designs due to its ability to predict possible reaction pathways

==== <u>1. PES minimum and TS</u> ====

==== Gradient and curvature relating to these points ====

==== Frequency calculation confirming structures ====

==== Methods used ====

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Anaylsis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. Caption
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
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From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Figure 3. Vibration of reaction path.

|<jmol>
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<color>white</color>
<size>250</size>
<script>frame 37; vibration 1;rotate x -20</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
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The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 1: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital analysis===
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. Caption
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
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<name>13DioxoleMOs</name>
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<script>mo 19</script>
<text>HOMO</text>
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<text>HOMO</text>
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<jmolbutton>
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<text>LUMO</text>
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<text>HOMO</text>
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<text>HOMO</text>
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<jmolbutton>
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<text>LUMO</text>
<target>CyclohexadieneMOs</target>
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<text>HOMO-1</text>
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<text>HOMO</text>
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<text>LUMO</text>
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<script>mo 43</script>
<text>LUMO+1</text>
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====<u>Endo</u>====
In contrast, the transition state shown in Table 4 indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. Caption
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
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<text>HOMO</text>
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<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs1</target>
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<text>HOMO</text>
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<text>HOMO</text>
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<text>LUMO</text>
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<text>HOMO-1</text>
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<text>HOMO</text>
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<text>LUMO</text>
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<jmolbutton>
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<text>LUMO+1</text>
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===Energy Calculations===
After running IRC calculations, the enthalpy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in Table 5.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1.90597E+13
| -1.90574E+13
| -1.90606E+13
| 160.0071622
| -64.72748504

|-
! Exo
| -1.90597E+13
| -1.90572E+13
| -1.90606E+13
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===

[[File: Exe3Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Reaction Coordinate===
Formation of Aromaticity
===Energy Calculations===
reaction profile

Rep:MOD:tyl214

2017-03-23T21:16:38Z

Tyl214: /* Reaction Scheme */

<b>Transition State Computational Lab</b>

== Introduction ==

Stereoselectivity is of extreme importance in the pharmaceutical industry, and a better understanding of the transition state in a reaction would a

Computational methods have become increasingly popular in synthetic designs due to its ability to predict possible reaction pathways

==== <u>1. PES minimum and TS</u> ====

==== Gradient and curvature relating to these points ====

==== Frequency calculation confirming structures ====

==== Methods used ====

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Anaylsis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. Caption
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
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<text>HOMO</text>
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<text>LUMO</text>
<target>etheneMOs</target>
</jmolbutton>
</jmol>

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</jmolbutton>
<jmolbutton>
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<text>LUMO</text>
<target>butadieneMOs</target>
</jmolbutton>
</jmol>

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From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Figure 3. Vibration of reaction path.

|<jmol>
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<script>frame 37; vibration 1;rotate x -20</script>
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The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 1: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital analysis===
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. Caption
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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====<u>Endo</u>====
In contrast, the transition state shown in Table 4 indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
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! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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===Energy Calculations===
After running IRC calculations, the enthalpy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in Table 5.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1.90597E+13
| -1.90574E+13
| -1.90606E+13
| 160.0071622
| -64.72748504

|-
! Exo
| -1.90597E+13
| -1.90572E+13
| -1.90606E+13
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===

Exe3Reactionscheme tyl214.png

===Reaction Coordinate===
Formation of Aromaticity
===Energy Calculations===
reaction profile

File:Exe3Reactionscheme tyl214.png

2017-03-23T21:16:15Z

Tyl214:

File:Exe3Reactionscheme tyl214.cdx

2017-03-23T21:15:49Z

Tyl214:

Rep:MOD:tyl214

2017-03-23T20:35:33Z

Tyl214: /* Exercise 3: Diels-Alder vs Cheletropic */

<b>Transition State Computational Lab</b>

== Introduction ==

Stereoselectivity is of extreme importance in the pharmaceutical industry, and a better understanding of the transition state in a reaction would a

Computational methods have become increasingly popular in synthetic designs due to its ability to predict possible reaction pathways

==== <u>1. PES minimum and TS</u> ====

==== Gradient and curvature relating to these points ====

==== Frequency calculation confirming structures ====

==== Methods used ====

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Anaylsis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. Caption
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
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<script>mo 6</script>
<text>HOMO</text>
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<target>etheneMOs</target>
</jmolbutton>
<jmolbutton>
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<text>LUMO</text>
<target>etheneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
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<target>butadieneMOs</target>
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<jmolbutton>
<script>mo 12</script>
<text>LUMO</text>
<target>butadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
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<text>LUMO</text>
<target>TSMOs</target>
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<jmolbutton>
<script>mo 19</script>
<text>LUMO+1</text>
<target>TSMOs</target>
</jmolbutton>
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|}

From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Figure 3. Vibration of reaction path.

|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 37; vibration 1;rotate x -20</script>
<uploadedFileContents>PM6_J.LOG</uploadedFileContents>
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</jmol>
|}
The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 1: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital analysis===
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. Caption
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
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<text>HOMO</text>
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<text>HOMO</text>
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<jmolbutton>
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<text>LUMO</text>
<target>13DioxoleMOs</target>
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</jmol>

||<jmol>
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<name>CyclohexadieneMOs</name>
</jmolApplet>
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<script>mo 22</script>
<text>HOMO</text>
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</jmolbutton>
<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs</target>
</jmolbutton>
</jmol>

||<jmol>
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<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
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<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
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<script>mo 41</script>
<text>HOMO</text>
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<script>mo 42</script>
<text>LUMO</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2exoTSMOs</target>
</jmolbutton>
</jmol>
|}

====<u>Endo</u>====
In contrast, the transition state shown in Table 4 indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. Caption
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
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<text>HOMO</text>
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<jmolbutton>
<script>mo 19</script>
<text>HOMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 20</script>
<text>LUMO</text>
<target>13DioxoleMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
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<text>HOMO</text>
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<jmolbutton>
<script>mo 22</script>
<text>HOMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
<jmolbutton>
<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
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<text>HOMO-1</text>
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<text>HOMO</text>
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<text>LUMO</text>
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===Energy Calculations===
After running IRC calculations, the enthalpy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in Table 5.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1.90597E+13
| -1.90574E+13
| -1.90606E+13
| 160.0071622
| -64.72748504

|-
! Exo
| -1.90597E+13
| -1.90572E+13
| -1.90606E+13
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===

===Reaction Coordinate===
Formation of Aromaticity
===Energy Calculations===
reaction profile

Rep:MOD:tyl214

2017-03-23T20:29:47Z

Tyl214: /* Reaction Coordinate */

<b>Transition State Computational Lab</b>

== Introduction ==

Stereoselectivity is of extreme importance in the pharmaceutical industry, and a better understanding of the transition state in a reaction would a

Computational methods have become increasingly popular in synthetic designs due to its ability to predict possible reaction pathways

==== <u>1. PES minimum and TS</u> ====

==== Gradient and curvature relating to these points ====

==== Frequency calculation confirming structures ====

==== Methods used ====

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Anaylsis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. Caption
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
||<jmol>
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From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Figure 3. Vibration of reaction path.

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The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 1: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital analysis===
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. Caption
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole MOs
! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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====<u>Endo</u>====
In contrast, the transition state shown in Table 4 indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 3. Caption
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! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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===Energy Calculations===
After running IRC calculations, the enthalpy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in Table 5.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1.90597E+13
| -1.90574E+13
| -1.90606E+13
| 160.0071622
| -64.72748504

|-
! Exo
| -1.90597E+13
| -1.90572E+13
| -1.90606E+13
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: Diels-Alder vs Cheletropic==

Rep:MOD:tyl214

2017-03-23T20:29:08Z

Tyl214: /* Bonds Analysis */

<b>Transition State Computational Lab</b>

== Introduction ==

Stereoselectivity is of extreme importance in the pharmaceutical industry, and a better understanding of the transition state in a reaction would a

Computational methods have become increasingly popular in synthetic designs due to its ability to predict possible reaction pathways

==== <u>1. PES minimum and TS</u> ====

==== Gradient and curvature relating to these points ====

==== Frequency calculation confirming structures ====

==== Methods used ====

==Exercise 1: [4 + 2] Cycloaddition of butadiene and ethene==
===Reaction Scheme===
The transition state in the Diels-Alder reaction of butadiene and ethene was simulated via a semi-empirical/PM6 method. The optimised structure was then used to perform an IRC calculation in order to investigate the bond lengths and orbital symmetry requirements of the reaction.

[[File: exe1scheme_tyl214.png|thumb|centre|x250px|500px|Fig. 1: Butadiene and Ethene reaction scheme.]]

===Theory===

[[File: tyl214_MOexe1.png|thumb|right|x200px|400px|Fig. 2: Molecular diagram of the butadiene/ethene transition state.]]
We would expect this reaction to undergo in a synchronous fashion with the butadiene being the electron rich species, where a normal electron demand [4+2] cycloaddition takes place. For a successful reaction to occur, the symmetry of the HOMO in butadiene should align with the LUMO in ethene in order to fulfil the Woodward-Hoffmann rule, resulting in a non-zero orbital overlap in the transition state. The general rule is stated as follows:

<div style="text-align: center;">
<b>symmetric + symmetric = non-zero overlap<br>
asymmetric + asymmetric = non-zero overlap<br>
symmetric + asymmetric = zero overlap</b>
</div>

Note that the energy difference between the HOMO and LUMO in ethene is expected to be larger than in butadiene, as an increase of π electrons in a delocalised system would decrease the energy gap according to Hückel Theory.
<br style="clear:right">

===Simulation Outcome===
====Orbital Anaylsis====
Semi-empirical/PM6 optimisations were performed for both of the starting materials, and the HOMO and LUMO of each are shown in <b>Table 1</b>.
{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 1. Caption
! style="background: #0D4F8B; color: white;" | Ethene MOs
! style="background: #0D4F8B; color: white;" | Butadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

|-
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From the table above, we can confirm that the HOMO of butadiene couples with the LUMO of ethene to form the HOMO and LUMO + 1 orbitals of the transition state, whereas the LUMO of butadiene and HOMO of ethene give rise to the HOMO - 1 and LUMO of the transition state. If we look at the corresponding molecular orbitals in detail, we can conclude that only orbitals with the same symmetry would interact, yielding the formation of two new C-C σ bonds seen in the cyclohexene product. The simulation outcome confirms with theory, suggesting that reactions are forbidden when orbital symmetries do not align.

====Bonds Analysis====
Comparing the original starting materal bond lengths to the simulated transition state, it is evident that the C-C σ bonds are generally shortened and the C=C π bonds are lengthened, resembling both the formation and breaking of C=C π bonds. These bonds were shown to be around 1.38 Å, which is in the range of the typical sp3 C-C σ bond length (1.54 Å) and the sp2 C=C π bond (1.34 Å), suggesting a partial double bond character. It is also worth noting that the distances between C2 - C3 and C6 - C1 in the transition state were lying between the typical C-C σ bond length and the combined covalent radii of carbon (3.4 Å), which is responsible for the new bond formation between the two merging molecules. The exact distances between the bonded carbon atoms can be found in <b>Table 2</b>.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Inter-carbon distances throughout the reaction profile.
! rowspan="2"|
! colspan="6 "| Bond Length / Å
|-
! C<sup>1</sup>-C<sup>2</sup>
! C<sup>2</sup>-C<sup>3</sup>
! C<sup>3</sup>-C<sup>4</sup>
! C<sup>4</sup>-C<sup>5</sup>
! C<sup>5</sup>-C<sup>6</sup>
! C<sup>6</sup>-C<sup>1</sup>
|-
! [[File:Exe1SM tyl214.png|thumb|centre|x200px|75px|Starting Material]]
| 1.32737
| N/A
| 1.33539
| 1.46833
| 1.33539
| N/A
|-
! [[File:Exe1TS tyl214.png|thumb|centre|x200px|75px|Transition State]]
| 1.38170
| 2.11466
| 1.37974
| 1.41107
| 1.37972
| 2.11509
|-
! [[File:Exe1product tyl214.png|thumb|centre|x200px|75px|Product]]
| 1.54091
| 1.54040
| 1.50090
| 1.33784
| 1.50090
| 1.54040
|}

====Reaction Coordinate====

{| class="wikitable" style="float: right;text-align: left; margin-left: auto; margin-right: auto;caption-side: bottom;"
|+ Figure 3. Vibration of reaction path.

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The frequency optimisation of the transition state structure showed a vibration at -948.16 cm-1, which depicts an imaginary frequency. This vibrational mode corresponds to the reaction pathway between the starting material and the product, which shows the molecules going towards and away from each other in a synchronous manner, suggesting the two new bonds form in a concerted fashion. <br style="clear:right">

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

===Reaction Scheme===
The following reaction is similar to the reaction of butadiene and ethene, only with the slight difference that there are now substituents attached to the double bonds. The presence of these substituents creates two possible product, exo and endo. From the simulation, we were able to calculate the corresponding energies and determined the kinetic and thermodynamic product of the reaction.
[[File: Exe2Reactionscheme tyl214.png|thumb|centre|x250px|500px|Fig. 1: Cyclohexadiene and 1,3-Dioxole reaction scheme.]]

===Orbital analysis===
The B3LYP/6-31G(d) method was used in this exercise to aid a more accurate simulation. Semi-empirical/PM6 method was first used to generate initial structures, as this is quicker than running all simulations with the B3LYP/6-31G(d) method.

====<u>Exo</u>====
In the reaction pathway that leads to the exo product, the HOMO of 1,3-Dioxole linearly combined with the LUMO of cyclohexadiene. From the simulated transition state, the two oxygens in the dioxole ring was shown to be away from the partially formed double bond. However, the methyl group in between the two oxygens shows a potential steric clash with the two sp3 carbons in the cyclohexadiene ring, which might affect the stability of both the transition state and the final product.
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! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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====<u>Endo</u>====
In contrast, the transition state shown in Table 4 indicates that the lone pair on the two oxygens form favourable π-interactions with the new forming double bond. From these secondary orbital interactions, we would expect the activation energy in forming the endo product would be lower than the exo product. The steric clash observed in the exo transition state does not appear in here, as the methyl group in the dioxole is now directly under two carbons with partial sp2 character, meaning the clashing hydrogens would be further away compared to the exo case.
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! style="background: #0D4F8B; color: white;" | Cyclohexadiene MOs
! style="background: #0D4F8B; color: white;" | TS MOs

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<script>mo 23</script>
<text>LUMO</text>
<target>CyclohexadieneMOs1</target>
</jmolbutton>
</jmol>

||<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Exe2 endo TS J 631.LOG</uploadedFileContents>
<name>exe2endoTSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 40</script>
<text>HOMO-1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 43</script>
<text>LUMO+1</text>
<target>exe2endoTSMOs</target>
</jmolbutton>
</jmol>
|}

===Energy Calculations===
After running IRC calculations, the enthalpy of reaction and the activation energy was extracted for both the endo and exo pathways, and the results are shown in Table 5.

{| class="wikitable" style="text-align: center; margin-left: auto; margin-right: auto;"
|+ style="text-align: left;"| Table 2. Caption
! rowspan="2"|
! colspan="6 "| Energy / kJ mol<sup>-1</sup>
|-
! S.M.
! T.S.
! Product
! E<sub>A</sub>
! ΔG<sub>r</sub>

|-
! Endo
| -1.90597E+13
| -1.90574E+13
| -1.90606E+13
| 160.0071622
| -64.72748504

|-
! Exo
| -1.90597E+13
| -1.90572E+13
| -1.90606E+13
| 167.7154406
| -61.24090679

|}

From the simulated results, the endo pathway was shown to require a lower activation energy as well as giving the more energetically stable product, meaning the endo product is both kinetically and thermodynamically favoured. This can be explained by the secondary orbital interactions between the lone pair on oxygen and the π system in the 6-membered ring, which appears in both the transition state and the final product.

==Exercise 3: Diels-Alder vs Cheletropic==