File:Ircgraphns2214.jpg

2017-03-23T22:40:17Z

Ns2214: Ns2214 uploaded a new version of File:Ircgraphns2214.jpg

Rep:Mod:tsns2214

2017-03-23T22:18:12Z

Ns2214: /* Exercise 2 */

'''Transition States'''
=Introduction=
Potential energy surfaces display the energy of a system with respect to positions of the molecules. They can therefore be used to display transition states in a molecule. Transition states are an energy maximum where the gradient is 0, i.e. a turning point.However, depending on the complexity of the reaction, there can be many maxima on a PES as there are different trajectories predicted. If a transition state has been correctly found, it will have a saddle-point geometry where it is the maximum on its particular reaction co-ordinate, but the minimum compared to other pathways. There is an equal probability of falling down the potential energy curve to form either reactants or products at a transition state.

In this lab, the transition states of Diels-Alder reactions were studied. This involves a [4+2] cycloaddition between a diene and dienophile. These double bonded structures are close enough in energy to interact and form 2 new sigma bonds and breaking one pi bond overall. The formation of theses sigma bonds lowers the energy of the system as electrons occupy bonding molecular orbitals.

Gaussian software was used to analyse the transition state formation of three Diels-Alder reactions. Method 3 in the tutorial was used for all the reactions, where the expected product molecule was optimised, the relevant bonds broken and frozen, and then the resulting transition state optimised. Two levels of optimisation were used: PM6 semi-empirical for exercises 1 and 3 and B3LYP-DFT for exercise 2. PM6 uses relevant parameters to fit experimental dipole moments and geometries, allowing for faster results as some integrals are pre-determined. B3LYP however uses electron density in the molecule to optimise the structure and base it calculations on. If the correct transition state was found, there was one negative frequency found in the vibrations, corresponding to..

Several consideration have to be taken into account when studying Diels-Alder reactions. One is that the diene and dienophile's HOMO and LUMOs are are relatively close to each other. The smaller energy gap between a HOMO-LUMO pair depended on the nature of the reactants and their electron densities. The checkpoint files obtained from optimisations gave insight into the closer energy levels and thus explained the products formed. Another consideration was that a molecule, such as xylylene, could have multiple reaction sites or the molecules could approach each other at different geometries. Once transition state structures had been optimised, IRC analysis was conducted to confirm the transition state path. If there were multiple approach possibilities and transition state structures, the free energy data could be extracted from the log files, in order to find the thermodynamic and kinetic products.
FIRST DERIVATIVE PF ORC
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=Exercise 1: 1,3-Butadiene and Ethene=
The first Diels-Alder reaction characterised was between 1,3-butadiene and ethene, forming cyclohexene. Visualising the molecular orbitals for the optimised reactants, products and transition state enabled for an orbital diagram to be drawn ('''Figure 1'''). It is evident that the formation of molecular orbitals is restricted by symmetry. Orbitals of the same symmetry/asymmetry can interact and bring stability to the molecule.
[[File:CyclohexadieneMODiagramns2214.jpg|300px|thumb|center|'''Figure 1''' Cyclohexene MO Diagram]]
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Looking at the values for the optimised reactants, the HOMO of the butadiene (-0.35899) and LUMO of the ethene (0.04256) are closer in energy and therefore the energy gap between the bonding and anti-bonding orbitals formed is larger. The energy difference between the HOMO ethene and LUMO butadiene is [(0.01943+0.39228)-(0.04256+0.35899)]=0.01006 larger giving a smaller energy gap in molecular orbitals formed. The orbital overlap is non-zero for a symmetric-symmetric or asymmetric-asymmetric interaction, and zero for an asymmetric-symmetric interaction, as in the latter interaction, one pair of p orbitals are in the phase and the other pair out of phase, effectively cancelling each other out.
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{| class="wikitable" style="margin: auto;"
|+ Exercise 1 Molecular Orbitals
|-
| style="text-align: center;"| PM6
! colspan="1" style="text-align: center;"|Ethene
! colspan="1" style="text-align: center;"|Butadiene
! colspan="2" style="text-align: center;"|Transition States
|-
! rowspan="1" style="text-align: center;"|LUMO
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|-
|}
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{| class="wikitable" border="1" align="right"
|+
|-
! colspan="5" style="text-align: center;"|Carbon numbering and bond lengths ('''Å''')
|-
| colspan="5" align="center"|[[File:TScarbonnumberns2214.jpg|250px|thumb|center|'''Figure 3''' Carbon numbering used by Gaussian]]
|-
! style="text-align: center;"|
! style="text-align: center;"|C1-C2/C5-C6
! style="text-align: center;"|C2-C3/C4-C5
! style="text-align: center;"|C3-C4
! style="text-align: center;"|C6-C1
|-
! rowspan="1" style="text-align: center;"| Reactants
| rowspan="1" style="text-align: center;"| -
| rowspan="1" style="text-align: center;"| 1.333
| rowspan="1" style="text-align: center;"| 1.471
| rowspan="1" style="text-align: center;"| 1.327
|-
! rowspan="1" style="text-align: center;"| Transition State
| rowspan="1" style="text-align: center;"| 2.115
| rowspan="1" style="text-align: center;"| 1.380
| rowspan="1" style="text-align: center;"| 1.411
| rowspan="1" style="text-align: center;"| 1.382
|-
! rowspan="1" style="text-align: center;"| Product
| rowspan="1" style="text-align: center;"| 1.537
| rowspan="1" style="text-align: center;"| 1.501
| rowspan="1" style="text-align: center;"| 1.337
| rowspan="1" style="text-align: center;"| 1.535
|-
|}
[[File:Ircgraphns2214.jpg|500px|thumb|left|'''Figure 2''' Graph showing internuclear distances during cyclohexene formation]]
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The graph in '''Figure 2''' displays how the C-C bonds change in length as the reactants approach the transition state and then form the products. Well before the transition state is reached, all bond lengths remain constant except for C1-C2 and C5-C6 as the ethene and butadiene molecules approach each other. Typical sp<sup>2</sup> C-C bond length at this stage is around 1.336 Å. Just before the transition state is approached, C1-C2 and C5-C6 continue to descend, but the other bond lengths appear to converge as the cyclisation occurs.

The four bond lengths converge just after the transition state. The bond length between the newly forming C1-C2 and C5-C6 is 2.115 Å at the transition state. This is significantly smaller than the Van Der Waal's radius of two Carbon atoms (1.7x2= 3.4 Å). This suggests that bond formation is occurring throughout the transition state, especially as the bond length continues to decrease linearly and plateau at a value of ~1.54 Å, the typical C-C sp<sup>3</sup> sigma bond length. What seems to define the transition state of cyclohexene is the convergence of the four other bond lengths
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The vibration at the transition state has a negative frequency. Looking at the vectors displayed for this vibration, it appears that the bond formation is synchronous. Therefore only one stereoisomer forms from the Diels-Alder reaction as there is no possibility of bond rotation before the second bond forms.
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=Exercise 2=
{| class="wikitable" border="1" align="left"
|+ Exercise 2 Molecular Orbitals
|-
| style="text-align: center;"| B3LYP
! colspan="2" style="text-align: center;"|EXO Transition States
! colspan="2" style="text-align: center;"|ENDO Transition States
|-
! rowspan="1" style="text-align: center;"|LUMO
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[[File:Cyclohexadiene13DDiagramNS2214.jpg|250px|thumb|right|'''Figure 4''' Cyclohexadiene and 1,3-Dioxole MO Diagram]]
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{| class="wikitable" border="1" align="right"
|+ Table of Gibbs Free Energies and Reaction Barriers
|-
! style="text-align: center;"| (B3LYP level)
! colspan="2" style="text-align: center;"|Gibbs Free Energy
! colspan="2" style="text-align: center;"|Reaction Barrier
|-
! rowspan="1" style="text-align: center;"|
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
|-
! rowspan="1" style="text-align: center;"| Exo
| rowspan="1" style="text-align: center;"| 0.138901
| rowspan="1" style="text-align: center;"|
| rowspan="1" style="text-align: center;"| 0.07429
| rowspan="1" style="text-align: center;"|
|-
! rowspan="1" style="text-align: center;"| Endo
| rowspan="1" style="text-align: center;"| 0.137942
| rowspan="1" style="text-align: center;"|
| rowspan="1" style="text-align: center;"| 0.073331
| rowspan="1" style="text-align: center;"|
|-
|}
Following the progress of the reaction between cyclohexadiene and 1,3-dioxole produced different results to exercise 1. Here, a typical inverse demand Diels-Alder reaction was seen, where the diene's HOMO and dienophile's LUMO formed the molecular HOMO and LUMO orbitals of the transition state ('''Figure 4'''). Energy levels of the HOMO and LUMO for each reactant were obtained from the checkpoint files. The energy gap between the diene's HOMO and dienophiles's LUMO is 0.18589 and therefore smaller than the diene's LUMO and dienophiles's HOMO energy gap of 0.21191. The smaller energy gap results in greater splitting. The electron rich nature of the diene 1,3-dioxole is due to the oxygen atoms adjacent to the double bond. The mixing of p orbitals raises the energy of the diene's HOMO and brings it closer to the dienophile's LUMO.

The Gibbs free energies were extracted from the log files of the reactants and transition states and the reaction barriers calculated accordingly ('''Figure 5'''). The endo-conformer of the product has a lower reaction barrier, being 7.842 KJmol<sup>-1</sup> smaller in value. This therefore makes it the kinetic product as less energy is required to overcome the barrier and thus over time, it will form more quickly. The stability of the transition state in the endo-form is most likely due to secondary orbital interaction. From the table and in '''Figure 6''' it can clearly be seen in the transition state HOMO where the p orbitals of cyclohexadiene are able to interact with the oxygen p orbitals, bringing some stability to the transition state. The endo product also has a lower product energy, final value being 0.446 KJmol<sup>-1</sup> lower than the exo product, making it the thermodynamic product too.
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[[File:Ex2rxncoordns2214.jpg|500px|thumb|center|alt text]]

=Exercise 3=
{| class="wikitable" border="1" align="right"
|+ Table of Gibbs Free Energies and Reaction Barriers for o-Xylylene-SO2 Cycloaddition
|-
! style="text-align: center;"|(PM6 level)
! colspan="2" style="text-align: center;"|Gibbs Free Energy
! colspan="2" style="text-align: center;"|Reaction Barrier
|-
! rowspan="1" style="text-align: center;"|
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
|-
! rowspan="1" style="text-align: center;"| Exo
| rowspan="1" style="text-align: center;"| 0.0326
| rowspan="1" style="text-align: center;"|85.497
| rowspan="1" style="text-align: center;"| -0.0381
| rowspan="1" style="text-align: center;"| -99.924
|-
! rowspan="1" style="text-align: center;"| Endo
| rowspan="1" style="text-align: center;"| 0.0310
| rowspan="1" style="text-align: center;"| 81.517
| rowspan="1" style="text-align: center;"| -0.0378
| rowspan="1" style="text-align: center;"| -99.283
|-
! rowspan="1" style="text-align: center;"| Chelotropic
| rowspan="1" style="text-align: center;"| 0.03955
| rowspan="1" style="text-align: center;"|103.839
| rowspan="1" style="text-align: center;"| -0.0583
| rowspan="1" style="text-align: center;"| -152.972
|-
! rowspan="1" style="text-align: center;"| Unfavourable Exo
| rowspan="1" style="text-align: center;"|0.045542
| rowspan="1" style="text-align: center;"|119.571
| rowspan="1" style="text-align: center;"| 0.007792
| rowspan="1" style="text-align: center;"| 20.458
|-
! rowspan="1" style="text-align: center;"| Unfavourable Endo
| rowspan="1" style="text-align: center;"| 0.042557
| rowspan="1" style="text-align: center;"|111.733
| rowspan="1" style="text-align: center;"| 0.006098
| rowspan="1" style="text-align: center;"| 16.010
|-
|}[[File:RXNCOORDNS2214.jpg|400px|thumb|right]]
Once again, the free energies of the reactants, transition states and products were extracted from the log files, optimised at the PM6 level. The endo conformer has the lowest energy barrier, 3.98 KJmol<sup>-1</sup> lower than exo, making it the kinetic product. The chelotropic and unfavourable transition states were significantly higher. The chelotropic has a high energy transition state because there are no possible stabilising orbital interactions as the sulphur dioxide approaches with the sulphur atom forward and oxygens facing away. The unfavourable endo and exo transition states have the highest energy. This is partly due to steric clashes with the xylylene molecule as sulphur dioxide approaches, resulting in destabilisation. The most significant factor is in fact the lack of aromaticity in the reaction. Conducting the Diels-Alder reaction with thee dienophile site in the ring means that it can't be aromatised and thus lower the energy of the system like with the other three reactions. The unfavourable conformers show just how unstable xylylene is compared to the products that can be formed. Both endo conformers are lower in transition state energy than the exo ones because of the secondary orbital overlap taking place, as mentioned in exercise 2.

The unfavourable endo and exo products also have the highest product energies. The positive value in the relative energies reaction co-ordinate makes it less stable than the reactants. There is no drive for the reaction as ∆G is positive. The high activation barrier and reaction energy makes these pathways kinetically and thermodynamically unfavourable. The chelotropic product has the lowest energy thereby making it the thermodynamic product. It is just over 50 KJmol<sup>-1</sup> more stable than the exo and endo products. Under reversible conditions, the chelotropic would be the majority product.
{| class="wikitable" border="1" align="center"
|+ IRC pathways for o-Xylylene-SO2 Cycloaddition
|-
! colspan="2" style="text-align: center;"|Diels-Alder
! colspan="1" style="text-align: center;"|Chelotropic
|-
! rowspan="1" style="text-align: center;"|Exo
! rowspan="1" style="text-align: center;"|Endo
! rowspan="1" style="text-align: center;"|
|-
|rowspan="1" style="text-align: center;"|[[File:IRC exo3ns2214.gif|400px|thumb|center]]
|rowspan="1" style="text-align: center;"|[[File:ENDOTStrajectoryns2214.gif|400px|thumb|center]]
|rowspan="1" style="text-align: center;"|[[File:IRCTSchelns2214traj.gif|400px|thumb|center]]
|-
! rowspan="1" style="text-align: center;"|Unfavourable Exo
! rowspan="1" style="text-align: center;"|Unfavourable Endo
|-
|rowspan="1" style="text-align: center;"|[[File:IRCexovidunfavns2214.gif|400px|thumb|center]]
|rowspan="1" style="text-align: center;"|[[File:IRCendovidunfavns2214.gif|400px|thumb|center]]
|-
|}
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=Conclusion=

File:Ex2rxncoordns2214.jpg

2017-03-23T22:14:32Z

Ns2214:

Rep:Mod:tsns2214

2017-03-23T22:13:39Z

Ns2214: /* Exercise 3 */

'''Transition States'''
=Introduction=
Potential energy surfaces display the energy of a system with respect to positions of the molecules. They can therefore be used to display transition states in a molecule. Transition states are an energy maximum where the gradient is 0, i.e. a turning point.However, depending on the complexity of the reaction, there can be many maxima on a PES as there are different trajectories predicted. If a transition state has been correctly found, it will have a saddle-point geometry where it is the maximum on its particular reaction co-ordinate, but the minimum compared to other pathways. There is an equal probability of falling down the potential energy curve to form either reactants or products at a transition state.

In this lab, the transition states of Diels-Alder reactions were studied. This involves a [4+2] cycloaddition between a diene and dienophile. These double bonded structures are close enough in energy to interact and form 2 new sigma bonds and breaking one pi bond overall. The formation of theses sigma bonds lowers the energy of the system as electrons occupy bonding molecular orbitals.

Gaussian software was used to analyse the transition state formation of three Diels-Alder reactions. Method 3 in the tutorial was used for all the reactions, where the expected product molecule was optimised, the relevant bonds broken and frozen, and then the resulting transition state optimised. Two levels of optimisation were used: PM6 semi-empirical for exercises 1 and 3 and B3LYP-DFT for exercise 2. PM6 uses relevant parameters to fit experimental dipole moments and geometries, allowing for faster results as some integrals are pre-determined. B3LYP however uses electron density in the molecule to optimise the structure and base it calculations on. If the correct transition state was found, there was one negative frequency found in the vibrations, corresponding to..

Several consideration have to be taken into account when studying Diels-Alder reactions. One is that the diene and dienophile's HOMO and LUMOs are are relatively close to each other. The smaller energy gap between a HOMO-LUMO pair depended on the nature of the reactants and their electron densities. The checkpoint files obtained from optimisations gave insight into the closer energy levels and thus explained the products formed. Another consideration was that a molecule, such as xylylene, could have multiple reaction sites or the molecules could approach each other at different geometries. Once transition state structures had been optimised, IRC analysis was conducted to confirm the transition state path. If there were multiple approach possibilities and transition state structures, the free energy data could be extracted from the log files, in order to find the thermodynamic and kinetic products.
FIRST DERIVATIVE PF ORC
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=Exercise 1: 1,3-Butadiene and Ethene=
The first Diels-Alder reaction characterised was between 1,3-butadiene and ethene, forming cyclohexene. Visualising the molecular orbitals for the optimised reactants, products and transition state enabled for an orbital diagram to be drawn ('''Figure 1'''). It is evident that the formation of molecular orbitals is restricted by symmetry. Orbitals of the same symmetry/asymmetry can interact and bring stability to the molecule.
[[File:CyclohexadieneMODiagramns2214.jpg|300px|thumb|center|'''Figure 1''' Cyclohexene MO Diagram]]
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Looking at the values for the optimised reactants, the HOMO of the butadiene (-0.35899) and LUMO of the ethene (0.04256) are closer in energy and therefore the energy gap between the bonding and anti-bonding orbitals formed is larger. The energy difference between the HOMO ethene and LUMO butadiene is [(0.01943+0.39228)-(0.04256+0.35899)]=0.01006 larger giving a smaller energy gap in molecular orbitals formed. The orbital overlap is non-zero for a symmetric-symmetric or asymmetric-asymmetric interaction, and zero for an asymmetric-symmetric interaction, as in the latter interaction, one pair of p orbitals are in the phase and the other pair out of phase, effectively cancelling each other out.
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{| class="wikitable" style="margin: auto;"
|+ Exercise 1 Molecular Orbitals
|-
| style="text-align: center;"| PM6
! colspan="1" style="text-align: center;"|Ethene
! colspan="1" style="text-align: center;"|Butadiene
! colspan="2" style="text-align: center;"|Transition States
|-
! rowspan="1" style="text-align: center;"|LUMO
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<uploadedFileContents>ETHENENS2214.LOG</uploadedFileContents>
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| rowspan="1" style="text-align: center;"| <jmol>
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| rowspan="1" style="text-align: center;"| <jmol>
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|-
! rowspan="1" style="text-align: center;"| HOMO
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|-
|}
<br style="clear:right">
<br style="clear:left">
{| class="wikitable" border="1" align="right"
|+
|-
! colspan="5" style="text-align: center;"|Carbon numbering and bond lengths ('''Å''')
|-
| colspan="5" align="center"|[[File:TScarbonnumberns2214.jpg|250px|thumb|center|'''Figure 3''' Carbon numbering used by Gaussian]]
|-
! style="text-align: center;"|
! style="text-align: center;"|C1-C2/C5-C6
! style="text-align: center;"|C2-C3/C4-C5
! style="text-align: center;"|C3-C4
! style="text-align: center;"|C6-C1
|-
! rowspan="1" style="text-align: center;"| Reactants
| rowspan="1" style="text-align: center;"| -
| rowspan="1" style="text-align: center;"| 1.333
| rowspan="1" style="text-align: center;"| 1.471
| rowspan="1" style="text-align: center;"| 1.327
|-
! rowspan="1" style="text-align: center;"| Transition State
| rowspan="1" style="text-align: center;"| 2.115
| rowspan="1" style="text-align: center;"| 1.380
| rowspan="1" style="text-align: center;"| 1.411
| rowspan="1" style="text-align: center;"| 1.382
|-
! rowspan="1" style="text-align: center;"| Product
| rowspan="1" style="text-align: center;"| 1.537
| rowspan="1" style="text-align: center;"| 1.501
| rowspan="1" style="text-align: center;"| 1.337
| rowspan="1" style="text-align: center;"| 1.535
|-
|}
[[File:Ircgraphns2214.jpg|500px|thumb|left|'''Figure 2''' Graph showing internuclear distances during cyclohexene formation]]
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The graph in '''Figure 2''' displays how the C-C bonds change in length as the reactants approach the transition state and then form the products. Well before the transition state is reached, all bond lengths remain constant except for C1-C2 and C5-C6 as the ethene and butadiene molecules approach each other. Typical sp<sup>2</sup> C-C bond length at this stage is around 1.336 Å. Just before the transition state is approached, C1-C2 and C5-C6 continue to descend, but the other bond lengths appear to converge as the cyclisation occurs.

The four bond lengths converge just after the transition state. The bond length between the newly forming C1-C2 and C5-C6 is 2.115 Å at the transition state. This is significantly smaller than the Van Der Waal's radius of two Carbon atoms (1.7x2= 3.4 Å). This suggests that bond formation is occurring throughout the transition state, especially as the bond length continues to decrease linearly and plateau at a value of ~1.54 Å, the typical C-C sp<sup>3</sup> sigma bond length. What seems to define the transition state of cyclohexene is the convergence of the four other bond lengths
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The vibration at the transition state has a negative frequency. Looking at the vectors displayed for this vibration, it appears that the bond formation is synchronous. Therefore only one stereoisomer forms from the Diels-Alder reaction as there is no possibility of bond rotation before the second bond forms.
<br style="clear:right">
<br style="clear:left">

=Exercise 2=
{| class="wikitable" border="1" align="left"
|+ Exercise 2 Molecular Orbitals
|-
| style="text-align: center;"| B3LYP
! colspan="2" style="text-align: center;"|EXO Transition States
! colspan="2" style="text-align: center;"|ENDO Transition States
|-
! rowspan="1" style="text-align: center;"|LUMO
| rowspan="1" style="text-align: center;"| <jmol>
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|-
! rowspan="1" style="text-align: center;"| HOMO
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|-
|}
[[File:Cyclohexadiene13DDiagramNS2214.jpg|250px|thumb|right|'''Figure 4''' Cyclohexadiene and 1,3-Dioxole MO Diagram]]
<br style="clear:right">
<br style="clear:left">
{| class="wikitable" border="1" align="right"
|+ Table of Gibbs Free Energies and Reaction Barriers
|-
! style="text-align: center;"| (B3LYP level)
! colspan="2" style="text-align: center;"|Gibbs Free Energy
! colspan="2" style="text-align: center;"|Reaction Barrier
|-
! rowspan="1" style="text-align: center;"|
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
|-
! rowspan="1" style="text-align: center;"| Exo
| rowspan="1" style="text-align: center;"| 0.138901
| rowspan="1" style="text-align: center;"|
| rowspan="1" style="text-align: center;"| 0.07429
| rowspan="1" style="text-align: center;"|
|-
! rowspan="1" style="text-align: center;"| Endo
| rowspan="1" style="text-align: center;"| 0.137942
| rowspan="1" style="text-align: center;"|
| rowspan="1" style="text-align: center;"| 0.073331
| rowspan="1" style="text-align: center;"|
|-
|}
Following the progress of the reaction between cyclohexadiene and 1,3-dioxole produced different results to exercise 1. Here, a typical inverse demand Diels-Alder reaction was seen, where the diene's HOMO and dienophile's LUMO formed the molecular HOMO and LUMO orbitals of the transition state ('''Figure 4'''). Energy levels of the HOMO and LUMO for each reactant were obtained from the checkpoint files. The energy gap between the diene's HOMO and dienophiles's LUMO is 0.18589 and therefore smaller than the diene's LUMO and dienophiles's HOMO energy gap of 0.21191. The smaller energy gap results in greater splitting. The electron rich nature of the diene 1,3-dioxole is due to the oxygen atoms adjacent to the double bond. The mixing of p orbitals raises the energy of the diene's HOMO and brings it closer to the dienophile's LUMO.

The Gibbs free energies were extracted from the log files of the reactants and transition states and the reaction barriers calculated accordingly ('''Figure 5'''). The endo-conformer of the product has a lower reaction barrier, being 7.842 KJmol<sup>-1</sup> smaller in value. This therefore makes it the kinetic product as less energy is required to overcome the barrier and thus over time, it will form more quickly. The stability of the transition state in the endo-form is most likely due to secondary orbital interaction. From the table and in '''Figure 6''' it can clearly be seen in the transition state HOMO where the p orbitals of cyclohexadiene are able to interact with the oxygen p orbitals, bringing some stability to the transition state. The endo product also has a lower product energy, final value being 0.446 KJmol<sup>-1</sup> lower than the exo product, making it the thermodynamic product too.
<br style="clear:right">
<br style="clear:left">

=Exercise 3=
{| class="wikitable" border="1" align="right"
|+ Table of Gibbs Free Energies and Reaction Barriers for o-Xylylene-SO2 Cycloaddition
|-
! style="text-align: center;"|(PM6 level)
! colspan="2" style="text-align: center;"|Gibbs Free Energy
! colspan="2" style="text-align: center;"|Reaction Barrier
|-
! rowspan="1" style="text-align: center;"|
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
|-
! rowspan="1" style="text-align: center;"| Exo
| rowspan="1" style="text-align: center;"| 0.0326
| rowspan="1" style="text-align: center;"|85.497
| rowspan="1" style="text-align: center;"| -0.0381
| rowspan="1" style="text-align: center;"| -99.924
|-
! rowspan="1" style="text-align: center;"| Endo
| rowspan="1" style="text-align: center;"| 0.0310
| rowspan="1" style="text-align: center;"| 81.517
| rowspan="1" style="text-align: center;"| -0.0378
| rowspan="1" style="text-align: center;"| -99.283
|-
! rowspan="1" style="text-align: center;"| Chelotropic
| rowspan="1" style="text-align: center;"| 0.03955
| rowspan="1" style="text-align: center;"|103.839
| rowspan="1" style="text-align: center;"| -0.0583
| rowspan="1" style="text-align: center;"| -152.972
|-
! rowspan="1" style="text-align: center;"| Unfavourable Exo
| rowspan="1" style="text-align: center;"|0.045542
| rowspan="1" style="text-align: center;"|119.571
| rowspan="1" style="text-align: center;"| 0.007792
| rowspan="1" style="text-align: center;"| 20.458
|-
! rowspan="1" style="text-align: center;"| Unfavourable Endo
| rowspan="1" style="text-align: center;"| 0.042557
| rowspan="1" style="text-align: center;"|111.733
| rowspan="1" style="text-align: center;"| 0.006098
| rowspan="1" style="text-align: center;"| 16.010
|-
|}[[File:RXNCOORDNS2214.jpg|400px|thumb|right]]
Once again, the free energies of the reactants, transition states and products were extracted from the log files, optimised at the PM6 level. The endo conformer has the lowest energy barrier, 3.98 KJmol<sup>-1</sup> lower than exo, making it the kinetic product. The chelotropic and unfavourable transition states were significantly higher. The chelotropic has a high energy transition state because there are no possible stabilising orbital interactions as the sulphur dioxide approaches with the sulphur atom forward and oxygens facing away. The unfavourable endo and exo transition states have the highest energy. This is partly due to steric clashes with the xylylene molecule as sulphur dioxide approaches, resulting in destabilisation. The most significant factor is in fact the lack of aromaticity in the reaction. Conducting the Diels-Alder reaction with thee dienophile site in the ring means that it can't be aromatised and thus lower the energy of the system like with the other three reactions. The unfavourable conformers show just how unstable xylylene is compared to the products that can be formed. Both endo conformers are lower in transition state energy than the exo ones because of the secondary orbital overlap taking place, as mentioned in exercise 2.

The unfavourable endo and exo products also have the highest product energies. The positive value in the relative energies reaction co-ordinate makes it less stable than the reactants. There is no drive for the reaction as ∆G is positive. The high activation barrier and reaction energy makes these pathways kinetically and thermodynamically unfavourable. The chelotropic product has the lowest energy thereby making it the thermodynamic product. It is just over 50 KJmol<sup>-1</sup> more stable than the exo and endo products. Under reversible conditions, the chelotropic would be the majority product.
{| class="wikitable" border="1" align="center"
|+ IRC pathways for o-Xylylene-SO2 Cycloaddition
|-
! colspan="2" style="text-align: center;"|Diels-Alder
! colspan="1" style="text-align: center;"|Chelotropic
|-
! rowspan="1" style="text-align: center;"|Exo
! rowspan="1" style="text-align: center;"|Endo
! rowspan="1" style="text-align: center;"|
|-
|rowspan="1" style="text-align: center;"|[[File:IRC exo3ns2214.gif|400px|thumb|center]]
|rowspan="1" style="text-align: center;"|[[File:ENDOTStrajectoryns2214.gif|400px|thumb|center]]
|rowspan="1" style="text-align: center;"|[[File:IRCTSchelns2214traj.gif|400px|thumb|center]]
|-
! rowspan="1" style="text-align: center;"|Unfavourable Exo
! rowspan="1" style="text-align: center;"|Unfavourable Endo
|-
|rowspan="1" style="text-align: center;"|[[File:IRCexovidunfavns2214.gif|400px|thumb|center]]
|rowspan="1" style="text-align: center;"|[[File:IRCendovidunfavns2214.gif|400px|thumb|center]]
|-
|}
<br style="clear:right">
<br style="clear:left">

=Conclusion=

2017-03-23T14:48:42Z

Ns2214: /* Exercise 3 */

'''Transition States'''
=Introduction=
Potential energy surfaces display the energy of a system with respect to positions of the molecules. They can therefore be used to display transition states in a molecule. Transition states are an energy maximum where the gradient is 0, i.e. a turning point.However, depending on the complexity of the reaction, there can be many maxima on a PES as there are different trajectories predicted. If a transition state has been correctly found, it will have a saddle-point geometry where it is the maximum on its particular reaction co-ordinate, but the minimum compared to other pathways. There is an equal probability of falling down the potential energy curve to form either reactants or products at a transition state.

In this lab, the transition states of Diels-Alder reactions were studied. This involves a [4+2] cycloaddition between a diene and dienophile. These double bonded structures are close enough in energy to interact and form 2 new sigma bonds and breaking one pi bond overall. The formation of theses sigma bonds lowers the energy of the system as electrons occupy bonding molecular orbitals.

Gaussian software was used to analyse the transition state formation of three Diels-Alder reactions. Method 3 in the tutorial was used for all the reactions, where the expected product molecule was optimised, the relevant bonds broken and frozen, and then the resulting transition state optimised. Two levels of optimisation were used: PM6 semi-empirical for exercises 1 and 3 and B3LYP-DFT for exercise 2. PM6 uses relevant parameters to fit experimental dipole moments and geometries, allowing for faster results as some integrals are pre-determined. B3LYP however uses electron density in the molecule to optimise the structure and base it calculations on. If the correct transition state was found, there was one negative frequency found in the vibrations, corresponding to..

Several consideration have to be taken into account when studying Diels-Alder reactions. One is that the diene and dienophile's HOMO and LUMOs are are relatively close to each other. The smaller energy gap between a HOMO-LUMO pair depended on the nature of the reactants and their electron densities. The checkpoint files obtained from optimisations gave insight into the closer energy levels and thus explained the products formed. Another consideration was that a molecule, such as xylylene, could have multiple reaction sites or the molecules could approach each other at different geometries. Once transition state structures had been optimised, IRC analysis was conducted to confirm the transition state path. If there were multiple approach possibilities and transition state structures, the free energy data could be extracted from the log files, in order to find the thermodynamic and kinetic products.
<br style="clear:right">
<br style="clear:left">

=Exercise 1=
The first Diels-Alder reaction characterised was between 1,3-butadiene and ethene, forming cyclohexene. Visualising the molecular orbitals for the optimised reactants, products and transition state enabled for an orbital diagram to be drawn ('''Figure 1'''). From the diagram it is evident that the formation of molecular orbitals is restricted by symmetry. Orbitals of the same symmetry/asymmetry are allowed to interact and bring stability to the moelcule. Looking at the values for the optimised reactants, the HOMO of the butadiene (-0.35899) and LUMO of the ethene (0.04256) are closer in energy and therefore the energy gap between the bonding and anti-bonding orbitals formed is larger. The orbital overlap is non-zero for a symmetric-symmetric or asymmetric-asymmetric interaction, and zero for an asymmetric-symmetric interaction.
<br style="clear:right">
<br style="clear:left">.
{| class="wikitable" border="1" align="right"
|+
|-
! colspan="5" style="text-align: center;"|Carbon numbering and bond lengths ('''Å''')
|-
| colspan="5" align="center"|[[File:TScarbonnumberns2214.jpg|250px|thumb|center|'''Figure 3''' Carbon numbering used by Gaussian]]
|-
! style="text-align: center;"|
! style="text-align: center;"|C1-C2/C5-C6
! style="text-align: center;"|C2-C3/C4-C5
! style="text-align: center;"|C3-C4
! style="text-align: center;"|C6-C1
|-
! rowspan="1" style="text-align: center;"| Reactants
| rowspan="1" style="text-align: center;"| -
| rowspan="1" style="text-align: center;"| 1.333
| rowspan="1" style="text-align: center;"| 1.471
| rowspan="1" style="text-align: center;"| 1.327
|-
! rowspan="1" style="text-align: center;"| Transition State
| rowspan="1" style="text-align: center;"| 2.115
| rowspan="1" style="text-align: center;"| 1.380
| rowspan="1" style="text-align: center;"| 1.411
| rowspan="1" style="text-align: center;"| 1.382
|-
! rowspan="1" style="text-align: center;"| Product
| rowspan="1" style="text-align: center;"| 1.537
| rowspan="1" style="text-align: center;"| 1.501
| rowspan="1" style="text-align: center;"| 1.337
| rowspan="1" style="text-align: center;"| 1.535
|-
|}
[[File:Ircgraphns2214.jpg|400px|thumb|left|'''Figure 2''' Graph showing internuclear distances during cyclohexene formation]]
<br style="clear:right">
<br style="clear:left">.
The graph in '''Figure 2''' displays how the C-C bonds change in length as the reactants approach the transition state and then form the products. Well before the transition state is reached, all bond lengths remain constant except for C1-C2 and C5-C6 as the ethene molecule approaches the butadiene. Typical sp<sup>2</sup> and sp<sup>3</sup> C-C bond lengths at this stage are around 1.336 and 1.468 Å respectively. Just before the transition state is approached,C1-C2 and C5-C6 continue to descend, but the other bond lengths appear to converge as the cyclisation occurs.

The four bond lengths converge just after the transition state. The bond length between the newly forming C1-C2 and C5-C6 is 2.115 at the transition state. This is significantly smaller than the Van Der Waal's radius of two Carbon atoms (1.7x2= 3.4 Å). This suggests that bond formation is occurring before, during and after the transition state, especially as the bond length continues to decrease linearly and plateau at a value of ~1.54 Å, the typical C-C sigma bond length. What defines the transition state of cyclohexene is the convergence of the four other bond lengths
<br style="clear:right">
<br style="clear:left">.
[[File:CyclohexadieneMODiagramns2214.jpg|400px|thumb|left]]
{| class="wikitable" border="1" align="right"
|+ Exercise 1 Molecular Orbitals
|-
| style="text-align: center;"| PM6
! colspan="1" style="text-align: center;"|Ethene
! colspan="1" style="text-align: center;"|Butadiene
! colspan="2" style="text-align: center;"|Transition States
|-
! rowspan="1" style="text-align: center;"|LUMO
| rowspan="1" style="text-align: center;"| <jmol>
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|-
! rowspan="1" style="text-align: center;"| HOMO
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<script> frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>ETHENENS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>BUTADIENENS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSOPTFREQPOPns2214.LOG</uploadedFileContents>
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| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
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<script> frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSOPTFREQPOPns2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<br style="clear:right">
<br style="clear:left">
<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script>frame 17; vectors 3; vectors scale 3.0; color vectors orange; vibration 2; </script>
<uploadedFileContents>TSOPTFREQns2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Formation of the two bonds is synchrous. ADD...
<br style="clear:right">
<br style="clear:left">

=Exercise 2=
{| class="wikitable" border="1" align="left"
|+ Exercise 2 Molecular Orbitals
|-
| style="text-align: center;"| B3LYP
! colspan="2" style="text-align: center;"|EXO Transition States
! colspan="2" style="text-align: center;"|ENDO Transition States
|-
! rowspan="1" style="text-align: center;"|LUMO
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 45; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSEXOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 44; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSEXOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSENDOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSENDOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! rowspan="1" style="text-align: center;"| HOMO
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSEXOPOPNS2214.LOG</uploadedFileContents>
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</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
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<script> frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSEXOPOPNS2214.LOG</uploadedFileContents>
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</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
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<script> frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSENDOPOPNS2214.LOG</uploadedFileContents>
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| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
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<uploadedFileContents>TSENDOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
[[File:Cyclohexadiene13DDiagramNS2214.jpg|250px|thumb|right|alt text]]
<br style="clear:right">
<br style="clear:left">
{| class="wikitable" border="1" align="right"
|+ Table of Gibbs Free Energies and Reaction Barriers
|-
! style="text-align: center;"| (B3LYP level)
! colspan="2" style="text-align: center;"|Gibbs Free Energy
! colspan="2" style="text-align: center;"|Reaction Barrier
|-
! rowspan="1" style="text-align: center;"|
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
|-
! rowspan="1" style="text-align: center;"| Exo
| rowspan="1" style="text-align: center;"| -500.329
| rowspan="1" style="text-align: center;"| 1313613.608
| rowspan="1" style="text-align: center;"| 0.0633
| rowspan="1" style="text-align: center;"| 166.310
|-
! rowspan="1" style="text-align: center;"| Endo
| rowspan="1" style="text-align: center;"| -500.332
| rowspan="1" style="text-align: center;"| 1313621.485
| rowspan="1" style="text-align: center;"| 0.0604
| rowspan="1" style="text-align: center;"| 158.467
|-
|}
Following the progress of the reaction between cyclohexadiene and 1,3-dioxole produced varying results to the ones above. Here, a typical inverse demand Diels-Alder reaction was seen, where the diene's HOMO and dienophile's LUMO formed the molecular HOMO and LUMO orbitals of the transition state. Energy levels of the HOMO and LUMO for each reactant were obtained from the checkpoint files and shown in '''Figure 4'''. The energy gap between the diene's HOMO and dienophiles's LUMO is 0.34597 and therefore smaller than the diene's LUMO and dienophiles's HOMO energy gap of 0.34806. Smaller energy gap results in greater splitting. The electron rich nature of the diene 1,3-dioxole is due to the oxygen atoms adjacent to the double bond. The mixing of p orbitals raises the energy of the diene's HOMO and brings it closer to the dienophile's LUMO.

The Gibbs free energies were extracted from the log files of the reactants and transition states and the reaction barriers calculated accordingly. The endo-conformer of the product has a lower reaction barrier, being 7.842 KJmol<sup>-1</sup> smaller in value. This therefore makes it the kinetic product as less energy is required to overcome the barrier and thus over time, it will form more quickly.
<br style="clear:right">
<br style="clear:left">

=Exercise 3=
{| class="wikitable" border="1" align="right"
|+ Table of Gibbs Free Energies and Reaction Barriers for o-Xylylene-SO2 Cycloaddition
|-
! style="text-align: center;"|(PM6 level)
! colspan="2" style="text-align: center;"|Gibbs Free Energy
! colspan="2" style="text-align: center;"|Reaction Barrier
|-
! rowspan="1" style="text-align: center;"|
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
|-
! rowspan="1" style="text-align: center;"| Exo
| rowspan="1" style="text-align: center;"| 0.092076
| rowspan="1" style="text-align: center;"|241.746
| rowspan="1" style="text-align: center;"| 0.032564
| rowspan="1" style="text-align: center;"| 85.497
|-
! rowspan="1" style="text-align: center;"| Endo
| rowspan="1" style="text-align: center;"| 0.090560
| rowspan="1" style="text-align: center;"| 237.765
| rowspan="1" style="text-align: center;"| 0.031048
| rowspan="1" style="text-align: center;"| 81.517
|-
! rowspan="1" style="text-align: center;"| Chelotropic
| rowspan="1" style="text-align: center;"| 0.099062
| rowspan="1" style="text-align: center;"|260.087
| rowspan="1" style="text-align: center;"| 0.03955
| rowspan="1" style="text-align: center;"| 103.839
|-
|}[[File:RXNCOORDNS2214.jpg|400px|thumb|right]]

Once again, the free energies of the reactants and transition were extracted from the log files, having been optimised at the PM6 level. The endo conformer has the lowest energy barrier, 3.98 KJmol<sup>-1</sup> lower than exo, making it the kinetic product.Plotting the reaction co-ordinate clearly displays the relative energies throughout the co-ordinate. The chelotropic product has the highest reaction barrier meaning it forms slowly as more energy is required to overcome the barrier. However, once the barrier has been overcome, the chelotropic product is lowest in energy and therefore the most stable, making it the thermodynamic product.
During the reaction, the 6-member-ed ring in xylylene is aromatised in order ot bring stability to the molecule.
{| class="wikitable" border="1" align="center"
|+ IRC pathways for o-Xylylene-SO2 Cycloaddition
|-
! colspan="2" style="text-align: center;"|Diels-Alder
! colspan="1" style="text-align: center;"|Chelotropic
|-
! rowspan="1" style="text-align: center;"|Exo
! rowspan="1" style="text-align: center;"|Endo
! rowspan="1" style="text-align: center;"|
|-
|rowspan="1" style="text-align: center;"|[[File:IRC exo3ns2214.gif|400px|thumb|center]]
|rowspan="1" style="text-align: center;"|[[File:ENDOTStrajectoryns2214.gif|400px|thumb|center]]
|rowspan="1" style="text-align: center;"|[[File:IRCTSchelns2214traj.gif|400px|thumb|center]]
|-
! rowspan="1" style="text-align: center;"|Unfavourable Exo
! rowspan="1" style="text-align: center;"|Unfavourable Endo
|-
|rowspan="1" style="text-align: center;"|[[File:IRCexovidunfavns2214.gif|400px|thumb|center]]
|rowspan="1" style="text-align: center;"|[[File:IRCendovidunfavns2214.gif|400px|thumb|center]]
|-
|}
<br style="clear:right">
<br style="clear:left">

=Conclusion=

File:IRCendovidunfavns2214.gif

2017-03-23T14:48:15Z

Ns2214:

File:IRCexovidunfavns2214.gif

2017-03-23T14:47:37Z

Ns2214:

Rep:Mod:tsns2214

2017-03-23T13:35:00Z

Ns2214: /* Exercise 2 */

'''Transition States'''
=Introduction=
Potential energy surfaces display the energy of a system with respect to positions of the molecules. They can therefore be used to display transition states in a molecule. Transition states are an energy maximum where the gradient is 0, i.e. a turning point.However, depending on the complexity of the reaction, there can be many maxima on a PES as there are different trajectories predicted. If a transition state has been correctly found, it will have a saddle-point geometry where it is the maximum on its particular reaction co-ordinate, but the minimum compared to other pathways. There is an equal probability of falling down the potential energy curve to form either reactants or products at a transition state.

In this lab, the transition states of Diels-Alder reactions were studied. This involves a [4+2] cycloaddition between a diene and dienophile. These double bonded structures are close enough in energy to interact and form 2 new sigma bonds and breaking one pi bond overall. The formation of theses sigma bonds lowers the energy of the system as electrons occupy bonding molecular orbitals.

Gaussian software was used to analyse the transition state formation of three Diels-Alder reactions. Method 3 in the tutorial was used for all the reactions, where the expected product molecule was optimised, the relevant bonds broken and frozen, and then the resulting transition state optimised. Two levels of optimisation were used: PM6 semi-empirical for exercises 1 and 3 and B3LYP-DFT for exercise 2. PM6 uses relevant parameters to fit experimental dipole moments and geometries, allowing for faster results as some integrals are pre-determined. B3LYP however uses electron density in the molecule to optimise the structure and base it calculations on. If the correct transition state was found, there was one negative frequency found in the vibrations, corresponding to..

Several consideration have to be taken into account when studying Diels-Alder reactions. One is that the diene and dienophile's HOMO and LUMOs are are relatively close to each other. The smaller energy gap between a HOMO-LUMO pair depended on the nature of the reactants and their electron densities. The checkpoint files obtained from optimisations gave insight into the closer energy levels and thus explained the products formed. Another consideration was that a molecule, such as xylylene, could have multiple reaction sites or the molecules could approach each other at different geometries. Once transition state structures had been optimised, IRC analysis was conducted to confirm the transition state path. If there were multiple approach possibilities and transition state structures, the free energy data could be extracted from the log files, in order to find the thermodynamic and kinetic products.
<br style="clear:right">
<br style="clear:left">

=Exercise 1=
The first Diels-Alder reaction characterised was between 1,3-butadiene and ethene, forming cyclohexene. Visualising the molecular orbitals for the optimised reactants, products and transition state enabled for an orbital diagram to be drawn ('''Figure 1'''). From the diagram it is evident that the formation of molecular orbitals is restricted by symmetry. Orbitals of the same symmetry/asymmetry are allowed to interact and bring stability to the moelcule. Looking at the values for the optimised reactants, the HOMO of the butadiene (-0.35899) and LUMO of the ethene (0.04256) are closer in energy and therefore the energy gap between the bonding and anti-bonding orbitals formed is larger. The orbital overlap is non-zero for a symmetric-symmetric or asymmetric-asymmetric interaction, and zero for an asymmetric-symmetric interaction.
<br style="clear:right">
<br style="clear:left">.
{| class="wikitable" border="1" align="right"
|+
|-
! colspan="5" style="text-align: center;"|Carbon numbering and bond lengths ('''Å''')
|-
| colspan="5" align="center"|[[File:TScarbonnumberns2214.jpg|250px|thumb|center|'''Figure 3''' Carbon numbering used by Gaussian]]
|-
! style="text-align: center;"|
! style="text-align: center;"|C1-C2/C5-C6
! style="text-align: center;"|C2-C3/C4-C5
! style="text-align: center;"|C3-C4
! style="text-align: center;"|C6-C1
|-
! rowspan="1" style="text-align: center;"| Reactants
| rowspan="1" style="text-align: center;"| -
| rowspan="1" style="text-align: center;"| 1.333
| rowspan="1" style="text-align: center;"| 1.471
| rowspan="1" style="text-align: center;"| 1.327
|-
! rowspan="1" style="text-align: center;"| Transition State
| rowspan="1" style="text-align: center;"| 2.115
| rowspan="1" style="text-align: center;"| 1.380
| rowspan="1" style="text-align: center;"| 1.411
| rowspan="1" style="text-align: center;"| 1.382
|-
! rowspan="1" style="text-align: center;"| Product
| rowspan="1" style="text-align: center;"| 1.537
| rowspan="1" style="text-align: center;"| 1.501
| rowspan="1" style="text-align: center;"| 1.337
| rowspan="1" style="text-align: center;"| 1.535
|-
|}
[[File:Ircgraphns2214.jpg|400px|thumb|left|'''Figure 2''' Graph showing internuclear distances during cyclohexene formation]]
<br style="clear:right">
<br style="clear:left">.
The graph in '''Figure 2''' displays how the C-C bonds change in length as the reactants approach the transition state and then form the products. Well before the transition state is reached, all bond lengths remain constant except for C1-C2 and C5-C6 as the ethene molecule approaches the butadiene. Typical sp<sup>2</sup> and sp<sup>3</sup> C-C bond lengths at this stage are around 1.336 and 1.468 Å respectively. Just before the transition state is approached,C1-C2 and C5-C6 continue to descend, but the other bond lengths appear to converge as the cyclisation occurs.

The four bond lengths converge just after the transition state. The bond length between the newly forming C1-C2 and C5-C6 is 2.115 at the transition state. This is significantly smaller than the Van Der Waal's radius of two Carbon atoms (1.7x2= 3.4 Å). This suggests that bond formation is occurring before, during and after the transition state, especially as the bond length continues to decrease linearly and plateau at a value of ~1.54 Å, the typical C-C sigma bond length. What defines the transition state of cyclohexene is the convergence of the four other bond lengths
<br style="clear:right">
<br style="clear:left">.
[[File:CyclohexadieneMODiagramns2214.jpg|400px|thumb|left]]
{| class="wikitable" border="1" align="right"
|+ Exercise 1 Molecular Orbitals
|-
| style="text-align: center;"| PM6
! colspan="1" style="text-align: center;"|Ethene
! colspan="1" style="text-align: center;"|Butadiene
! colspan="2" style="text-align: center;"|Transition States
|-
! rowspan="1" style="text-align: center;"|LUMO
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
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<uploadedFileContents>ETHENENS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
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<uploadedFileContents>BUTADIENENS2214.LOG</uploadedFileContents>
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</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title>LUMO+1</title>
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| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
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<uploadedFileContents>TSOPTFREQPOPns2214.LOG</uploadedFileContents>
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</jmol>
|-
! rowspan="1" style="text-align: center;"| HOMO
| rowspan="1" style="text-align: center;"| <jmol>
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| rowspan="1" style="text-align: center;"| <jmol>
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| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title>HOMO-1</title>
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<uploadedFileContents>TSOPTFREQPOPns2214.LOG</uploadedFileContents>
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| rowspan="1" style="text-align: center;"| <jmol>
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</jmol>
|-
|}
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<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script>frame 17; vectors 3; vectors scale 3.0; color vectors orange; vibration 2; </script>
<uploadedFileContents>TSOPTFREQns2214.LOG</uploadedFileContents>
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</jmol>

Formation of the two bonds is synchrous. ADD...
<br style="clear:right">
<br style="clear:left">

=Exercise 2=
{| class="wikitable" border="1" align="left"
|+ Exercise 2 Molecular Orbitals
|-
| style="text-align: center;"| B3LYP
! colspan="2" style="text-align: center;"|EXO Transition States
! colspan="2" style="text-align: center;"|ENDO Transition States
|-
! rowspan="1" style="text-align: center;"|LUMO
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
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<script> frame 6; mo 45; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSEXOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 44; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSEXOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSENDOPOPNS2214.LOG</uploadedFileContents>
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</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
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<uploadedFileContents>TSENDOPOPNS2214.LOG</uploadedFileContents>
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</jmol>
|-
! rowspan="1" style="text-align: center;"| HOMO
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
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</jmolApplet>
</jmol>
|-
|}
[[File:Cyclohexadiene13DDiagramNS2214.jpg|250px|thumb|right|alt text]]
<br style="clear:right">
<br style="clear:left">
{| class="wikitable" border="1" align="right"
|+ Table of Gibbs Free Energies and Reaction Barriers
|-
! style="text-align: center;"| (B3LYP level)
! colspan="2" style="text-align: center;"|Gibbs Free Energy
! colspan="2" style="text-align: center;"|Reaction Barrier
|-
! rowspan="1" style="text-align: center;"|
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
|-
! rowspan="1" style="text-align: center;"| Exo
| rowspan="1" style="text-align: center;"| -500.329
| rowspan="1" style="text-align: center;"| 1313613.608
| rowspan="1" style="text-align: center;"| 0.0633
| rowspan="1" style="text-align: center;"| 166.310
|-
! rowspan="1" style="text-align: center;"| Endo
| rowspan="1" style="text-align: center;"| -500.332
| rowspan="1" style="text-align: center;"| 1313621.485
| rowspan="1" style="text-align: center;"| 0.0604
| rowspan="1" style="text-align: center;"| 158.467
|-
|}
Following the progress of the reaction between cyclohexadiene and 1,3-dioxole produced varying results to the ones above. Here, a typical inverse demand Diels-Alder reaction was seen, where the diene's HOMO and dienophile's LUMO formed the molecular HOMO and LUMO orbitals of the transition state. Energy levels of the HOMO and LUMO for each reactant were obtained from the checkpoint files and shown in '''Figure 4'''. The energy gap between the diene's HOMO and dienophiles's LUMO is 0.34597 and therefore smaller than the diene's LUMO and dienophiles's HOMO energy gap of 0.34806. Smaller energy gap results in greater splitting. The electron rich nature of the diene 1,3-dioxole is due to the oxygen atoms adjacent to the double bond. The mixing of p orbitals raises the energy of the diene's HOMO and brings it closer to the dienophile's LUMO.

The Gibbs free energies were extracted from the log files of the reactants and transition states and the reaction barriers calculated accordingly. The endo-conformer of the product has a lower reaction barrier, being 7.842 KJmol<sup>-1</sup> smaller in value. This therefore makes it the kinetic product as less energy is required to overcome the barrier and thus over time, it will form more quickly.
<br style="clear:right">
<br style="clear:left">

=Exercise 3=
{| class="wikitable" border="1" align="right"
|+ Table of Gibbs Free Energies and Reaction Barriers for o-Xylylene-SO2 Cycloaddition
|-
! style="text-align: center;"|(PM6 level)
! colspan="2" style="text-align: center;"|Gibbs Free Energy
! colspan="2" style="text-align: center;"|Reaction Barrier
|-
! rowspan="1" style="text-align: center;"|
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
|-
! rowspan="1" style="text-align: center;"| Exo
| rowspan="1" style="text-align: center;"| 0.092076
| rowspan="1" style="text-align: center;"|241.746
| rowspan="1" style="text-align: center;"| 0.032564
| rowspan="1" style="text-align: center;"| 85.497
|-
! rowspan="1" style="text-align: center;"| Endo
| rowspan="1" style="text-align: center;"| 0.090560
| rowspan="1" style="text-align: center;"| 237.765
| rowspan="1" style="text-align: center;"| 0.031048
| rowspan="1" style="text-align: center;"| 81.517
|-
! rowspan="1" style="text-align: center;"| Chelotropic
| rowspan="1" style="text-align: center;"| 0.099062
| rowspan="1" style="text-align: center;"|260.087
| rowspan="1" style="text-align: center;"| 0.03955
| rowspan="1" style="text-align: center;"| 103.839
|-
|}[[File:RXNCOORDNS2214.jpg|400px|thumb|right]]

Once again, the free energies of the reactants and transition were extracted from the log files, having been optimised at the PM6 level. The endo conformer has the lowest energy barrier, 3.98 KJmol<sup>-1</sup> lower than exo, making it the kinetic product.Plotting the reaction co-ordinate clearly displays the relative energies throughout the co-ordinate. The chelotropic product has the highest reaction barrier meaning it forms slowly as more energy is required to overcome the barrier. However, once the barrier has been overcome, the chelotropic product is lowest in energy and therefore the most stable, making it the thermodynamic product.
During the reaction, the 6-member-ed ring in xylylene is aromatised in order ot bring stability to the molecule.
{| class="wikitable" border="1" align="center"
|+ IRC pathways for o-Xylylene-SO2 Cycloaddition
|-
! colspan="2" style="text-align: center;"|Diels-Alder
! colspan="1" style="text-align: center;"|Chelotropic
|-
! rowspan="1" style="text-align: center;"|Exo
! rowspan="1" style="text-align: center;"|Endo
! rowspan="1" style="text-align: center;"|
|-
|rowspan="1" style="text-align: center;"|[[File:IRC exo3ns2214.gif|400px|thumb|center]]
|rowspan="1" style="text-align: center;"|[[File:ENDOTStrajectoryns2214.gif|400px|thumb|center]]
|rowspan="1" style="text-align: center;"|[[File:IRCTSchelns2214traj.gif|400px|thumb|center]]
|}
<br style="clear:right">
<br style="clear:left">
=Conclusion=

Rep:Mod:tsns2214

2017-03-23T13:03:26Z

Ns2214:

'''Transition States'''
=Introduction=
Potential energy surfaces display the energy of a system with respect to positions of the molecules. They can therefore be used to display transition states in a molecule. Transition states are an energy maximum where the gradient is 0, i.e. a turning point.However, depending on the complexity of the reaction, there can be many maxima on a PES as there are different trajectories predicted. If a transition state has been correctly found, it will have a saddle-point geometry where it is the maximum on its particular reaction co-ordinate, but the minimum compared to other pathways. There is an equal probability of falling down the potential energy curve to form either reactants or products at a transition state.

In this lab, the transition states of Diels-Alder reactions were studied. This involves a [4+2] cycloaddition between a diene and dienophile. These double bonded structures are close enough in energy to interact and form 2 new sigma bonds and breaking one pi bond overall. The formation of theses sigma bonds lowers the energy of the system as electrons occupy bonding molecular orbitals.

Gaussian software was used to analyse the transition state formation of three Diels-Alder reactions. Method 3 in the tutorial was used for all the reactions, where the expected product molecule was optimised, the relevant bonds broken and frozen, and then the resulting transition state optimised. Two levels of optimisation were used: PM6 semi-empirical for exercises 1 and 3 and B3LYP-DFT for exercise 2. PM6 uses relevant parameters to fit experimental dipole moments and geometries, allowing for faster results as some integrals are pre-determined. B3LYP however uses electron density in the molecule to optimise the structure and base it calculations on. If the correct transition state was found, there was one negative frequency found in the vibrations, corresponding to..

Several consideration have to be taken into account when studying Diels-Alder reactions. One is that the diene and dienophile's HOMO and LUMOs are are relatively close to each other. The smaller energy gap between a HOMO-LUMO pair depended on the nature of the reactants and their electron densities. The checkpoint files obtained from optimisations gave insight into the closer energy levels and thus explained the products formed. Another consideration was that a molecule, such as xylylene, could have multiple reaction sites or the molecules could approach each other at different geometries. Once transition state structures had been optimised, IRC analysis was conducted to confirm the transition state path. If there were multiple approach possibilities and transition state structures, the free energy data could be extracted from the log files, in order to find the thermodynamic and kinetic products.
<br style="clear:right">
<br style="clear:left">

=Exercise 1=
The first Diels-Alder reaction characterised was between 1,3-butadiene and ethene, forming cyclohexene. Visualising the molecular orbitals for the optimised reactants, products and transition state enabled for an orbital diagram to be drawn ('''Figure 1'''). From the diagram it is evident that the formation of molecular orbitals is restricted by symmetry. Orbitals of the same symmetry/asymmetry are allowed to interact and bring stability to the moelcule. Looking at the values for the optimised reactants, the HOMO of the butadiene (-0.35899) and LUMO of the ethene (0.04256) are closer in energy and therefore the energy gap between the bonding and anti-bonding orbitals formed is larger. The orbital overlap is non-zero for a symmetric-symmetric or asymmetric-asymmetric interaction, and zero for an asymmetric-symmetric interaction.
<br style="clear:right">
<br style="clear:left">.
{| class="wikitable" border="1" align="right"
|+
|-
! colspan="5" style="text-align: center;"|Carbon numbering and bond lengths ('''Å''')
|-
| colspan="5" align="center"|[[File:TScarbonnumberns2214.jpg|250px|thumb|center|'''Figure 3''' Carbon numbering used by Gaussian]]
|-
! style="text-align: center;"|
! style="text-align: center;"|C1-C2/C5-C6
! style="text-align: center;"|C2-C3/C4-C5
! style="text-align: center;"|C3-C4
! style="text-align: center;"|C6-C1
|-
! rowspan="1" style="text-align: center;"| Reactants
| rowspan="1" style="text-align: center;"| -
| rowspan="1" style="text-align: center;"| 1.333
| rowspan="1" style="text-align: center;"| 1.471
| rowspan="1" style="text-align: center;"| 1.327
|-
! rowspan="1" style="text-align: center;"| Transition State
| rowspan="1" style="text-align: center;"| 2.115
| rowspan="1" style="text-align: center;"| 1.380
| rowspan="1" style="text-align: center;"| 1.411
| rowspan="1" style="text-align: center;"| 1.382
|-
! rowspan="1" style="text-align: center;"| Product
| rowspan="1" style="text-align: center;"| 1.537
| rowspan="1" style="text-align: center;"| 1.501
| rowspan="1" style="text-align: center;"| 1.337
| rowspan="1" style="text-align: center;"| 1.535
|-
|}
[[File:Ircgraphns2214.jpg|400px|thumb|left|'''Figure 2''' Graph showing internuclear distances during cyclohexene formation]]
<br style="clear:right">
<br style="clear:left">.
The graph in '''Figure 2''' displays how the C-C bonds change in length as the reactants approach the transition state and then form the products. Well before the transition state is reached, all bond lengths remain constant except for C1-C2 and C5-C6 as the ethene molecule approaches the butadiene. Typical sp<sup>2</sup> and sp<sup>3</sup> C-C bond lengths at this stage are around 1.336 and 1.468 Å respectively. Just before the transition state is approached,C1-C2 and C5-C6 continue to descend, but the other bond lengths appear to converge as the cyclisation occurs.

The four bond lengths converge just after the transition state. The bond length between the newly forming C1-C2 and C5-C6 is 2.115 at the transition state. This is significantly smaller than the Van Der Waal's radius of two Carbon atoms (1.7x2= 3.4 Å). This suggests that bond formation is occurring before, during and after the transition state, especially as the bond length continues to decrease linearly and plateau at a value of ~1.54 Å, the typical C-C sigma bond length. What defines the transition state of cyclohexene is the convergence of the four other bond lengths
<br style="clear:right">
<br style="clear:left">.
[[File:CyclohexadieneMODiagramns2214.jpg|400px|thumb|left]]
{| class="wikitable" border="1" align="right"
|+ Exercise 1 Molecular Orbitals
|-
| style="text-align: center;"| PM6
! colspan="1" style="text-align: center;"|Ethene
! colspan="1" style="text-align: center;"|Butadiene
! colspan="2" style="text-align: center;"|Transition States
|-
! rowspan="1" style="text-align: center;"|LUMO
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>ETHENENS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>BUTADIENENS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSOPTFREQPOPns2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSOPTFREQPOPns2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! rowspan="1" style="text-align: center;"| HOMO
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>ETHENENS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>BUTADIENENS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSOPTFREQPOPns2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSOPTFREQPOPns2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<br style="clear:right">
<br style="clear:left">
<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script>frame 17; vectors 3; vectors scale 3.0; color vectors orange; vibration 2; </script>
<uploadedFileContents>TSOPTFREQns2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Formation of the two bonds is synchrous. ADD...
<br style="clear:right">
<br style="clear:left">

=Exercise 2=
{| class="wikitable" border="1" align="left"
|+ Exercise 2 Molecular Orbitals
|-
| style="text-align: center;"| B3LYP
! colspan="2" style="text-align: center;"|EXO Transition States
! colspan="2" style="text-align: center;"|ENDO Transition States
|-
! rowspan="1" style="text-align: center;"|LUMO
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 45; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSEXOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 44; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSEXOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSENDOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSENDOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! rowspan="1" style="text-align: center;"| HOMO
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSEXOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSEXOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSENDOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSENDOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
[[File:Cyclohexadiene13DDiagramNS2214.jpg|400px|thumb|right|alt text]]
<br style="clear:right">
<br style="clear:left">
{| class="wikitable" border="1" align="right"
|+ Table of Gibbs Free Energies and Reaction Barriers
|-
! style="text-align: center;"| (B3LYP level)
! colspan="2" style="text-align: center;"|Gibbs Free Energy
! colspan="2" style="text-align: center;"|Reaction Barrier
|-
! rowspan="1" style="text-align: center;"|
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
|-
! rowspan="1" style="text-align: center;"| Exo
| rowspan="1" style="text-align: center;"| -500.329
| rowspan="1" style="text-align: center;"| 1313613.608
| rowspan="1" style="text-align: center;"| 0.0633
| rowspan="1" style="text-align: center;"| 166.310
|-
! rowspan="1" style="text-align: center;"| Endo
| rowspan="1" style="text-align: center;"| -500.332
| rowspan="1" style="text-align: center;"| 1313621.485
| rowspan="1" style="text-align: center;"| 0.0604
| rowspan="1" style="text-align: center;"| 158.467
|-
|}
Following the progress of the reaction between cyclohexadiene and 1,3-dioxole produced varying results to the ones above. Here, a typical inverse demand Diels-Alder reaction was seen, where the diene's HOMO and dienophile's LUMO formed the molecular HOMO and LUMO orbitals of the transition state. Energy levels of the HOMO and LUMO for each reactant were obtained from the checkpoint files and shown in '''Figure 4'''. The energy gap between the diene's HOMO and dienophiles's LUMO is 0.34597 and therefore smaller than the diene's LUMO and dienophiles's HOMO energy gap of 0.34806. Smaller energy gap results in greater splitting. The electron rich nature of the diene 1,3-dioxole is due to the oxygen atoms adjacent to the double bond. The mixing of p orbitals raises the energy of the diene's HOMO and brings it closer to the dienophile's LUMO.

The Gibbs free energies were extracted from the log files of the reactants and transition states and the reaction barriers calculated accordingly. The endo-conformer of the product has a lower reaction barrier, being 7.842 KJmol<sup>-1</sup> smaller in value. This therefore makes it the kinetic product as less energy is required to overcome the barrier and thus over time, it will form more quickly.
<br style="clear:right">
<br style="clear:left">

=Exercise 3=
{| class="wikitable" border="1" align="right"
|+ Table of Gibbs Free Energies and Reaction Barriers for o-Xylylene-SO2 Cycloaddition
|-
! style="text-align: center;"|(PM6 level)
! colspan="2" style="text-align: center;"|Gibbs Free Energy
! colspan="2" style="text-align: center;"|Reaction Barrier
|-
! rowspan="1" style="text-align: center;"|
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
|-
! rowspan="1" style="text-align: center;"| Exo
| rowspan="1" style="text-align: center;"| 0.092076
| rowspan="1" style="text-align: center;"|241.746
| rowspan="1" style="text-align: center;"| 0.032564
| rowspan="1" style="text-align: center;"| 85.497
|-
! rowspan="1" style="text-align: center;"| Endo
| rowspan="1" style="text-align: center;"| 0.090560
| rowspan="1" style="text-align: center;"| 237.765
| rowspan="1" style="text-align: center;"| 0.031048
| rowspan="1" style="text-align: center;"| 81.517
|-
! rowspan="1" style="text-align: center;"| Chelotropic
| rowspan="1" style="text-align: center;"| 0.099062
| rowspan="1" style="text-align: center;"|260.087
| rowspan="1" style="text-align: center;"| 0.03955
| rowspan="1" style="text-align: center;"| 103.839
|-
|}[[File:RXNCOORDNS2214.jpg|400px|thumb|right]]

Once again, the free energies of the reactants and transition were extracted from the log files, having been optimised at the PM6 level. The endo conformer has the lowest energy barrier, 3.98 KJmol<sup>-1</sup> lower than exo, making it the kinetic product.Plotting the reaction co-ordinate clearly displays the relative energies throughout the co-ordinate. The chelotropic product has the highest reaction barrier meaning it forms slowly as more energy is required to overcome the barrier. However, once the barrier has been overcome, the chelotropic product is lowest in energy and therefore the most stable, making it the thermodynamic product.
During the reaction, the 6-member-ed ring in xylylene is aromatised in order ot bring stability to the molecule.
{| class="wikitable" border="1" align="center"
|+ IRC pathways for o-Xylylene-SO2 Cycloaddition
|-
! colspan="2" style="text-align: center;"|Diels-Alder
! colspan="1" style="text-align: center;"|Chelotropic
|-
! rowspan="1" style="text-align: center;"|Exo
! rowspan="1" style="text-align: center;"|Endo
! rowspan="1" style="text-align: center;"|
|-
|rowspan="1" style="text-align: center;"|[[File:IRC exo3ns2214.gif|400px|thumb|center]]
|rowspan="1" style="text-align: center;"|[[File:ENDOTStrajectoryns2214.gif|400px|thumb|center]]
|rowspan="1" style="text-align: center;"|[[File:IRCTSchelns2214traj.gif|400px|thumb|center]]
|}
<br style="clear:right">
<br style="clear:left">
=Conclusion=

Rep:Mod:tsns2214

2017-03-23T13:01:33Z

Ns2214: /* Exercise 2 */

'''Transition States'''
=Introduction=
Potential energy surfaces display the energy of a system with respect to positions of the molecules. They can therefore be used to display transition states in a molecule. Transition states are an energy maximum where the gradient is 0, i.e. a turning point.However, depending on the complexity of the reaction, there can be many maxima on a PES as there are different trajectories predicted. If a transition state has been correctly found, it will have a saddle-point geometry where it is the maximum on its particular reaction co-ordinate, but the minimum compared to other pathways. There is an equal probability of falling down the potential energy curve to form either reactants or products at a transition state.

In this lab, the transition states of Diels-Alder reactions were studied. This involves a [4+2] cycloaddition between a diene and dienophile. These double bonded structures are close enough in energy to interact and form 2 new sigma bonds and breaking one pi bond overall. The formation of theses sigma bonds lowers the energy of the system as electrons occupy bonding molecular orbitals.

Gaussian software was used to analyse the transition state formation of three Diels-Alder reactions. Method 3 in the tutorial was used for all the reactions, where the expected product molecule was optimised, the relevant bonds broken and frozen, and then the resulting transition state optimised. Two levels of optimisation were used: PM6 semi-empirical for exercises 1 and 3 and B3LYP-DFT for exercise 2. PM6 uses relevant parameters to fit experimental dipole moments and geometries, allowing for faster results as some integrals are pre-determined. B3LYP however uses electron density in the molecule to optimise the structure and base it calculations on. If the correct transition state was found, there was one negative frequency found in the vibrations, corresponding to..

Several consideration have to be taken into account when studying Diels-Alder reactions. One is that the diene and dienophile's HOMO and LUMOs are are relatively close to each other. The smaller energy gap between a HOMO-LUMO pair depended on the nature of the reactants and their electron densities. The checkpoint files obtained from optimisations gave insight into the closer energy levels and thus explained the products formed. Another consideration was that a molecule, such as xylylene, could have multiple reaction sites or the molecules could approach each other at different geometries. Once transition state structures had been optimised, IRC analysis was conducted to confirm the transition state path. If there were multiple approach possibilities and transition state structures, the free energy data could be extracted from the log files, in order to find the thermodynamic and kinetic products.
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=Exercise 1=
The first Diels-Alder reaction characterised was between 1,3-butadiene and ethene, forming cyclohexene. Visualising the molecular orbitals for the optimised reactants, products and transition state enabled for an orbital diagram to be drawn ('''Figure 1'''). From the diagram it is evident that the formation of molecular orbitals is restricted by symmetry. Orbitals of the same symmetry/asymmetry are allowed to interact and bring stability to the moelcule. Looking at the values for the optimised reactants, the HOMO of the butadiene (-0.35899) and LUMO of the ethene (0.04256) are closer in energy and therefore the energy gap between the bonding and anti-bonding orbitals formed is larger. The orbital overlap is non-zero for a symmetric-symmetric or asymmetric-asymmetric interaction, and zero for an asymmetric-symmetric interaction.
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{| class="wikitable" border="1" align="right"
|+
|-
! colspan="5" style="text-align: center;"|Carbon numbering and bond lengths ('''Å''')
|-
| colspan="5" align="center"|[[File:TScarbonnumberns2214.jpg|250px|thumb|center|'''Figure 3''' Carbon numbering used by Gaussian]]
|-
! style="text-align: center;"|
! style="text-align: center;"|C1-C2/C5-C6
! style="text-align: center;"|C2-C3/C4-C5
! style="text-align: center;"|C3-C4
! style="text-align: center;"|C6-C1
|-
! rowspan="1" style="text-align: center;"| Reactants
| rowspan="1" style="text-align: center;"| -
| rowspan="1" style="text-align: center;"| 1.333
| rowspan="1" style="text-align: center;"| 1.471
| rowspan="1" style="text-align: center;"| 1.327
|-
! rowspan="1" style="text-align: center;"| Transition State
| rowspan="1" style="text-align: center;"| 2.115
| rowspan="1" style="text-align: center;"| 1.380
| rowspan="1" style="text-align: center;"| 1.411
| rowspan="1" style="text-align: center;"| 1.382
|-
! rowspan="1" style="text-align: center;"| Product
| rowspan="1" style="text-align: center;"| 1.537
| rowspan="1" style="text-align: center;"| 1.501
| rowspan="1" style="text-align: center;"| 1.337
| rowspan="1" style="text-align: center;"| 1.535
|-
|}
[[File:Ircgraphns2214.jpg|400px|thumb|left|'''Figure 2''' Graph showing internuclear distances during cyclohexene formation]]
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The graph in '''Figure 2''' displays how the C-C bonds change in length as the reactants approach the transition state and then form the products. Well before the transition state is reached, all bond lengths remain constant except for C1-C2 and C5-C6 as the ethene molecule approaches the butadiene. Typical sp<sup>2</sup> and sp<sup>3</sup> C-C bond lengths at this stage are around 1.336 and 1.468 Å respectively. Just before the transition state is approached,C1-C2 and C5-C6 continue to descend, but the other bond lengths appear to converge as the cyclisation occurs.

The four bond lengths converge just after the transition state. The bond length between the newly forming C1-C2 and C5-C6 is 2.115 at the transition state. This is significantly smaller than the Van Der Waal's radius of two Carbon atoms (1.7x2= 3.4 Å). This suggests that bond formation is occurring before, during and after the transition state, especially as the bond length continues to decrease linearly and plateau at a value of ~1.54 Å, the typical C-C sigma bond length. What defines the transition state of cyclohexene is the convergence of the four other bond lengths
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<br style="clear:left">.
[[File:CyclohexadieneMODiagramns2214.jpg|400px|thumb|left]]
{| class="wikitable" border="1" align="right"
|+ Exercise 1 Molecular Orbitals
|-
| style="text-align: center;"| PM6
! colspan="1" style="text-align: center;"|Ethene
! colspan="1" style="text-align: center;"|Butadiene
! colspan="2" style="text-align: center;"|Transition States
|-
! rowspan="1" style="text-align: center;"|LUMO
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
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|-
! rowspan="1" style="text-align: center;"| HOMO
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|-
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Formation of the two bonds is synchrous. ADD...
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=Exercise 2=
{| class="wikitable"
|+ Exercise 2 Molecular Orbitals
|-
| style="text-align: center;"| B3LYP
! colspan="2" style="text-align: center;"|EXO Transition States
! colspan="2" style="text-align: center;"|ENDO Transition States
|-
! rowspan="1" style="text-align: center;"|LUMO
| rowspan="1" style="text-align: center;"| <jmol>
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| rowspan="1" style="text-align: center;"| <jmol>
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| rowspan="1" style="text-align: center;"| <jmol>
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|-
! rowspan="1" style="text-align: center;"| HOMO
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|-
|}
[[File:Cyclohexadiene13DDiagramNS2214.jpg|400px|thumb|right|alt text]]
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{| class="wikitable" border="1" align="right"
|+ Table of Gibbs Free Energies and Reaction Barriers
|-
! style="text-align: center;"| (B3LYP level)
! colspan="2" style="text-align: center;"|Gibbs Free Energy
! colspan="2" style="text-align: center;"|Reaction Barrier
|-
! rowspan="1" style="text-align: center;"|
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
|-
! rowspan="1" style="text-align: center;"| Exo
| rowspan="1" style="text-align: center;"| -500.329
| rowspan="1" style="text-align: center;"| 1313613.608
| rowspan="1" style="text-align: center;"| 0.0633
| rowspan="1" style="text-align: center;"| 166.310
|-
! rowspan="1" style="text-align: center;"| Endo
| rowspan="1" style="text-align: center;"| -500.332
| rowspan="1" style="text-align: center;"| 1313621.485
| rowspan="1" style="text-align: center;"| 0.0604
| rowspan="1" style="text-align: center;"| 158.467
|-
|}
Following the progress of the reaction between cyclohexadiene and 1,3-dioxole produced varying results to the ones above. Here, a typical inverse demand Diels-Alder reaction was seen, where the diene's HOMO and dienophile's LUMO formed the molecular HOMO and LUMO orbitals of the transition state. Energy levels of the HOMO and LUMO for each reactant were obtained from the checkpoint files and shown in '''Figure 4'''. The energy gap between the diene's HOMO and dienophiles's LUMO is 0.34597 and therefore smaller than the diene's LUMO and dienophiles's HOMO energy gap of 0.34806. Smaller energy gap results in greater splitting. The electron rich nature of the diene 1,3-dioxole is due to the oxygen atoms adjacent to the double bond. The mixing of p orbitals raises the energy of the diene's HOMO and brings it closer to the dienophile's LUMO.

The Gibbs free energies were extracted from the log files of the reactants and transition states and the reaction barriers calculated accordingly. The endo-conformer of the product has a lower reaction barrier, being 7.842 KJmol<sup>-1</sup> smaller in value. This therefore makes it the kinetic product as less energy is required to overcome the barrier and thus over time, it will form more quickly.
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<br style="clear:left">

=Exercise 3=
{| class="wikitable" border="1" align="right"
|+ Table of Gibbs Free Energies and Reaction Barriers for o-Xylylene-SO2 Cycloaddition
|-
! style="text-align: center;"|(PM6 level)
! colspan="2" style="text-align: center;"|Gibbs Free Energy
! colspan="2" style="text-align: center;"|Reaction Barrier
|-
! rowspan="1" style="text-align: center;"|
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
|-
! rowspan="1" style="text-align: center;"| Exo
| rowspan="1" style="text-align: center;"| 0.092076
| rowspan="1" style="text-align: center;"|241.746
| rowspan="1" style="text-align: center;"| 0.032564
| rowspan="1" style="text-align: center;"| 85.497
|-
! rowspan="1" style="text-align: center;"| Endo
| rowspan="1" style="text-align: center;"| 0.090560
| rowspan="1" style="text-align: center;"| 237.765
| rowspan="1" style="text-align: center;"| 0.031048
| rowspan="1" style="text-align: center;"| 81.517
|-
! rowspan="1" style="text-align: center;"| Chelotropic
| rowspan="1" style="text-align: center;"| 0.099062
| rowspan="1" style="text-align: center;"|260.087
| rowspan="1" style="text-align: center;"| 0.03955
| rowspan="1" style="text-align: center;"| 103.839
|-
|}[[File:RXNCOORDNS2214.jpg|400px|thumb|right]]

Once again, the free energies of the reactants and transition were extracted from the log files, having been optimised at the PM6 level. The endo conformer has the lowest energy barrier, 3.98 KJmol<sup>-1</sup> lower than exo, making it the kinetic product.Plotting the reaction co-ordinate clearly displays the relative energies throughout the co-ordinate. The chelotropic product has the highest reaction barrier meaning it forms slowly as more energy is required to overcome the barrier. However, once the barrier has been overcome, the chelotropic product is lowest in energy and therefore the most stable, making it the thermodynamic product.
During the reaction, the 6-member-ed ring in xylylene is aromatised in order ot bring stability to the molecule.
{| class="wikitable" border="1" align="center"
|+ IRC pathways for o-Xylylene-SO2 Cycloaddition
|-
! colspan="2" style="text-align: center;"|Diels-Alder
! colspan="1" style="text-align: center;"|Chelotropic
|-
! rowspan="1" style="text-align: center;"|Exo
! rowspan="1" style="text-align: center;"|Endo
! rowspan="1" style="text-align: center;"|
|-
|rowspan="1" style="text-align: center;"|[[File:IRC exo3ns2214.gif|400px|thumb|center]]
|rowspan="1" style="text-align: center;"|[[File:ENDOTStrajectoryns2214.gif|400px|thumb|center]]
|rowspan="1" style="text-align: center;"|[[File:IRCTSchelns2214traj.gif|400px|thumb|center]]
|}
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<br style="clear:left">
=Conclusion=

Rep:Mod:tsns2214

2017-03-23T12:59:43Z

Ns2214: /* Exercise 2 */

'''Transition States'''
=Introduction=
Potential energy surfaces display the energy of a system with respect to positions of the molecules. They can therefore be used to display transition states in a molecule. Transition states are an energy maximum where the gradient is 0, i.e. a turning point.However, depending on the complexity of the reaction, there can be many maxima on a PES as there are different trajectories predicted. If a transition state has been correctly found, it will have a saddle-point geometry where it is the maximum on its particular reaction co-ordinate, but the minimum compared to other pathways. There is an equal probability of falling down the potential energy curve to form either reactants or products at a transition state.

In this lab, the transition states of Diels-Alder reactions were studied. This involves a [4+2] cycloaddition between a diene and dienophile. These double bonded structures are close enough in energy to interact and form 2 new sigma bonds and breaking one pi bond overall. The formation of theses sigma bonds lowers the energy of the system as electrons occupy bonding molecular orbitals.

Gaussian software was used to analyse the transition state formation of three Diels-Alder reactions. Method 3 in the tutorial was used for all the reactions, where the expected product molecule was optimised, the relevant bonds broken and frozen, and then the resulting transition state optimised. Two levels of optimisation were used: PM6 semi-empirical for exercises 1 and 3 and B3LYP-DFT for exercise 2. PM6 uses relevant parameters to fit experimental dipole moments and geometries, allowing for faster results as some integrals are pre-determined. B3LYP however uses electron density in the molecule to optimise the structure and base it calculations on. If the correct transition state was found, there was one negative frequency found in the vibrations, corresponding to..

Several consideration have to be taken into account when studying Diels-Alder reactions. One is that the diene and dienophile's HOMO and LUMOs are are relatively close to each other. The smaller energy gap between a HOMO-LUMO pair depended on the nature of the reactants and their electron densities. The checkpoint files obtained from optimisations gave insight into the closer energy levels and thus explained the products formed. Another consideration was that a molecule, such as xylylene, could have multiple reaction sites or the molecules could approach each other at different geometries. Once transition state structures had been optimised, IRC analysis was conducted to confirm the transition state path. If there were multiple approach possibilities and transition state structures, the free energy data could be extracted from the log files, in order to find the thermodynamic and kinetic products.
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<br style="clear:left">

=Exercise 1=
The first Diels-Alder reaction characterised was between 1,3-butadiene and ethene, forming cyclohexene. Visualising the molecular orbitals for the optimised reactants, products and transition state enabled for an orbital diagram to be drawn ('''Figure 1'''). From the diagram it is evident that the formation of molecular orbitals is restricted by symmetry. Orbitals of the same symmetry/asymmetry are allowed to interact and bring stability to the moelcule. Looking at the values for the optimised reactants, the HOMO of the butadiene (-0.35899) and LUMO of the ethene (0.04256) are closer in energy and therefore the energy gap between the bonding and anti-bonding orbitals formed is larger. The orbital overlap is non-zero for a symmetric-symmetric or asymmetric-asymmetric interaction, and zero for an asymmetric-symmetric interaction.
<br style="clear:right">
<br style="clear:left">.
{| class="wikitable" border="1" align="right"
|+
|-
! colspan="5" style="text-align: center;"|Carbon numbering and bond lengths ('''Å''')
|-
| colspan="5" align="center"|[[File:TScarbonnumberns2214.jpg|250px|thumb|center|'''Figure 3''' Carbon numbering used by Gaussian]]
|-
! style="text-align: center;"|
! style="text-align: center;"|C1-C2/C5-C6
! style="text-align: center;"|C2-C3/C4-C5
! style="text-align: center;"|C3-C4
! style="text-align: center;"|C6-C1
|-
! rowspan="1" style="text-align: center;"| Reactants
| rowspan="1" style="text-align: center;"| -
| rowspan="1" style="text-align: center;"| 1.333
| rowspan="1" style="text-align: center;"| 1.471
| rowspan="1" style="text-align: center;"| 1.327
|-
! rowspan="1" style="text-align: center;"| Transition State
| rowspan="1" style="text-align: center;"| 2.115
| rowspan="1" style="text-align: center;"| 1.380
| rowspan="1" style="text-align: center;"| 1.411
| rowspan="1" style="text-align: center;"| 1.382
|-
! rowspan="1" style="text-align: center;"| Product
| rowspan="1" style="text-align: center;"| 1.537
| rowspan="1" style="text-align: center;"| 1.501
| rowspan="1" style="text-align: center;"| 1.337
| rowspan="1" style="text-align: center;"| 1.535
|-
|}
[[File:Ircgraphns2214.jpg|400px|thumb|left|'''Figure 2''' Graph showing internuclear distances during cyclohexene formation]]
<br style="clear:right">
<br style="clear:left">.
The graph in '''Figure 2''' displays how the C-C bonds change in length as the reactants approach the transition state and then form the products. Well before the transition state is reached, all bond lengths remain constant except for C1-C2 and C5-C6 as the ethene molecule approaches the butadiene. Typical sp<sup>2</sup> and sp<sup>3</sup> C-C bond lengths at this stage are around 1.336 and 1.468 Å respectively. Just before the transition state is approached,C1-C2 and C5-C6 continue to descend, but the other bond lengths appear to converge as the cyclisation occurs.

The four bond lengths converge just after the transition state. The bond length between the newly forming C1-C2 and C5-C6 is 2.115 at the transition state. This is significantly smaller than the Van Der Waal's radius of two Carbon atoms (1.7x2= 3.4 Å). This suggests that bond formation is occurring before, during and after the transition state, especially as the bond length continues to decrease linearly and plateau at a value of ~1.54 Å, the typical C-C sigma bond length. What defines the transition state of cyclohexene is the convergence of the four other bond lengths
<br style="clear:right">
<br style="clear:left">.
[[File:CyclohexadieneMODiagramns2214.jpg|400px|thumb|left]]
{| class="wikitable" border="1" align="right"
|+ Exercise 1 Molecular Orbitals
|-
| style="text-align: center;"| PM6
! colspan="1" style="text-align: center;"|Ethene
! colspan="1" style="text-align: center;"|Butadiene
! colspan="2" style="text-align: center;"|Transition States
|-
! rowspan="1" style="text-align: center;"|LUMO
| rowspan="1" style="text-align: center;"| <jmol>
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</jmol>
|-
! rowspan="1" style="text-align: center;"| HOMO
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>ETHENENS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>BUTADIENENS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSOPTFREQPOPns2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSOPTFREQPOPns2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<br style="clear:right">
<br style="clear:left">
<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script>frame 17; vectors 3; vectors scale 3.0; color vectors orange; vibration 2; </script>
<uploadedFileContents>TSOPTFREQns2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Formation of the two bonds is synchrous. ADD...
<br style="clear:right">
<br style="clear:left">

=Exercise 2=
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Exercise 2 Molecular Orbitals
|-
| style="text-align: center;"| B3LYP
! colspan="2" style="text-align: center;"|EXO Transition States
! colspan="2" style="text-align: center;"|ENDO Transition States
|-
! rowspan="1" style="text-align: center;"|LUMO
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 45; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSEXOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 44; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSEXOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSENDOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSENDOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! rowspan="1" style="text-align: center;"| HOMO
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSEXOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSEXOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSENDOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSENDOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
[[File:Cyclohexadiene13DDiagramNS2214.jpg|400px|thumb|left|alt text]]
<br style="clear:right">
<br style="clear:left">
{| class="wikitable" border="1" align="right"
|+ Table of Gibbs Free Energies and Reaction Barriers
|-
! style="text-align: center;"| (B3LYP level)
! colspan="2" style="text-align: center;"|Gibbs Free Energy
! colspan="2" style="text-align: center;"|Reaction Barrier
|-
! rowspan="1" style="text-align: center;"|
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
|-
! rowspan="1" style="text-align: center;"| Exo
| rowspan="1" style="text-align: center;"| -500.329
| rowspan="1" style="text-align: center;"| 1313613.608
| rowspan="1" style="text-align: center;"| 0.0633
| rowspan="1" style="text-align: center;"| 166.310
|-
! rowspan="1" style="text-align: center;"| Endo
| rowspan="1" style="text-align: center;"| -500.332
| rowspan="1" style="text-align: center;"| 1313621.485
| rowspan="1" style="text-align: center;"| 0.0604
| rowspan="1" style="text-align: center;"| 158.467
|-
|}
Following the progress of the reaction between cyclohexadiene and 1,3-dioxole produced varying results to the ones above. Here, a typical inverse demand Diels-Alder reaction was seen, where the diene's HOMO and dienophile's LUMO formed the molecular HOMO and LUMO orbitals of the transition state. Energy levels of the HOMO and LUMO for each reactant were obtained from the checkpoint files and shown in '''Figure 4'''. The energy gap between the diene's HOMO and dienophiles's LUMO is 0.34597 and therefore smaller than the diene's LUMO and dienophiles's HOMO energy gap of 0.34806. Smaller energy gap results in greater splitting. The electron rich nature of the diene 1,3-dioxole is due to the oxygen atoms adjacent to the double bond. The mixing of p orbitals raises the energy of the diene's HOMO and brings it closer to the dienophile's LUMO.

The Gibbs free energies were extracted from the log files of the reactants and transition states and the reaction barriers calculated accordingly. The endo-conformer of the product has a lower reaction barrier, being 7.842 KJmol<sup>-1</sup> smaller in value. This therefore makes it the kinetic product as less energy is required to overcome the barrier and thus over time, it will form more quickly.
<br style="clear:right">
<br style="clear:left">

=Exercise 3=
{| class="wikitable" border="1" align="right"
|+ Table of Gibbs Free Energies and Reaction Barriers for o-Xylylene-SO2 Cycloaddition
|-
! style="text-align: center;"|(PM6 level)
! colspan="2" style="text-align: center;"|Gibbs Free Energy
! colspan="2" style="text-align: center;"|Reaction Barrier
|-
! rowspan="1" style="text-align: center;"|
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
|-
! rowspan="1" style="text-align: center;"| Exo
| rowspan="1" style="text-align: center;"| 0.092076
| rowspan="1" style="text-align: center;"|241.746
| rowspan="1" style="text-align: center;"| 0.032564
| rowspan="1" style="text-align: center;"| 85.497
|-
! rowspan="1" style="text-align: center;"| Endo
| rowspan="1" style="text-align: center;"| 0.090560
| rowspan="1" style="text-align: center;"| 237.765
| rowspan="1" style="text-align: center;"| 0.031048
| rowspan="1" style="text-align: center;"| 81.517
|-
! rowspan="1" style="text-align: center;"| Chelotropic
| rowspan="1" style="text-align: center;"| 0.099062
| rowspan="1" style="text-align: center;"|260.087
| rowspan="1" style="text-align: center;"| 0.03955
| rowspan="1" style="text-align: center;"| 103.839
|-
|}[[File:RXNCOORDNS2214.jpg|400px|thumb|right]]

Once again, the free energies of the reactants and transition were extracted from the log files, having been optimised at the PM6 level. The endo conformer has the lowest energy barrier, 3.98 KJmol<sup>-1</sup> lower than exo, making it the kinetic product.Plotting the reaction co-ordinate clearly displays the relative energies throughout the co-ordinate. The chelotropic product has the highest reaction barrier meaning it forms slowly as more energy is required to overcome the barrier. However, once the barrier has been overcome, the chelotropic product is lowest in energy and therefore the most stable, making it the thermodynamic product.
During the reaction, the 6-member-ed ring in xylylene is aromatised in order ot bring stability to the molecule.
{| class="wikitable" border="1" align="center"
|+ IRC pathways for o-Xylylene-SO2 Cycloaddition
|-
! colspan="2" style="text-align: center;"|Diels-Alder
! colspan="1" style="text-align: center;"|Chelotropic
|-
! rowspan="1" style="text-align: center;"|Exo
! rowspan="1" style="text-align: center;"|Endo
! rowspan="1" style="text-align: center;"|
|-
|rowspan="1" style="text-align: center;"|[[File:IRC exo3ns2214.gif|400px|thumb|center]]
|rowspan="1" style="text-align: center;"|[[File:ENDOTStrajectoryns2214.gif|400px|thumb|center]]
|rowspan="1" style="text-align: center;"|[[File:IRCTSchelns2214traj.gif|400px|thumb|center]]
|}
<br style="clear:right">
<br style="clear:left">
=Conclusion=

File:Cyclohexadiene13DDiagramNS2214.jpg

2017-03-23T12:58:44Z

Ns2214:

Rep:Mod:tsns2214

2017-03-23T12:41:07Z

Ns2214: /* Exercise 1 */

'''Transition States'''
=Introduction=
Potential energy surfaces display the energy of a system with respect to positions of the molecules. They can therefore be used to display transition states in a molecule. Transition states are an energy maximum where the gradient is 0, i.e. a turning point.However, depending on the complexity of the reaction, there can be many maxima on a PES as there are different trajectories predicted. If a transition state has been correctly found, it will have a saddle-point geometry where it is the maximum on its particular reaction co-ordinate, but the minimum compared to other pathways. There is an equal probability of falling down the potential energy curve to form either reactants or products at a transition state.

In this lab, the transition states of Diels-Alder reactions were studied. This involves a [4+2] cycloaddition between a diene and dienophile. These double bonded structures are close enough in energy to interact and form 2 new sigma bonds and breaking one pi bond overall. The formation of theses sigma bonds lowers the energy of the system as electrons occupy bonding molecular orbitals.

Gaussian software was used to analyse the transition state formation of three Diels-Alder reactions. Method 3 in the tutorial was used for all the reactions, where the expected product molecule was optimised, the relevant bonds broken and frozen, and then the resulting transition state optimised. Two levels of optimisation were used: PM6 semi-empirical for exercises 1 and 3 and B3LYP-DFT for exercise 2. PM6 uses relevant parameters to fit experimental dipole moments and geometries, allowing for faster results as some integrals are pre-determined. B3LYP however uses electron density in the molecule to optimise the structure and base it calculations on. If the correct transition state was found, there was one negative frequency found in the vibrations, corresponding to..

Several consideration have to be taken into account when studying Diels-Alder reactions. One is that the diene and dienophile's HOMO and LUMOs are are relatively close to each other. The smaller energy gap between a HOMO-LUMO pair depended on the nature of the reactants and their electron densities. The checkpoint files obtained from optimisations gave insight into the closer energy levels and thus explained the products formed. Another consideration was that a molecule, such as xylylene, could have multiple reaction sites or the molecules could approach each other at different geometries. Once transition state structures had been optimised, IRC analysis was conducted to confirm the transition state path. If there were multiple approach possibilities and transition state structures, the free energy data could be extracted from the log files, in order to find the thermodynamic and kinetic products.
<br style="clear:right">
<br style="clear:left">

=Exercise 1=
The first Diels-Alder reaction characterised was between 1,3-butadiene and ethene, forming cyclohexene. Visualising the molecular orbitals for the optimised reactants, products and transition state enabled for an orbital diagram to be drawn ('''Figure 1'''). From the diagram it is evident that the formation of molecular orbitals is restricted by symmetry. Orbitals of the same symmetry/asymmetry are allowed to interact and bring stability to the moelcule. Looking at the values for the optimised reactants, the HOMO of the butadiene (-0.35899) and LUMO of the ethene (0.04256) are closer in energy and therefore the energy gap between the bonding and anti-bonding orbitals formed is larger. The orbital overlap is non-zero for a symmetric-symmetric or asymmetric-asymmetric interaction, and zero for an asymmetric-symmetric interaction.
<br style="clear:right">
<br style="clear:left">.
{| class="wikitable" border="1" align="right"
|+
|-
! colspan="5" style="text-align: center;"|Carbon numbering and bond lengths ('''Å''')
|-
| colspan="5" align="center"|[[File:TScarbonnumberns2214.jpg|250px|thumb|center|'''Figure 3''' Carbon numbering used by Gaussian]]
|-
! style="text-align: center;"|
! style="text-align: center;"|C1-C2/C5-C6
! style="text-align: center;"|C2-C3/C4-C5
! style="text-align: center;"|C3-C4
! style="text-align: center;"|C6-C1
|-
! rowspan="1" style="text-align: center;"| Reactants
| rowspan="1" style="text-align: center;"| -
| rowspan="1" style="text-align: center;"| 1.333
| rowspan="1" style="text-align: center;"| 1.471
| rowspan="1" style="text-align: center;"| 1.327
|-
! rowspan="1" style="text-align: center;"| Transition State
| rowspan="1" style="text-align: center;"| 2.115
| rowspan="1" style="text-align: center;"| 1.380
| rowspan="1" style="text-align: center;"| 1.411
| rowspan="1" style="text-align: center;"| 1.382
|-
! rowspan="1" style="text-align: center;"| Product
| rowspan="1" style="text-align: center;"| 1.537
| rowspan="1" style="text-align: center;"| 1.501
| rowspan="1" style="text-align: center;"| 1.337
| rowspan="1" style="text-align: center;"| 1.535
|-
|}
[[File:Ircgraphns2214.jpg|400px|thumb|left|'''Figure 2''' Graph showing internuclear distances during cyclohexene formation]]
<br style="clear:right">
<br style="clear:left">.
The graph in '''Figure 2''' displays how the C-C bonds change in length as the reactants approach the transition state and then form the products. Well before the transition state is reached, all bond lengths remain constant except for C1-C2 and C5-C6 as the ethene molecule approaches the butadiene. Typical sp<sup>2</sup> and sp<sup>3</sup> C-C bond lengths at this stage are around 1.336 and 1.468 Å respectively. Just before the transition state is approached,C1-C2 and C5-C6 continue to descend, but the other bond lengths appear to converge as the cyclisation occurs.

The four bond lengths converge just after the transition state. The bond length between the newly forming C1-C2 and C5-C6 is 2.115 at the transition state. This is significantly smaller than the Van Der Waal's radius of two Carbon atoms (1.7x2= 3.4 Å). This suggests that bond formation is occurring before, during and after the transition state, especially as the bond length continues to decrease linearly and plateau at a value of ~1.54 Å, the typical C-C sigma bond length. What defines the transition state of cyclohexene is the convergence of the four other bond lengths
<br style="clear:right">
<br style="clear:left">.
[[File:CyclohexadieneMODiagramns2214.jpg|400px|thumb|left]]
{| class="wikitable" border="1" align="right"
|+ Exercise 1 Molecular Orbitals
|-
| style="text-align: center;"| PM6
! colspan="1" style="text-align: center;"|Ethene
! colspan="1" style="text-align: center;"|Butadiene
! colspan="2" style="text-align: center;"|Transition States
|-
! rowspan="1" style="text-align: center;"|LUMO
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>ETHENENS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>BUTADIENENS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSOPTFREQPOPns2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSOPTFREQPOPns2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! rowspan="1" style="text-align: center;"| HOMO
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>ETHENENS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>BUTADIENENS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSOPTFREQPOPns2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSOPTFREQPOPns2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<br style="clear:right">
<br style="clear:left">
<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script>frame 17; vectors 3; vectors scale 3.0; color vectors orange; vibration 2; </script>
<uploadedFileContents>TSOPTFREQns2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Formation of the two bonds is synchrous. ADD...
<br style="clear:right">
<br style="clear:left">

=Exercise 2=
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Exercise 2 Molecular Orbitals
|-
| style="text-align: center;"| B3LYP
! colspan="2" style="text-align: center;"|EXO Transition States
! colspan="2" style="text-align: center;"|ENDO Transition States
|-
! rowspan="1" style="text-align: center;"|LUMO
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 45; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSEXOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 44; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSEXOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSENDOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSENDOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! rowspan="1" style="text-align: center;"| HOMO
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
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<uploadedFileContents>TSEXOPOPNS2214.LOG</uploadedFileContents>
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</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
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<script> frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSEXOPOPNS2214.LOG</uploadedFileContents>
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</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSENDOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
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<script> frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSENDOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<br style="clear:right">
<br style="clear:left">
{| class="wikitable" border="1" align="right"
|+ Table of Gibbs Free Energies and Reaction Barriers
|-
! style="text-align: center;"| (B3LYP level)
! colspan="2" style="text-align: center;"|Gibbs Free Energy
! colspan="2" style="text-align: center;"|Reaction Barrier
|-
! rowspan="1" style="text-align: center;"|
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
|-
! rowspan="1" style="text-align: center;"| Exo
| rowspan="1" style="text-align: center;"| -500.329
| rowspan="1" style="text-align: center;"| 1313613.608
| rowspan="1" style="text-align: center;"| 0.0633
| rowspan="1" style="text-align: center;"| 166.310
|-
! rowspan="1" style="text-align: center;"| Endo
| rowspan="1" style="text-align: center;"| -500.332
| rowspan="1" style="text-align: center;"| 1313621.485
| rowspan="1" style="text-align: center;"| 0.0604
| rowspan="1" style="text-align: center;"| 158.467
|-
|}
Following the progress of the reaction between cyclohexadiene and 1,3-dioxole produced varying results to the ones above. Here, a typical inverse demand Diels-Alder reaction was seen, where the diene's HOMO and dienophile's LUMO formed the molecular HOMO and LUMO orbitals of the transition state. Energy levels of the HOMO and LUMO for each reactant were obtained from the checkpoint files and shown in '''Figure 4'''. The energy gap between the diene's HOMO and dienophiles's LUMO is 0.34597 and therefore smaller than the diene's LUMO and dienophiles's HOMO energy gap of 0.34806. Smaller energy gap results in greater splitting. The electron rich nature of the diene 1,3-dioxole is due to the oxygen atoms adjacent to the double bond. The mixing of p orbitals raises the energy of the diene's HOMO and brings it closer to the dienophile's LUMO.

The Gibbs free energies were extracted from the log files of the reactants and transition states and the reaction barriers calculated accordingly. The endo-conformer of the product has a lower reaction barrier, being 7.842 KJmol<sup>-1</sup> smaller in value. This therefore makes it the kinetic product as less energy is required to overcome the barrier and thus over time, it will form more quickly.
<br style="clear:right">
<br style="clear:left">

=Exercise 3=
{| class="wikitable" border="1" align="right"
|+ Table of Gibbs Free Energies and Reaction Barriers for o-Xylylene-SO2 Cycloaddition
|-
! style="text-align: center;"|(PM6 level)
! colspan="2" style="text-align: center;"|Gibbs Free Energy
! colspan="2" style="text-align: center;"|Reaction Barrier
|-
! rowspan="1" style="text-align: center;"|
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
|-
! rowspan="1" style="text-align: center;"| Exo
| rowspan="1" style="text-align: center;"| 0.092076
| rowspan="1" style="text-align: center;"|241.746
| rowspan="1" style="text-align: center;"| 0.032564
| rowspan="1" style="text-align: center;"| 85.497
|-
! rowspan="1" style="text-align: center;"| Endo
| rowspan="1" style="text-align: center;"| 0.090560
| rowspan="1" style="text-align: center;"| 237.765
| rowspan="1" style="text-align: center;"| 0.031048
| rowspan="1" style="text-align: center;"| 81.517
|-
! rowspan="1" style="text-align: center;"| Chelotropic
| rowspan="1" style="text-align: center;"| 0.099062
| rowspan="1" style="text-align: center;"|260.087
| rowspan="1" style="text-align: center;"| 0.03955
| rowspan="1" style="text-align: center;"| 103.839
|-
|}[[File:RXNCOORDNS2214.jpg|400px|thumb|right]]

Once again, the free energies of the reactants and transition were extracted from the log files, having been optimised at the PM6 level. The endo conformer has the lowest energy barrier, 3.98 KJmol<sup>-1</sup> lower than exo, making it the kinetic product.Plotting the reaction co-ordinate clearly displays the relative energies throughout the co-ordinate. The chelotropic product has the highest reaction barrier meaning it forms slowly as more energy is required to overcome the barrier. However, once the barrier has been overcome, the chelotropic product is lowest in energy and therefore the most stable, making it the thermodynamic product.
During the reaction, the 6-member-ed ring in xylylene is aromatised in order ot bring stability to the molecule.
{| class="wikitable" border="1" align="center"
|+ IRC pathways for o-Xylylene-SO2 Cycloaddition
|-
! colspan="2" style="text-align: center;"|Diels-Alder
! colspan="1" style="text-align: center;"|Chelotropic
|-
! rowspan="1" style="text-align: center;"|Exo
! rowspan="1" style="text-align: center;"|Endo
! rowspan="1" style="text-align: center;"|
|-
|rowspan="1" style="text-align: center;"|[[File:IRC exo3ns2214.gif|400px|thumb|center]]
|rowspan="1" style="text-align: center;"|[[File:ENDOTStrajectoryns2214.gif|400px|thumb|center]]
|rowspan="1" style="text-align: center;"|[[File:IRCTSchelns2214traj.gif|400px|thumb|center]]
|}
<br style="clear:right">
<br style="clear:left">
=Conclusion=

Rep:Mod:tsns2214

2017-03-23T12:40:11Z

Ns2214: /* Exercise 1 */

'''Transition States'''
=Introduction=
Potential energy surfaces display the energy of a system with respect to positions of the molecules. They can therefore be used to display transition states in a molecule. Transition states are an energy maximum where the gradient is 0, i.e. a turning point.However, depending on the complexity of the reaction, there can be many maxima on a PES as there are different trajectories predicted. If a transition state has been correctly found, it will have a saddle-point geometry where it is the maximum on its particular reaction co-ordinate, but the minimum compared to other pathways. There is an equal probability of falling down the potential energy curve to form either reactants or products at a transition state.

In this lab, the transition states of Diels-Alder reactions were studied. This involves a [4+2] cycloaddition between a diene and dienophile. These double bonded structures are close enough in energy to interact and form 2 new sigma bonds and breaking one pi bond overall. The formation of theses sigma bonds lowers the energy of the system as electrons occupy bonding molecular orbitals.

Gaussian software was used to analyse the transition state formation of three Diels-Alder reactions. Method 3 in the tutorial was used for all the reactions, where the expected product molecule was optimised, the relevant bonds broken and frozen, and then the resulting transition state optimised. Two levels of optimisation were used: PM6 semi-empirical for exercises 1 and 3 and B3LYP-DFT for exercise 2. PM6 uses relevant parameters to fit experimental dipole moments and geometries, allowing for faster results as some integrals are pre-determined. B3LYP however uses electron density in the molecule to optimise the structure and base it calculations on. If the correct transition state was found, there was one negative frequency found in the vibrations, corresponding to..

Several consideration have to be taken into account when studying Diels-Alder reactions. One is that the diene and dienophile's HOMO and LUMOs are are relatively close to each other. The smaller energy gap between a HOMO-LUMO pair depended on the nature of the reactants and their electron densities. The checkpoint files obtained from optimisations gave insight into the closer energy levels and thus explained the products formed. Another consideration was that a molecule, such as xylylene, could have multiple reaction sites or the molecules could approach each other at different geometries. Once transition state structures had been optimised, IRC analysis was conducted to confirm the transition state path. If there were multiple approach possibilities and transition state structures, the free energy data could be extracted from the log files, in order to find the thermodynamic and kinetic products.
<br style="clear:right">
<br style="clear:left">

=Exercise 1=
The first Diels-Alder reaction characterised was between 1,3-butadiene and ethene, forming cyclohexene. Visualising the molecular orbitals for the optimised reactants, products and transition state enabled for an orbital diagram to be drawn ('''Figure 1'''). From the diagram it is evident that the formation of molecular orbitals is restricted by symmetry. Orbitals of the same symmetry/asymmetry are allowed to interact and bring stability to the moelcule. Looking at the values for the optimised reactants, the HOMO of the butadiene (-0.35899) and LUMO of the ethene (0.04256) are closer in energy and therefore the energy gap between the bonding and anti-bonding orbitals formed is larger. The orbital overlap is non-zero for a symmetric-symmetric or asymmetric-asymmetric interaction, and zero for an asymmetric-symmetric interaction.
<br style="clear:right">
<br style="clear:left">.
{| class="wikitable" border="1" align="right"
|+
|-
! colspan="5" style="text-align: center;"|Carbon numbering and bond lengths ('''Å''')
|-
| colspan="5" align="center"|[[File:TScarbonnumberns2214.jpg|250px|thumb|center|'''Figure 3''' Carbon numbering used by Gaussian]]
|-
! style="text-align: center;"|
! style="text-align: center;"|C1-C2/C5-C6
! style="text-align: center;"|C2-C3/C4-C5
! style="text-align: center;"|C3-C4
! style="text-align: center;"|C6-C1
|-
! rowspan="1" style="text-align: center;"| Reactants
| rowspan="1" style="text-align: center;"| -
| rowspan="1" style="text-align: center;"| 1.333
| rowspan="1" style="text-align: center;"| 1.471
| rowspan="1" style="text-align: center;"| 1.327
|-
! rowspan="1" style="text-align: center;"| Transition State
| rowspan="1" style="text-align: center;"| 2.115
| rowspan="1" style="text-align: center;"| 1.380
| rowspan="1" style="text-align: center;"| 1.411
| rowspan="1" style="text-align: center;"| 1.382
|-
! rowspan="1" style="text-align: center;"| Product
| rowspan="1" style="text-align: center;"| 1.537
| rowspan="1" style="text-align: center;"| 1.501
| rowspan="1" style="text-align: center;"| 1.337
| rowspan="1" style="text-align: center;"| 1.535
|-
|}
[[File:Ircgraphns2214.jpg|400px|thumb|right|'''Figure 2''' Graph showing internuclear distances during cyclohexene formation]]
<br style="clear:right">
<br style="clear:left">.
The graph in '''Figure 2''' displays how the C-C bonds change in length as the reactants approach the transition state and then form the products. Well before the transition state is reached, all bond lengths remain constant except for C1-C2 and C5-C6 as the ethene molecule approaches the butadiene. Typical sp<sup>2</sup> and sp<sup>3</sup> C-C bond lengths at this stage are around 1.336 and 1.468 Å respectively. Just before the transition state is approached,C1-C2 and C5-C6 continue to descend, but the other bond lengths appear to converge as the cyclisation occurs.

The four bond lengths converge just after the transition state. The bond length between the newly forming C1-C2 and C5-C6 is 2.115 at the transition state. This is significantly smaller than the Van Der Waal's radius of two Carbon atoms (1.7x2= 3.4 Å). This suggests that bond formation is occurring before, during and after the transition state, especially as the bond length continues to decrease linearly and plateau at a value of ~1.54 Å, the typical C-C sigma bond length. What defines the transition state of cyclohexene is the convergence of the four other bond lengths
<br style="clear:right">
<br style="clear:left">.
[[File:CyclohexadieneMODiagramns2214.jpg|400px|thumb|left]]
{| class="wikitable" border="1" align="right"
|+ Exercise 1 Molecular Orbitals
|-
| style="text-align: center;"| PM6
! colspan="1" style="text-align: center;"|Ethene
! colspan="1" style="text-align: center;"|Butadiene
! colspan="2" style="text-align: center;"|Transition States
|-
! rowspan="1" style="text-align: center;"|LUMO
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>ETHENENS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>BUTADIENENS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSOPTFREQPOPns2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSOPTFREQPOPns2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! rowspan="1" style="text-align: center;"| HOMO
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>ETHENENS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>BUTADIENENS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSOPTFREQPOPns2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSOPTFREQPOPns2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<br style="clear:right">
<br style="clear:left">
<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script>frame 17; vectors 3; vectors scale 3.0; color vectors orange; vibration 2; </script>
<uploadedFileContents>TSOPTFREQns2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Formation of the two bonds is synchrous. ADD...
<br style="clear:right">
<br style="clear:left">

=Exercise 2=
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Exercise 2 Molecular Orbitals
|-
| style="text-align: center;"| B3LYP
! colspan="2" style="text-align: center;"|EXO Transition States
! colspan="2" style="text-align: center;"|ENDO Transition States
|-
! rowspan="1" style="text-align: center;"|LUMO
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 45; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSEXOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 44; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSEXOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSENDOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSENDOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! rowspan="1" style="text-align: center;"| HOMO
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSEXOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSEXOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSENDOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSENDOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<br style="clear:right">
<br style="clear:left">
{| class="wikitable" border="1" align="right"
|+ Table of Gibbs Free Energies and Reaction Barriers
|-
! style="text-align: center;"| (B3LYP level)
! colspan="2" style="text-align: center;"|Gibbs Free Energy
! colspan="2" style="text-align: center;"|Reaction Barrier
|-
! rowspan="1" style="text-align: center;"|
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
|-
! rowspan="1" style="text-align: center;"| Exo
| rowspan="1" style="text-align: center;"| -500.329
| rowspan="1" style="text-align: center;"| 1313613.608
| rowspan="1" style="text-align: center;"| 0.0633
| rowspan="1" style="text-align: center;"| 166.310
|-
! rowspan="1" style="text-align: center;"| Endo
| rowspan="1" style="text-align: center;"| -500.332
| rowspan="1" style="text-align: center;"| 1313621.485
| rowspan="1" style="text-align: center;"| 0.0604
| rowspan="1" style="text-align: center;"| 158.467
|-
|}
Following the progress of the reaction between cyclohexadiene and 1,3-dioxole produced varying results to the ones above. Here, a typical inverse demand Diels-Alder reaction was seen, where the diene's HOMO and dienophile's LUMO formed the molecular HOMO and LUMO orbitals of the transition state. Energy levels of the HOMO and LUMO for each reactant were obtained from the checkpoint files and shown in '''Figure 4'''. The energy gap between the diene's HOMO and dienophiles's LUMO is 0.34597 and therefore smaller than the diene's LUMO and dienophiles's HOMO energy gap of 0.34806. Smaller energy gap results in greater splitting. The electron rich nature of the diene 1,3-dioxole is due to the oxygen atoms adjacent to the double bond. The mixing of p orbitals raises the energy of the diene's HOMO and brings it closer to the dienophile's LUMO.

The Gibbs free energies were extracted from the log files of the reactants and transition states and the reaction barriers calculated accordingly. The endo-conformer of the product has a lower reaction barrier, being 7.842 KJmol<sup>-1</sup> smaller in value. This therefore makes it the kinetic product as less energy is required to overcome the barrier and thus over time, it will form more quickly.
<br style="clear:right">
<br style="clear:left">

=Exercise 3=
{| class="wikitable" border="1" align="right"
|+ Table of Gibbs Free Energies and Reaction Barriers for o-Xylylene-SO2 Cycloaddition
|-
! style="text-align: center;"|(PM6 level)
! colspan="2" style="text-align: center;"|Gibbs Free Energy
! colspan="2" style="text-align: center;"|Reaction Barrier
|-
! rowspan="1" style="text-align: center;"|
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
|-
! rowspan="1" style="text-align: center;"| Exo
| rowspan="1" style="text-align: center;"| 0.092076
| rowspan="1" style="text-align: center;"|241.746
| rowspan="1" style="text-align: center;"| 0.032564
| rowspan="1" style="text-align: center;"| 85.497
|-
! rowspan="1" style="text-align: center;"| Endo
| rowspan="1" style="text-align: center;"| 0.090560
| rowspan="1" style="text-align: center;"| 237.765
| rowspan="1" style="text-align: center;"| 0.031048
| rowspan="1" style="text-align: center;"| 81.517
|-
! rowspan="1" style="text-align: center;"| Chelotropic
| rowspan="1" style="text-align: center;"| 0.099062
| rowspan="1" style="text-align: center;"|260.087
| rowspan="1" style="text-align: center;"| 0.03955
| rowspan="1" style="text-align: center;"| 103.839
|-
|}[[File:RXNCOORDNS2214.jpg|400px|thumb|right]]

Once again, the free energies of the reactants and transition were extracted from the log files, having been optimised at the PM6 level. The endo conformer has the lowest energy barrier, 3.98 KJmol<sup>-1</sup> lower than exo, making it the kinetic product.Plotting the reaction co-ordinate clearly displays the relative energies throughout the co-ordinate. The chelotropic product has the highest reaction barrier meaning it forms slowly as more energy is required to overcome the barrier. However, once the barrier has been overcome, the chelotropic product is lowest in energy and therefore the most stable, making it the thermodynamic product.
During the reaction, the 6-member-ed ring in xylylene is aromatised in order ot bring stability to the molecule.
{| class="wikitable" border="1" align="center"
|+ IRC pathways for o-Xylylene-SO2 Cycloaddition
|-
! colspan="2" style="text-align: center;"|Diels-Alder
! colspan="1" style="text-align: center;"|Chelotropic
|-
! rowspan="1" style="text-align: center;"|Exo
! rowspan="1" style="text-align: center;"|Endo
! rowspan="1" style="text-align: center;"|
|-
|rowspan="1" style="text-align: center;"|[[File:IRC exo3ns2214.gif|400px|thumb|center]]
|rowspan="1" style="text-align: center;"|[[File:ENDOTStrajectoryns2214.gif|400px|thumb|center]]
|rowspan="1" style="text-align: center;"|[[File:IRCTSchelns2214traj.gif|400px|thumb|center]]
|}
<br style="clear:right">
<br style="clear:left">
=Conclusion=

Rep:Mod:tsns2214

2017-03-23T12:37:54Z

Ns2214: /* Exercise 1 */

'''Transition States'''
=Introduction=
Potential energy surfaces display the energy of a system with respect to positions of the molecules. They can therefore be used to display transition states in a molecule. Transition states are an energy maximum where the gradient is 0, i.e. a turning point.However, depending on the complexity of the reaction, there can be many maxima on a PES as there are different trajectories predicted. If a transition state has been correctly found, it will have a saddle-point geometry where it is the maximum on its particular reaction co-ordinate, but the minimum compared to other pathways. There is an equal probability of falling down the potential energy curve to form either reactants or products at a transition state.

In this lab, the transition states of Diels-Alder reactions were studied. This involves a [4+2] cycloaddition between a diene and dienophile. These double bonded structures are close enough in energy to interact and form 2 new sigma bonds and breaking one pi bond overall. The formation of theses sigma bonds lowers the energy of the system as electrons occupy bonding molecular orbitals.

Gaussian software was used to analyse the transition state formation of three Diels-Alder reactions. Method 3 in the tutorial was used for all the reactions, where the expected product molecule was optimised, the relevant bonds broken and frozen, and then the resulting transition state optimised. Two levels of optimisation were used: PM6 semi-empirical for exercises 1 and 3 and B3LYP-DFT for exercise 2. PM6 uses relevant parameters to fit experimental dipole moments and geometries, allowing for faster results as some integrals are pre-determined. B3LYP however uses electron density in the molecule to optimise the structure and base it calculations on. If the correct transition state was found, there was one negative frequency found in the vibrations, corresponding to..

Several consideration have to be taken into account when studying Diels-Alder reactions. One is that the diene and dienophile's HOMO and LUMOs are are relatively close to each other. The smaller energy gap between a HOMO-LUMO pair depended on the nature of the reactants and their electron densities. The checkpoint files obtained from optimisations gave insight into the closer energy levels and thus explained the products formed. Another consideration was that a molecule, such as xylylene, could have multiple reaction sites or the molecules could approach each other at different geometries. Once transition state structures had been optimised, IRC analysis was conducted to confirm the transition state path. If there were multiple approach possibilities and transition state structures, the free energy data could be extracted from the log files, in order to find the thermodynamic and kinetic products.
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=Exercise 1=
{| class="wikitable" border="1" align="right"
|+
|-
! colspan="5" style="text-align: center;"|Carbon numbering and bond lengths ('''Å''')
|-
| colspan="5" align="center"|[[File:TScarbonnumberns2214.jpg|250px|thumb|center|'''Figure 3''' Carbon numbering used by Gaussian]]
|-
! style="text-align: center;"|
! style="text-align: center;"|C1-C2/C5-C6
! style="text-align: center;"|C2-C3/C4-C5
! style="text-align: center;"|C3-C4
! style="text-align: center;"|C6-C1
|-
! rowspan="1" style="text-align: center;"| Reactants
| rowspan="1" style="text-align: center;"| -
| rowspan="1" style="text-align: center;"| 1.333
| rowspan="1" style="text-align: center;"| 1.471
| rowspan="1" style="text-align: center;"| 1.327
|-
! rowspan="1" style="text-align: center;"| Transition State
| rowspan="1" style="text-align: center;"| 2.115
| rowspan="1" style="text-align: center;"| 1.380
| rowspan="1" style="text-align: center;"| 1.411
| rowspan="1" style="text-align: center;"| 1.382
|-
! rowspan="1" style="text-align: center;"| Product
| rowspan="1" style="text-align: center;"| 1.537
| rowspan="1" style="text-align: center;"| 1.501
| rowspan="1" style="text-align: center;"| 1.337
| rowspan="1" style="text-align: center;"| 1.535
|-
|}
[[File:Ircgraphns2214.jpg|400px|thumb|right|'''Figure 2''' Graph showing internuclear distances during cyclohexene formation]]
The first Diels-Alder reaction characterised was between 1,3-butadiene and ethene, forming cyclohexene. Visualising the molecular orbitals for the optimised reactants, products and transition state enabled for an orbital diagram to be drawn ('''Figure 1'''). From the diagram it is evident that the formation of molecular orbitals is restricted by symmetry. Orbitals of the same symmetry/asymmetry are allowed to interact and bring stability to the moelcule. Looking at the values for the optimised reactants, the HOMO of the butadiene (-0.35899) and LUMO of the ethene (0.04256) are closer in energy and therefore the energy gap between the bonding and anti-bonding orbitals formed is larger. The orbital overlap is non-zero for a symmetric-symmetric or asymmetric-asymmetric interaction, and zero for an asymmetric-symmetric interaction.

The graph in '''Figure 2''' displays how the C-C bonds change in length as the reactants approach the transition state and then form the products. Well before the transition state is reached, all bond lengths remain constant except for C1-C2 and C5-C6 as the ethene molecule approaches the butadiene. Typical sp<sup>2</sup> and sp<sup>3</sup> C-C bond lengths at this stage are around 1.336 and 1.468 Å respectively. Just before the transition state is approached,C1-C2 and C5-C6 continue to descend, but the other bond lengths appear to converge as the cyclisation occurs.

The four bond lengths converge just after the transition state. The bond length between the newly forming C1-C2 and C5-C6 is 2.115 at the transition state. This is significantly smaller than the Van Der Waal's radius of two Carbon atoms (1.7x2= 3.4 Å). This suggests that bond formation is occurring before, during and after the transition state, especially as the bond length continues to decrease linearly and plateau at a value of ~1.54 Å, the typical C-C sigma bond length. What defines the transition state of cyclohexene is the convergence of the four other bond lengths
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[[File:CyclohexadieneMODiagramns2214.jpg|400px|thumb|left]]
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{| class="wikitable" border="1" align="right"
|+ Exercise 1 Molecular Orbitals
|-
| style="text-align: center;"| PM6
! colspan="1" style="text-align: center;"|Ethene
! colspan="1" style="text-align: center;"|Butadiene
! colspan="2" style="text-align: center;"|Transition States
|-
! rowspan="1" style="text-align: center;"|LUMO
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
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| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>BUTADIENENS2214.LOG</uploadedFileContents>
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| rowspan="1" style="text-align: center;"| <jmol>
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<title>LUMO+1</title>
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| rowspan="1" style="text-align: center;"| <jmol>
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|-
! rowspan="1" style="text-align: center;"| HOMO
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|-
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Formation of the two bonds is synchrous. ADD...
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=Exercise 2=
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Exercise 2 Molecular Orbitals
|-
| style="text-align: center;"| B3LYP
! colspan="2" style="text-align: center;"|EXO Transition States
! colspan="2" style="text-align: center;"|ENDO Transition States
|-
! rowspan="1" style="text-align: center;"|LUMO
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 45; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSEXOPOPNS2214.LOG</uploadedFileContents>
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</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 44; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSEXOPOPNS2214.LOG</uploadedFileContents>
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| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSENDOPOPNS2214.LOG</uploadedFileContents>
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| rowspan="1" style="text-align: center;"| <jmol>
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|-
! rowspan="1" style="text-align: center;"| HOMO
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|-
|}
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{| class="wikitable" border="1" align="right"
|+ Table of Gibbs Free Energies and Reaction Barriers
|-
! style="text-align: center;"| (B3LYP level)
! colspan="2" style="text-align: center;"|Gibbs Free Energy
! colspan="2" style="text-align: center;"|Reaction Barrier
|-
! rowspan="1" style="text-align: center;"|
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
|-
! rowspan="1" style="text-align: center;"| Exo
| rowspan="1" style="text-align: center;"| -500.329
| rowspan="1" style="text-align: center;"| 1313613.608
| rowspan="1" style="text-align: center;"| 0.0633
| rowspan="1" style="text-align: center;"| 166.310
|-
! rowspan="1" style="text-align: center;"| Endo
| rowspan="1" style="text-align: center;"| -500.332
| rowspan="1" style="text-align: center;"| 1313621.485
| rowspan="1" style="text-align: center;"| 0.0604
| rowspan="1" style="text-align: center;"| 158.467
|-
|}
Following the progress of the reaction between cyclohexadiene and 1,3-dioxole produced varying results to the ones above. Here, a typical inverse demand Diels-Alder reaction was seen, where the diene's HOMO and dienophile's LUMO formed the molecular HOMO and LUMO orbitals of the transition state. Energy levels of the HOMO and LUMO for each reactant were obtained from the checkpoint files and shown in '''Figure 4'''. The energy gap between the diene's HOMO and dienophiles's LUMO is 0.34597 and therefore smaller than the diene's LUMO and dienophiles's HOMO energy gap of 0.34806. Smaller energy gap results in greater splitting. The electron rich nature of the diene 1,3-dioxole is due to the oxygen atoms adjacent to the double bond. The mixing of p orbitals raises the energy of the diene's HOMO and brings it closer to the dienophile's LUMO.

The Gibbs free energies were extracted from the log files of the reactants and transition states and the reaction barriers calculated accordingly. The endo-conformer of the product has a lower reaction barrier, being 7.842 KJmol<sup>-1</sup> smaller in value. This therefore makes it the kinetic product as less energy is required to overcome the barrier and thus over time, it will form more quickly.
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=Exercise 3=
{| class="wikitable" border="1" align="right"
|+ Table of Gibbs Free Energies and Reaction Barriers for o-Xylylene-SO2 Cycloaddition
|-
! style="text-align: center;"|(PM6 level)
! colspan="2" style="text-align: center;"|Gibbs Free Energy
! colspan="2" style="text-align: center;"|Reaction Barrier
|-
! rowspan="1" style="text-align: center;"|
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
|-
! rowspan="1" style="text-align: center;"| Exo
| rowspan="1" style="text-align: center;"| 0.092076
| rowspan="1" style="text-align: center;"|241.746
| rowspan="1" style="text-align: center;"| 0.032564
| rowspan="1" style="text-align: center;"| 85.497
|-
! rowspan="1" style="text-align: center;"| Endo
| rowspan="1" style="text-align: center;"| 0.090560
| rowspan="1" style="text-align: center;"| 237.765
| rowspan="1" style="text-align: center;"| 0.031048
| rowspan="1" style="text-align: center;"| 81.517
|-
! rowspan="1" style="text-align: center;"| Chelotropic
| rowspan="1" style="text-align: center;"| 0.099062
| rowspan="1" style="text-align: center;"|260.087
| rowspan="1" style="text-align: center;"| 0.03955
| rowspan="1" style="text-align: center;"| 103.839
|-
|}[[File:RXNCOORDNS2214.jpg|400px|thumb|right]]

Once again, the free energies of the reactants and transition were extracted from the log files, having been optimised at the PM6 level. The endo conformer has the lowest energy barrier, 3.98 KJmol<sup>-1</sup> lower than exo, making it the kinetic product.Plotting the reaction co-ordinate clearly displays the relative energies throughout the co-ordinate. The chelotropic product has the highest reaction barrier meaning it forms slowly as more energy is required to overcome the barrier. However, once the barrier has been overcome, the chelotropic product is lowest in energy and therefore the most stable, making it the thermodynamic product.
During the reaction, the 6-member-ed ring in xylylene is aromatised in order ot bring stability to the molecule.
{| class="wikitable" border="1" align="center"
|+ IRC pathways for o-Xylylene-SO2 Cycloaddition
|-
! colspan="2" style="text-align: center;"|Diels-Alder
! colspan="1" style="text-align: center;"|Chelotropic
|-
! rowspan="1" style="text-align: center;"|Exo
! rowspan="1" style="text-align: center;"|Endo
! rowspan="1" style="text-align: center;"|
|-
|rowspan="1" style="text-align: center;"|[[File:IRC exo3ns2214.gif|400px|thumb|center]]
|rowspan="1" style="text-align: center;"|[[File:ENDOTStrajectoryns2214.gif|400px|thumb|center]]
|rowspan="1" style="text-align: center;"|[[File:IRCTSchelns2214traj.gif|400px|thumb|center]]
|}
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<br style="clear:left">
=Conclusion=

Rep:Mod:tsns2214

2017-03-23T12:36:52Z

Ns2214: /* Exercise 1 */

'''Transition States'''
=Introduction=
Potential energy surfaces display the energy of a system with respect to positions of the molecules. They can therefore be used to display transition states in a molecule. Transition states are an energy maximum where the gradient is 0, i.e. a turning point.However, depending on the complexity of the reaction, there can be many maxima on a PES as there are different trajectories predicted. If a transition state has been correctly found, it will have a saddle-point geometry where it is the maximum on its particular reaction co-ordinate, but the minimum compared to other pathways. There is an equal probability of falling down the potential energy curve to form either reactants or products at a transition state.

In this lab, the transition states of Diels-Alder reactions were studied. This involves a [4+2] cycloaddition between a diene and dienophile. These double bonded structures are close enough in energy to interact and form 2 new sigma bonds and breaking one pi bond overall. The formation of theses sigma bonds lowers the energy of the system as electrons occupy bonding molecular orbitals.

Gaussian software was used to analyse the transition state formation of three Diels-Alder reactions. Method 3 in the tutorial was used for all the reactions, where the expected product molecule was optimised, the relevant bonds broken and frozen, and then the resulting transition state optimised. Two levels of optimisation were used: PM6 semi-empirical for exercises 1 and 3 and B3LYP-DFT for exercise 2. PM6 uses relevant parameters to fit experimental dipole moments and geometries, allowing for faster results as some integrals are pre-determined. B3LYP however uses electron density in the molecule to optimise the structure and base it calculations on. If the correct transition state was found, there was one negative frequency found in the vibrations, corresponding to..

Several consideration have to be taken into account when studying Diels-Alder reactions. One is that the diene and dienophile's HOMO and LUMOs are are relatively close to each other. The smaller energy gap between a HOMO-LUMO pair depended on the nature of the reactants and their electron densities. The checkpoint files obtained from optimisations gave insight into the closer energy levels and thus explained the products formed. Another consideration was that a molecule, such as xylylene, could have multiple reaction sites or the molecules could approach each other at different geometries. Once transition state structures had been optimised, IRC analysis was conducted to confirm the transition state path. If there were multiple approach possibilities and transition state structures, the free energy data could be extracted from the log files, in order to find the thermodynamic and kinetic products.
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<br style="clear:left">

=Exercise 1=
{| class="wikitable" border="1" align="right"
|+
|-
! colspan="5" style="text-align: center;"|Carbon numbering and bond lengths ('''Å''')
|-
| colspan="5" align="center"|[[File:TScarbonnumberns2214.jpg|250px|thumb|center|'''Figure 3''' Carbon numbering used by Gaussian]]
|-
! style="text-align: center;"|
! style="text-align: center;"|C1-C2/C5-C6
! style="text-align: center;"|C2-C3/C4-C5
! style="text-align: center;"|C3-C4
! style="text-align: center;"|C6-C1
|-
! rowspan="1" style="text-align: center;"| Reactants
| rowspan="1" style="text-align: center;"| -
| rowspan="1" style="text-align: center;"| 1.333
| rowspan="1" style="text-align: center;"| 1.471
| rowspan="1" style="text-align: center;"| 1.327
|-
! rowspan="1" style="text-align: center;"| Transition State
| rowspan="1" style="text-align: center;"| 2.115
| rowspan="1" style="text-align: center;"| 1.380
| rowspan="1" style="text-align: center;"| 1.411
| rowspan="1" style="text-align: center;"| 1.382
|-
! rowspan="1" style="text-align: center;"| Product
| rowspan="1" style="text-align: center;"| 1.537
| rowspan="1" style="text-align: center;"| 1.501
| rowspan="1" style="text-align: center;"| 1.337
| rowspan="1" style="text-align: center;"| 1.535
|-
|}
[[File:Ircgraphns2214.jpg|400px|thumb|right|'''Figure 2''' Graph showing internuclear distances during cyclohexene formation]]
The first Diels-Alder reaction characterised was between 1,3-butadiene and ethene, forming cyclohexene. Visualising the molecular orbitals for the optimised reactants, products and transition state enabled for an orbital diagram to be drawn ('''Figure 1'''). From the diagram it is evident that the formation of molecular orbitals is restricted by symmetry. Orbitals of the same symmetry/asymmetry are allowed to interact and bring stability to the moelcule. Looking at the values for the optimised reactants, the HOMO of the butadiene (-0.35899) and LUMO of the ethene (0.04256) are closer in energy and therefore the energy gap between the bonding and anti-bonding orbitals formed is larger. The orbital overlap is non-zero for a symmetric-symmetric or asymmetric-asymmetric interaction, and zero for an asymmetric-symmetric interaction.

The graph in '''Figure 2''' displays how the C-C bonds change in length as the reactants approach the transition state and then form the products. Well before the transition state is reached, all bond lengths remain constant except for C1-C2 and C5-C6 as the ethene molecule approaches the butadiene. Typical sp<sup>2</sup> and sp<sup>3</sup> C-C bond lengths at this stage are around 1.336 and 1.468 Å respectively. Just before the transition state is approached,C1-C2 and C5-C6 continue to descend, but the other bond lengths appear to converge as the cyclisation occurs.

The four bond lengths converge just after the transition state. The bond length between the newly forming C1-C2 and C5-C6 is 2.115 at the transition state. This is significantly smaller than the Van Der Waal's radius of two Carbon atoms (1.7x2= 3.4 Å). This suggests that bond formation is occurring before, during and after the transition state, especially as the bond length continues to decrease linearly and plateau at a value of ~1.54 Å, the typical C-C sigma bond length. What defines the transition state of cyclohexene is the convergence of the four other bond lengths.
[[File:CyclohexadieneMODiagramns2214.jpg|400px|thumb|left]]
{| class="wikitable" border="1" align="right"
|+ Exercise 1 Molecular Orbitals
|-
| style="text-align: center;"| PM6
! colspan="1" style="text-align: center;"|Ethene
! colspan="1" style="text-align: center;"|Butadiene
! colspan="2" style="text-align: center;"|Transition States
|-
! rowspan="1" style="text-align: center;"|LUMO
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
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</jmolApplet>
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| rowspan="1" style="text-align: center;"| <jmol>
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| rowspan="1" style="text-align: center;"| <jmol>
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|-
! rowspan="1" style="text-align: center;"| HOMO
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<jmolApplet>
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<size>200</size>
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<uploadedFileContents>ETHENENS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>BUTADIENENS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSOPTFREQPOPns2214.LOG</uploadedFileContents>
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</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
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<size>200</size>
<script> frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSOPTFREQPOPns2214.LOG</uploadedFileContents>
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</jmol>
|-
|}
<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script>frame 17; vectors 3; vectors scale 3.0; color vectors orange; vibration 2; </script>
<uploadedFileContents>TSOPTFREQns2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Formation of the two bonds is synchrous. ADD...
<br style="clear:right">
<br style="clear:left">

=Exercise 2=
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Exercise 2 Molecular Orbitals
|-
| style="text-align: center;"| B3LYP
! colspan="2" style="text-align: center;"|EXO Transition States
! colspan="2" style="text-align: center;"|ENDO Transition States
|-
! rowspan="1" style="text-align: center;"|LUMO
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 45; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSEXOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 44; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSEXOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSENDOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSENDOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! rowspan="1" style="text-align: center;"| HOMO
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSEXOPOPNS2214.LOG</uploadedFileContents>
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</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSEXOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSENDOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSENDOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<br style="clear:right">
<br style="clear:left">
{| class="wikitable" border="1" align="right"
|+ Table of Gibbs Free Energies and Reaction Barriers
|-
! style="text-align: center;"| (B3LYP level)
! colspan="2" style="text-align: center;"|Gibbs Free Energy
! colspan="2" style="text-align: center;"|Reaction Barrier
|-
! rowspan="1" style="text-align: center;"|
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
|-
! rowspan="1" style="text-align: center;"| Exo
| rowspan="1" style="text-align: center;"| -500.329
| rowspan="1" style="text-align: center;"| 1313613.608
| rowspan="1" style="text-align: center;"| 0.0633
| rowspan="1" style="text-align: center;"| 166.310
|-
! rowspan="1" style="text-align: center;"| Endo
| rowspan="1" style="text-align: center;"| -500.332
| rowspan="1" style="text-align: center;"| 1313621.485
| rowspan="1" style="text-align: center;"| 0.0604
| rowspan="1" style="text-align: center;"| 158.467
|-
|}
Following the progress of the reaction between cyclohexadiene and 1,3-dioxole produced varying results to the ones above. Here, a typical inverse demand Diels-Alder reaction was seen, where the diene's HOMO and dienophile's LUMO formed the molecular HOMO and LUMO orbitals of the transition state. Energy levels of the HOMO and LUMO for each reactant were obtained from the checkpoint files and shown in '''Figure 4'''. The energy gap between the diene's HOMO and dienophiles's LUMO is 0.34597 and therefore smaller than the diene's LUMO and dienophiles's HOMO energy gap of 0.34806. Smaller energy gap results in greater splitting. The electron rich nature of the diene 1,3-dioxole is due to the oxygen atoms adjacent to the double bond. The mixing of p orbitals raises the energy of the diene's HOMO and brings it closer to the dienophile's LUMO.

The Gibbs free energies were extracted from the log files of the reactants and transition states and the reaction barriers calculated accordingly. The endo-conformer of the product has a lower reaction barrier, being 7.842 KJmol<sup>-1</sup> smaller in value. This therefore makes it the kinetic product as less energy is required to overcome the barrier and thus over time, it will form more quickly.
<br style="clear:right">
<br style="clear:left">

=Exercise 3=
{| class="wikitable" border="1" align="right"
|+ Table of Gibbs Free Energies and Reaction Barriers for o-Xylylene-SO2 Cycloaddition
|-
! style="text-align: center;"|(PM6 level)
! colspan="2" style="text-align: center;"|Gibbs Free Energy
! colspan="2" style="text-align: center;"|Reaction Barrier
|-
! rowspan="1" style="text-align: center;"|
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
|-
! rowspan="1" style="text-align: center;"| Exo
| rowspan="1" style="text-align: center;"| 0.092076
| rowspan="1" style="text-align: center;"|241.746
| rowspan="1" style="text-align: center;"| 0.032564
| rowspan="1" style="text-align: center;"| 85.497
|-
! rowspan="1" style="text-align: center;"| Endo
| rowspan="1" style="text-align: center;"| 0.090560
| rowspan="1" style="text-align: center;"| 237.765
| rowspan="1" style="text-align: center;"| 0.031048
| rowspan="1" style="text-align: center;"| 81.517
|-
! rowspan="1" style="text-align: center;"| Chelotropic
| rowspan="1" style="text-align: center;"| 0.099062
| rowspan="1" style="text-align: center;"|260.087
| rowspan="1" style="text-align: center;"| 0.03955
| rowspan="1" style="text-align: center;"| 103.839
|-
|}[[File:RXNCOORDNS2214.jpg|400px|thumb|right]]

Once again, the free energies of the reactants and transition were extracted from the log files, having been optimised at the PM6 level. The endo conformer has the lowest energy barrier, 3.98 KJmol<sup>-1</sup> lower than exo, making it the kinetic product.Plotting the reaction co-ordinate clearly displays the relative energies throughout the co-ordinate. The chelotropic product has the highest reaction barrier meaning it forms slowly as more energy is required to overcome the barrier. However, once the barrier has been overcome, the chelotropic product is lowest in energy and therefore the most stable, making it the thermodynamic product.
During the reaction, the 6-member-ed ring in xylylene is aromatised in order ot bring stability to the molecule.
{| class="wikitable" border="1" align="center"
|+ IRC pathways for o-Xylylene-SO2 Cycloaddition
|-
! colspan="2" style="text-align: center;"|Diels-Alder
! colspan="1" style="text-align: center;"|Chelotropic
|-
! rowspan="1" style="text-align: center;"|Exo
! rowspan="1" style="text-align: center;"|Endo
! rowspan="1" style="text-align: center;"|
|-
|rowspan="1" style="text-align: center;"|[[File:IRC exo3ns2214.gif|400px|thumb|center]]
|rowspan="1" style="text-align: center;"|[[File:ENDOTStrajectoryns2214.gif|400px|thumb|center]]
|rowspan="1" style="text-align: center;"|[[File:IRCTSchelns2214traj.gif|400px|thumb|center]]
|}
<br style="clear:right">
<br style="clear:left">
=Conclusion=

2017-03-21T15:42:35Z

Ns2214:

Rep:Mod:tsns2214

2017-03-21T15:38:12Z

Ns2214: /* Exercise 2 */

'''Transition States'''
=Introduction=

=Exercise 1=
{| class="wikitable" border="1" align="right"
|+
|-
! colspan="5" style="text-align: center;"|Carbon numbering and bond lengths ('''Å''')
|-
| colspan="5" align="center"|[[File:TScarbonnumberns2214.jpg|250px|thumb|center|'''Figure 3''' Carbon numbering used by Gaussian]]
|-
! style="text-align: center;"|
! style="text-align: center;"|C1-C2/C5-C6
! style="text-align: center;"|C2-C3/C4-C5
! style="text-align: center;"|C3-C4
! style="text-align: center;"|C6-C1
|-
! rowspan="1" style="text-align: center;"| Reactants
| rowspan="1" style="text-align: center;"| -
| rowspan="1" style="text-align: center;"| 1.333
| rowspan="1" style="text-align: center;"| 1.471
| rowspan="1" style="text-align: center;"| 1.327
|-
! rowspan="1" style="text-align: center;"| Transition State
| rowspan="1" style="text-align: center;"| 2.115
| rowspan="1" style="text-align: center;"| 1.380
| rowspan="1" style="text-align: center;"| 1.411
| rowspan="1" style="text-align: center;"| 1.382
|-
! rowspan="1" style="text-align: center;"| Product
| rowspan="1" style="text-align: center;"| 1.537
| rowspan="1" style="text-align: center;"| 1.501
| rowspan="1" style="text-align: center;"| 1.337
| rowspan="1" style="text-align: center;"| 1.535
|-
|}
[[File:Ircgraphns2214.jpg|400px|thumb|right|'''Figure 2''' Graph showing internuclear distances during cyclohexene formation]]
The first Diels-Alder reaction characterised was between 1,3-butadiene and ethene, forming cyclohexene. Visualising the molecular orbitals for the optimised reactants, products and transition state enabled for an orbital diagram to be drawn ('''Figure 1'''). From the diagram it is evident that the formation of molecular orbitals is restricted by symmetry. Orbitals of the same symmetry/asymmetry are allowed to interact and bring stability to the moelcule. Looking at the values for the optimised reactants, the HOMO of the butadiene (-0.35899) and LUMO of the ethene (0.04256) are closer in energy and therefore the energy gap between the bonding and anti-bonding orbitals formed is larger. The orbital overlap is non-zero for a symmetric-symmetric or asymmetric-asymmetric interaction, and zero for an asymmetric-symmetric interaction.

The graph in '''Figure 2''' displays how the C-C bonds change in length as the reactants approach the transition state and then form the products. Well before the transition state is reached, all bond lengths remain constant except for C1-C2 and C5-C6 as the ethene molecule approaches the butadiene. Typical sp<sup>2</sup> and sp<sup>3</sup> C-C bond lengths at this stage are around 1.336 and 1.468 Å respectively. Just before the transition state is approached,C1-C2 and C5-C6 continue to descend, but the other bond lengths appear to converge as the cyclisation occurs.

The four bond lengths converge just after the transition state. The bond length between the newly forming C1-C2 and C5-C6 is 2.115 at the transition state. This is significantly smaller than the Van Der Waal's radius of two Carbon atoms (1.7x2= 3.4 Å). This suggests that bond formation is occurring before, during and after the transition state, especially as the bond length continues to decrease linearly and plateau at a value of ~1.54 Å, the typical C-C sigma bond length. What defines the transition state of cyclohexene is the convergence of the four other bond lengths.
{| class="wikitable" border="1" align="right"
|+ Table of Gibbs Free Energies and Reaction Barriers
|-
| style="text-align: center;"| Molecular Orbitals
! colspan="1" style="text-align: center;"|Ethene
! colspan="1" style="text-align: center;"|Butadiene
! colspan="2" style="text-align: center;"|Transition States
|-
! rowspan="1" style="text-align: center;"|LUMO
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>ETHENENS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>BUTADIENENS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSOPTFREQPOPns2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSOPTFREQPOPns2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! rowspan="1" style="text-align: center;"| HOMO
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
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</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
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<script> frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>BUTADIENENS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSOPTFREQPOPns2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
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<uploadedFileContents>TSOPTFREQPOPns2214.LOG</uploadedFileContents>
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</jmol>
|-
|}
<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script>frame 17; vectors 3; vectors scale 3.0; color vectors orange; vibration 2; </script>
<uploadedFileContents>TSOPTFREQns2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Formation of the two bonds is synchrous.

<br style="clear:right">
<br style="clear:left">

=Exercise 2=
{| class="wikitable" border="1" align="center"
|+ Table of Gibbs Free Energies and Reaction Barriers
|-
| style="text-align: center;"| Molecular Orbitals
! colspan="1" style="text-align: center;"|Cyclohexadiene
! colspan="1" style="text-align: center;"|1,3-dioxole
! colspan="2" style="text-align: center;"|Transition States
|-
! rowspan="1" style="text-align: center;"|LUMO
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 24; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>CYPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>13DPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSEXOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSOPTFREQPOPns2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! rowspan="1" style="text-align: center;"| HOMO
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>CYPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>13DPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSEXOPOPNS2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="1" style="text-align: center;"| <jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script> frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>TSOPTFREQPOPns2214.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<br style="clear:right">
<br style="clear:left">
{| class="wikitable" border="1" align="right"
|+ Table of Gibbs Free Energies and Reaction Barriers
|-
! style="text-align: center;"| (B3LYP level)
! colspan="2" style="text-align: center;"|Gibbs Free Energy
! colspan="2" style="text-align: center;"|Reaction Barrier
|-
! rowspan="1" style="text-align: center;"|
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
|-
! rowspan="1" style="text-align: center;"| Exo
| rowspan="1" style="text-align: center;"| -500.329
| rowspan="1" style="text-align: center;"| 1313613.608
| rowspan="1" style="text-align: center;"| 0.0633
| rowspan="1" style="text-align: center;"| 166.310
|-
! rowspan="1" style="text-align: center;"| Endo
| rowspan="1" style="text-align: center;"| -500.332
| rowspan="1" style="text-align: center;"| 1313621.485
| rowspan="1" style="text-align: center;"| 0.0604
| rowspan="1" style="text-align: center;"| 158.467
|-
|}
Following the progress of the reaction between cyclohexadiene and 1,3-dioxole produced varying results to the ones above. Here, a typical inverse demand Diels-Alder reaction was seen, where the diene's HOMO and dienophile's LUMO formed the molecular HOMO and LUMO orbitals of the transition state. Energy levels of the HOMO and LUMO for each reactant were obtained from the checkpoint files and shown in '''Figure 4'''. The energy gap between the diene's HOMO and dienophiles's LUMO is 0.34597 and therefore smaller than the diene's LUMO and dienophiles's HOMO energy gap of 0.34806. Smaller energy gap results in greater splitting. The electron rich nature of the diene 1,3-dioxole is due to the oxygen atoms adjacent to the double bond. The mixing of p orbitals raises the energy of the diene's HOMO and brings it closer to the dienophile's LUMO.

The Gibbs free energies were extracted from the log files of the reactants and transition states and the reaction barriers calculated accordingly. The endo-conformer of the product has a lower reaction barrier, being 7.842 KJmol<sup>-1</sup> smaller in value. This therefore makes it the kinetic product as less energy is required to overcome the barrier and thus over time, it will form more quickly.

=Exercise 3=
{| class="wikitable" border="1" align="right"
|+ Table of Gibbs Free Energies and Reaction Barriers for o-Xylylene-SO2 Cycloaddition
|-
! style="text-align: center;"|(PM6 level)
! colspan="2" style="text-align: center;"|Gibbs Free Energy
! colspan="2" style="text-align: center;"|Reaction Barrier
|-
! rowspan="1" style="text-align: center;"|
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
| rowspan="1" style="text-align: center;"| Hartree/particle
| rowspan="1" style="text-align: center;"| KJmol<sup>-1</sup>
|-
! rowspan="1" style="text-align: center;"| Exo
| rowspan="1" style="text-align: center;"| 0.092076
| rowspan="1" style="text-align: center;"|241.746
| rowspan="1" style="text-align: center;"| 0.032564
| rowspan="1" style="text-align: center;"| 85.497
|-
! rowspan="1" style="text-align: center;"| Endo
| rowspan="1" style="text-align: center;"| 0.090560
| rowspan="1" style="text-align: center;"| 237.765
| rowspan="1" style="text-align: center;"| 0.031048
| rowspan="1" style="text-align: center;"| 81.517
|-
! rowspan="1" style="text-align: center;"| Chelotropic
| rowspan="1" style="text-align: center;"| 0.099062
| rowspan="1" style="text-align: center;"|260.087
| rowspan="1" style="text-align: center;"| 0.03955
| rowspan="1" style="text-align: center;"| 103.839
|-
|}[[File:RXNCOORDNS2214.jpg|400px|thumb|right]]

Once again, the free energies of the reactants and transition were extracted from the log files, having been optimised at the PM6 level. The endo conformer has the lowest energy barrier, 3.98 KJmol<sup>-1</sup> lower than exo, making it the kinetic product.Plotting the reaction co-ordinate clearly displays the relative energies throughout the co-ordinate. The chelotropic product has the highest reaction barrier meaning it forms slowly as more energy is required to overcome the barrier. However, once the barrier has been overcome, the chelotropic product is lowest in energy and therefore the most stable, making it the thermodynamic product.
During the reaction, the 6-member-ed ring in xylylene is aromatised in order ot bring stability to the molecule.
{| class="wikitable" border="1" align="center"
|+ IRC pathways for o-Xylylene-SO2 Cycloaddition
|-
! colspan="2" style="text-align: center;"|Diels-Alder
! colspan="1" style="text-align: center;"|Chelotropic
|-
! rowspan="1" style="text-align: center;"|Exo
! rowspan="1" style="text-align: center;"|Endo
! rowspan="1" style="text-align: center;"|
|-
|rowspan="1" style="text-align: center;"|[[File:IRC exo3ns2214.gif|400px|thumb|center]]
|rowspan="1" style="text-align: center;"|[[File:ENDOTStrajectoryns2214.gif|400px|thumb|center]]
|rowspan="1" style="text-align: center;"|[[File:IRCTSchelns2214traj.gif|400px|thumb|center]]
|}