=Transition states and reactivity=

==Introduction==
This experiment involves using computational quantum chemistry methods to analyse molecular structures, their molecular orbitals (MO's) and energetics. Providing information about reaction pathways, activation energies and transition state (TS) intermediates. The transition state structures that are investigated are based on the shape of the potential energy surface; these are found through computational molecular-orbital based methods by solving the Schrödinger equation. The computational methods used to optimise and run frequency calculations on molecular structures are the semi-empirical method PM6 and the density Functional Theory (DFT) method B3LYP.
<br>

The Potential Energy Surface (PES) describes the energy of a system in terms of parameters such as the positions of atoms in a structure. For a molecule with N<sub>atoms</sub> there are 3N<sub>atoms</sub>-6 independent geometric variables that are determined;including bond lengths, bond angles and torsional angles. Using computational methods the points of a potential energy curve can be determined and analysis of its first and second derivatives yields important information about the systems reaction energetics. The first derivatives give the gradient and the second derivatives give the curvature of the (PES). Points with zero gradient are minima which correspond to products, or can be saddle points, energy maxima, that represent transition state species. The transition state is an intermediate structure between reactants and products in the reaction pathway that requires maximum energy to be overcome resulting in products, it is a maximum in the potential energy curve.
<br>

The curve's first derivative can be related to the force acting on atoms which acts in the direction that will lower potential energy, giving it a negative value. At bond length distances above the equilibrium bond length the potential energy curve gradient is positive and the force acting upon it to reach the minimum equilibrium length point on the curve is negative. At bond length distances below the equilibrium bond length the potential energy curve gradient is negative and the force acting on it to increase the bond length is positive<ref name="intro" />. Since the TS is at the maxima the force acts on it in the direction to minimise bond length to reach products indicating it has a negative force constant. A TS can therefore be identified by an imaginary frequency in its first vibrational mode since calculating the frequency of a harmonic oscillator with a negative force constant yields this imaginary frequency. This frequency calculation was a method to confirm if a TS structure was created after optimisation.
<br>

The reactions that will be studied using these computational methods are pericyclic reactions which occur through a cyclic TS in a concerted fashion. More specifically Diels-Alder cycloadditions will be looked into where a [4+2] cycloaddition occurs to form a 6-membered ring system.

==Exercise 1==

[[File:Overall reaction pk1615.PNG|thumb|400px|centre|Scheme 1:Diels-Alder reaction of butadiene and ethene]]

The transition state of the Diels-Alder reaction between butadiene and ethene, shown above in scheme 1, will be studied. This reaction involves a [4+2] cycloaddition between the two reactant molecules resulting in a ring product. The PM6 optimisation method was used in this exercise to optimise the reaction molecules.
<br>

===Molecular orbital analysis===

Optimising the reactants, transition state and product molecules revealed the energies and shape of the molecular orbitals for each structure. This then helped to identify the reactant HOMO and LUMO MO's that reacted to form the transition state, leading to the construction of the molecular orbital diagram for the transition state, figure 2.
{|style="margin: 0 auto;"
| [[File:Mos of butadiene ethene word pk1615.PNG|thumb|upright|344x344px|Figure 1:Molecular orbital energy levels of butadiene and ethene.]]
| [[File:Mo diagram butadiene pk1615.PNG|thumb|upright|500x500px|Figure 2:Molecular orbital diagram of the Diels-Alder transition state.]]
|}
<br>

{| class="wikitable"
! Ethene MO's
! Butadiene MO's
! Transition state Mo's
|-
| Ethene-φ1 HOMO
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT MINpk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| Butadiene-φ2 HOMO
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE OPT MIN PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| Transition state HOMO 1
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Ethene-φ2 LUMO
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT MINpk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| Butadiene-φ3 LUMO
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE OPT MIN PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| Transition state HOMO 2
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|
|
| Transition state LUMO 1
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|
|
| Transition state LUMO 2
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The Jmols of the MO's of the reactants and TS have been displayed above. It is observed that for a molecular orbital to react successfully and produce a product they need to be of the same symmetry. In the MO diagram it can be seen that symmetric reacts with symmetric and anti-symmetric reacts with anti-symmetric orbitals to product a TS HOMO or LUMO of the same symmetry.If they are of different symmetry the reaction is disallowed. This is seen where the butadiene HOMO which is asymmetric reacts with the ethene LUMO, also asymmetric, to product TS HOMO 1 and LUMO 2 which are both asymmetric.

The overlap integral for a symmetric-antisymmetric interaction is zero, whereas for a symmetric-symmetric or antisymmetric-antisymmetric interaction a non-zero value is obtained. The transition state MO diagram reveals that the transition state orbitals produced arise from s-s or a-a interactions, these inteaction contain non-zero overlap integrals, yielding true MO's.

===Carbon-Carbon bond length analysis===

{| class="wikitable"
|+ Table 1-Carbon-Carbon bond lengths of the reactants, TS and products.
! Carbon bonds
! Ethene bond lengths (Å)
[[File:Ethene pk1615.PNG]]
! Butadiene bond lengths (Å)
[[File:Butadiene pk1615.PNG]]
! Transition state bond lengths (Å)
[[File:Ts pk1615.PNG]]
! Cyclohexene bond lengths (Å)
[[File:Product pk1615.PNG]]
! Bond length change
|-
| C<sub>1</sub>-C<sub>2</sub>
| 1.327
| -
| 1.380
| 1.538
|Increase
|-
| C<sub>2</sub>-C<sub>3</sub>
| -
| -
| 2.115
| 1.536
|Decrease
|-
| C<sub>3</sub>-C<sub>4</sub>
| -
| 1.333
| 1.380
| 1.493
|Increase
|-
| C<sub>4</sub>-C<sub>5</sub>
| -
| 1.471
| 1.411
| 1.333
|Decrease
|-
| C<sub>5</sub>-C<sub>6</sub>
| -
| 1.333
| 1.380
| 1.493
|Increase
|-
| C<sub>6</sub>-C<sub>1</sub>
| -
| -
| 2.114
| 1.536
|Decrease
|}

The typical length for a C-C sp<sup>3</sup> bond is 1.54 Å, whereas the length of a C-C sp<sup>2</sup> bond is 1.34 Å <ref name="C length" />. In table 1 it can be seen that single and double bond values are approximately the same length as the typical values expected, confirming the structures obtained through optimisation. For example the bond between C<sub>1</sub>-C<sub>2</sub> is seen to increase as the bond becomes sp<sup>3</sup> hybridised from sp<sup>2</sup>.
<br>
The Van der Waals radius of a carbon atom is 1.7 Å <ref name="C radius" />. In the Diels-Alder transition state is can be seen that the bonds that form between C<sub>6</sub>-C<sub>1</sub> and C<sub>2</sub>-C<sub>3</sub>, 2.1 Å, are shorter than two carbon Van der Waals radii values, 3.4 Å. This confirms that in the TS the molecules, that were far apart, gradually come closer; when they are found within less than two carbon Van der Waals radii they are able to approach the formation of a single bond that is found in the products.
<br>

===Transition state vibration===
The vibration that corresponds to the reaction path at the transition state is identified as the one with a negative frequency, known as the imaginary frequency stated above. The Diels-Alder transition state at this vibration is displayed below. It can be seen that at this transition state vibration the bonds between the two reactants form in a synchronous manner, this is seen by the movement of the displacement vectors that move towards each other at the same time. This synchronous bond formation is further confirmed by the analysis of the IRC that shows the reactions proceeds through a concerted mechanism. This is the typical mechanism pathway found for Diels-Alder cycloadditions.

<jmol>
<jmolApplet>
<title>Transition state vibration</title>
<color>white</color>
<size>300</size>
<script>frame 17; vibration 1;rotate x -20; </script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The IRC for the Diels-Alder transition state can be found [[Media:CH IRC PM6 pk1615.LOG|here]]
<br>
The .log file for the PM6 optimised cyclohexene TS can be found [[Media:CH OPT TS PM6 pk1615.LOG|here]]
<br>
The .log file for the PM6 optimised cyclohexene product can be found [[Media:CH OPT MIN PRODUCTS pk1615.LOG|here]]

==Exercise 2==
[[File:Exercise 2 overall reactionpk1615.PNG|thumb|400px|centre|Scheme 2:Diels-Alder reaction of Cyclohexadiene and 1,3-Dioxole]]
In this exercise the [4+2] cycloaddition reaction between cyclohexadiene and 1,3-dioxole is investigated. This Diels-Alder reaction yields two products, the exo and endo products, due to the different symmetries of the transition state.
<br>
===Molecular orbital analysis===
Using the B3LYP optimisation method the TS for both the exo and endo molecules was determined. This yielded the occupied, HOMO, and unoccupied, LUMO, orbitals and their energies for each TS. The HOMO and LUMO orbitals for both symmetries are displayed below. These were then used to construct an MO diagram for this Diels-Alder reaction, figure 3, which was based on the MO diagram of the butadiene and ethene TS as these reacting molecules are symmetrically similar.

{|style="margin: 0 auto;"
| <jmol>
<jmolApplet>
<title>EXO HOMO 1</title>
<color>white</color>
<size>200</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS OPT FREQ B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>EXO HOMO 2</title>
<color>white</color>
<size>200</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS OPT FREQ B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>EXO LUMO 1</title>
<color>white</color>
<size>200</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS OPT FREQ B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>EXO LUMO 2</title>
<color>white</color>
<size>200</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS OPT FREQ B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
<br>
{|style="margin: 0 auto;"
| <jmol>
<jmolApplet>
<title>ENDO HOMO 1</title>
<color>white</color>
<size>200</size>
<script>frame 30; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS OPT FREQ TS B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>ENDO HOMO 2</title>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS OPT FREQ TS B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>ENDO LUMO 1</title>
<color>white</color>
<size>200</size>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS OPT FREQ TS B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>ENDO LUMO 2</title>
<color>white</color>
<size>200</size>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS OPT FREQ TS B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
<br>
[[File:Exercise 2 mo edited pk1615.PNG|thumb|400px|centre|Figure 3:Molecular orbital diagram of Cyclohexadiene and 1,3-Dioxole TS (the exo TS has been draw, however, the same orbitals apply for the endo TS)]]

According to symmetry the cyclohexadiene and 1,3-dioxole MO's can be considered as the butadiene and ethene MO's from figure 2 respectively. The energy levels of the reactant and TS orbitals has been determined from their B3LYP/6-31G(d) optimised .chk file MO's, and have been positioned accordingly. It is observed that the energy level of these MO's is slightly shifted compared to the butadiene ethene MO's. The cyclohexadiene HOMO is lower in energy than the 1,3-dioxole HOMO, whereas, in figure 2, the butadiene HOMO is higher in energy compared to the ethene HOMO. It is to be noted that both the exo and endo TS have different geometries, however,they both contain the same molecular orbital combinations, therefore, one molecular orbital diagram has been drawn for both.
<br>
The .log files for the B3LYP/6-31G(d) optimised molecules can be found here:[[Media:CYCLOHEXANE OPT FREQ MIN B pk1615.LOG|Cyclohexadiene]], [[Media:CYCLOPENTADIENE OPT FREQ MIN B pk1615.LOG|1,3-dioxole]], [[Media:EXO TS OPT FREQ B pk1615.LOG |Exo TS]], [[Media:ENDO_TS_OPT_FREQ_TS_B pk1615.LOG|Endo TS]], [[Media:EXO PRODUCT OPT FREQ MIN B. pk1615LOG|Exo product]], [[Media:ENDO PRODUCT OPT FREQ MIN B pk1615.LOG|Endo product]].

===Normal and Inverse demand Diels-Alder reaction analysis===
In a normal demand Diels-Alder reaction the HOMO of the electron rich diene reacts with the LUMO, π<sup>*</sup> bond, of the electron deficient dienophile ( the substituted alkene). In a normal demand reaction the HOMO of the diene reacts with the LUMO of the dienophile to form the HOMO and LUMO of the TS, this is seen in the reaction between butadiene (diene) and ethene (dienophile), figure 2, which produces HOMO 2 and LUMO 1.
<br>
In an inverse demand reaction, an electron deficient diene's LUMO now reacts with an electron rich dienophile's HOMO. This occurs due to a switch in energies of the diene's and dienophile's orbitals which occurs when an electron withdrawing group is attached to the diene, lowering its HOMO, and/or an electron donating group is attached to the dienophile, raising its π orbital's energy making it's HOMO higher in energy. This leads to the dienophile HOMO being high enough in energy to react with the diene's LUMO. This case is seen in the reaction between cyclohexadiene and 1,3-dioxole, figure 3, in which the dienophile, 1,3-dioxole, has electron donating oxygen atoms attached to it, raising its HOMO and allowing the TS HOMO 2 and LUMO 1 to be reached in an inverse demand reaction.
[[File:Inverse demand pk1615 .PNG|thumb|400px|centre|Figure 4:Diels-Alder normal and inverse reaction molecular orbital analysis]]

===Energy calculations===
The Sum of electronic and thermal Free Energies for each molecule has been taken from the B3LYP/6-31G(d) optimised .log files
{| class="wikitable"
|+ Table 2-Molecule energies.
! Molecule
! Energy (Hatree)
! Energy (kJ/mol)
|-
| Cyclohexadiene
| -233.324374
| -612593.1906
|-
| 1,3-dioxole
| -267.068642
| -701188.773
|-
| Reactants combined
| -500.393016
| -1313781.964
|-
| Endo TS
| -500.332146
| -1313622.149
|-
| Exo TS
| -500.329167
| -1313614.328
|-
| Endo product
| -500.418692
| -1313849.376
|-
| Exo product
| -500.417319
| -1313845.771
|}

{| class="wikitable"
|+ Table 3-Endo and Exo reaction barriers and energies.
! Reaction
! Reaction barrier (kJ/mol)
! Reaction energy (kJ/mol)
|-
| Endo
| 159.8142
| -67.41234
|-
| Exo
| 167.63557
| -63.80753
|}

Table 2 gives energy values of reactants, TS's and products for both the exo and endo geometries. These energy values were used to obtain calculations of the reaction barriers, also known as the activation energies, and the reaction energies for the endo and exo reaction pathways, table 3. The reaction barrier is the maximum energy in the reaction pathway which needs to be overcome for a reaction to proceed to its product. The reaction barrier energy is calculated as the TS minus the reactants and is the energy value needed to reach the maximum in the potential energy surface of the system. Furthermore, the reaction energy is calculated as the reactant minus the products and is the energy obtained when the minimum of the potential energy surface is reached. The results of the energy barriers and energies shown that the endo product is both the kinetically and thermodynamically stable product. This is explained through secondary orbital interactions that occur in the endo product between the ring π bond and the oxygen p-orbitals displayed in figure 5.
<br>
[[File:Endo stabilisation pk1615.PNG|thumb|400px|centre|Figure 5:Endo product secondary orbital stabilisation interaction]]
<br>
These secondary orbital interactions stabilise the product, making the endo product the lowest energy product, the thermodynamic one. Additionally, through stabilising the product these secondary orbital interactions lower the energy barrier of the endo reaction making it the more kinetically stable one as well. The kinetic product has the lower energy barrier i.e less energy is needed to overcome its activation energy. Moreover, steric reasons that may affect the exo product, making it both thermodynamically and kinetically less stable, are the repulsive interactions that could occur between the bridgehead carbons of the ring and the 1,3-dioxole oxygens that are closer in the exo geometry. This could lead to destabilisation of the exo product molecule.

==Exercise 3==
[[File:Diels alder cheletropic pk1615.PNG|thumb|400px|centre|Scheme 3:Diels-Alder/Cheletropic reaction of o-Xylylene and SO<sub>2</sub>]]
This exercise involves studying the Diels-Alder and Cheletropic reactions between o-Xylylene- and SO<sub>2</sub>, dispayed in scheme 3.
<br>
The IRC for the three reaction pathways can be found here: [[Media:XYLENE ENDO IRC pk1615.LOG|Diels-Alder endo]], [[Media:XYLENE EXO IRC PM6 pk1615.LOG|Diels-Alder exo]], [[Media:ISO-INDENE IRC PM6 pk1615.LOG|Cheletropic]].
<br>
The PM6 optimised .log files for the reaction molecules can be found here: [[Media:XYLYLENE REACTANT OPT MIN PM6 pk1615.LOG|o-Xylylene]], [[Media:SO2 OPT MIN PM6 pk1615.LOG|SO<sub>2</sub>]], [[Media:XYLENE OPT TS PM6 ENDO pk1615.LOG|Endo TS]], [[Media:XYLENE OPT TS PM6 exo pk1615.LOG|Exo TS]], [[Media:ISO-INDENE OPT TS PM6 pk1615.LOG|Cheletropic TS]], [[Media:XYLENE OPT MIN PM6 ENDO pk1615.LOG|Endo product]], [[Media:XYLENE OPT MIN PM6 pk1615 exo.LOG|Exo product]], [[Media:ISO-INDENE OPT MIN PM6 pk1615.LOG|Cheletropic product]].
===Energy calculations===
The Sum of electronic and thermal Free Energies for each molecule has been taken from the PM6 optimised .log files.
{| class="wikitable"
|+ Table 4-Molecule energies.
! Molecule
! Energy (Hatree)
! Energy (kJ/mol)
|-
| ortho-Xylylene
| 0.177678
| 466.493625
|-
| SO<sub>2</sub>
| -0.119269
| -313.1407834
|-
| Reactants
| 0.058409
| 153.352841
|-
| DA Endo TS
| 0.090560
| 237.765298
|-
| DA Exo TS
| 0.092077
| 241.748182
|-
| Cheletropic TS
| 0.099061
| 260.084675
|-
| DA Endo product
| 0.021705
| 56.9864818
|-
| DA Exo product
| 0.021454
| 56.3274813
|-
| Cheletropic Product
| 0.000005
| 0.013127501
|}

{| class="wikitable"
|+ Table 5-Reaction barriers and energies.
! Reaction
! Reaction barrier (kJ/mol)
! Reaction energy (kJ/mol)
|-
| Endo
| 84.4124569
| -96.3663593
|-
| Exo
| 88.3953407
| -97.0253599
|-
| Cheletropic
| 106.731834
| -153.339714
|}
<br>
The most favourable route in this reaction is the endo route. As seen in table 5 the endo TS has the lowest reaction barrier energy, therefore, it is easier to overcome this reaction barrier to reach the TS and get a product. This lower energy barrier value is due to the endo TS and product having the secondary orbital interactions stated above; now between the oxygen p orbital and the pi orbitals of the conjugated benzene ring. These secondary orbital interactions stabilise the molecule, lowering its reaction energies. It is to be noted that the cheletropic product is the more thermodynamically stable one but has a very high energy barrier which is unfavourable to reach as a lot of energy is needed to overcome it; this is an undesirable route. The endo product is the kinetically stable one and is the route that is preferred.
<br>
[[File:Exercise 3 reaction coordinate 3.PNG|thumb|400px|centre|Figure 6:Reaction profile diagram]]
<br>
Observing the IRC paths for the three reaction TS's, it can be seen that the xylylene 6-membered ring bonds change in length as the reaction proceeds from reactants to products through the TS. The xylylene ring obtains aromaticity as the bond length changes, this could be a considered a driving force for the reaction and proves the molecule's instability as it readily rearranges as the reaction proceeds to the product.

===An alternative reaction route===
An alternative reaction route can occur in the Diels-Alder reaction between o-Xylylene and SO<sub>2</sub>, where the SO<sub>2</sub> molecule reacts with the diene inside the six-membered ring of the xylylene molecule. This approach is displayed in scheme 4.
[[File:Alternative route pk1615.PNG|thumb|400px|centre|Scheme 4:Diels-Alder alternative reaction of o-Xylylene and SO<sub>2</sub>]]
{| class="wikitable"
|+ Table 6-Reaction barriers and energies.
! Reaction
! Energy barrier (kJ/mol)
! Reaction energy (kJ/mol)
|-
| Endo
| 114.631969
| -18.906229
|-
| Exo
| 122.469083
| -23.353824
|}
<br>
This endo and exo route are neither thermodynamically or kinetically stable since they have high reaction energies (are not stable) and have high energy barriers. These high energy barriers require large amounts of energy to be overcome which is undesirable and would lead to products that are not very thermodynamically stable.
<br>
The IRC for the the alternative reaction pathways can be found here: [[Media:ENDO TS IRC pk1615.LOG|Alternative Diels-Alder endo]], [[Media:EXO TS IRC pk1615.LOG|Alternative Diels-Alder exo]].

==Further work==
An electrocyclic reaction is a pericyclic reaction that involves a rearrangement of a pi to a sigma bond to form a ring product, such as the one displayed in scheme 5.
[[File:Electrocyclic pk1615.PNG|thumb|400px|centre|Scheme 5: Electrocyclic reaction.]]
<br>
[[File:Further work disrotation pk1615.PNG|thumb|400px|centre|Figure 7: Electrocyclic reaction orbital alignment.]]
<br>
The molecular orbital interactions that yield the ring product are shown in figure 7. It can be seen that the orbitals move in a disrotary fashion. The TS of the molecule was optimised to the PM6 level and the MO's where identified in order to confirm their movement.
<br>
{|style="margin: 0 auto;"
| [[File:Further work reactant MO pk1615.PNG|thumb|upright|344x344px|Figure 8: Reactant MO (1).]]
| [[File:Further work TS MO pk1615.PNG|thumb|upright|344x344px|Figure 9: TS MO (3).]]
|}
<br>
Even though the PM6 level of optimisation is not the most accurate for viewing the correct symmetry of the MO's; it is concluded through the MO's that this electrocyclic reaction proceeds with disrotation, as the orbitals allign as expected in the TS of the molecule leading to the formation of the sigma bond. A higher level of optimisation would be more suitable to determine the direction of orbital movement.
<br>
The IRC for the TS can be found [[Media:TS IRC pk1615.LOG|here]].
<br>
The PM6 optimised .log files can be found here: [[Media:REACTANTS OPT MIN PM6 pk1615.LOG|Reactant]], [[Media:PRODUCT OPT TS PM6 pk1615.LOG|TS]], [[Media:PRODUCT OPT MIN PM6 pk1615.LOG|Product]].

==Conclusion==
==References==
<references>
<ref name="intro">Computational Quantum Chemistry. Chapter 1, 2013, Pages 1-62.</ref>
<ref name="C length">B.P. Stoicheff. "The variation of carbon-carbon bond lengths with environment as determined by spectroscopic studies of simple polyatomic molecules". Tetrahedron, Vol 17, Issues 3–4, 1962, Pages 135-145.</ref>
<ref name="C radius">A Bondi. "Van der Waals Volumes and Radii". J. Phys. Chem., 68 (3), 1964, Pages 441–451.</ref>
</references>

Rep:Mod:pk1615Yr3

2018-03-11T14:39:21Z

Pk1615: /* Further work */

=Transition states and reactivity=

==Introduction==
This experiment involves using computational quantum chemistry methods to analyse molecular structures, their molecular orbitals (MO's) and energetics. Providing information about reaction pathways, activation energies and transition state (TS) intermediates. The transition state structures that are investigated are based on the shape of the potential energy surface; these are found through computational molecular-orbital based methods by solving the Schrödinger equation. The computational methods used to optimise and run frequency calculations on molecular structures are the semi-empirical method PM6 and the density Functional Theory (DFT) method B3LYP.
<br>

The Potential Energy Surface (PES) describes the energy of a system in terms of parameters such as the positions of atoms in a structure. For a molecule with N<sub>atoms</sub> there are 3N<sub>atoms</sub>-6 independent geometric variables that are determined;including bond lengths, bond angles and torsional angles. Using computational methods the points of a potential energy curve can be determined and analysis of its first and second derivatives yields important information about the systems reaction energetics. The first derivatives give the gradient and the second derivatives give the curvature of the (PES). Points with zero gradient are minima which correspond to products, or can be saddle points, energy maxima, that represent transition state species. The transition state is an intermediate structure between reactants and products in the reaction pathway that requires maximum energy to be overcome resulting in products, it is a maximum in the potential energy curve.
<br>

The curve's first derivative can be related to the force acting on atoms which acts in the direction that will lower potential energy, giving it a negative value. At bond length distances above the equilibrium bond length the potential energy curve gradient is positive and the force acting upon it to reach the minimum equilibrium length point on the curve is negative. At bond length distances below the equilibrium bond length the potential energy curve gradient is negative and the force acting on it to increase the bond length is positive<ref name="intro" />. Since the TS is at the maxima the force acts on it in the direction to minimise bond length to reach products indicating it has a negative force constant. A TS can therefore be identified by an imaginary frequency in its first vibrational mode since calculating the frequency of a harmonic oscillator with a negative force constant yields this imaginary frequency. This frequency calculation was a method to confirm if a TS structure was created after optimisation.
<br>

The reactions that will be studied using these computational methods are pericyclic reactions which occur through a cyclic TS in a concerted fashion. More specifically Diels-Alder cycloadditions will be looked into where a [4+2] cycloaddition occurs to form a 6-membered ring system.

==Exercise 1==

[[File:Overall reaction pk1615.PNG|thumb|400px|centre|Scheme 1:Diels-Alder reaction of butadiene and ethene]]

The transition state of the Diels-Alder reaction between butadiene and ethene, shown above in scheme 1, will be studied. This reaction involves a [4+2] cycloaddition between the two reactant molecules resulting in a ring product. The PM6 optimisation method was used in this exercise to optimise the reaction molecules.
<br>

===Molecular orbital analysis===

Optimising the reactants, transition state and product molecules revealed the energies and shape of the molecular orbitals for each structure. This then helped to identify the reactant HOMO and LUMO MO's that reacted to form the transition state, leading to the construction of the molecular orbital diagram for the transition state, figure 2.
{|style="margin: 0 auto;"
| [[File:Mos of butadiene ethene word pk1615.PNG|thumb|upright|344x344px|Figure 1:Molecular orbital energy levels of butadiene and ethene.]]
| [[File:Mo diagram butadiene pk1615.PNG|thumb|upright|500x500px|Figure 2:Molecular orbital diagram of the Diels-Alder transition state.]]
|}
<br>

{| class="wikitable"
! Ethene MO's
! Butadiene MO's
! Transition state Mo's
|-
| Ethene-φ1 HOMO
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT MINpk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| Butadiene-φ2 HOMO
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE OPT MIN PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| Transition state HOMO 1
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Ethene-φ2 LUMO
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT MINpk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| Butadiene-φ3 LUMO
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE OPT MIN PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| Transition state HOMO 2
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|
|
| Transition state LUMO 1
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|
|
| Transition state LUMO 2
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The Jmols of the MO's of the reactants and TS have been displayed above. It is observed that for a molecular orbital to react successfully and produce a product they need to be of the same symmetry. In the MO diagram it can be seen that symmetric reacts with symmetric and anti-symmetric reacts with anti-symmetric orbitals to product a TS HOMO or LUMO of the same symmetry.If they are of different symmetry the reaction is disallowed. This is seen where the butadiene HOMO which is asymmetric reacts with the ethene LUMO, also asymmetric, to product TS HOMO 1 and LUMO 2 which are both asymmetric.

The overlap integral for a symmetric-antisymmetric interaction is zero, whereas for a symmetric-symmetric or antisymmetric-antisymmetric interaction a non-zero value is obtained. The transition state MO diagram reveals that the transition state orbitals produced arise from s-s or a-a interactions, these inteaction contain non-zero overlap integrals, yielding true MO's.

===Carbon-Carbon bond length analysis===

{| class="wikitable"
|+ Table 1-Carbon-Carbon bond lengths of the reactants, TS and products.
! Carbon bonds
! Ethene bond lengths (Å)
[[File:Ethene pk1615.PNG]]
! Butadiene bond lengths (Å)
[[File:Butadiene pk1615.PNG]]
! Transition state bond lengths (Å)
[[File:Ts pk1615.PNG]]
! Cyclohexene bond lengths (Å)
[[File:Product pk1615.PNG]]
! Bond length change
|-
| C<sub>1</sub>-C<sub>2</sub>
| 1.327
| -
| 1.380
| 1.538
|Increase
|-
| C<sub>2</sub>-C<sub>3</sub>
| -
| -
| 2.115
| 1.536
|Decrease
|-
| C<sub>3</sub>-C<sub>4</sub>
| -
| 1.333
| 1.380
| 1.493
|Increase
|-
| C<sub>4</sub>-C<sub>5</sub>
| -
| 1.471
| 1.411
| 1.333
|Decrease
|-
| C<sub>5</sub>-C<sub>6</sub>
| -
| 1.333
| 1.380
| 1.493
|Increase
|-
| C<sub>6</sub>-C<sub>1</sub>
| -
| -
| 2.114
| 1.536
|Decrease
|}

The typical length for a C-C sp<sup>3</sup> bond is 1.54 Å, whereas the length of a C-C sp<sup>2</sup> bond is 1.34 Å <ref name="C length" />. In table 1 it can be seen that single and double bond values are approximately the same length as the typical values expected, confirming the structures obtained through optimisation. For example the bond between C<sub>1</sub>-C<sub>2</sub> is seen to increase as the bond becomes sp<sup>3</sup> hybridised from sp<sup>2</sup>.
<br>
The Van der Waals radius of a carbon atom is 1.7 Å <ref name="C radius" />. In the Diels-Alder transition state is can be seen that the bonds that form between C<sub>6</sub>-C<sub>1</sub> and C<sub>2</sub>-C<sub>3</sub>, 2.1 Å, are shorter than two carbon Van der Waals radii values, 3.4 Å. This confirms that in the TS the molecules, that were far apart, gradually come closer; when they are found within less than two carbon Van der Waals radii they are able to approach the formation of a single bond that is found in the products.
<br>

===Transition state vibration===
The vibration that corresponds to the reaction path at the transition state is identified as the one with a negative frequency, known as the imaginary frequency stated above. The Diels-Alder transition state at this vibration is displayed below. It can be seen that at this transition state vibration the bonds between the two reactants form in a synchronous manner, this is seen by the movement of the displacement vectors that move towards each other at the same time. This synchronous bond formation is further confirmed by the analysis of the IRC that shows the reactions proceeds through a concerted mechanism. This is the typical mechanism pathway found for Diels-Alder cycloadditions.

<jmol>
<jmolApplet>
<title>Transition state vibration</title>
<color>white</color>
<size>300</size>
<script>frame 17; vibration 1;rotate x -20; </script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The IRC for the Diels-Alder transition state can be found [[Media:CH IRC PM6 pk1615.LOG|here]]
<br>
The .log file for the PM6 optimised cyclohexene TS can be found [[Media:CH OPT TS PM6 pk1615.LOG|here]]
<br>
The .log file for the PM6 optimised cyclohexene product can be found [[Media:CH OPT MIN PRODUCTS pk1615.LOG|here]]

==Exercise 2==
[[File:Exercise 2 overall reactionpk1615.PNG|thumb|400px|centre|Scheme 2:Diels-Alder reaction of Cyclohexadiene and 1,3-Dioxole]]
In this exercise the [4+2] cycloaddition reaction between cyclohexadiene and 1,3-dioxole is investigated. This Diels-Alder reaction yields two products, the exo and endo products, due to the different symmetries of the transition state.
<br>
===Molecular orbital analysis===
Using the B3LYP optimisation method the TS for both the exo and endo molecules was determined. This yielded the occupied, HOMO, and unoccupied, LUMO, orbitals and their energies for each TS. The HOMO and LUMO orbitals for both symmetries are displayed below. These were then used to construct an MO diagram for this Diels-Alder reaction, figure 3, which was based on the MO diagram of the butadiene and ethene TS as these reacting molecules are symmetrically similar.

{|style="margin: 0 auto;"
| <jmol>
<jmolApplet>
<title>EXO HOMO 1</title>
<color>white</color>
<size>200</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS OPT FREQ B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>EXO HOMO 2</title>
<color>white</color>
<size>200</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS OPT FREQ B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>EXO LUMO 1</title>
<color>white</color>
<size>200</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS OPT FREQ B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>EXO LUMO 2</title>
<color>white</color>
<size>200</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS OPT FREQ B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
<br>
{|style="margin: 0 auto;"
| <jmol>
<jmolApplet>
<title>ENDO HOMO 1</title>
<color>white</color>
<size>200</size>
<script>frame 30; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS OPT FREQ TS B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>ENDO HOMO 2</title>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS OPT FREQ TS B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>ENDO LUMO 1</title>
<color>white</color>
<size>200</size>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS OPT FREQ TS B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>ENDO LUMO 2</title>
<color>white</color>
<size>200</size>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS OPT FREQ TS B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
<br>
[[File:Exercise 2 mo edited pk1615.PNG|thumb|400px|centre|Figure 3:Molecular orbital diagram of Cyclohexadiene and 1,3-Dioxole TS (the exo TS has been draw, however, the same orbitals apply for the endo TS)]]

According to symmetry the cyclohexadiene and 1,3-dioxole MO's can be considered as the butadiene and ethene MO's from figure 2 respectively. The energy levels of the reactant and TS orbitals has been determined from their B3LYP/6-31G(d) optimised .chk file MO's, and have been positioned accordingly. It is observed that the energy level of these MO's is slightly shifted compared to the butadiene ethene MO's. The cyclohexadiene HOMO is lower in energy than the 1,3-dioxole HOMO, whereas, in figure 2, the butadiene HOMO is higher in energy compared to the ethene HOMO. It is to be noted that both the exo and endo TS have different geometries, however,they both contain the same molecular orbital combinations, therefore, one molecular orbital diagram has been drawn for both.
<br>
The .log files for the B3LYP/6-31G(d) optimised molecules can be found here:[[Media:CYCLOHEXANE OPT FREQ MIN B pk1615.LOG|Cyclohexadiene]], [[Media:CYCLOPENTADIENE OPT FREQ MIN B pk1615.LOG|1,3-dioxole]], [[Media:EXO TS OPT FREQ B pk1615.LOG |Exo TS]], [[Media:ENDO_TS_OPT_FREQ_TS_B pk1615.LOG|Endo TS]], [[Media:EXO PRODUCT OPT FREQ MIN B. pk1615LOG|Exo product]], [[Media:ENDO PRODUCT OPT FREQ MIN B pk1615.LOG|Endo product]].

===Normal and Inverse demand Diels-Alder reaction analysis===
In a normal demand Diels-Alder reaction the HOMO of the electron rich diene reacts with the LUMO, π<sup>*</sup> bond, of the electron deficient dienophile ( the substituted alkene). In a normal demand reaction the HOMO of the diene reacts with the LUMO of the dienophile to form the HOMO and LUMO of the TS, this is seen in the reaction between butadiene (diene) and ethene (dienophile), figure 2, which produces HOMO 2 and LUMO 1.
<br>
In an inverse demand reaction, an electron deficient diene's LUMO now reacts with an electron rich dienophile's HOMO. This occurs due to a switch in energies of the diene's and dienophile's orbitals which occurs when an electron withdrawing group is attached to the diene, lowering its HOMO, and/or an electron donating group is attached to the dienophile, raising its π orbital's energy making it's HOMO higher in energy. This leads to the dienophile HOMO being high enough in energy to react with the diene's LUMO. This case is seen in the reaction between cyclohexadiene and 1,3-dioxole, figure 3, in which the dienophile, 1,3-dioxole, has electron donating oxygen atoms attached to it, raising its HOMO and allowing the TS HOMO 2 and LUMO 1 to be reached in an inverse demand reaction.
[[File:Inverse demand pk1615 .PNG|thumb|400px|centre|Figure 4:Diels-Alder normal and inverse reaction molecular orbital analysis]]

===Energy calculations===
The Sum of electronic and thermal Free Energies for each molecule has been taken from the B3LYP/6-31G(d) optimised .log files
{| class="wikitable"
|+ Table 2-Molecule energies.
! Molecule
! Energy (Hatree)
! Energy (kJ/mol)
|-
| Cyclohexadiene
| -233.324374
| -612593.1906
|-
| 1,3-dioxole
| -267.068642
| -701188.773
|-
| Reactants combined
| -500.393016
| -1313781.964
|-
| Endo TS
| -500.332146
| -1313622.149
|-
| Exo TS
| -500.329167
| -1313614.328
|-
| Endo product
| -500.418692
| -1313849.376
|-
| Exo product
| -500.417319
| -1313845.771
|}

{| class="wikitable"
|+ Table 3-Endo and Exo reaction barriers and energies.
! Reaction
! Reaction barrier (kJ/mol)
! Reaction energy (kJ/mol)
|-
| Endo
| 159.8142
| -67.41234
|-
| Exo
| 167.63557
| -63.80753
|}

Table 2 gives energy values of reactants, TS's and products for both the exo and endo geometries. These energy values were used to obtain calculations of the reaction barriers, also known as the activation energies, and the reaction energies for the endo and exo reaction pathways, table 3. The reaction barrier is the maximum energy in the reaction pathway which needs to be overcome for a reaction to proceed to its product. The reaction barrier energy is calculated as the TS minus the reactants and is the energy value needed to reach the maximum in the potential energy surface of the system. Furthermore, the reaction energy is calculated as the reactant minus the products and is the energy obtained when the minimum of the potential energy surface is reached. The results of the energy barriers and energies shown that the endo product is both the kinetically and thermodynamically stable product. This is explained through secondary orbital interactions that occur in the endo product between the ring π bond and the oxygen p-orbitals displayed in figure 5.
<br>
[[File:Endo stabilisation pk1615.PNG|thumb|400px|centre|Figure 5:Endo product secondary orbital stabilisation interaction]]
<br>
These secondary orbital interactions stabilise the product, making the endo product the lowest energy product, the thermodynamic one. Additionally, through stabilising the product these secondary orbital interactions lower the energy barrier of the endo reaction making it the more kinetically stable one as well. The kinetic product has the lower energy barrier i.e less energy is needed to overcome its activation energy. Moreover, steric reasons that may affect the exo product, making it both thermodynamically and kinetically less stable, are the repulsive interactions that could occur between the bridgehead carbons of the ring and the 1,3-dioxole oxygens that are closer in the exo geometry. This could lead to destabilisation of the exo product molecule.

==Exercise 3==
[[File:Diels alder cheletropic pk1615.PNG|thumb|400px|centre|Scheme 3:Diels-Alder/Cheletropic reaction of o-Xylylene and SO<sub>2</sub>]]
This exercise involves studying the Diels-Alder and Cheletropic reactions between o-Xylylene- and SO<sub>2</sub>, dispayed in scheme 3.
<br>
The IRC for the three reaction pathways can be found here: [[Media:XYLENE ENDO IRC pk1615.LOG|Diels-Alder endo]], [[Media:XYLENE EXO IRC PM6 pk1615.LOG|Diels-Alder exo]], [[Media:ISO-INDENE IRC PM6 pk1615.LOG|Cheletropic]].
<br>
The PM6 optimised .log files for the reaction molecules can be found here: [[Media:XYLYLENE REACTANT OPT MIN PM6 pk1615.LOG|o-Xylylene]], [[Media:SO2 OPT MIN PM6 pk1615.LOG|SO<sub>2</sub>]], [[Media:XYLENE OPT TS PM6 ENDO pk1615.LOG|Endo TS]], [[Media:XYLENE OPT TS PM6 exo pk1615.LOG|Exo TS]], [[Media:ISO-INDENE OPT TS PM6 pk1615.LOG|Cheletropic TS]], [[Media:XYLENE OPT MIN PM6 ENDO pk1615.LOG|Endo product]], [[Media:XYLENE OPT MIN PM6 pk1615 exo.LOG|Exo product]], [[Media:ISO-INDENE OPT MIN PM6 pk1615.LOG|Cheletropic product]].
===Energy calculations===
The Sum of electronic and thermal Free Energies for each molecule has been taken from the PM6 optimised .log files.
{| class="wikitable"
|+ Table 4-Molecule energies.
! Molecule
! Energy (Hatree)
! Energy (kJ/mol)
|-
| ortho-Xylylene
| 0.177678
| 466.493625
|-
| SO<sub>2</sub>
| -0.119269
| -313.1407834
|-
| Reactants
| 0.058409
| 153.352841
|-
| DA Endo TS
| 0.090560
| 237.765298
|-
| DA Exo TS
| 0.092077
| 241.748182
|-
| Cheletropic TS
| 0.099061
| 260.084675
|-
| DA Endo product
| 0.021705
| 56.9864818
|-
| DA Exo product
| 0.021454
| 56.3274813
|-
| Cheletropic Product
| 0.000005
| 0.013127501
|}

{| class="wikitable"
|+ Table 5-Reaction barriers and energies.
! Reaction
! Reaction barrier (kJ/mol)
! Reaction energy (kJ/mol)
|-
| Endo
| 84.4124569
| -96.3663593
|-
| Exo
| 88.3953407
| -97.0253599
|-
| Cheletropic
| 106.731834
| -153.339714
|}
<br>
The most favourable route in this reaction is the endo route. As seen in table 5 the endo TS has the lowest reaction barrier energy, therefore, it is easier to overcome this reaction barrier to reach the TS and get a product. This lower energy barrier value is due to the endo TS and product having the secondary orbital interactions stated above; now between the oxygen p orbital and the pi orbitals of the conjugated benzene ring. These secondary orbital interactions stabilise the molecule, lowering its reaction energies. It is to be noted that the cheletropic product is the more thermodynamically stable one but has a very high energy barrier which is unfavourable to reach as a lot of energy is needed to overcome it; this is an undesirable route. The endo product is the kinetically stable one and is the route that is preferred.
<br>
[[File:Exercise 3 reaction coordinate 3.PNG|thumb|400px|centre|Figure 6:Reaction profile diagram]]
<br>
Observing the IRC paths for the three reaction TS's, it can be seen that the xylylene 6-membered ring bonds change in length as the reaction proceeds from reactants to products through the TS. The xylylene ring obtains aromaticity as the bond length changes, this could be a considered a driving force for the reaction and proves the molecule's instability as it readily rearranges as the reaction proceeds to the product.

===An alternative reaction route===
An alternative reaction route can occur in the Diels-Alder reaction between o-Xylylene and SO<sub>2</sub>, where the SO<sub>2</sub> molecule reacts with the diene inside the six-membered ring of the xylylene molecule. This approach is displayed in scheme 4.
[[File:Alternative route pk1615.PNG|thumb|400px|centre|Scheme 4:Diels-Alder alternative reaction of o-Xylylene and SO<sub>2</sub>]]
{| class="wikitable"
|+ Table 6-Reaction barriers and energies.
! Reaction
! Energy barrier (kJ/mol)
! Reaction energy (kJ/mol)
|-
| Endo
| 114.631969
| -18.906229
|-
| Exo
| 122.469083
| -23.353824
|}
<br>
This endo and exo route are neither thermodynamically or kinetically stable since they have high reaction energies (are not stable) and have high energy barriers. These high energy barriers require large amounts of energy to be overcome which is undesirable and would lead to products that are not very thermodynamically stable.
<br>
The IRC for the the alternative reaction pathways can be found here: [[Media:ENDO TS IRC pk1615.LOG|Alternative Diels-Alder endo]], [[Media:EXO TS IRC pk1615.LOG|Alternative Diels-Alder exo]].

==Further work==
An electrocyclic reaction is a pericyclic reaction that involves a rearrangement of a pi to a sigma bond to form a ring product, such as the one displayed in scheme 5.
[[File:Electrocyclic pk1615.PNG|thumb|400px|centre|Scheme 5: Electrocyclic reaction.]]
<br>
[[File:Further work disrotation pk1615.PNG|thumb|400px|centre|Figure 7: Electrocyclic reaction orbital alignment.]]
<br>
The molecular orbital interactions that yield the ring product are shown in figure 7. It can be seen that the orbitals move in a disrotary fashion. The TS of the molecule was optimised to the PM6 level and the MO's where identified in order to confirm their movement.
<br>
{|style="margin: 0 auto;"
| [[File:Further work reactant MO pk1615.PNG|thumb|upright|344x344px|Figure 8: Reactant MO (1).]]
| [[File:Further work TS MO pk1615.PNG|thumb|upright|344x344px|Figure 9: TS MO (3).]]
|}
<br>
Even though the PM6 level of optimisation is the most accurate for viewing the correct symmetry of the MO's; it is concluded through the MO's that this electrocyclic reaction proceeds with disrotation, as they allign as expects in the TS of the molecule leading to the formation of the sigma bond. A higher level of optimisation would be more suitable to determine the direction of orbital movement.
<br>
The IRC for the TS can be found [[Media:TS IRC pk1615.LOG|here]].
<br>
The PM6 optimised .log files can be found here: [[Media:REACTANTS OPT MIN PM6 pk1615.LOG|Reactant]], [[Media:PRODUCT OPT TS PM6 pk1615.LOG|TS]], [[Media:PRODUCT OPT MIN PM6 pk1615.LOG|Product]].

==Conclusion==
==References==
<references>
<ref name="intro">Computational Quantum Chemistry. Chapter 1, 2013, Pages 1-62.</ref>
<ref name="C length">B.P. Stoicheff. "The variation of carbon-carbon bond lengths with environment as determined by spectroscopic studies of simple polyatomic molecules". Tetrahedron, Vol 17, Issues 3–4, 1962, Pages 135-145.</ref>
<ref name="C radius">A Bondi. "Van der Waals Volumes and Radii". J. Phys. Chem., 68 (3), 1964, Pages 441–451.</ref>
</references>

2018-03-10T20:41:28Z

Pk1615: /* Carbon-Carbon bond length analysis */

=Transition states and reactivity=

==Introduction==
This experiment involves using computational quantum chemistry methods to analyse molecular structures, their molecular orbitals and energetics. Providing information about reaction pathways, activation energies and transition state intermediates. The transition state structures are based on the shape of the potential energy surface; these are found through computational molecular-orbital based methods by solving the Schrödinger equation.
<br>
The potential Energy Surface describes the energy of a system in terms of parameters such as the positions of atoms in a structure. Using computational methods the points of a potential energy surface can be determined and analysis of their first and second derivatives yields important information about the systems reaction energetics. The first derivatives give the gradient and the second derivatives give the curvature of the potential energy surface. Points with zero gradient can be minima which correspond to reactants or products or can be saddle points, energy maxima, that represent transition state species. The transition state is an intermediate in the reaction pathway that requires maximum energy to be overcome leading to products, it is an intermediate structure between reactants and products and is a maximum in the potential energy surface.
<br>
The computational methods used to optimise and run frequency calculations is the semi-empirical method PM6 and the density Functional Theory (DFT) method B3LYP. The optimised structure results yield vibrational frequencies that can be studied to give results about if a structure is at the minimum or maximum of the potential energy surface. A negative frequency calculation indicates that a structure is at a minimum since less energy needed to jump over surface ?????????
<br>

==Exercise 1==

[[File:Overall reaction pk1615.PNG|thumb|400px|centre|Scheme 1:Diels-Alder reaction of butadiene and ethene]]

The transition state of the Diels-Alder reaction between butadiene and ethene, shown above in scheme 1, will be studied. This reaction involves a [4+2] cycloaddition between the two reactant molecules resulting in a ring product. Using the PM6 optimisation for both reactants, the energy levels of the MO's were obtained and are diplayed below.
<br>

===Molecular orbital analysis===

Optimising the reactants, transition state and product molecules revealed the energies and shape of the molecular orbitals for each structure. This then helped to identify the reactant HOMO and LUMO MO's that reacted to form the transition state, leading to the construction of the molecular orbital diagram for the transition state, figure 2.
{|style="margin: 0 auto;"
| [[File:Mos of butadiene ethene word pk1615.PNG|thumb|upright|344x344px|Figure 1:Molecular orbital energy levels of butadiene and ethene.]]
| [[File:Mo diagram butadiene pk1615.PNG|thumb|upright|500x500px|Figure 2:Molecular orbital diagram of the Diels-Alder transition state.]]
|}

{| class="wikitable"
! Ethene MO's
! Butadiene MO's
! Transition state Mo's
|-
| Ethene-φ1 HOMO
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT MINpk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| Butadiene-φ2 HOMO
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE OPT MIN PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| Transition state HOMO 1
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Ethene-φ2 LUMO
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT MINpk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| Butadiene-φ3 LUMO
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE OPT MIN PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| Transition state HOMO 2
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|
|
| Transition state LUMO 1
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|
|
| Transition state LUMO 2
<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The Jmols of the MO of the reactants and TS have been displayed above. It is observed that for a molecular orbital to react successfully and produce a product they need to be of the same symmetry. In the MO diagram it can be seen that symmetric reacts with symmetric and anti-symmetric reacts with anti-symmetric orbitals.If they are of different symmetry the reaction is disallowed.

The overlap integral for a symmetric-antisymmetric interaction is zero, whereas for a symmetric-symmetric or antisymmetric-antisymmetric interaction a non-zero value is obtained. The transition state MO diagram reveals that the transition state orbitals produced arise from s-s or a-a interactions, these inteaction contain non-zero overlap integrals, yielding true MO's.

===Carbon-Carbon bond length analysis===

{| class="wikitable"
|+ Table 1-Carbon-Carbon bond lengths of the reactants, TS and products.
! Carbon bonds
! Ethene bond lengths (Å)
[[File:Ethene pk1615.PNG]]
! Butadiene bond lengths (Å)
[[File:Butadiene pk1615.PNG]]
! Transition state bond lengths (Å)
[[File:Ts pk1615.PNG]]
! Cyclohexene bond lengths (Å)
[[File:Product pk1615.PNG]]
! Bond length change
|-
| C<sub>1</sub>-C<sub>2</sub>
| 1.327
| -
| 1.380
| 1.538
|Increase
|-
| C<sub>2</sub>-C<sub>3</sub>
| -
| -
| 2.115
| 1.536
|Decrease
|-
| C<sub>3</sub>-C<sub>4</sub>
| -
| 1.333
| 1.380
| 1.493
|Increase
|-
| C<sub>4</sub>-C<sub>5</sub>
| -
| 1.471
| 1.411
| 1.333
|Decrease
|-
| C<sub>5</sub>-C<sub>6</sub>
| -
| 1.333
| 1.380
| 1.493
|Increase
|-
| C<sub>6</sub>-C<sub>1</sub>
| -
| -
| 2.114
| 1.536
|Decrease
|}

The typical length for a C-C sp<sup>3</sup> bond is 1.54 Å, whereas the length of a C-C sp<sup>2</sup> bond is 1.34 Å <ref name="C length" />. In table 1 it can be seen that single and double bond values are approximately the same length as the typical values expected, confirming the structures obtained through optimisation. For example the bond between C<sub>1</sub>-<sub>2</sub> is seen to increase as the bond becomes sp<sup>3</sup> hybridised from sp<sup>2</sup>.
<br>
The Van der Waals radius of a carbon atom is 1.7 Å <ref name="C radius" />. In the Diels-Alder transition state is can be seen that the bonds that form between C<sub>6</sub>-C<sub>1</sub> and C<sub>2</sub>-C<sub>3</sub>, 2.1 Å, are shorter than two carbon Van der Waals radii values, 3.4 Å. This confirms that in the TS the molecules, that were far apart gradually come closer, when they are found within less than two carbon Van der Waals radii they approach the formation of a single bond that is found in the products.
<br>

===Transition state vibration===
The vibration that corresponds to the reaction path at the transition state is identified as the one with a negative frequency. The Diels-Alder transition state at this vibration is displayed below. It can be seen that at the transition state the bonds between the two reactants form in a synchronous manner, this is seen by the movement of the displacement vectors and is further confirmed by the analysis of the IRC that shows the reactions proceeds through a concerted mechanism. This is the typical mechanism pathway found for Diels-Alder cycloadditions.

<jmol>
<jmolApplet>
<title>Transition state vibration</title>
<color>white</color>
<size>300</size>
<script>frame 17; vibration 1;rotate x -20; </script>
<uploadedFileContents>CH OPT TS PM6 pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The IRC for the Diels-Alder transition state can be found [[Media:CH IRC PM6 pk1615.LOG|here]]
<br>
The .log file for the PM6 optimised cyclohexene TS can be found [[Media:CH OPT TS PM6 pk1615.LOG|here]]
<br>
The .log file for the PM6 optimised cyclohexene product can be found [[Media:CH OPT MIN PRODUCTS pk1615.LOG|here]]

==Exercise 2==
[[File:Exercise 2 overall reactionpk1615.PNG|thumb|400px|centre|Scheme 2:Diels-Alder reaction of Cyclohexadiene and 1,3-Dioxole]]
In this exercise the [4+2] cycloaddition reaction between cyclohexadiene and 1,3-dioxole is investigated. This Diels-Alder reaction yields two products, the exo and endo products, due to the different symmetries in the transition state.
<br>
===Molecular orbital analysis===

{|style="margin: 0 auto;"
| <jmol>
<jmolApplet>
<title>EXO HOMO 1</title>
<color>white</color>
<size>200</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS OPT FREQ B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>EXO HOMO 2</title>
<color>white</color>
<size>200</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS OPT FREQ B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>EXO LUMO 1</title>
<color>white</color>
<size>200</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS OPT FREQ B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>EXO LUMO 2</title>
<color>white</color>
<size>200</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS OPT FREQ B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
<br>
{|style="margin: 0 auto;"
| <jmol>
<jmolApplet>
<title>ENDO HOMO 1</title>
<color>white</color>
<size>200</size>
<script>frame 30; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS OPT FREQ TS B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>ENDO HOMO 2</title>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS OPT FREQ TS B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>ENDO LUMO 1</title>
<color>white</color>
<size>200</size>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS OPT FREQ TS B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>ENDO LUMO 2</title>
<color>white</color>
<size>200</size>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS OPT FREQ TS B pk1615.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
<br>
[[File:Exercise 2 mo edited pk1615.PNG|thumb|400px|centre|Figure 3:Molecular orbital diagram of Cyclohexadiene and 1,3-Dioxole TS (the exo TS has been draw, however, the same orbitals apply for the endo TS]]

According to symmetry the cyclohexadiene and 1,3-dioxole MO's can be considered as the butadiene and ethene MO's from figure 2 respectively. The energy levels of the reactant and TS orbitals has been determined from their B3LYP/6-31G(d) optimised .chk file MO's, and thave been positioned accordingly. However, the energy level of these MO's is slightly shifted. The cyclohexadiene HOMO is lower in energy than the 1,3-dioxole HOMO, whereas, in figure 2, the butadiene HOMO is higher in energy compared to the ethene HOMO. The molecular orbital diagram for the Cyclohexadiene and 1,3-Dioxole TS's have been drawn. It is to be noted that both the exo and endo TS have different geometries, however,they both contain the same molecular orbital combinations, therefore, one molecular orbital diagram has been drawn for both.
<br>
The .log files for the B3LYP/6-31G(d) optimised molecules can be found here:[[Media:CYCLOHEXANE OPT FREQ MIN B pk1615.LOG|Cyclohexadiene]], [[Media:CYCLOPENTADIENE OPT FREQ MIN B pk1615.LOG|1,3-dioxole]], [[Media:EXO TS OPT FREQ B pk1615.LOG |Exo TS]], [[Media:ENDO_TS_OPT_FREQ_TS_B pk1615.LOG|Endo TS]], [[Media:EXO PRODUCT OPT FREQ MIN B. pk1615LOG|Exo product]], [[Media:ENDO PRODUCT OPT FREQ MIN B pk1615.LOG|Endo product]].

===Normal and Inverse demand Diels-Alder reaction analysis===
In a normal demand Diels-Alder reaction the HOMO of the electron rich diene reacts with the LUMO, π<sup>*</sup> bond, of the electron deficient dienophile ( the substituted alkene). In a normal demand reaction the HOMO of the diene reacts with the LUMO of the dienophile, this is seen in the reaction between butadiene (diene) and ethene (dienophile), figure 2.
<br>
In an inverse demand reaction, an electron deficient diene's LUMO now reacts with an electron rich dienophile's HOMO. This occurs due to a switch in energies of the diene's and dienophile's orbitals which occurs when an electron withdrawing group is attached to the diene, lowering its HOMO, and/or an electron donating group is attached to the dienophile, raising its π orbital's energy making it's HOMO higher in energy. This leads to the dienophile HOMO being high enough in energy to react with the diene's LUMO. This case is seen in the reaction between cyclohexadiene and 1,3-dioxole, figure 3, in which the dienophile, 1,3-dioxole, has electron donating oxygen atoms attached to it, raising its HOMO and allowing the TS to be reached in an inverse demand reaction.
[[File:Inverse demand pk1615 .PNG|thumb|400px|centre|Figure 4:Diels-Alder normal and inverse reaction molecular orbital analysis]]

===Energy calculations===
The Sum of electronic and thermal Free Energies for each molecule has been taken from the B3LYP/6-31G(d) optimised .log files
{| class="wikitable"
|+ Table 2-Molecule energies.
! Molecule
! Energy (Hatree)
! Energy (kJ/mol)
|-
| Cyclohexadiene
| -233.324374
| -612593.1906
|-
| 1,3-dioxole
| -267.068642
| -701188.773
|-
| Reactants combined
| -500.393016
| -1313781.964
|-
| Endo TS
| -500.332146
| -1313622.149
|-
| Exo TS
| -500.329167
| -1313614.328
|-
| Endo product
| -500.418692
| -1313849.376
|-
| Exo product
| -500.417319
| -1313845.771
|}

{| class="wikitable"
|+ Table 3-Endo and Exo reaction barriers and energies.
! Reaction
! Reaction barrier (kJ/mol)
! Reaction energy (kJ/mol)
|-
| Endo
| 159.8142
| -67.41234
|-
| Exo
| 167.63557
| -63.80753
|}

Table 2 gives energy values of reactants, TS's and products for both the exo and endo geometries. These energy values were used to obtain calculation of the reaction barriers, also known as the activation energies, and the reaction energies for the endo and exo reaction pathways, table 3. The reaction barrier is known as the maximum energy in the reaction pathway which needs to be overcome for a reaction to proceed to its product. The results of the energy barriers and energies shown that the endo product is both the kinetically and thermodynamically stable product. This is explained through secondary orbital interactions that occur in the endo product displayed in figure 5.
<br>
[[File:Endo stabilisation pk1615.PNG|thumb|400px|centre|Figure 5:Endo product secondary orbital stabilisation interaction]]
<br>
These secondary orbital interactions stabilise the product, making the endo product the lowest energy product, the thermodynamic one. Additionally, through stabilising the product these secondary orbital interactions lower the energy barrier of the endo reaction making it the more kinetically stable one as well. The kinetic product has the lower energy barrier i.e less energy is needed to overcome its activation energy.

==Exercise 3==
This exercise involves studying the Diels-Alder and Cheletropic reactions between o-Xylylene- and SO<sub>2</sub>, dispayed in scheme 3.
[[File:Diels alder cheletropic pk1615.PNG|thumb|400px|centre|Scheme 3:Diels-Alder/Cheletropic reaction of o-Xylylene and SO<sub>2</sub>]]
<br>
The IRC for the three reaction pathways can be found here: [[Media:XYLENE ENDO IRC pk1615.LOG|Diels-Alder endo]], [[Media:XYLENE EXO IRC PM6 pk1615.LOG|Diels-Alder exo]], [[Media:ISO-INDENE IRC PM6 pk1615.LOG|Cheletropic]].
<br>
The PM6 optimised files for the reaction molecules can be found here: [[Media:XYLYLENE REACTANT OPT MIN PM6 pk1615.LOG|o-Xylylene]], [[Media:SO2 OPT MIN PM6 pk1615.LOG|SO<sub>2</sub>]], [[Media:XYLENE OPT TS PM6 ENDO pk1615.LOG|Endo TS]], [[Media:XYLENE OPT TS PM6 exo pk1615.LOG|Exo TS]], [[Media:ISO-INDENE OPT TS PM6 pk1615.LOG|Cheletropic TS]], [[Media:XYLENE OPT MIN PM6 ENDO pk1615.LOG|Endo product]], [[Media:XYLENE OPT MIN PM6 pk1615 exo.LOG|Exo product]], [[Media:ISO-INDENE OPT MIN PM6 pk1615.LOG|Cheletropic product]].
===Energy calculations===
The Sum of electronic and thermal Free Energies for each molecule has been taken from the PM6 optimised .log files.
{| class="wikitable"
|+ Table 4-Molecule energies.
! Molecule
! Energy (Hatree)
! Energy (kJ/mol)
|-
| ortho-Xylylene
| 0.177678
| 466.493625
|-
| SO<sub>2</sub>
| -0.119269
| -313.1407834
|-
| Reactants
| 0.058409
| 153.352841
|-
| DA Endo TS
| 0.090560
| 237.765298
|-
| DA Exo TS
| 0.092077
| 241.748182
|-
| Cheletropic TS
| 0.099061
| 260.084675
|-
| DA Endo product
| 0.021705
| 56.9864818
|-
| DA Exo product
| 0.021454
| 56.3274813
|-
| Cheletropic Product
| 0.000005
| 0.013127501
|}

{| class="wikitable"
|+ Table 5-Reaction barriers and energies.
! Reaction
! Reaction barrier (kJ/mol)
! Reaction energy (kJ/mol)
|-
| Endo
| 84.4124569
| -96.3663593
|-
| Exo
| 88.3953407
| -97.0253599
|-
| Cheletropic
| 106.731834
| -153.339714
|}
<br>
The most favourable route in this reaction is the endo route. As seen in table 5 the endo TS has the lowest energy, therefore, it is easier to overcome this TS and get products. This lower value is due to the endo TS and product having the secondary orbital interactions that were stated above, stabilising the molecules, lowering the reaction energies. It is to be noted that the cheletropic product is the most thermodynamically stable one but has a very high energy barrier which is unfavourable to reach as a lot of energy is needed; this is an undesirable route. The endo product is the kinetically stable one and is the route that is preferred.
<br>
[[File:Exercise 3 reaction coordinate 3.PNG|thumb|400px|centre|Figure 6:Reaction profile diagram]]
<br>
Observing the IRC paths for the three reaction TS's, it can be seen that the xylene 6-membered ring bonds change in legth as the reaction proceeds since the ring obtains aromaticity through resonance forms.

===An alternative reaction route===
An alternative reaction route can occur in the Diels-Alder reaction between o-Xylylene and SO<sub>2</sub>, where the SO<sub>2</sub> molecule reacts with the diene inside the six-membered ring of the xylylene molecule. This approach is displayed in scheme 4.
[[File:Alternative route pk1615.PNG|thumb|400px|centre|Scheme 4:Diels-Alder alternative reaction of o-Xylylene and SO<sub>2</sub>]]
{| class="wikitable"
|+ Table 6-Reaction barriers and energies.
! Reaction
! Energy barrier (kJ/mol)
! Reaction energy (kJ/mol)
|-
| Endo
| 114.631969
| -18.906229
|-
| Exo
| 122.469083
| -23.353824
|}
<br>
This endo and exo route are neither thermodynamically or kinetically stable since they have high reaction energies (are not stable) and have high energy barriers.
<br>
The IRC for the the alternative reaction pathways can be found here: [[Media:ENDO TS IRC pk1615.LOG|Alternative Diels-Alder endo]], [[Media:EXO TS IRC pk1615.LOG|Alternative Diels-Alder exo]].

==Further work==
[[File:Further work scheme pk1615.PNG|thumb|400px|centre|Scheme 5: Electrocyclic reaction.]]
<br>
[[File:Further work disrotation pk1615.PNG|thumb|400px|centre|Figure 7: Electrocyclic reaction orbital alignment.]]
<br>
{|style="margin: 0 auto;"
| [[File:Further work reactant MO pk1615.PNG|thumb|upright|344x344px|Figure 8: Reactant MO (1).]]
| [[File:Further work TS MO pk1615.PNG|thumb|upright|344x344px|Figure 9: TS MO (3).]]
|}

<br>

It is concluded through the MO's that this electrocyclic reaction proceeds with disrotation.
<br>
The IRC for the TS can be found [[Media:TS IRC pk1615.LOG|here]].
<br>
The PM6 optimised .log files can be found here: [[Media:REACTANTS OPT MIN PM6 pk1615.LOG|Reactant]], [[Media:PRODUCT OPT TS PM6 pk1615.LOG|TS]], [[Media:PRODUCT OPT MIN PM6 pk1615.LOG|Product]].

==References==
<references>
<ref name="C length">B.P. Stoicheff. "The variation of carbon-carbon bond lengths with environment as determined by spectroscopic studies of simple polyatomic molecules". Tetrahedron, Vol 17, Issues 3–4, 1962, Pages 135-145.</ref>
<ref name="C radius">A Bondi. "Van der Waals Volumes and Radii". J. Phys. Chem., 68 (3), 1964, Pages 441–451.</ref>
</references>