ChemWiki - User contributions [en]

Rep:Transition States and Reactivity ZWL115

2018-02-28T10:26:49Z

Zwl115: /* Conclusion */

==Introduction==

===What is a potential energy surface?===

A potential energy surface (PES) describes the potential energy of a chemical system in terms of certain parameters such as time and extent of reactions. Each geometry of the atoms in a system has its own unique potential energy due to the varying distances of the different atoms. Two atoms which are very far apart will have no interactions while 2 atoms which are very close together will have strong repulsive forces between them. This results in the creation of a smooth energy landscape such as the one shown in Figure 1. In Figure 1, the vertical coordinate gives the potential energy which varies with the 2 horizontal coordinates which are the bond lengths of atoms AB and atoms BC

[[File:PES_zwl115.jpg|centre|frame|Figure 1. Example of a PES<sup>1</sup>]]

===What is a transition state?===

Minima in a PES are assiociated with the structures of the reactants, products or intermediates of a reaction system. The reaction path is the lowest energy pathway between the reactant minimum and the product minimum which is denoted as a red line in Figure 1. The highest point on the reaction path corresponds to the transition state. A minimum and a transition state are both stationary points as they have zero gradient on the PES. For a stationary point, the Hessian Index, which is the number of negative eigenvalues of a force constant matrix, corresponds to the number of internal degrees of freedom along which that point is a potential energy maximum<sup>2</sup>. The Hessian Index is also equal to the number of imaginary vibrational frequencies. A minimum and a transition state can be distinguished via this Hessian Index. A minimum will have only positive eigenvalues of the Hessian and have an Hessian Index of 0. Hence, there will be no imaginary frequencies. However, since a transition state is the maximum of the lowest energy pathway, it will have a single negative Hessian eigenvalue and have a Hessian Index of 0. Hence, it will have a single imaginary vibrational frequency.

===Quantum Chemical methods used===
The semi-empirical PM6 method was used for initial calculations, followed by the more accurate DFT (Density Functional Theory) method B3LYP. The PM6 method was used to speed up initial calculations due to the method replacing some of the two-electron integrals, the Coulomb and the exchange integrals (which are difficult to calculate), used in the Hartree Fock, with empirical parameters.<sup>3</sup> The DFT method is a computational method that derives the properties of a molecular system based on the determination of the electron density of the molecule.<sup>4</sup> Unlike a wavefunction, which becomes increasingly complex as the number of electrons increase, the determination of electron density is independent of the number of electrons. The B3LYP method is a hybrid method which utilises the useful features from <i>ab initio</i> methods and improves the accuracy of the calculation by DFT mathematics. The 6-31G basis set was chosen as a larger basis set gave a better approximation to the atomic orbitals as they placed fewer restrictions on the wavefunction while the split basis sets allowed for size changes during bonding.<sup>5</sup>

==Exercise 1: Reaction of Butadiene and Ethene==
===Reaction Scheme===
[[File:Reaction_Scheme_Ex1_zwl115.PNG]]
===Jmol Files===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_PDT_OPT_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

===MO Diagram===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! MO diagram for the formation of the Butadiene/Ethene transition state !! Ethene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of butadiene||rowspan="2"|[[File:MO_Diagram_Ex_1_3_zwl115.PNG|centre|frame]] || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Ethene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Butadiene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Ethene
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! MO 1 !! MO 2 !! MO 3 !! MO 4
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

Referring to the MO diagram above, the HOMO of butadiene is higher in energy than that of ethene, indicating that this is a normal electron demand cycloaddition. Bonding MOs (MOs 1 and 2) of the transition state formed from the MOs of the reactants are much higher in energy than what is expected for a product. Similarly, the anti-bonding MOs of the transition state are lower in energy than the corresponding MOs of the product. This is due to the fact that the transition state lies at the maximum of the lowest energy pathway and the overlap of orbitals are not as strong as what would be seen in the products of the reaction. This leads to an overall destabilisation of the structure as the electrons are occupying MOs which are higher in energy than that of the reactants.

===Symmetry===

[[File:WH_analysis__2_EX1_zwl115.PNG|frame|100px|Figure 2. Woodward-Hoffmann analysis of cycloaddition of butadiene and ethene.]]

For a thermal pericyclic reaction, whether a reaction is 'allowed' or 'forbidden' depends on the Woodward-Hoffmann rules which states that the total number of (4q+2)<sub>s</sub> and (4r)<sub>a</sub> components must be odd.<sup>6</sup> The suffix 's' represents suprafacial where the new bonds are formed on the same side at both ends of the component. The suffix 'a' represents antarafacial where the new bonds formed are on opposite sides of both ends of the component. As seen from Figure 2, when both components are suprafacial, it would allow for good orbital overlap and the Woodward-Hoffmann rules are obeyed. This is in agreement with the results obtained for the combination of the Frontier Orbitals of butadiene and ethene in the MO diagram. Reactions are only allowed when the symmetry of the FO of butadiene is the same as that for the FO of ethene as this would lead to a non-zero orbital overlap. Conversely, an overlap between a symmetric FO and an anti-symmetric FO would lead to an orbital overlap integral of 0 and hence, no reaction will occur.

===Bond Length Analysis===

[[File:Bond_lengths_Ex1.PNG|centre|frame| Figure 3: Reaction Scheme showing the bond lengths of the reactants, transition state and the products]]
The C-C bond lengths for the reactants, transition state and the products are summarised in the Figure 3. Butadiene has shorter C=C terminal bonds of 1.34 Å and a longer C-C internal bond of 1.47 Å while ethene has a bond length of 1.33 Å. The shorter bond lengths observed in butadiene are due to the overlap between sp<sup>2</sup> C atoms which have a typical value of 1.34 Å<sup>7</sup> while the longer C-C bonds observed are due to the overlap between sp<sup>3</sup> C atoms which have a typical value of 1.54 Å.<sup>7</sup> At the transition state, the C=C terminal bonds of butadiene and the C=C bond in ethene lengthen to 1.38 Å, moving towards the value of a bond length observed between sp<sup>3</sup> C atoms. This indicates that the bond order has decreased from 2 to a value between 1 and 2. In contrast, the internal bond shortens to 1.41 Å, moving towards the value of a bond length observed between sp<sup>2</sup> C atoms and the bond order has increased from 1 to a value between 1 and 2, similar to the bond lengths of the terminal bonds. Finally in the products, the bond lengths continue to change in the same way. C5-C6 which was previously the internal bond of the butadiene has the shortest bond length of 1.34 Å due to the overlap between sp<sup>2</sup> C atoms. C1-C2, C2-C3 and C3-C4 have very similar bond lengths of 1.53-1.54 Å which reflects the overlap between sp<sup>3</sup> C atoms. C1-C6 and C4-C5 which were previously the terminal bonds of the butadiene have a bond length of 1.50 Å which is slightly shorter than the other single bonds in the molecule. This is due to the sp<sup>2</sup>-sp<sup>3</sup> overlap of the C atoms. The greater s character of the sp<sup>2</sup> C atom results in a stronger and shorter sigma bond. The length of the partially formed C-C bonds in the transition state is 2.11 Å which is significantly greater than the Van Der Waals radius of C (1.70 Å).<sup>8</sup> This indicates that at the transition state, no new C-C bonds were formed.

===Reaction path towards the products from the transition state===

[[File:Vibration_TS_Ex1_zwl115.gif|centre|frame| Figure 3. Illustration of vibration of reaction path at the Transition state]]
As seen from the illustration showing the vibration corresponding to the transition state, the formation of the 2 bonds is synchronous. The ends of the butadiene and ethene fragments move towards each other in a symmetric fashion showing a concerted mechanism.

==Link to Exercise 2==
https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_States_and_Reactivity_Exercise2_ZWL115

==Link to Exercise 3==
https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_States_and_Reactivity_Exercise3_ZWL115

==Conclusion==
The use of the semi-empirical method PM6, followed by the DFT method B3LYP has provided the tools required to locate the transition states for several reactions, allowing great insight into the nature of the reactions. Following a successful vibration calculation, an IRC can be carried out to ensure that the minima of the reactants and the products were reached and were connected. In Exercise 1, the energy levels of the individual MOs of the reactants, transition states and the products were obtained, allowing for the construction of the MO diagram which was useful in studying the symmetry of the 'allowed' and 'forbidden' reactions. Exercise 2 involved an inverse electron demand Diels-Alder reaction due to the different ordering of energies of the HOMO and LUMO of the dienophile and the diene as compared to Exercise 1. This allowed for the comparison between the MO diagrams of a normal versus an inverse electron demand Diels-Alder. It was found that the MO diagrams for the 2 reactions had similar relative energy levels for their respective transition states. The study of the reaction thermodynamics in Exercises 2 and 3 confirmed the role of steric clashes and secondary orbital interactions in determining which transition states and products are favourable and vice versa. Steric clashes raised the energy of the compound while secondary orbital interactions helped to lower the energy of the chemical system. Exercise 3 also showed the role of aromaticity in providing stability to a molecule and lowering its energy while anti-aromatic compounds are highly unstable.

==References==
1. Potential Energy Surface. Encyclopedia of Human thermodynamics.

2. Potential Energy Surfaces. C, David Sherrill. School of Chemistry and Biochemistry Georgia Institute of Technology.

3. Computational Quantum Chemistry. C, David Sherrill.

4. Introduction to Computational Quantum Chemistry: Theory. A, Gilbert. The Australian National University.

5. Introduction to Computational Chemistry. V H¨anninen. University of Helsinki

6. Woodward, R. B.; Hoffmann, R. J. Am. Chem. Soc. 1965, 87(2), 395-397.

7. Bond Length. Wikipedia.

8. Van der Waals radius. Wikipedia.

Rep:Transition States and Reactivity Exercise3 ZWL115

2018-02-28T10:21:39Z

Zwl115: /* Reaction Coordinate */

==Exercise 3==

===Reaction Scheme===

O-Xylylene can react with SO<sub>2</sub> via 2 different Diels-Alder cycloadditions and a chelotropic pathway. These pathways are illustrated in Figure. 5.
[[File:Reaction_scheme_ex3_zwl115.PNG|left|frame| Figure 5. Reaction scheme showing the Exo, Endo Diels-Alder cycloadditions and the Chelotropic reaction mechanisms possible.]]

{| class="wikitable"
|-
! Reactants
! Transition States
! Products
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> SO2_OPT_PM6_2_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> SO<sub>2</sub>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_ENDO_TS_FREQ_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 50; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_PDT_ENDO_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> XYLYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Xylylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_EXO_TS_FREQ1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 72; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_PDT_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
|-
|
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 48; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>C_TS_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Chelotropic
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>C_PDT_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Chelotropic
|}

===Reaction Coordinate===
{| class="wikitable"
|+IRC pathways
|-
! Endo
! Exo
! Chelotropic
|-
| [[File:DA_endo_TS_freq_IRC_PM6_zwl115.gif|500px]]
| [[File:DA_exo_TS_freq_IRC_PM6_zwl115.gif|500px]]
| [[File:C_TS_freq_IRC_PM6_zwl115.gif|500px]]
|}

The instability of Xylylene can be rationalised using Hückel's Molecular Orbital Theory. According to the theory, a compound is stable when all of its bonding orbitals are filled and no electrons fill the anti-bonding orbitals. This is especially true in aromatic compounds, where 2 electrons fill the lowest energy molecular orbital and 4 electrons fill the subsequent degenerate pair of orbitals (the number of pairs of orbitals is denoted by the by <i>n</i>). This gives rise to Hückel's rule where aromatic compounds have 4n+2 π electrons which are in a conjugated ring system and are highly stabilised. On the contrary, compounds with 4n π electrons show anti-aromatic behaviour and are highly unstable due to the filling of anti-bonding orbitals.<sup>9</sup> O-Xylylene only has 4π electrons in the ring resulting in anti-aromatic instability due to filling of the anti-bonding orbitals. During the course of the reactions, the 6-membered ring of Xylylene becomes a stabilised benzene ring in all 3 pathways as seen in the IRCs. The benzene ring has 6π electrons in a conjugated ring system which obeys Hückel's rule (where <i>n</i> = 1), making it aromatic. Hence the resulting products are more stabilised and the reactions occur favourably.

===Gibbs Free Energies===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
!
! Xylylene
! Sulfur Dioxide
! Exo Transition State
! Endo Transition State
! Chelotropic Transition State
! Exo Product
! Endo Product
! Chelotropic Product
|-
| '''Energy/Hartrees'''
| -0.119269
| 0.178119
| 0.092077
| 0.090559
| 0.099062
| 0.021452
| 0.021697
| -0.000018
|-
| '''Energy/kJmol<sup>-1</sup>'''
| -313.141
| 467.651
| 241.748
| 237.762
| 260.087
| 56.3222
| 56.9654
| -0.04726
|}

===Energy Profile Diagram===
[[File:Energy_profile_diagram_ex3_1_zwl115.PNG|centre|frame|Figure 6. Energy Profile Diagram showing the 3 different reaction pathways for the reaction between Xylylene and SO<sub>2</sub>]]

==Diels-Alder reaction with second cis-butadiene fragment==

===Reaction Scheme===
[[File:Reaction_scheme_ex3_part_2_zwl115.PNG|centre|frame| Figure 7. Reaction scheme showing the Exo and Endo Diels-Alder cycloadditions mechanisms possible.]]

===Jmol Files===
{| class="wikitable"
|-
! Reactants
! Transition States
! Products
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> SO2_OPT_PM6_2_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> SO<sub>2</sub>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_DA_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 50; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_PDT_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> XYLYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Xylylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_DA_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 72; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_PDT_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
|}

===Reaction Profile Diagram===
[[File:Energy_profile_diagram_ex3_part_2_zwl115.PNG|centre|frame|Figure 8. Energy Profile diagram showing the thermodynamics of the 2 Diels-Alder cycloaddition pathways]]
The Endo and Exo Diels-Alder reactions for this cis-butadiene fragment is thermodynamically and kinetically unfavourable. Comparing Figures 6 and 8, the activation energies for both the exo and endo Diels-Alder cycloadditions at this site are much greater than those of the terminal butadiene fragment. Furthermore, the products of the reactions for the non-terminal cis-butadiene fragment are much higher in energy than those for the terminal cis butadiene fragment. The overall reaction for both endo and exo pathways are endothermic in this case. The kinetic and thermodynamic consequences can be rationalised by the greater steric clash present in the transition state and the products when SO<sub>2</sub> reacts with the non-terminal cis-butadiene fragment which are absent with the terminal cis-butadiene fragment.

==References==

9. Aromaticity and the Hückel 4n + 2 Rule. Chemistry Libretexts.

Rep:Transition States and Reactivity Exercise2 ZWL115

2018-02-28T10:08:21Z

Zwl115: /* Inverse Demand Diels-Alder Reaction */

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==
===Reaction Scheme===
[[File:Reaction_Scheme_Ex2_zwl115.PNG]]

===Inverse Demand Diels-Alder Reaction===
By running an IRC on the transition states, the structure of the unreacted reactants can be used to run a single point energy calculation. This placed the reactants on the same potential energy surface, allowing the visualisation of the order of the energies of the MOs of the 2 reactants.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! HOMO of Cyclohexadiene !! HOMO of 1,3-Dioxole !! LUMO of Cyclohexadiene !! LUMO of 1,3-Dioxole
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_ENERGY_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 30; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_ENERGY_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_ENERGY_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_ENERGY_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
The MOs in the table are shown in ascending order based on their energies. The HOMO of cyclohexadiene (diene) has a lower energy than the HOMO of 1,3-dioxole (dienophile). This is the opposite from what was observed in Exercise 1 between the reaction of butadiene and ethene. There is a stronger interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene as they are closer in energy as compared to the LUMO of 1,3-dioxole and the HOMO of cyclohexadiene. Hence this is indicative of a inverse electron demand Diels-Alder reaction . The high energy of the dienophile can be rationalised through the presence of oxygen atoms adjacent to either side of the alkene which have readily available lone pairs of electrons to donate into the π* of the C=C.

===MO diagrams for the formation of the Cyclohexadienediene/1,3-Dioxole transition states ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Cyclohexadiene !! Endo Transition State !! Exo Transition State !! 1,3-Dioxole
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXADIENE_2_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Cyclohexadiene||rowspan="2"|[[File:MO_Diagram_Ex_2_1_zwl115endo.PNG|500px]] || rowspan="2"|[[File:MO_Diagram_Ex_2_exdo_1_zwl115.PNG|500px]] ||<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIOXOLE_FREQ_1_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of 1,3-Dioxole
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXADIENE_2_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Cyclohexadiene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIOXOLE_FREQ_1_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of 1,3-Dioxole
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! !! MO 1 !! MO 2 !! MO 3 !! MO 4
|-
|'''Endo'''
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 44; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 44; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 44; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 44; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''Exo'''
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_EXO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_EXO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_EXO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_EXO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

As mentioned in the previous section, this is an inverse electron demand cycloaddition and hence the HOMO of the dienophile (1,3-Dioxole) is higher in energy than the HOMO of cyclohexadiene. The overall ordering of the energies of the MOs of the transition states are very similar to what was observed in the normal electron demand cycloaddition reaction between butadiene and ethene. The HOMO of the diene interacts with the LUMO of the dienophile to give the bonding MO1 which is lower in energy than the corresponding bonding MO2 between the interaction between the LUMO of the diene and the HOMO of the dienophile. The anti-bonding MO4 from the interaction between the HOMO of the diene and the LUMO of the dienophile is higher in energy than the corresponding MO3 formed from the interaction between the LUMO of the diene and the HOMO of the dienophile. Hence, there is a similar overall destabilisation of the electrons in the transition state as that in the normal electron demand cycloaddition, with weaker bonding and anti-bonding interactions than what would be seen in the corresponding MOs of the products. At the transition state, the overlap of the orbitals are not as strong as those found in the products. Furthermore, it was found that the exo and endo transition states had MOs which were very close in energy. The electrons in the exo transition state occupied electrons which were slightly higher in energy than those in the endo transition state, causing it to be slightly more destabilised.

===Gibbs Free Energies===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
!
! Cyclohexadiene
! 1,3-Dioxole
! Exo Transition State
! Endo Transition State
! Exo Product
! Endo Product
|-
| '''Energy/Hartrees'''
| -233.3243
| -267.0686
| -500.3291
| -500.3321
| -500.4173
| -500.4187
|-
| '''Energy/kJmol<sup>-1</sup>'''
| -6.125930 × 10<sup>5</sup>
| -7.011890 × 10<sup>5</sup>
| -1.313614 × 10<sup>6</sup>
| -1.313622 × 10<sup>6</sup>
| -1.313846 × 10<sup>6</sup>
| -1.313849 × 10<sup>6</sup>
|}

===Energy Profile Diagram===
[[File:Energy_profile_diagram_ex2_zwl115.PNG|centre|frame|Figure 4. Energy profile diagram showing the reaction barriers and reaction energies of the Endo and Exo products ]]

===Kinetic and Thermodynamic Products===
{| class="wikitable"
|-
! HOMO of Endo Transition State
! HOMO of Exo Transition State
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 44; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_EXO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Referring to the Figure 4, the endo product has a lower activation barrier than the exo product. This can be rationalised using the Jmol images of the HOMOs of the endo and exo transition states. In the HOMO of the Endo transition state, there is a good overlap between the p orbitals of the oxygen atoms of dioxole and C=C orbitals of cyclohexadiene. This interaction is absent in the Exo transition state. Furthermore, the greater steric clash of the CH<sub>2</sub> units of both the reactants is greater in the Exo transition state than the Endo transition state. Hence, the presence of secondary orbital interactions coupled with the favourable sterics contributes to a lower energy transition state of the endo product. The exo transition state is more unfavourable due to the more significant steric clash present in the transition state and the absence of the secondary orbital interactions. Therefore, the endo product is formed faster than the exo product and the endo product is the kinetic product. The same steric clash present in the transition states is also present in the product, destabilising the exo product. Therefore, the exo product has a higher energy than the endo product. Hence the endo product is also the thermodynamically favoured product.

Rep:Transition States and Reactivity Exercise2 ZWL115

2018-02-28T10:04:58Z

Zwl115: /* MO diagrams for the formation of the Cyclohexadienediene/1,3-Dioxole transition states */

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==
===Reaction Scheme===
[[File:Reaction_Scheme_Ex2_zwl115.PNG]]

===Inverse Demand Diels-Alder Reaction===
By running an IRC on the transition states, the structure of the unreacted reactants can be used to run a single point energy calculation. This allows the visualisation of the order of the energies of the MOs of the 2 reactants.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! HOMO of Cyclohexadiene !! HOMO of 1,3-Dioxole !! LUMO of Cyclohexadiene !! LUMO of 1,3-Dioxole
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_ENERGY_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 30; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_ENERGY_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_ENERGY_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_ENERGY_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
The MOs in the table are shown in ascending order based on their energies. The HOMO of cyclohexadiene (diene) has a lower energy than the HOMO of 1,3-dioxole (dienophile). This is the opposite from what was observed in Exercise 1 between the reaction of butadiene and ethene. There is a stronger interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene as they are closer in energy as compared to the LUMO of 1,3-dioxole and the HOMO of cyclohexadiene. Hence this is indicative of a inverse electron demand Diels-Alder reaction . The high energy of the dienophile can be rationalised through the presence of oxygen atoms adjacent to either side of the alkene which have readily available lone pairs of electrons to donate into the π* of the C=C.

===MO diagrams for the formation of the Cyclohexadienediene/1,3-Dioxole transition states ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Cyclohexadiene !! Endo Transition State !! Exo Transition State !! 1,3-Dioxole
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXADIENE_2_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Cyclohexadiene||rowspan="2"|[[File:MO_Diagram_Ex_2_1_zwl115endo.PNG|500px]] || rowspan="2"|[[File:MO_Diagram_Ex_2_exdo_1_zwl115.PNG|500px]] ||<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIOXOLE_FREQ_1_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of 1,3-Dioxole
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXADIENE_2_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Cyclohexadiene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIOXOLE_FREQ_1_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of 1,3-Dioxole
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! !! MO 1 !! MO 2 !! MO 3 !! MO 4
|-
|'''Endo'''
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 44; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 44; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 44; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 44; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''Exo'''
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_EXO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_EXO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_EXO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_EXO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

As mentioned in the previous section, this is an inverse electron demand cycloaddition and hence the HOMO of the dienophile (1,3-Dioxole) is higher in energy than the HOMO of cyclohexadiene. The overall ordering of the energies of the MOs of the transition states are very similar to what was observed in the normal electron demand cycloaddition reaction between butadiene and ethene. The HOMO of the diene interacts with the LUMO of the dienophile to give the bonding MO1 which is lower in energy than the corresponding bonding MO2 between the interaction between the LUMO of the diene and the HOMO of the dienophile. The anti-bonding MO4 from the interaction between the HOMO of the diene and the LUMO of the dienophile is higher in energy than the corresponding MO3 formed from the interaction between the LUMO of the diene and the HOMO of the dienophile. Hence, there is a similar overall destabilisation of the electrons in the transition state as that in the normal electron demand cycloaddition, with weaker bonding and anti-bonding interactions than what would be seen in the corresponding MOs of the products. At the transition state, the overlap of the orbitals are not as strong as those found in the products. Furthermore, it was found that the exo and endo transition states had MOs which were very close in energy. The electrons in the exo transition state occupied electrons which were slightly higher in energy than those in the endo transition state, causing it to be slightly more destabilised.

===Gibbs Free Energies===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
!
! Cyclohexadiene
! 1,3-Dioxole
! Exo Transition State
! Endo Transition State
! Exo Product
! Endo Product
|-
| '''Energy/Hartrees'''
| -233.3243
| -267.0686
| -500.3291
| -500.3321
| -500.4173
| -500.4187
|-
| '''Energy/kJmol<sup>-1</sup>'''
| -6.125930 × 10<sup>5</sup>
| -7.011890 × 10<sup>5</sup>
| -1.313614 × 10<sup>6</sup>
| -1.313622 × 10<sup>6</sup>
| -1.313846 × 10<sup>6</sup>
| -1.313849 × 10<sup>6</sup>
|}

===Energy Profile Diagram===
[[File:Energy_profile_diagram_ex2_zwl115.PNG|centre|frame|Figure 4. Energy profile diagram showing the reaction barriers and reaction energies of the Endo and Exo products ]]

===Kinetic and Thermodynamic Products===
{| class="wikitable"
|-
! HOMO of Endo Transition State
! HOMO of Exo Transition State
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 44; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_EXO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Referring to the Figure 4, the endo product has a lower activation barrier than the exo product. This can be rationalised using the Jmol images of the HOMOs of the endo and exo transition states. In the HOMO of the Endo transition state, there is a good overlap between the p orbitals of the oxygen atoms of dioxole and C=C orbitals of cyclohexadiene. This interaction is absent in the Exo transition state. Furthermore, the greater steric clash of the CH<sub>2</sub> units of both the reactants is greater in the Exo transition state than the Endo transition state. Hence, the presence of secondary orbital interactions coupled with the favourable sterics contributes to a lower energy transition state of the endo product. The exo transition state is more unfavourable due to the more significant steric clash present in the transition state and the absence of the secondary orbital interactions. Therefore, the endo product is formed faster than the exo product and the endo product is the kinetic product. The same steric clash present in the transition states is also present in the product, destabilising the exo product. Therefore, the exo product has a higher energy than the endo product. Hence the endo product is also the thermodynamically favoured product.

Rep:Transition States and Reactivity ZWL115

2018-02-28T09:47:07Z

Zwl115: /* Quantum Chemical methods used */

==Introduction==

===What is a potential energy surface?===

A potential energy surface (PES) describes the potential energy of a chemical system in terms of certain parameters such as time and extent of reactions. Each geometry of the atoms in a system has its own unique potential energy due to the varying distances of the different atoms. Two atoms which are very far apart will have no interactions while 2 atoms which are very close together will have strong repulsive forces between them. This results in the creation of a smooth energy landscape such as the one shown in Figure 1. In Figure 1, the vertical coordinate gives the potential energy which varies with the 2 horizontal coordinates which are the bond lengths of atoms AB and atoms BC

[[File:PES_zwl115.jpg|centre|frame|Figure 1. Example of a PES<sup>1</sup>]]

===What is a transition state?===

Minima in a PES are assiociated with the structures of the reactants, products or intermediates of a reaction system. The reaction path is the lowest energy pathway between the reactant minimum and the product minimum which is denoted as a red line in Figure 1. The highest point on the reaction path corresponds to the transition state. A minimum and a transition state are both stationary points as they have zero gradient on the PES. For a stationary point, the Hessian Index, which is the number of negative eigenvalues of a force constant matrix, corresponds to the number of internal degrees of freedom along which that point is a potential energy maximum<sup>2</sup>. The Hessian Index is also equal to the number of imaginary vibrational frequencies. A minimum and a transition state can be distinguished via this Hessian Index. A minimum will have only positive eigenvalues of the Hessian and have an Hessian Index of 0. Hence, there will be no imaginary frequencies. However, since a transition state is the maximum of the lowest energy pathway, it will have a single negative Hessian eigenvalue and have a Hessian Index of 0. Hence, it will have a single imaginary vibrational frequency.

===Quantum Chemical methods used===
The semi-empirical PM6 method was used for initial calculations, followed by the more accurate DFT (Density Functional Theory) method B3LYP. The PM6 method was used to speed up initial calculations due to the method replacing some of the two-electron integrals, the Coulomb and the exchange integrals (which are difficult to calculate), used in the Hartree Fock, with empirical parameters.<sup>3</sup> The DFT method is a computational method that derives the properties of a molecular system based on the determination of the electron density of the molecule.<sup>4</sup> Unlike a wavefunction, which becomes increasingly complex as the number of electrons increase, the determination of electron density is independent of the number of electrons. The B3LYP method is a hybrid method which utilises the useful features from <i>ab initio</i> methods and improves the accuracy of the calculation by DFT mathematics. The 6-31G basis set was chosen as a larger basis set gave a better approximation to the atomic orbitals as they placed fewer restrictions on the wavefunction while the split basis sets allowed for size changes during bonding.<sup>5</sup>

==Exercise 1: Reaction of Butadiene and Ethene==
===Reaction Scheme===
[[File:Reaction_Scheme_Ex1_zwl115.PNG]]
===Jmol Files===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_PDT_OPT_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

===MO Diagram===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! MO diagram for the formation of the Butadiene/Ethene transition state !! Ethene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of butadiene||rowspan="2"|[[File:MO_Diagram_Ex_1_3_zwl115.PNG|centre|frame]] || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Ethene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Butadiene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Ethene
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! MO 1 !! MO 2 !! MO 3 !! MO 4
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

Referring to the MO diagram above, the HOMO of butadiene is higher in energy than that of ethene, indicating that this is a normal electron demand cycloaddition. Bonding MOs (MOs 1 and 2) of the transition state formed from the MOs of the reactants are much higher in energy than what is expected for a product. Similarly, the anti-bonding MOs of the transition state are lower in energy than the corresponding MOs of the product. This is due to the fact that the transition state lies at the maximum of the lowest energy pathway and the overlap of orbitals are not as strong as what would be seen in the products of the reaction. This leads to an overall destabilisation of the structure as the electrons are occupying MOs which are higher in energy than that of the reactants.

===Symmetry===

[[File:WH_analysis__2_EX1_zwl115.PNG|frame|100px|Figure 2. Woodward-Hoffmann analysis of cycloaddition of butadiene and ethene.]]

For a thermal pericyclic reaction, whether a reaction is 'allowed' or 'forbidden' depends on the Woodward-Hoffmann rules which states that the total number of (4q+2)<sub>s</sub> and (4r)<sub>a</sub> components must be odd.<sup>6</sup> The suffix 's' represents suprafacial where the new bonds are formed on the same side at both ends of the component. The suffix 'a' represents antarafacial where the new bonds formed are on opposite sides of both ends of the component. As seen from Figure 2, when both components are suprafacial, it would allow for good orbital overlap and the Woodward-Hoffmann rules are obeyed. This is in agreement with the results obtained for the combination of the Frontier Orbitals of butadiene and ethene in the MO diagram. Reactions are only allowed when the symmetry of the FO of butadiene is the same as that for the FO of ethene as this would lead to a non-zero orbital overlap. Conversely, an overlap between a symmetric FO and an anti-symmetric FO would lead to an orbital overlap integral of 0 and hence, no reaction will occur.

===Bond Length Analysis===

[[File:Bond_lengths_Ex1.PNG|centre|frame| Figure 3: Reaction Scheme showing the bond lengths of the reactants, transition state and the products]]
The C-C bond lengths for the reactants, transition state and the products are summarised in the Figure 3. Butadiene has shorter C=C terminal bonds of 1.34 Å and a longer C-C internal bond of 1.47 Å while ethene has a bond length of 1.33 Å. The shorter bond lengths observed in butadiene are due to the overlap between sp<sup>2</sup> C atoms which have a typical value of 1.34 Å<sup>7</sup> while the longer C-C bonds observed are due to the overlap between sp<sup>3</sup> C atoms which have a typical value of 1.54 Å.<sup>7</sup> At the transition state, the C=C terminal bonds of butadiene and the C=C bond in ethene lengthen to 1.38 Å, moving towards the value of a bond length observed between sp<sup>3</sup> C atoms. This indicates that the bond order has decreased from 2 to a value between 1 and 2. In contrast, the internal bond shortens to 1.41 Å, moving towards the value of a bond length observed between sp<sup>2</sup> C atoms and the bond order has increased from 1 to a value between 1 and 2, similar to the bond lengths of the terminal bonds. Finally in the products, the bond lengths continue to change in the same way. C5-C6 which was previously the internal bond of the butadiene has the shortest bond length of 1.34 Å due to the overlap between sp<sup>2</sup> C atoms. C1-C2, C2-C3 and C3-C4 have very similar bond lengths of 1.53-1.54 Å which reflects the overlap between sp<sup>3</sup> C atoms. C1-C6 and C4-C5 which were previously the terminal bonds of the butadiene have a bond length of 1.50 Å which is slightly shorter than the other single bonds in the molecule. This is due to the sp<sup>2</sup>-sp<sup>3</sup> overlap of the C atoms. The greater s character of the sp<sup>2</sup> C atom results in a stronger and shorter sigma bond. The length of the partially formed C-C bonds in the transition state is 2.11 Å which is significantly greater than the Van Der Waals radius of C (1.70 Å).<sup>8</sup> This indicates that at the transition state, no new C-C bonds were formed.

===Reaction path towards the products from the transition state===

[[File:Vibration_TS_Ex1_zwl115.gif|centre|frame| Figure 3. Illustration of vibration of reaction path at the Transition state]]
As seen from the illustration showing the vibration corresponding to the transition state, the formation of the 2 bonds is synchronous. The ends of the butadiene and ethene fragments move towards each other in a symmetric fashion showing a concerted mechanism.

==Link to Exercise 2==
https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_States_and_Reactivity_Exercise2_ZWL115

==Link to Exercise 3==
https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_States_and_Reactivity_Exercise3_ZWL115

==Conclusion==
The use of the semi-empirical method PM6, followed by the DFT method B3LYP has provided the tools required to locate the transition states for several reactions, allowing great insight into the nature of the reactions. In Exercise 1, the energy levels of the individual MOs of the reactants, transition states and the products were obtained, allowing for the construction of the MO diagram which was useful in studying the symmetry of the 'allowed' and 'forbidden' reactions. Exercise 2 involved an inverse electron demand Diels-Alder reaction due to the different ordering of energies of the HOMO and LUMO of the dienophile and the diene as compared to Exercise 1. This allowed for the comparison between the MO diagrams of a normal versus an inverse electron demand Diels-Alder. It was found that the MO diagrams for the 2 reactions had similar relative energy levels for their respective transition states. The study of the reaction thermodynamics in Exercises 2 and 3 confirmed the role of steric clashes and secondary orbital interactions in determining which transition states and products are favourable and vice versa. Steric clashes raised the energy of the compound while secondary orbital interactions helped to lower the energy of the chemical system. Exercise 3 also showed the role of aromaticity in providing stability to a molecule and lowering its energy while anti-aromatic compounds are highly unstable.

==References==
1. Potential Energy Surface. Encyclopedia of Human thermodynamics.

2. Potential Energy Surfaces. C, David Sherrill. School of Chemistry and Biochemistry Georgia Institute of Technology.

3. Computational Quantum Chemistry. C, David Sherrill.

4. Introduction to Computational Quantum Chemistry: Theory. A, Gilbert. The Australian National University.

5. Introduction to Computational Chemistry. V H¨anninen. University of Helsinki

6. Woodward, R. B.; Hoffmann, R. J. Am. Chem. Soc. 1965, 87(2), 395-397.

7. Bond Length. Wikipedia.

8. Van der Waals radius. Wikipedia.

Rep:Transition States and Reactivity ZWL115

2018-02-28T02:37:32Z

Zwl115: /* Conclusion */

==Introduction==

===What is a potential energy surface?===

A potential energy surface (PES) describes the potential energy of a chemical system in terms of certain parameters such as time and extent of reactions. Each geometry of the atoms in a system has its own unique potential energy due to the varying distances of the different atoms. Two atoms which are very far apart will have no interactions while 2 atoms which are very close together will have strong repulsive forces between them. This results in the creation of a smooth energy landscape such as the one shown in Figure 1. In Figure 1, the vertical coordinate gives the potential energy which varies with the 2 horizontal coordinates which are the bond lengths of atoms AB and atoms BC

[[File:PES_zwl115.jpg|centre|frame|Figure 1. Example of a PES<sup>1</sup>]]

===What is a transition state?===

Minima in a PES are assiociated with the structures of the reactants, products or intermediates of a reaction system. The reaction path is the lowest energy pathway between the reactant minimum and the product minimum which is denoted as a red line in Figure 1. The highest point on the reaction path corresponds to the transition state. A minimum and a transition state are both stationary points as they have zero gradient on the PES. For a stationary point, the Hessian Index, which is the number of negative eigenvalues of a force constant matrix, corresponds to the number of internal degrees of freedom along which that point is a potential energy maximum<sup>2</sup>. The Hessian Index is also equal to the number of imaginary vibrational frequencies. A minimum and a transition state can be distinguished via this Hessian Index. A minimum will have only positive eigenvalues of the Hessian and have an Hessian Index of 0. Hence, there will be no imaginary frequencies. However, since a transition state is the maximum of the lowest energy pathway, it will have a single negative Hessian eigenvalue and have a Hessian Index of 0. Hence, it will have a single imaginary vibrational frequency.

===Quantum Chemical methods used===
The semi-empirical PM6 method was used for initial calculations, followed by the more accurate DFT (Density Functional Theory) method B3LYP. The PM6 method was used to speed up initial calculations due to the method replacing some of the two-electron integrals, the Coulomb and the exchange integrals (which are difficult to calculate), used in the Hartree Fock, with empirical parameters.<sup>3</sup> The DFT method is a computational method that derives the properties of a molecular system based on the determination of the electron density of the molecule.<sup>4</sup> Unlike a wavefunction, which becomes increasingly complex as the number of electrons increase, the determination of electron density is independent of the number of electrons. The B3LYP method is a hybrid method which utilises the useful features from <i>ab initio</i> methods and improves the accuracy of the calculation by DFT mathematics. The 6-31G basis set was chosen as a larger basis set gave a better approximation to the atomic orbitals as they place fewer restrictions on the wavefunction while the split basis sets allowed for size changes during bonding.<sup>5</sup>

==Exercise 1: Reaction of Butadiene and Ethene==
===Reaction Scheme===
[[File:Reaction_Scheme_Ex1_zwl115.PNG]]
===Jmol Files===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_PDT_OPT_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

===MO Diagram===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! MO diagram for the formation of the Butadiene/Ethene transition state !! Ethene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of butadiene||rowspan="2"|[[File:MO_Diagram_Ex_1_3_zwl115.PNG|centre|frame]] || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Ethene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Butadiene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Ethene
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! MO 1 !! MO 2 !! MO 3 !! MO 4
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

Referring to the MO diagram above, the HOMO of butadiene is higher in energy than that of ethene, indicating that this is a normal electron demand cycloaddition. Bonding MOs (MOs 1 and 2) of the transition state formed from the MOs of the reactants are much higher in energy than what is expected for a product. Similarly, the anti-bonding MOs of the transition state are lower in energy than the corresponding MOs of the product. This is due to the fact that the transition state lies at the maximum of the lowest energy pathway and the overlap of orbitals are not as strong as what would be seen in the products of the reaction. This leads to an overall destabilisation of the structure as the electrons are occupying MOs which are higher in energy than that of the reactants.

===Symmetry===

[[File:WH_analysis__2_EX1_zwl115.PNG|frame|100px|Figure 2. Woodward-Hoffmann analysis of cycloaddition of butadiene and ethene.]]

For a thermal pericyclic reaction, whether a reaction is 'allowed' or 'forbidden' depends on the Woodward-Hoffmann rules which states that the total number of (4q+2)<sub>s</sub> and (4r)<sub>a</sub> components must be odd.<sup>6</sup> The suffix 's' represents suprafacial where the new bonds are formed on the same side at both ends of the component. The suffix 'a' represents antarafacial where the new bonds formed are on opposite sides of both ends of the component. As seen from Figure 2, when both components are suprafacial, it would allow for good orbital overlap and the Woodward-Hoffmann rules are obeyed. This is in agreement with the results obtained for the combination of the Frontier Orbitals of butadiene and ethene in the MO diagram. Reactions are only allowed when the symmetry of the FO of butadiene is the same as that for the FO of ethene as this would lead to a non-zero orbital overlap. Conversely, an overlap between a symmetric FO and an anti-symmetric FO would lead to an orbital overlap integral of 0 and hence, no reaction will occur.

===Bond Length Analysis===

[[File:Bond_lengths_Ex1.PNG|centre|frame| Figure 3: Reaction Scheme showing the bond lengths of the reactants, transition state and the products]]
The C-C bond lengths for the reactants, transition state and the products are summarised in the Figure 3. Butadiene has shorter C=C terminal bonds of 1.34 Å and a longer C-C internal bond of 1.47 Å while ethene has a bond length of 1.33 Å. The shorter bond lengths observed in butadiene are due to the overlap between sp<sup>2</sup> C atoms which have a typical value of 1.34 Å<sup>7</sup> while the longer C-C bonds observed are due to the overlap between sp<sup>3</sup> C atoms which have a typical value of 1.54 Å.<sup>7</sup> At the transition state, the C=C terminal bonds of butadiene and the C=C bond in ethene lengthen to 1.38 Å, moving towards the value of a bond length observed between sp<sup>3</sup> C atoms. This indicates that the bond order has decreased from 2 to a value between 1 and 2. In contrast, the internal bond shortens to 1.41 Å, moving towards the value of a bond length observed between sp<sup>2</sup> C atoms and the bond order has increased from 1 to a value between 1 and 2, similar to the bond lengths of the terminal bonds. Finally in the products, the bond lengths continue to change in the same way. C5-C6 which was previously the internal bond of the butadiene has the shortest bond length of 1.34 Å due to the overlap between sp<sup>2</sup> C atoms. C1-C2, C2-C3 and C3-C4 have very similar bond lengths of 1.53-1.54 Å which reflects the overlap between sp<sup>3</sup> C atoms. C1-C6 and C4-C5 which were previously the terminal bonds of the butadiene have a bond length of 1.50 Å which is slightly shorter than the other single bonds in the molecule. This is due to the sp<sup>2</sup>-sp<sup>3</sup> overlap of the C atoms. The greater s character of the sp<sup>2</sup> C atom results in a stronger and shorter sigma bond. The length of the partially formed C-C bonds in the transition state is 2.11 Å which is significantly greater than the Van Der Waals radius of C (1.70 Å).<sup>8</sup> This indicates that at the transition state, no new C-C bonds were formed.

===Reaction path towards the products from the transition state===

[[File:Vibration_TS_Ex1_zwl115.gif|centre|frame| Figure 3. Illustration of vibration of reaction path at the Transition state]]
As seen from the illustration showing the vibration corresponding to the transition state, the formation of the 2 bonds is synchronous. The ends of the butadiene and ethene fragments move towards each other in a symmetric fashion showing a concerted mechanism.

==Link to Exercise 2==
https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_States_and_Reactivity_Exercise2_ZWL115

==Link to Exercise 3==
https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_States_and_Reactivity_Exercise3_ZWL115

==Conclusion==
The use of the semi-empirical method PM6, followed by the DFT method B3LYP has provided the tools required to locate the transition states for several reactions, allowing great insight into the nature of the reactions. In Exercise 1, the energy levels of the individual MOs of the reactants, transition states and the products were obtained, allowing for the construction of the MO diagram which was useful in studying the symmetry of the 'allowed' and 'forbidden' reactions. Exercise 2 involved an inverse electron demand Diels-Alder reaction due to the different ordering of energies of the HOMO and LUMO of the dienophile and the diene as compared to Exercise 1. This allowed for the comparison between the MO diagrams of a normal versus an inverse electron demand Diels-Alder. It was found that the MO diagrams for the 2 reactions had similar relative energy levels for their respective transition states. The study of the reaction thermodynamics in Exercises 2 and 3 confirmed the role of steric clashes and secondary orbital interactions in determining which transition states and products are favourable and vice versa. Steric clashes raised the energy of the compound while secondary orbital interactions helped to lower the energy of the chemical system. Exercise 3 also showed the role of aromaticity in providing stability to a molecule and lowering its energy while anti-aromatic compounds are highly unstable.

==References==
1. Potential Energy Surface. Encyclopedia of Human thermodynamics.

2. Potential Energy Surfaces. C, David Sherrill. School of Chemistry and Biochemistry Georgia Institute of Technology.

3. Computational Quantum Chemistry. C, David Sherrill.

4. Introduction to Computational Quantum Chemistry: Theory. A, Gilbert. The Australian National University.

5. Introduction to Computational Chemistry. V H¨anninen. University of Helsinki

6. Woodward, R. B.; Hoffmann, R. J. Am. Chem. Soc. 1965, 87(2), 395-397.

7. Bond Length. Wikipedia.

8. Van der Waals radius. Wikipedia.

Rep:Transition States and Reactivity ZWL115

2018-02-28T02:34:17Z

Zwl115: /* Link to Exercise 3 */

==Introduction==

===What is a potential energy surface?===

A potential energy surface (PES) describes the potential energy of a chemical system in terms of certain parameters such as time and extent of reactions. Each geometry of the atoms in a system has its own unique potential energy due to the varying distances of the different atoms. Two atoms which are very far apart will have no interactions while 2 atoms which are very close together will have strong repulsive forces between them. This results in the creation of a smooth energy landscape such as the one shown in Figure 1. In Figure 1, the vertical coordinate gives the potential energy which varies with the 2 horizontal coordinates which are the bond lengths of atoms AB and atoms BC

[[File:PES_zwl115.jpg|centre|frame|Figure 1. Example of a PES<sup>1</sup>]]

===What is a transition state?===

Minima in a PES are assiociated with the structures of the reactants, products or intermediates of a reaction system. The reaction path is the lowest energy pathway between the reactant minimum and the product minimum which is denoted as a red line in Figure 1. The highest point on the reaction path corresponds to the transition state. A minimum and a transition state are both stationary points as they have zero gradient on the PES. For a stationary point, the Hessian Index, which is the number of negative eigenvalues of a force constant matrix, corresponds to the number of internal degrees of freedom along which that point is a potential energy maximum<sup>2</sup>. The Hessian Index is also equal to the number of imaginary vibrational frequencies. A minimum and a transition state can be distinguished via this Hessian Index. A minimum will have only positive eigenvalues of the Hessian and have an Hessian Index of 0. Hence, there will be no imaginary frequencies. However, since a transition state is the maximum of the lowest energy pathway, it will have a single negative Hessian eigenvalue and have a Hessian Index of 0. Hence, it will have a single imaginary vibrational frequency.

===Quantum Chemical methods used===
The semi-empirical PM6 method was used for initial calculations, followed by the more accurate DFT (Density Functional Theory) method B3LYP. The PM6 method was used to speed up initial calculations due to the method replacing some of the two-electron integrals, the Coulomb and the exchange integrals (which are difficult to calculate), used in the Hartree Fock, with empirical parameters.<sup>3</sup> The DFT method is a computational method that derives the properties of a molecular system based on the determination of the electron density of the molecule.<sup>4</sup> Unlike a wavefunction, which becomes increasingly complex as the number of electrons increase, the determination of electron density is independent of the number of electrons. The B3LYP method is a hybrid method which utilises the useful features from <i>ab initio</i> methods and improves the accuracy of the calculation by DFT mathematics. The 6-31G basis set was chosen as a larger basis set gave a better approximation to the atomic orbitals as they place fewer restrictions on the wavefunction while the split basis sets allowed for size changes during bonding.<sup>5</sup>

==Exercise 1: Reaction of Butadiene and Ethene==
===Reaction Scheme===
[[File:Reaction_Scheme_Ex1_zwl115.PNG]]
===Jmol Files===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_PDT_OPT_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

===MO Diagram===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! MO diagram for the formation of the Butadiene/Ethene transition state !! Ethene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of butadiene||rowspan="2"|[[File:MO_Diagram_Ex_1_3_zwl115.PNG|centre|frame]] || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Ethene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Butadiene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Ethene
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! MO 1 !! MO 2 !! MO 3 !! MO 4
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

Referring to the MO diagram above, the HOMO of butadiene is higher in energy than that of ethene, indicating that this is a normal electron demand cycloaddition. Bonding MOs (MOs 1 and 2) of the transition state formed from the MOs of the reactants are much higher in energy than what is expected for a product. Similarly, the anti-bonding MOs of the transition state are lower in energy than the corresponding MOs of the product. This is due to the fact that the transition state lies at the maximum of the lowest energy pathway and the overlap of orbitals are not as strong as what would be seen in the products of the reaction. This leads to an overall destabilisation of the structure as the electrons are occupying MOs which are higher in energy than that of the reactants.

===Symmetry===

[[File:WH_analysis__2_EX1_zwl115.PNG|frame|100px|Figure 2. Woodward-Hoffmann analysis of cycloaddition of butadiene and ethene.]]

For a thermal pericyclic reaction, whether a reaction is 'allowed' or 'forbidden' depends on the Woodward-Hoffmann rules which states that the total number of (4q+2)<sub>s</sub> and (4r)<sub>a</sub> components must be odd.<sup>6</sup> The suffix 's' represents suprafacial where the new bonds are formed on the same side at both ends of the component. The suffix 'a' represents antarafacial where the new bonds formed are on opposite sides of both ends of the component. As seen from Figure 2, when both components are suprafacial, it would allow for good orbital overlap and the Woodward-Hoffmann rules are obeyed. This is in agreement with the results obtained for the combination of the Frontier Orbitals of butadiene and ethene in the MO diagram. Reactions are only allowed when the symmetry of the FO of butadiene is the same as that for the FO of ethene as this would lead to a non-zero orbital overlap. Conversely, an overlap between a symmetric FO and an anti-symmetric FO would lead to an orbital overlap integral of 0 and hence, no reaction will occur.

===Bond Length Analysis===

[[File:Bond_lengths_Ex1.PNG|centre|frame| Figure 3: Reaction Scheme showing the bond lengths of the reactants, transition state and the products]]
The C-C bond lengths for the reactants, transition state and the products are summarised in the Figure 3. Butadiene has shorter C=C terminal bonds of 1.34 Å and a longer C-C internal bond of 1.47 Å while ethene has a bond length of 1.33 Å. The shorter bond lengths observed in butadiene are due to the overlap between sp<sup>2</sup> C atoms which have a typical value of 1.34 Å<sup>7</sup> while the longer C-C bonds observed are due to the overlap between sp<sup>3</sup> C atoms which have a typical value of 1.54 Å.<sup>7</sup> At the transition state, the C=C terminal bonds of butadiene and the C=C bond in ethene lengthen to 1.38 Å, moving towards the value of a bond length observed between sp<sup>3</sup> C atoms. This indicates that the bond order has decreased from 2 to a value between 1 and 2. In contrast, the internal bond shortens to 1.41 Å, moving towards the value of a bond length observed between sp<sup>2</sup> C atoms and the bond order has increased from 1 to a value between 1 and 2, similar to the bond lengths of the terminal bonds. Finally in the products, the bond lengths continue to change in the same way. C5-C6 which was previously the internal bond of the butadiene has the shortest bond length of 1.34 Å due to the overlap between sp<sup>2</sup> C atoms. C1-C2, C2-C3 and C3-C4 have very similar bond lengths of 1.53-1.54 Å which reflects the overlap between sp<sup>3</sup> C atoms. C1-C6 and C4-C5 which were previously the terminal bonds of the butadiene have a bond length of 1.50 Å which is slightly shorter than the other single bonds in the molecule. This is due to the sp<sup>2</sup>-sp<sup>3</sup> overlap of the C atoms. The greater s character of the sp<sup>2</sup> C atom results in a stronger and shorter sigma bond. The length of the partially formed C-C bonds in the transition state is 2.11 Å which is significantly greater than the Van Der Waals radius of C (1.70 Å).<sup>8</sup> This indicates that at the transition state, no new C-C bonds were formed.

===Reaction path towards the products from the transition state===

[[File:Vibration_TS_Ex1_zwl115.gif|centre|frame| Figure 3. Illustration of vibration of reaction path at the Transition state]]
As seen from the illustration showing the vibration corresponding to the transition state, the formation of the 2 bonds is synchronous. The ends of the butadiene and ethene fragments move towards each other in a symmetric fashion showing a concerted mechanism.

==Link to Exercise 2==
https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_States_and_Reactivity_Exercise2_ZWL115

==Link to Exercise 3==
https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_States_and_Reactivity_Exercise3_ZWL115

==Conclusion==
The use of the semi-empirical method PM6, followed by the DFT method B3LYP has provided the tools required to locate the transition states for several reactions, allowing great insight into the nature of the reactions. In Exercise 1, the energy levels of the individual MOs of the reactants, transition states and the products were obtained, allowing for the construction of the MO diagram which was useful in studying the symmetry of the 'allowed' and 'forbidden' reactions. Exercise 2 involved an inverse electron demand Diels-Alder reaction due to the different ordering of energies of the HOMO and LUMO of the dienophile and the diene as compared to Exercise 1. This allowed for the comparison between the MO diagrams of a normal versus an inverse electron demand Diels-Alder. The study of the reaction thermodynamics in Exercises 2 and 3 confirmed the role of steric clashes and secondary orbital interactions in determining which transition states and products are favourable and vice versa. Steric clashes raised the energy of the compound while secondary orbital interactions helped to lower the energy of the chemical system. Exercise 3 also showed the role of aromaticity in providing stability to a molecule and lowering its energy while anti-aromatic compounds are highly unstable.

==References==
1. Potential Energy Surface. Encyclopedia of Human thermodynamics.

2. Potential Energy Surfaces. C, David Sherrill. School of Chemistry and Biochemistry Georgia Institute of Technology.

3. Computational Quantum Chemistry. C, David Sherrill.

4. Introduction to Computational Quantum Chemistry: Theory. A, Gilbert. The Australian National University.

5. Introduction to Computational Chemistry. V H¨anninen. University of Helsinki

6. Woodward, R. B.; Hoffmann, R. J. Am. Chem. Soc. 1965, 87(2), 395-397.

7. Bond Length. Wikipedia.

8. Van der Waals radius. Wikipedia.

Rep:Transition States and Reactivity Exercise3 ZWL115

2018-02-28T02:11:35Z

Zwl115:

==Exercise 3==

===Reaction Scheme===

O-Xylylene can react with SO<sub>2</sub> via 2 different Diels-Alder cycloadditions and a chelotropic pathway. These pathways are illustrated in Figure. 5.
[[File:Reaction_scheme_ex3_zwl115.PNG|left|frame| Figure 5. Reaction scheme showing the Exo, Endo Diels-Alder cycloadditions and the Chelotropic reaction mechanisms possible.]]

{| class="wikitable"
|-
! Reactants
! Transition States
! Products
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> SO2_OPT_PM6_2_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> SO<sub>2</sub>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_ENDO_TS_FREQ_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 50; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_PDT_ENDO_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> XYLYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Xylylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_EXO_TS_FREQ1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 72; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_PDT_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
|-
|
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 48; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>C_TS_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Chelotropic
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>C_PDT_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Chelotropic
|}

===Reaction Coordinate===
{| class="wikitable"
|+IRC pathways
|-
! Endo
! Exo
! Chelotropic
|-
| [[File:DA_endo_TS_freq_IRC_PM6_zwl115.gif|500px]]
| [[File:DA_exo_TS_freq_IRC_PM6_zwl115.gif|500px]]
| [[File:C_TS_freq_IRC_PM6_zwl115.gif|500px]]
|}

The instability of Xylylene can be rationalised using Hückel's Molecular Orbital Theory. According to the theory, a compound is stable when all of its bonding orbitals are filled and no electrons fill the anti-bonding orbitals. This is especially true in aromatic compounds, where 2 electrons fill the lowest energy molecular orbital and 4 electrons fill the subsequent degenerate pair of orbitals (the number of pairs of orbitals is denoted by the by <i>n</i>). This gives rise to Hückel's rule where aromatic compounds have 4n+2 π electrons which are in a conjugated ring system while compounds with 4n π electrons show anti-aromatic behaviour and are highly unstable.<sup>9</sup> O-Xylylene only has 4π electrons in the ring resulting in anti-aromatic instability due to filling of the anti-bonding orbitals. During the course of the reactions, the 6-membered ring of Xylylene becomes a stabilised benzene ring in all 3 pathways as seen in the IRCs. The benzene ring has 6π electrons in a conjugated ring system which obeys Hückel's rule (where <i>n</i> = 1), making it aromatic. Hence the resulting products are more stabilised and the reactions occur favourably.

===Gibbs Free Energies===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
!
! Xylylene
! Sulfur Dioxide
! Exo Transition State
! Endo Transition State
! Chelotropic Transition State
! Exo Product
! Endo Product
! Chelotropic Product
|-
| '''Energy/Hartrees'''
| -0.119269
| 0.178119
| 0.092077
| 0.090559
| 0.099062
| 0.021452
| 0.021697
| -0.000018
|-
| '''Energy/kJmol<sup>-1</sup>'''
| -313.141
| 467.651
| 241.748
| 237.762
| 260.087
| 56.3222
| 56.9654
| -0.04726
|}

===Energy Profile Diagram===
[[File:Energy_profile_diagram_ex3_1_zwl115.PNG|centre|frame|Figure 6. Energy Profile Diagram showing the 3 different reaction pathways for the reaction between Xylylene and SO<sub>2</sub>]]

==Diels-Alder reaction with second cis-butadiene fragment==

===Reaction Scheme===
[[File:Reaction_scheme_ex3_part_2_zwl115.PNG|centre|frame| Figure 7. Reaction scheme showing the Exo and Endo Diels-Alder cycloadditions mechanisms possible.]]

===Jmol Files===
{| class="wikitable"
|-
! Reactants
! Transition States
! Products
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> SO2_OPT_PM6_2_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> SO<sub>2</sub>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_DA_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 50; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_PDT_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> XYLYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Xylylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_DA_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 72; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_PDT_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
|}

===Reaction Profile Diagram===
[[File:Energy_profile_diagram_ex3_part_2_zwl115.PNG|centre|frame|Figure 8. Energy Profile diagram showing the thermodynamics of the 2 Diels-Alder cycloaddition pathways]]
The Endo and Exo Diels-Alder reactions for this cis-butadiene fragment is thermodynamically and kinetically unfavourable. Comparing Figures 6 and 8, the activation energies for both the exo and endo Diels-Alder cycloadditions at this site are much greater than those of the terminal butadiene fragment. Furthermore, the products of the reactions for the non-terminal cis-butadiene fragment are much higher in energy than those for the terminal cis butadiene fragment. The overall reaction for both endo and exo pathways are endothermic in this case. The kinetic and thermodynamic consequences can be rationalised by the greater steric clash present in the transition state and the products when SO<sub>2</sub> reacts with the non-terminal cis-butadiene fragment which are absent with the terminal cis-butadiene fragment.

==References==

9. Aromaticity and the Hückel 4n + 2 Rule. Chemistry Libretexts.

Rep:Transition States and Reactivity Exercise3 ZWL115

2018-02-28T02:08:04Z

Zwl115: /* Diels-Alder reaction with second cis-butadiene fragment */

==Exercise 3==

===Reaction Scheme===

O-Xylylene can react with SO<sub>2</sub> via 2 different Diels-Alder cycloadditions and a chelotropic pathway. These pathways are illustrated in Figure. 5.
[[File:Reaction_scheme_ex3_zwl115.PNG|left|frame| Figure 5. Reaction scheme showing the Exo, Endo Diels-Alder cycloadditions and the Chelotropic reaction mechanisms possible.]]

{| class="wikitable"
|-
! Reactants
! Transition States
! Products
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> SO2_OPT_PM6_2_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> SO<sub>2</sub>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_ENDO_TS_FREQ_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 50; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_PDT_ENDO_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> XYLYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Xylylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_EXO_TS_FREQ1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 72; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_PDT_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
|-
|
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 48; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>C_TS_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Chelotropic
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>C_PDT_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Chelotropic
|}

===Reaction Coordinate===
{| class="wikitable"
|+IRC pathways
|-
! Endo
! Exo
! Chelotropic
|-
| [[File:DA_endo_TS_freq_IRC_PM6_zwl115.gif|500px]]
| [[File:DA_exo_TS_freq_IRC_PM6_zwl115.gif|500px]]
| [[File:C_TS_freq_IRC_PM6_zwl115.gif|500px]]
|}

The instability of Xylylene can be rationalised using Hückel's Molecular Orbital Theory. According to the theory, a compound is stable when all of its bonding orbitals are filled and no electrons fill the anti-bonding orbitals. This is especially true in aromatic compounds, where 2 electrons fill the lowest energy molecular orbital and 4 electrons fill the subsequent degenerate pair of orbitals (the number of pairs of orbitals is denoted by the by <i>n</i>). This gives rise to Hückel's rule where aromatic compounds have 4n+2 π electrons which are in a conjugated ring system while compounds with 4n π electrons show anti-aromatic behaviour and are highly unstable. O-Xylylene only has 4π electrons in the ring resulting in anti-aromatic instability due to filling of the anti-bonding orbitals. During the course of the reactions, the 6-membered ring of Xylylene becomes a stabilised benzene ring in all 3 pathways as seen in the IRCs. The benzene ring has 6π electrons in a conjugated ring system which obeys Hückel's rule (where <i>n</i> = 1), making it aromatic. Hence the resulting products are more stabilised and the reactions occur favourably.

===Gibbs Free Energies===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
!
! Xylylene
! Sulfur Dioxide
! Exo Transition State
! Endo Transition State
! Chelotropic Transition State
! Exo Product
! Endo Product
! Chelotropic Product
|-
| '''Energy/Hartrees'''
| -0.119269
| 0.178119
| 0.092077
| 0.090559
| 0.099062
| 0.021452
| 0.021697
| -0.000018
|-
| '''Energy/kJmol<sup>-1</sup>'''
| -313.141
| 467.651
| 241.748
| 237.762
| 260.087
| 56.3222
| 56.9654
| -0.04726
|}

===Energy Profile Diagram===
[[File:Energy_profile_diagram_ex3_1_zwl115.PNG|centre|frame|Figure 6. Energy Profile Diagram showing the 3 different reaction pathways for the reaction between Xylylene and SO<sub>2</sub>]]

==Diels-Alder reaction with second cis-butadiene fragment==

===Reaction Scheme===
[[File:Reaction_scheme_ex3_part_2_zwl115.PNG|centre|frame| Figure 7. Reaction scheme showing the Exo and Endo Diels-Alder cycloadditions mechanisms possible.]]

===Jmol Files===
{| class="wikitable"
|-
! Reactants
! Transition States
! Products
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> SO2_OPT_PM6_2_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> SO<sub>2</sub>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_DA_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 50; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_PDT_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> XYLYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Xylylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_DA_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 72; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_PDT_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
|}

===Reaction Profile Diagram===
[[File:Energy_profile_diagram_ex3_part_2_zwl115.PNG|centre|frame|Figure 8. Energy Profile diagram showing the thermodynamics of the 2 Diels-Alder cycloaddition pathways]]
The Endo and Exo Diels-Alder reactions for this cis-butadiene fragment is thermodynamically and kinetically unfavourable. Comparing Figures 6 and 8, the activation energies for both the exo and endo Diels-Alder cycloadditions at this site are much greater than those of the terminal butadiene fragment. Furthermore, the products of the reactions for the non-terminal cis-butadiene fragment are much higher in energy than those for the terminal cis butadiene fragment. The overall reaction for both endo and exo pathways are endothermic in this case. The kinetic and thermodynamic consequences can be rationalised by the greater steric clash present in the transition state and the products when SO<sub>2</sub> reacts with the non-terminal cis-butadiene fragment which are absent with the terminal cis-butadiene fragment.

Rep:Transition States and Reactivity Exercise3 ZWL115

2018-02-28T02:07:27Z

Zwl115: /* Energy Profile Diagram */

==Exercise 3==

===Reaction Scheme===

O-Xylylene can react with SO<sub>2</sub> via 2 different Diels-Alder cycloadditions and a chelotropic pathway. These pathways are illustrated in Figure. 5.
[[File:Reaction_scheme_ex3_zwl115.PNG|left|frame| Figure 5. Reaction scheme showing the Exo, Endo Diels-Alder cycloadditions and the Chelotropic reaction mechanisms possible.]]

{| class="wikitable"
|-
! Reactants
! Transition States
! Products
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> SO2_OPT_PM6_2_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> SO<sub>2</sub>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_ENDO_TS_FREQ_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 50; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_PDT_ENDO_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> XYLYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Xylylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_EXO_TS_FREQ1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 72; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_PDT_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
|-
|
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 48; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>C_TS_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Chelotropic
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>C_PDT_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Chelotropic
|}

===Reaction Coordinate===
{| class="wikitable"
|+IRC pathways
|-
! Endo
! Exo
! Chelotropic
|-
| [[File:DA_endo_TS_freq_IRC_PM6_zwl115.gif|500px]]
| [[File:DA_exo_TS_freq_IRC_PM6_zwl115.gif|500px]]
| [[File:C_TS_freq_IRC_PM6_zwl115.gif|500px]]
|}

The instability of Xylylene can be rationalised using Hückel's Molecular Orbital Theory. According to the theory, a compound is stable when all of its bonding orbitals are filled and no electrons fill the anti-bonding orbitals. This is especially true in aromatic compounds, where 2 electrons fill the lowest energy molecular orbital and 4 electrons fill the subsequent degenerate pair of orbitals (the number of pairs of orbitals is denoted by the by <i>n</i>). This gives rise to Hückel's rule where aromatic compounds have 4n+2 π electrons which are in a conjugated ring system while compounds with 4n π electrons show anti-aromatic behaviour and are highly unstable. O-Xylylene only has 4π electrons in the ring resulting in anti-aromatic instability due to filling of the anti-bonding orbitals. During the course of the reactions, the 6-membered ring of Xylylene becomes a stabilised benzene ring in all 3 pathways as seen in the IRCs. The benzene ring has 6π electrons in a conjugated ring system which obeys Hückel's rule (where <i>n</i> = 1), making it aromatic. Hence the resulting products are more stabilised and the reactions occur favourably.

===Gibbs Free Energies===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
!
! Xylylene
! Sulfur Dioxide
! Exo Transition State
! Endo Transition State
! Chelotropic Transition State
! Exo Product
! Endo Product
! Chelotropic Product
|-
| '''Energy/Hartrees'''
| -0.119269
| 0.178119
| 0.092077
| 0.090559
| 0.099062
| 0.021452
| 0.021697
| -0.000018
|-
| '''Energy/kJmol<sup>-1</sup>'''
| -313.141
| 467.651
| 241.748
| 237.762
| 260.087
| 56.3222
| 56.9654
| -0.04726
|}

===Energy Profile Diagram===
[[File:Energy_profile_diagram_ex3_1_zwl115.PNG|centre|frame|Figure 6. Energy Profile Diagram showing the 3 different reaction pathways for the reaction between Xylylene and SO<sub>2</sub>]]

==Diels-Alder reaction with second cis-butadiene fragment==

===Reaction Scheme===
[[File:Reaction_scheme_ex3_part_2_zwl115.PNG|centre|frame| Figure XX. Reaction scheme showing the Exo and Endo Diels-Alder cycloadditions mechanisms possible.]]

===Jmol Files===
{| class="wikitable"
|-
! Reactants
! Transition States
! Products
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> SO2_OPT_PM6_2_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> SO<sub>2</sub>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_DA_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 50; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_PDT_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> XYLYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Xylylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_DA_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 72; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_PDT_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
|}

===Reaction Profile Diagram===
[[File:Energy_profile_diagram_ex3_part_2_zwl115.PNG|centre|frame|Figure XX. Energy Profile diagram showing the thermodynamics of the 2 Diels-Alder cycloaddition pathways]]
The Endo and Exo Diels-Alder reactions for this cis-butadiene fragment is thermodynamically and kinetically unfavourable. Comparing Figures XX and XX, the activation energies for both the exo and endo Diels-Alder cycloadditions at this site are much greater than those of the terminal butadiene fragment. Furthermore, the products of the reactions for the non-terminal cis-butadiene fragment are much higher in energy than those for the terminal cis butadiene fragment. The overall reaction for both endo and exo pathways are endothermic in this case. The kinetic and thermodynamic consequences can be rationalised by the greater steric clash present in the transition state and the products when SO<sub>2</sub> reacts with the non-terminal cis-butadiene fragment which are absent with the terminal cis-butadiene fragment.

Rep:Transition States and Reactivity Exercise3 ZWL115

2018-02-28T02:06:34Z

Zwl115: /* Reaction Scheme */

==Exercise 3==

===Reaction Scheme===

O-Xylylene can react with SO<sub>2</sub> via 2 different Diels-Alder cycloadditions and a chelotropic pathway. These pathways are illustrated in Figure. 5.
[[File:Reaction_scheme_ex3_zwl115.PNG|left|frame| Figure 5. Reaction scheme showing the Exo, Endo Diels-Alder cycloadditions and the Chelotropic reaction mechanisms possible.]]

{| class="wikitable"
|-
! Reactants
! Transition States
! Products
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> SO2_OPT_PM6_2_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> SO<sub>2</sub>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_ENDO_TS_FREQ_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 50; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_PDT_ENDO_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> XYLYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Xylylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_EXO_TS_FREQ1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 72; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_PDT_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
|-
|
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 48; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>C_TS_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Chelotropic
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>C_PDT_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Chelotropic
|}

===Reaction Coordinate===
{| class="wikitable"
|+IRC pathways
|-
! Endo
! Exo
! Chelotropic
|-
| [[File:DA_endo_TS_freq_IRC_PM6_zwl115.gif|500px]]
| [[File:DA_exo_TS_freq_IRC_PM6_zwl115.gif|500px]]
| [[File:C_TS_freq_IRC_PM6_zwl115.gif|500px]]
|}

The instability of Xylylene can be rationalised using Hückel's Molecular Orbital Theory. According to the theory, a compound is stable when all of its bonding orbitals are filled and no electrons fill the anti-bonding orbitals. This is especially true in aromatic compounds, where 2 electrons fill the lowest energy molecular orbital and 4 electrons fill the subsequent degenerate pair of orbitals (the number of pairs of orbitals is denoted by the by <i>n</i>). This gives rise to Hückel's rule where aromatic compounds have 4n+2 π electrons which are in a conjugated ring system while compounds with 4n π electrons show anti-aromatic behaviour and are highly unstable. O-Xylylene only has 4π electrons in the ring resulting in anti-aromatic instability due to filling of the anti-bonding orbitals. During the course of the reactions, the 6-membered ring of Xylylene becomes a stabilised benzene ring in all 3 pathways as seen in the IRCs. The benzene ring has 6π electrons in a conjugated ring system which obeys Hückel's rule (where <i>n</i> = 1), making it aromatic. Hence the resulting products are more stabilised and the reactions occur favourably.

===Gibbs Free Energies===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
!
! Xylylene
! Sulfur Dioxide
! Exo Transition State
! Endo Transition State
! Chelotropic Transition State
! Exo Product
! Endo Product
! Chelotropic Product
|-
| '''Energy/Hartrees'''
| -0.119269
| 0.178119
| 0.092077
| 0.090559
| 0.099062
| 0.021452
| 0.021697
| -0.000018
|-
| '''Energy/kJmol<sup>-1</sup>'''
| -313.141
| 467.651
| 241.748
| 237.762
| 260.087
| 56.3222
| 56.9654
| -0.04726
|}

===Energy Profile Diagram===
[[File:Energy_profile_diagram_ex3_1_zwl115.PNG|centre|frame|Figure xx. Energy Profile Diagram showing the 3 different reaction pathways for the reaction between Xylylene and SO<sub>2</sub>]]

==Diels-Alder reaction with second cis-butadiene fragment==

===Reaction Scheme===
[[File:Reaction_scheme_ex3_part_2_zwl115.PNG|centre|frame| Figure XX. Reaction scheme showing the Exo and Endo Diels-Alder cycloadditions mechanisms possible.]]

===Jmol Files===
{| class="wikitable"
|-
! Reactants
! Transition States
! Products
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> SO2_OPT_PM6_2_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> SO<sub>2</sub>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_DA_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 50; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_PDT_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> XYLYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Xylylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_DA_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 72; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_PDT_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
|}

===Reaction Profile Diagram===
[[File:Energy_profile_diagram_ex3_part_2_zwl115.PNG|centre|frame|Figure XX. Energy Profile diagram showing the thermodynamics of the 2 Diels-Alder cycloaddition pathways]]
The Endo and Exo Diels-Alder reactions for this cis-butadiene fragment is thermodynamically and kinetically unfavourable. Comparing Figures XX and XX, the activation energies for both the exo and endo Diels-Alder cycloadditions at this site are much greater than those of the terminal butadiene fragment. Furthermore, the products of the reactions for the non-terminal cis-butadiene fragment are much higher in energy than those for the terminal cis butadiene fragment. The overall reaction for both endo and exo pathways are endothermic in this case. The kinetic and thermodynamic consequences can be rationalised by the greater steric clash present in the transition state and the products when SO<sub>2</sub> reacts with the non-terminal cis-butadiene fragment which are absent with the terminal cis-butadiene fragment.

Rep:Transition States and Reactivity Exercise2 ZWL115

2018-02-28T02:05:09Z

Zwl115: /* MO diagrams for the formation of the Cyclohexadienediene/1,3-Dioxole transition states */

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==
===Reaction Scheme===
[[File:Reaction_Scheme_Ex2_zwl115.PNG]]

===Inverse Demand Diels-Alder Reaction===
By running an IRC on the transition states, the structure of the unreacted reactants can be used to run a single point energy calculation. This allows the visualisation of the order of the energies of the MOs of the 2 reactants.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! HOMO of Cyclohexadiene !! HOMO of 1,3-Dioxole !! LUMO of Cyclohexadiene !! LUMO of 1,3-Dioxole
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_ENERGY_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 30; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_ENERGY_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_ENERGY_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_ENERGY_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
The MOs in the table are shown in ascending order based on their energies. The HOMO of cyclohexadiene (diene) has a lower energy than the HOMO of 1,3-dioxole (dienophile). This is the opposite from what was observed in Exercise 1 between the reaction of butadiene and ethene. There is a stronger interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene as they are closer in energy as compared to the LUMO of 1,3-dioxole and the HOMO of cyclohexadiene. Hence this is indicative of a inverse electron demand Diels-Alder reaction . The high energy of the dienophile can be rationalised through the presence of oxygen atoms adjacent to either side of the alkene which have readily available lone pairs of electrons to donate into the π* of the C=C.

===MO diagrams for the formation of the Cyclohexadienediene/1,3-Dioxole transition states ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Cyclohexadiene !! Endo Transition State !! Exo Transition State !! 1,3-Dioxole
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXADIENE_2_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Cyclohexadiene||rowspan="2"|[[File:MO_Diagram_Ex_2_1_zwl115endo.PNG|500px]] || rowspan="2"|[[File:MO_Diagram_Ex_2_exdo_1_zwl115.PNG|500px]] ||<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIOXOLE_FREQ_1_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of 1,3-Dioxole
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXADIENE_2_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Cyclohexadiene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIOXOLE_FREQ_1_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of 1,3-Dioxole
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! !! MO 1 !! MO 2 !! MO 3 !! MO 4
|-
|'''Endo'''
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 44; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 44; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 44; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 44; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''Exo'''
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_EXO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_EXO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_EXO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_EXO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

As mentioned in the previous section, this is an inverse electron demand cycloaddition and hence the HOMO of the dienophile (1,3-Dioxole) is higher in energy than the HOMO of cyclohexadiene. The overall energy of the MOs of the transition states are very similar to what was observed in the reaction of butadiene and ethene. There is an overall destabilisation of the electrons in the transition state with weaker bonding and anti-bonding interactions than what would be seen in the corresponding MOs of the products. At the transition state, the overlap of the orbitals are not as strong as those found in the products.

===Gibbs Free Energies===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
!
! Cyclohexadiene
! 1,3-Dioxole
! Exo Transition State
! Endo Transition State
! Exo Product
! Endo Product
|-
| '''Energy/Hartrees'''
| -233.3243
| -267.0686
| -500.3291
| -500.3321
| -500.4173
| -500.4187
|-
| '''Energy/kJmol<sup>-1</sup>'''
| -6.125930 × 10<sup>5</sup>
| -7.011890 × 10<sup>5</sup>
| -1.313614 × 10<sup>6</sup>
| -1.313622 × 10<sup>6</sup>
| -1.313846 × 10<sup>6</sup>
| -1.313849 × 10<sup>6</sup>
|}

===Energy Profile Diagram===
[[File:Energy_profile_diagram_ex2_zwl115.PNG|centre|frame|Figure 4. Energy profile diagram showing the reaction barriers and reaction energies of the Endo and Exo products ]]

===Kinetic and Thermodynamic Products===
{| class="wikitable"
|-
! HOMO of Endo Transition State
! HOMO of Exo Transition State
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 44; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_EXO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Referring to the Figure 4, the endo product has a lower activation barrier than the exo product. This can be rationalised using the Jmol images of the HOMOs of the endo and exo transition states. In the HOMO of the Endo transition state, there is a good overlap between the p orbitals of the oxygen atoms of dioxole and C=C orbitals of cyclohexadiene. This interaction is absent in the Exo transition state. Furthermore, the greater steric clash of the CH<sub>2</sub> units of both the reactants is greater in the Exo transition state than the Endo transition state. Hence, the presence of secondary orbital interactions coupled with the favourable sterics contributes to a lower energy transition state of the endo product. The exo transition state is more unfavourable due to the more significant steric clash present in the transition state and the absence of the secondary orbital interactions. Therefore, the endo product is formed faster than the exo product and the endo product is the kinetic product. The same steric clash present in the transition states is also present in the product, destabilising the exo product. Therefore, the exo product has a higher energy than the endo product. Hence the endo product is also the thermodynamically favoured product.

Rep:Transition States and Reactivity Exercise2 ZWL115

2018-02-28T02:04:37Z

Zwl115: /* MO diagrams for the formation of the Cyclohexadienediene/1,3-Dioxole transition states */

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==
===Reaction Scheme===
[[File:Reaction_Scheme_Ex2_zwl115.PNG]]

===Inverse Demand Diels-Alder Reaction===
By running an IRC on the transition states, the structure of the unreacted reactants can be used to run a single point energy calculation. This allows the visualisation of the order of the energies of the MOs of the 2 reactants.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! HOMO of Cyclohexadiene !! HOMO of 1,3-Dioxole !! LUMO of Cyclohexadiene !! LUMO of 1,3-Dioxole
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_ENERGY_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 30; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_ENERGY_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_ENERGY_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_ENERGY_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
The MOs in the table are shown in ascending order based on their energies. The HOMO of cyclohexadiene (diene) has a lower energy than the HOMO of 1,3-dioxole (dienophile). This is the opposite from what was observed in Exercise 1 between the reaction of butadiene and ethene. There is a stronger interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene as they are closer in energy as compared to the LUMO of 1,3-dioxole and the HOMO of cyclohexadiene. Hence this is indicative of a inverse electron demand Diels-Alder reaction . The high energy of the dienophile can be rationalised through the presence of oxygen atoms adjacent to either side of the alkene which have readily available lone pairs of electrons to donate into the π* of the C=C.

===MO diagrams for the formation of the Cyclohexadienediene/1,3-Dioxole transition states ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Cyclohexadiene !! Endo Transition State !! Exo Transition State !! 1,3-Dioxole
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXADIENE_2_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Cyclohexadiene||rowspan="2"|[[File:MO_Diagram_Ex_2_1_zwl115endo.PNG|500px]] || rowspan="2"|[[File:MO_Diagram_Ex_2_1_exdo_zwl115.PNG|500px]] ||<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIOXOLE_FREQ_1_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of 1,3-Dioxole
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXADIENE_2_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Cyclohexadiene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIOXOLE_FREQ_1_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of 1,3-Dioxole
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! !! MO 1 !! MO 2 !! MO 3 !! MO 4
|-
|'''Endo'''
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 44; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 44; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 44; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 44; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''Exo'''
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_EXO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_EXO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_EXO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_EXO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

As mentioned in the previous section, this is an inverse electron demand cycloaddition and hence the HOMO of the dienophile (1,3-Dioxole) is higher in energy than the HOMO of cyclohexadiene. The overall energy of the MOs of the transition states are very similar to what was observed in the reaction of butadiene and ethene. There is an overall destabilisation of the electrons in the transition state with weaker bonding and anti-bonding interactions than what would be seen in the corresponding MOs of the products. At the transition state, the overlap of the orbitals are not as strong as those found in the products.

===Gibbs Free Energies===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
!
! Cyclohexadiene
! 1,3-Dioxole
! Exo Transition State
! Endo Transition State
! Exo Product
! Endo Product
|-
| '''Energy/Hartrees'''
| -233.3243
| -267.0686
| -500.3291
| -500.3321
| -500.4173
| -500.4187
|-
| '''Energy/kJmol<sup>-1</sup>'''
| -6.125930 × 10<sup>5</sup>
| -7.011890 × 10<sup>5</sup>
| -1.313614 × 10<sup>6</sup>
| -1.313622 × 10<sup>6</sup>
| -1.313846 × 10<sup>6</sup>
| -1.313849 × 10<sup>6</sup>
|}

===Energy Profile Diagram===
[[File:Energy_profile_diagram_ex2_zwl115.PNG|centre|frame|Figure 4. Energy profile diagram showing the reaction barriers and reaction energies of the Endo and Exo products ]]

===Kinetic and Thermodynamic Products===
{| class="wikitable"
|-
! HOMO of Endo Transition State
! HOMO of Exo Transition State
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 44; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_EXO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Referring to the Figure 4, the endo product has a lower activation barrier than the exo product. This can be rationalised using the Jmol images of the HOMOs of the endo and exo transition states. In the HOMO of the Endo transition state, there is a good overlap between the p orbitals of the oxygen atoms of dioxole and C=C orbitals of cyclohexadiene. This interaction is absent in the Exo transition state. Furthermore, the greater steric clash of the CH<sub>2</sub> units of both the reactants is greater in the Exo transition state than the Endo transition state. Hence, the presence of secondary orbital interactions coupled with the favourable sterics contributes to a lower energy transition state of the endo product. The exo transition state is more unfavourable due to the more significant steric clash present in the transition state and the absence of the secondary orbital interactions. Therefore, the endo product is formed faster than the exo product and the endo product is the kinetic product. The same steric clash present in the transition states is also present in the product, destabilising the exo product. Therefore, the exo product has a higher energy than the endo product. Hence the endo product is also the thermodynamically favoured product.

File:MO Diagram Ex 2 exdo 1 zwl115.PNG

2018-02-28T02:04:19Z

Zwl115:

File:MO Diagram Ex 2 1 zwl115endo.PNG

2018-02-28T02:03:08Z

Zwl115:

Rep:Transition States and Reactivity Exercise2 ZWL115

2018-02-28T01:59:22Z

Zwl115: /* Kinetic and Thermodynamic Products */

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==
===Reaction Scheme===
[[File:Reaction_Scheme_Ex2_zwl115.PNG]]

===Inverse Demand Diels-Alder Reaction===
By running an IRC on the transition states, the structure of the unreacted reactants can be used to run a single point energy calculation. This allows the visualisation of the order of the energies of the MOs of the 2 reactants.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! HOMO of Cyclohexadiene !! HOMO of 1,3-Dioxole !! LUMO of Cyclohexadiene !! LUMO of 1,3-Dioxole
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_ENERGY_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 30; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_ENERGY_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_ENERGY_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_ENERGY_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
The MOs in the table are shown in ascending order based on their energies. The HOMO of cyclohexadiene (diene) has a lower energy than the HOMO of 1,3-dioxole (dienophile). This is the opposite from what was observed in Exercise 1 between the reaction of butadiene and ethene. There is a stronger interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene as they are closer in energy as compared to the LUMO of 1,3-dioxole and the HOMO of cyclohexadiene. Hence this is indicative of a inverse electron demand Diels-Alder reaction . The high energy of the dienophile can be rationalised through the presence of oxygen atoms adjacent to either side of the alkene which have readily available lone pairs of electrons to donate into the π* of the C=C.

===MO diagrams for the formation of the Cyclohexadienediene/1,3-Dioxole transition states ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Cyclohexadiene !! Endo Transition State !! Exo Transition State !! 1,3-Dioxole
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXADIENE_2_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Cyclohexadiene||rowspan="2"|[[File:MO_Diagram_Ex_2_endo_zwl115.PNG|500px]] || rowspan="2"|[[File:MO_Diagram_Ex_2_exdo_zwl115.PNG|500px]] ||<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIOXOLE_FREQ_1_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of 1,3-Dioxole
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXADIENE_2_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Cyclohexadiene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIOXOLE_FREQ_1_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of 1,3-Dioxole
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! !! MO 1 !! MO 2 !! MO 3 !! MO 4
|-
|'''Endo'''
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 44; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 44; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 44; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 44; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''Exo'''
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_EXO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_EXO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_EXO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_EXO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

As mentioned in the previous section, this is an inverse electron demand cycloaddition and hence the HOMO of the dienophile (1,3-Dioxole) is higher in energy than the HOMO of cyclohexadiene. The overall energy of the MOs of the transition states are very similar to what was observed in the reaction of butadiene and ethene. There is an overall destabilisation of the electrons in the transition state with weaker bonding and anti-bonding interactions than what would be seen in the corresponding MOs of the products. At the transition state, the overlap of the orbitals are not as strong as those found in the products.

===Gibbs Free Energies===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
!
! Cyclohexadiene
! 1,3-Dioxole
! Exo Transition State
! Endo Transition State
! Exo Product
! Endo Product
|-
| '''Energy/Hartrees'''
| -233.3243
| -267.0686
| -500.3291
| -500.3321
| -500.4173
| -500.4187
|-
| '''Energy/kJmol<sup>-1</sup>'''
| -6.125930 × 10<sup>5</sup>
| -7.011890 × 10<sup>5</sup>
| -1.313614 × 10<sup>6</sup>
| -1.313622 × 10<sup>6</sup>
| -1.313846 × 10<sup>6</sup>
| -1.313849 × 10<sup>6</sup>
|}

===Energy Profile Diagram===
[[File:Energy_profile_diagram_ex2_zwl115.PNG|centre|frame|Figure 4. Energy profile diagram showing the reaction barriers and reaction energies of the Endo and Exo products ]]

===Kinetic and Thermodynamic Products===
{| class="wikitable"
|-
! HOMO of Endo Transition State
! HOMO of Exo Transition State
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 44; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_EXO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Referring to the Figure 4, the endo product has a lower activation barrier than the exo product. This can be rationalised using the Jmol images of the HOMOs of the endo and exo transition states. In the HOMO of the Endo transition state, there is a good overlap between the p orbitals of the oxygen atoms of dioxole and C=C orbitals of cyclohexadiene. This interaction is absent in the Exo transition state. Furthermore, the greater steric clash of the CH<sub>2</sub> units of both the reactants is greater in the Exo transition state than the Endo transition state. Hence, the presence of secondary orbital interactions coupled with the favourable sterics contributes to a lower energy transition state of the endo product. The exo transition state is more unfavourable due to the more significant steric clash present in the transition state and the absence of the secondary orbital interactions. Therefore, the endo product is formed faster than the exo product and the endo product is the kinetic product. The same steric clash present in the transition states is also present in the product, destabilising the exo product. Therefore, the exo product has a higher energy than the endo product. Hence the endo product is also the thermodynamically favoured product.

Rep:Transition States and Reactivity Exercise2 ZWL115

2018-02-28T01:58:56Z

Zwl115: /* Energy Profile Diagram */

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==
===Reaction Scheme===
[[File:Reaction_Scheme_Ex2_zwl115.PNG]]

===Inverse Demand Diels-Alder Reaction===
By running an IRC on the transition states, the structure of the unreacted reactants can be used to run a single point energy calculation. This allows the visualisation of the order of the energies of the MOs of the 2 reactants.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! HOMO of Cyclohexadiene !! HOMO of 1,3-Dioxole !! LUMO of Cyclohexadiene !! LUMO of 1,3-Dioxole
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_ENERGY_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 30; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_ENERGY_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 31; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_ENERGY_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 32; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_ENERGY_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
The MOs in the table are shown in ascending order based on their energies. The HOMO of cyclohexadiene (diene) has a lower energy than the HOMO of 1,3-dioxole (dienophile). This is the opposite from what was observed in Exercise 1 between the reaction of butadiene and ethene. There is a stronger interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene as they are closer in energy as compared to the LUMO of 1,3-dioxole and the HOMO of cyclohexadiene. Hence this is indicative of a inverse electron demand Diels-Alder reaction . The high energy of the dienophile can be rationalised through the presence of oxygen atoms adjacent to either side of the alkene which have readily available lone pairs of electrons to donate into the π* of the C=C.

===MO diagrams for the formation of the Cyclohexadienediene/1,3-Dioxole transition states ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Cyclohexadiene !! Endo Transition State !! Exo Transition State !! 1,3-Dioxole
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXADIENE_2_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Cyclohexadiene||rowspan="2"|[[File:MO_Diagram_Ex_2_endo_zwl115.PNG|500px]] || rowspan="2"|[[File:MO_Diagram_Ex_2_exdo_zwl115.PNG|500px]] ||<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIOXOLE_FREQ_1_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of 1,3-Dioxole
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXADIENE_2_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Cyclohexadiene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIOXOLE_FREQ_1_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of 1,3-Dioxole
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! !! MO 1 !! MO 2 !! MO 3 !! MO 4
|-
|'''Endo'''
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 44; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 44; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 44; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 44; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''Exo'''
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_EXO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_EXO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_EXO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_EXO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

As mentioned in the previous section, this is an inverse electron demand cycloaddition and hence the HOMO of the dienophile (1,3-Dioxole) is higher in energy than the HOMO of cyclohexadiene. The overall energy of the MOs of the transition states are very similar to what was observed in the reaction of butadiene and ethene. There is an overall destabilisation of the electrons in the transition state with weaker bonding and anti-bonding interactions than what would be seen in the corresponding MOs of the products. At the transition state, the overlap of the orbitals are not as strong as those found in the products.

===Gibbs Free Energies===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
!
! Cyclohexadiene
! 1,3-Dioxole
! Exo Transition State
! Endo Transition State
! Exo Product
! Endo Product
|-
| '''Energy/Hartrees'''
| -233.3243
| -267.0686
| -500.3291
| -500.3321
| -500.4173
| -500.4187
|-
| '''Energy/kJmol<sup>-1</sup>'''
| -6.125930 × 10<sup>5</sup>
| -7.011890 × 10<sup>5</sup>
| -1.313614 × 10<sup>6</sup>
| -1.313622 × 10<sup>6</sup>
| -1.313846 × 10<sup>6</sup>
| -1.313849 × 10<sup>6</sup>
|}

===Energy Profile Diagram===
[[File:Energy_profile_diagram_ex2_zwl115.PNG|centre|frame|Figure 4. Energy profile diagram showing the reaction barriers and reaction energies of the Endo and Exo products ]]

===Kinetic and Thermodynamic Products===
{| class="wikitable"
|-
! HOMO of Endo Transition State
! HOMO of Exo Transition State
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 44; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_ENDO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXER2_EXO_TS_FREQ_B3LYP_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Referring to the Figure XX, the endo product has a lower activation barrier than the exo product. This can be rationalised using the Jmol images of the HOMOs of the endo and exo transition states. In the HOMO of the Endo transition state, there is a good overlap between the p orbitals of the oxygen atoms of dioxole and C=C orbitals of cyclohexadiene. This interaction is absent in the Exo transition state. Furthermore, the greater steric clash of the CH<sub>2</sub> units of both the reactants is greater in the Exo transition state than the Endo transition state. Hence, the presence of secondary orbital interactions coupled with the favourable sterics contributes to a lower energy transition state of the endo product. The exo transition state is more unfavourable due to the more significant steric clash present in the transition state and the absence of the secondary orbital interactions. Therefore, the endo product is formed faster than the exo product and the endo product is the kinetic product. The same steric clash present in the transition states is also present in the product, destabilising the exo product. Therefore, the exo product has a higher energy than the endo product. Hence the endo product is also the thermodynamically favoured product.

Rep:Transition States and Reactivity ZWL115

2018-02-28T01:57:40Z

Zwl115: /* MO Diagram */

==Introduction==

===What is a potential energy surface?===

A potential energy surface (PES) describes the potential energy of a chemical system in terms of certain parameters such as time and extent of reactions. Each geometry of the atoms in a system has its own unique potential energy due to the varying distances of the different atoms. Two atoms which are very far apart will have no interactions while 2 atoms which are very close together will have strong repulsive forces between them. This results in the creation of a smooth energy landscape such as the one shown in Figure 1. In Figure 1, the vertical coordinate gives the potential energy which varies with the 2 horizontal coordinates which are the bond lengths of atoms AB and atoms BC

[[File:PES_zwl115.jpg|centre|frame|Figure 1. Example of a PES<sup>1</sup>]]

===What is a transition state?===

Minima in a PES are assiociated with the structures of the reactants, products or intermediates of a reaction system. The reaction path is the lowest energy pathway between the reactant minimum and the product minimum which is denoted as a red line in Figure 1. The highest point on the reaction path corresponds to the transition state. A minimum and a transition state are both stationary points as they have zero gradient on the PES. For a stationary point, the Hessian Index, which is the number of negative eigenvalues of a force constant matrix, corresponds to the number of internal degrees of freedom along which that point is a potential energy maximum<sup>2</sup>. The Hessian Index is also equal to the number of imaginary vibrational frequencies. A minimum and a transition state can be distinguished via this Hessian Index. A minimum will have only positive eigenvalues of the Hessian and have an Hessian Index of 0. Hence, there will be no imaginary frequencies. However, since a transition state is the maximum of the lowest energy pathway, it will have a single negative Hessian eigenvalue and have a Hessian Index of 0. Hence, it will have a single imaginary vibrational frequency.

===Quantum Chemical methods used===
The semi-empirical PM6 method was used for initial calculations, followed by the more accurate DFT (Density Functional Theory) method B3LYP. The PM6 method was used to speed up initial calculations due to the method replacing some of the two-electron integrals, the Coulomb and the exchange integrals (which are difficult to calculate), used in the Hartree Fock, with empirical parameters.<sup>3</sup> The DFT method is a computational method that derives the properties of a molecular system based on the determination of the electron density of the molecule.<sup>4</sup> Unlike a wavefunction, which becomes increasingly complex as the number of electrons increase, the determination of electron density is independent of the number of electrons. The B3LYP method is a hybrid method which utilises the useful features from <i>ab initio</i> methods and improves the accuracy of the calculation by DFT mathematics. The 6-31G basis set was chosen as a larger basis set gave a better approximation to the atomic orbitals as they place fewer restrictions on the wavefunction while the split basis sets allowed for size changes during bonding.<sup>5</sup>

==Exercise 1: Reaction of Butadiene and Ethene==
===Reaction Scheme===
[[File:Reaction_Scheme_Ex1_zwl115.PNG]]
===Jmol Files===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_PDT_OPT_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

===MO Diagram===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! MO diagram for the formation of the Butadiene/Ethene transition state !! Ethene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of butadiene||rowspan="2"|[[File:MO_Diagram_Ex_1_3_zwl115.PNG|centre|frame]] || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Ethene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Butadiene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Ethene
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! MO 1 !! MO 2 !! MO 3 !! MO 4
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

Referring to the MO diagram above, the HOMO of butadiene is higher in energy than that of ethene, indicating that this is a normal electron demand cycloaddition. Bonding MOs (MOs 1 and 2) of the transition state formed from the MOs of the reactants are much higher in energy than what is expected for a product. Similarly, the anti-bonding MOs of the transition state are lower in energy than the corresponding MOs of the product. This is due to the fact that the transition state lies at the maximum of the lowest energy pathway and the overlap of orbitals are not as strong as what would be seen in the products of the reaction. This leads to an overall destabilisation of the structure as the electrons are occupying MOs which are higher in energy than that of the reactants.

===Symmetry===

[[File:WH_analysis__2_EX1_zwl115.PNG|frame|100px|Figure 2. Woodward-Hoffmann analysis of cycloaddition of butadiene and ethene.]]

For a thermal pericyclic reaction, whether a reaction is 'allowed' or 'forbidden' depends on the Woodward-Hoffmann rules which states that the total number of (4q+2)<sub>s</sub> and (4r)<sub>a</sub> components must be odd.<sup>6</sup> The suffix 's' represents suprafacial where the new bonds are formed on the same side at both ends of the component. The suffix 'a' represents antarafacial where the new bonds formed are on opposite sides of both ends of the component. As seen from Figure 2, when both components are suprafacial, it would allow for good orbital overlap and the Woodward-Hoffmann rules are obeyed. This is in agreement with the results obtained for the combination of the Frontier Orbitals of butadiene and ethene in the MO diagram. Reactions are only allowed when the symmetry of the FO of butadiene is the same as that for the FO of ethene as this would lead to a non-zero orbital overlap. Conversely, an overlap between a symmetric FO and an anti-symmetric FO would lead to an orbital overlap integral of 0 and hence, no reaction will occur.

===Bond Length Analysis===

[[File:Bond_lengths_Ex1.PNG|centre|frame| Figure 3: Reaction Scheme showing the bond lengths of the reactants, transition state and the products]]
The C-C bond lengths for the reactants, transition state and the products are summarised in the Figure 3. Butadiene has shorter C=C terminal bonds of 1.34 Å and a longer C-C internal bond of 1.47 Å while ethene has a bond length of 1.33 Å. The shorter bond lengths observed in butadiene are due to the overlap between sp<sup>2</sup> C atoms which have a typical value of 1.34 Å<sup>7</sup> while the longer C-C bonds observed are due to the overlap between sp<sup>3</sup> C atoms which have a typical value of 1.54 Å.<sup>7</sup> At the transition state, the C=C terminal bonds of butadiene and the C=C bond in ethene lengthen to 1.38 Å, moving towards the value of a bond length observed between sp<sup>3</sup> C atoms. This indicates that the bond order has decreased from 2 to a value between 1 and 2. In contrast, the internal bond shortens to 1.41 Å, moving towards the value of a bond length observed between sp<sup>2</sup> C atoms and the bond order has increased from 1 to a value between 1 and 2, similar to the bond lengths of the terminal bonds. Finally in the products, the bond lengths continue to change in the same way. C5-C6 which was previously the internal bond of the butadiene has the shortest bond length of 1.34 Å due to the overlap between sp<sup>2</sup> C atoms. C1-C2, C2-C3 and C3-C4 have very similar bond lengths of 1.53-1.54 Å which reflects the overlap between sp<sup>3</sup> C atoms. C1-C6 and C4-C5 which were previously the terminal bonds of the butadiene have a bond length of 1.50 Å which is slightly shorter than the other single bonds in the molecule. This is due to the sp<sup>2</sup>-sp<sup>3</sup> overlap of the C atoms. The greater s character of the sp<sup>2</sup> C atom results in a stronger and shorter sigma bond. The length of the partially formed C-C bonds in the transition state is 2.11 Å which is significantly greater than the Van Der Waals radius of C (1.70 Å).<sup>8</sup> This indicates that at the transition state, no new C-C bonds were formed.

===Reaction path towards the products from the transition state===

[[File:Vibration_TS_Ex1_zwl115.gif|centre|frame| Figure 3. Illustration of vibration of reaction path at the Transition state]]
As seen from the illustration showing the vibration corresponding to the transition state, the formation of the 2 bonds is synchronous. The ends of the butadiene and ethene fragments move towards each other in a symmetric fashion showing a concerted mechanism.

==Link to Exercise 2==
https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_States_and_Reactivity_Exercise2_ZWL115

==Link to Exercise 3==
https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_States_and_Reactivity_Exercise3_ZWL115

==References==
1. Potential Energy Surface. Encyclopedia of Human thermodynamics.

2. Potential Energy Surfaces. C, David Sherrill. School of Chemistry and Biochemistry Georgia Institute of Technology.

3. Computational Quantum Chemistry. C, David Sherrill.

4. Introduction to Computational Quantum Chemistry: Theory. A, Gilbert. The Australian National University.

5. Introduction to Computational Chemistry. V H¨anninen. University of Helsinki

6. Woodward, R. B.; Hoffmann, R. J. Am. Chem. Soc. 1965, 87(2), 395-397.

7. Bond Length. Wikipedia.

8. Van der Waals radius. Wikipedia.

File:MO Diagram Ex 1 3 zwl115.PNG

2018-02-28T01:57:29Z

Zwl115:

Rep:Transition States and Reactivity ZWL115

2018-02-28T01:54:15Z

Zwl115: /* Bond Length Analysis */

==Introduction==

===What is a potential energy surface?===

A potential energy surface (PES) describes the potential energy of a chemical system in terms of certain parameters such as time and extent of reactions. Each geometry of the atoms in a system has its own unique potential energy due to the varying distances of the different atoms. Two atoms which are very far apart will have no interactions while 2 atoms which are very close together will have strong repulsive forces between them. This results in the creation of a smooth energy landscape such as the one shown in Figure 1. In Figure 1, the vertical coordinate gives the potential energy which varies with the 2 horizontal coordinates which are the bond lengths of atoms AB and atoms BC

[[File:PES_zwl115.jpg|centre|frame|Figure 1. Example of a PES<sup>1</sup>]]

===What is a transition state?===

Minima in a PES are assiociated with the structures of the reactants, products or intermediates of a reaction system. The reaction path is the lowest energy pathway between the reactant minimum and the product minimum which is denoted as a red line in Figure 1. The highest point on the reaction path corresponds to the transition state. A minimum and a transition state are both stationary points as they have zero gradient on the PES. For a stationary point, the Hessian Index, which is the number of negative eigenvalues of a force constant matrix, corresponds to the number of internal degrees of freedom along which that point is a potential energy maximum<sup>2</sup>. The Hessian Index is also equal to the number of imaginary vibrational frequencies. A minimum and a transition state can be distinguished via this Hessian Index. A minimum will have only positive eigenvalues of the Hessian and have an Hessian Index of 0. Hence, there will be no imaginary frequencies. However, since a transition state is the maximum of the lowest energy pathway, it will have a single negative Hessian eigenvalue and have a Hessian Index of 0. Hence, it will have a single imaginary vibrational frequency.

===Quantum Chemical methods used===
The semi-empirical PM6 method was used for initial calculations, followed by the more accurate DFT (Density Functional Theory) method B3LYP. The PM6 method was used to speed up initial calculations due to the method replacing some of the two-electron integrals, the Coulomb and the exchange integrals (which are difficult to calculate), used in the Hartree Fock, with empirical parameters.<sup>3</sup> The DFT method is a computational method that derives the properties of a molecular system based on the determination of the electron density of the molecule.<sup>4</sup> Unlike a wavefunction, which becomes increasingly complex as the number of electrons increase, the determination of electron density is independent of the number of electrons. The B3LYP method is a hybrid method which utilises the useful features from <i>ab initio</i> methods and improves the accuracy of the calculation by DFT mathematics. The 6-31G basis set was chosen as a larger basis set gave a better approximation to the atomic orbitals as they place fewer restrictions on the wavefunction while the split basis sets allowed for size changes during bonding.<sup>5</sup>

==Exercise 1: Reaction of Butadiene and Ethene==
===Reaction Scheme===
[[File:Reaction_Scheme_Ex1_zwl115.PNG]]
===Jmol Files===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_PDT_OPT_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

===MO Diagram===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! MO diagram for the formation of the Butadiene/Ethene transition state !! Ethene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of butadiene||rowspan="2"|[[File:MO_Diagram_Ex_1_2_zwl115.PNG|centre|frame]] || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Ethene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Butadiene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Ethene
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! MO 1 !! MO 2 !! MO 3 !! MO 4
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

Referring to the MO diagram above, the HOMO of butadiene is higher in energy than that of ethene, indicating that this is a normal electron demand cycloaddition. Bonding MOs (MOs 1 and 2) of the transition state formed from the MOs of the reactants are much higher in energy than what is expected for a product. Similarly, the anti-bonding MOs of the transition state are lower in energy than the corresponding MOs of the product. This is due to the fact that the transition state lies at the maximum of the lowest energy pathway and the overlap of orbitals are not as strong as what would be seen in the products of the reaction. This leads to an overall destabilisation of the structure as the electrons are occupying MOs which are higher in energy than that of the reactants.

===Symmetry===

[[File:WH_analysis__2_EX1_zwl115.PNG|frame|100px|Figure 2. Woodward-Hoffmann analysis of cycloaddition of butadiene and ethene.]]

For a thermal pericyclic reaction, whether a reaction is 'allowed' or 'forbidden' depends on the Woodward-Hoffmann rules which states that the total number of (4q+2)<sub>s</sub> and (4r)<sub>a</sub> components must be odd.<sup>6</sup> The suffix 's' represents suprafacial where the new bonds are formed on the same side at both ends of the component. The suffix 'a' represents antarafacial where the new bonds formed are on opposite sides of both ends of the component. As seen from Figure 2, when both components are suprafacial, it would allow for good orbital overlap and the Woodward-Hoffmann rules are obeyed. This is in agreement with the results obtained for the combination of the Frontier Orbitals of butadiene and ethene in the MO diagram. Reactions are only allowed when the symmetry of the FO of butadiene is the same as that for the FO of ethene as this would lead to a non-zero orbital overlap. Conversely, an overlap between a symmetric FO and an anti-symmetric FO would lead to an orbital overlap integral of 0 and hence, no reaction will occur.

===Bond Length Analysis===

[[File:Bond_lengths_Ex1.PNG|centre|frame| Figure 3: Reaction Scheme showing the bond lengths of the reactants, transition state and the products]]
The C-C bond lengths for the reactants, transition state and the products are summarised in the Figure 3. Butadiene has shorter C=C terminal bonds of 1.34 Å and a longer C-C internal bond of 1.47 Å while ethene has a bond length of 1.33 Å. The shorter bond lengths observed in butadiene are due to the overlap between sp<sup>2</sup> C atoms which have a typical value of 1.34 Å<sup>7</sup> while the longer C-C bonds observed are due to the overlap between sp<sup>3</sup> C atoms which have a typical value of 1.54 Å.<sup>7</sup> At the transition state, the C=C terminal bonds of butadiene and the C=C bond in ethene lengthen to 1.38 Å, moving towards the value of a bond length observed between sp<sup>3</sup> C atoms. This indicates that the bond order has decreased from 2 to a value between 1 and 2. In contrast, the internal bond shortens to 1.41 Å, moving towards the value of a bond length observed between sp<sup>2</sup> C atoms and the bond order has increased from 1 to a value between 1 and 2, similar to the bond lengths of the terminal bonds. Finally in the products, the bond lengths continue to change in the same way. C5-C6 which was previously the internal bond of the butadiene has the shortest bond length of 1.34 Å due to the overlap between sp<sup>2</sup> C atoms. C1-C2, C2-C3 and C3-C4 have very similar bond lengths of 1.53-1.54 Å which reflects the overlap between sp<sup>3</sup> C atoms. C1-C6 and C4-C5 which were previously the terminal bonds of the butadiene have a bond length of 1.50 Å which is slightly shorter than the other single bonds in the molecule. This is due to the sp<sup>2</sup>-sp<sup>3</sup> overlap of the C atoms. The greater s character of the sp<sup>2</sup> C atom results in a stronger and shorter sigma bond. The length of the partially formed C-C bonds in the transition state is 2.11 Å which is significantly greater than the Van Der Waals radius of C (1.70 Å).<sup>8</sup> This indicates that at the transition state, no new C-C bonds were formed.

===Reaction path towards the products from the transition state===

[[File:Vibration_TS_Ex1_zwl115.gif|centre|frame| Figure 3. Illustration of vibration of reaction path at the Transition state]]
As seen from the illustration showing the vibration corresponding to the transition state, the formation of the 2 bonds is synchronous. The ends of the butadiene and ethene fragments move towards each other in a symmetric fashion showing a concerted mechanism.

==Link to Exercise 2==
https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_States_and_Reactivity_Exercise2_ZWL115

==Link to Exercise 3==
https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_States_and_Reactivity_Exercise3_ZWL115

==References==
1. Potential Energy Surface. Encyclopedia of Human thermodynamics.

2. Potential Energy Surfaces. C, David Sherrill. School of Chemistry and Biochemistry Georgia Institute of Technology.

3. Computational Quantum Chemistry. C, David Sherrill.

4. Introduction to Computational Quantum Chemistry: Theory. A, Gilbert. The Australian National University.

5. Introduction to Computational Chemistry. V H¨anninen. University of Helsinki

6. Woodward, R. B.; Hoffmann, R. J. Am. Chem. Soc. 1965, 87(2), 395-397.

7. Bond Length. Wikipedia.

8. Van der Waals radius. Wikipedia.

Rep:Transition States and Reactivity ZWL115

2018-02-28T01:53:53Z

Zwl115: /* Symmetry */

==Introduction==

===What is a potential energy surface?===

A potential energy surface (PES) describes the potential energy of a chemical system in terms of certain parameters such as time and extent of reactions. Each geometry of the atoms in a system has its own unique potential energy due to the varying distances of the different atoms. Two atoms which are very far apart will have no interactions while 2 atoms which are very close together will have strong repulsive forces between them. This results in the creation of a smooth energy landscape such as the one shown in Figure 1. In Figure 1, the vertical coordinate gives the potential energy which varies with the 2 horizontal coordinates which are the bond lengths of atoms AB and atoms BC

[[File:PES_zwl115.jpg|centre|frame|Figure 1. Example of a PES<sup>1</sup>]]

===What is a transition state?===

Minima in a PES are assiociated with the structures of the reactants, products or intermediates of a reaction system. The reaction path is the lowest energy pathway between the reactant minimum and the product minimum which is denoted as a red line in Figure 1. The highest point on the reaction path corresponds to the transition state. A minimum and a transition state are both stationary points as they have zero gradient on the PES. For a stationary point, the Hessian Index, which is the number of negative eigenvalues of a force constant matrix, corresponds to the number of internal degrees of freedom along which that point is a potential energy maximum<sup>2</sup>. The Hessian Index is also equal to the number of imaginary vibrational frequencies. A minimum and a transition state can be distinguished via this Hessian Index. A minimum will have only positive eigenvalues of the Hessian and have an Hessian Index of 0. Hence, there will be no imaginary frequencies. However, since a transition state is the maximum of the lowest energy pathway, it will have a single negative Hessian eigenvalue and have a Hessian Index of 0. Hence, it will have a single imaginary vibrational frequency.

===Quantum Chemical methods used===
The semi-empirical PM6 method was used for initial calculations, followed by the more accurate DFT (Density Functional Theory) method B3LYP. The PM6 method was used to speed up initial calculations due to the method replacing some of the two-electron integrals, the Coulomb and the exchange integrals (which are difficult to calculate), used in the Hartree Fock, with empirical parameters.<sup>3</sup> The DFT method is a computational method that derives the properties of a molecular system based on the determination of the electron density of the molecule.<sup>4</sup> Unlike a wavefunction, which becomes increasingly complex as the number of electrons increase, the determination of electron density is independent of the number of electrons. The B3LYP method is a hybrid method which utilises the useful features from <i>ab initio</i> methods and improves the accuracy of the calculation by DFT mathematics. The 6-31G basis set was chosen as a larger basis set gave a better approximation to the atomic orbitals as they place fewer restrictions on the wavefunction while the split basis sets allowed for size changes during bonding.<sup>5</sup>

==Exercise 1: Reaction of Butadiene and Ethene==
===Reaction Scheme===
[[File:Reaction_Scheme_Ex1_zwl115.PNG]]
===Jmol Files===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_PDT_OPT_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

===MO Diagram===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! MO diagram for the formation of the Butadiene/Ethene transition state !! Ethene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of butadiene||rowspan="2"|[[File:MO_Diagram_Ex_1_2_zwl115.PNG|centre|frame]] || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Ethene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Butadiene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Ethene
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! MO 1 !! MO 2 !! MO 3 !! MO 4
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

Referring to the MO diagram above, the HOMO of butadiene is higher in energy than that of ethene, indicating that this is a normal electron demand cycloaddition. Bonding MOs (MOs 1 and 2) of the transition state formed from the MOs of the reactants are much higher in energy than what is expected for a product. Similarly, the anti-bonding MOs of the transition state are lower in energy than the corresponding MOs of the product. This is due to the fact that the transition state lies at the maximum of the lowest energy pathway and the overlap of orbitals are not as strong as what would be seen in the products of the reaction. This leads to an overall destabilisation of the structure as the electrons are occupying MOs which are higher in energy than that of the reactants.

===Symmetry===

[[File:WH_analysis__2_EX1_zwl115.PNG|frame|100px|Figure 2. Woodward-Hoffmann analysis of cycloaddition of butadiene and ethene.]]

For a thermal pericyclic reaction, whether a reaction is 'allowed' or 'forbidden' depends on the Woodward-Hoffmann rules which states that the total number of (4q+2)<sub>s</sub> and (4r)<sub>a</sub> components must be odd.<sup>6</sup> The suffix 's' represents suprafacial where the new bonds are formed on the same side at both ends of the component. The suffix 'a' represents antarafacial where the new bonds formed are on opposite sides of both ends of the component. As seen from Figure 2, when both components are suprafacial, it would allow for good orbital overlap and the Woodward-Hoffmann rules are obeyed. This is in agreement with the results obtained for the combination of the Frontier Orbitals of butadiene and ethene in the MO diagram. Reactions are only allowed when the symmetry of the FO of butadiene is the same as that for the FO of ethene as this would lead to a non-zero orbital overlap. Conversely, an overlap between a symmetric FO and an anti-symmetric FO would lead to an orbital overlap integral of 0 and hence, no reaction will occur.

===Bond Length Analysis===

[[File:Bond_lengths_Ex1.PNG|centre|frame| Figure 2: Reaction Scheme showing the bond lengths of the reactants, transition state and the products]]
The C-C bond lengths for the reactants, transition state and the products are summarised in the Figure 2. Butadiene has shorter C=C terminal bonds of 1.34 Å and a longer C-C internal bond of 1.47 Å while ethene has a bond length of 1.33 Å. The shorter bond lengths observed in butadiene are due to the overlap between sp<sup>2</sup> C atoms which have a typical value of 1.34 Å<sup>7</sup> while the longer C-C bonds observed are due to the overlap between sp<sup>3</sup> C atoms which have a typical value of 1.54 Å.<sup>7</sup> At the transition state, the C=C terminal bonds of butadiene and the C=C bond in ethene lengthen to 1.38 Å, moving towards the value of a bond length observed between sp<sup>3</sup> C atoms. This indicates that the bond order has decreased from 2 to a value between 1 and 2. In contrast, the internal bond shortens to 1.41 Å, moving towards the value of a bond length observed between sp<sup>2</sup> C atoms and the bond order has increased from 1 to a value between 1 and 2, similar to the bond lengths of the terminal bonds. Finally in the products, the bond lengths continue to change in the same way. C5-C6 which was previously the internal bond of the butadiene has the shortest bond length of 1.34 Å due to the overlap between sp<sup>2</sup> C atoms. C1-C2, C2-C3 and C3-C4 have very similar bond lengths of 1.53-1.54 Å which reflects the overlap between sp<sup>3</sup> C atoms. C1-C6 and C4-C5 which were previously the terminal bonds of the butadiene have a bond length of 1.50 Å which is slightly shorter than the other single bonds in the molecule. This is due to the sp<sup>2</sup>-sp<sup>3</sup> overlap of the C atoms. The greater s character of the sp<sup>2</sup> C atom results in a stronger and shorter sigma bond. The length of the partially formed C-C bonds in the transition state is 2.11 Å which is significantly greater than the Van Der Waals radius of C (1.70 Å).<sup>8</sup> This indicates that at the transition state, no new C-C bonds were formed.

===Reaction path towards the products from the transition state===

[[File:Vibration_TS_Ex1_zwl115.gif|centre|frame| Figure 3. Illustration of vibration of reaction path at the Transition state]]
As seen from the illustration showing the vibration corresponding to the transition state, the formation of the 2 bonds is synchronous. The ends of the butadiene and ethene fragments move towards each other in a symmetric fashion showing a concerted mechanism.

==Link to Exercise 2==
https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_States_and_Reactivity_Exercise2_ZWL115

==Link to Exercise 3==
https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_States_and_Reactivity_Exercise3_ZWL115

==References==
1. Potential Energy Surface. Encyclopedia of Human thermodynamics.

2. Potential Energy Surfaces. C, David Sherrill. School of Chemistry and Biochemistry Georgia Institute of Technology.

3. Computational Quantum Chemistry. C, David Sherrill.

4. Introduction to Computational Quantum Chemistry: Theory. A, Gilbert. The Australian National University.

5. Introduction to Computational Chemistry. V H¨anninen. University of Helsinki

6. Woodward, R. B.; Hoffmann, R. J. Am. Chem. Soc. 1965, 87(2), 395-397.

7. Bond Length. Wikipedia.

8. Van der Waals radius. Wikipedia.

Rep:Transition States and Reactivity ZWL115

2018-02-28T01:35:58Z

Zwl115: /* Link to Exercise 3 */

==Introduction==

===What is a potential energy surface?===

A potential energy surface (PES) describes the potential energy of a chemical system in terms of certain parameters such as time and extent of reactions. Each geometry of the atoms in a system has its own unique potential energy due to the varying distances of the different atoms. Two atoms which are very far apart will have no interactions while 2 atoms which are very close together will have strong repulsive forces between them. This results in the creation of a smooth energy landscape such as the one shown in Figure 1. In Figure 1, the vertical coordinate gives the potential energy which varies with the 2 horizontal coordinates which are the bond lengths of atoms AB and atoms BC

[[File:PES_zwl115.jpg|centre|frame|Figure 1. Example of a PES<sup>1</sup>]]

===What is a transition state?===

Minima in a PES are assiociated with the structures of the reactants, products or intermediates of a reaction system. The reaction path is the lowest energy pathway between the reactant minimum and the product minimum which is denoted as a red line in Figure 1. The highest point on the reaction path corresponds to the transition state. A minimum and a transition state are both stationary points as they have zero gradient on the PES. For a stationary point, the Hessian Index, which is the number of negative eigenvalues of a force constant matrix, corresponds to the number of internal degrees of freedom along which that point is a potential energy maximum<sup>2</sup>. The Hessian Index is also equal to the number of imaginary vibrational frequencies. A minimum and a transition state can be distinguished via this Hessian Index. A minimum will have only positive eigenvalues of the Hessian and have an Hessian Index of 0. Hence, there will be no imaginary frequencies. However, since a transition state is the maximum of the lowest energy pathway, it will have a single negative Hessian eigenvalue and have a Hessian Index of 0. Hence, it will have a single imaginary vibrational frequency.

===Quantum Chemical methods used===
The semi-empirical PM6 method was used for initial calculations, followed by the more accurate DFT (Density Functional Theory) method B3LYP. The PM6 method was used to speed up initial calculations due to the method replacing some of the two-electron integrals, the Coulomb and the exchange integrals (which are difficult to calculate), used in the Hartree Fock, with empirical parameters.<sup>3</sup> The DFT method is a computational method that derives the properties of a molecular system based on the determination of the electron density of the molecule.<sup>4</sup> Unlike a wavefunction, which becomes increasingly complex as the number of electrons increase, the determination of electron density is independent of the number of electrons. The B3LYP method is a hybrid method which utilises the useful features from <i>ab initio</i> methods and improves the accuracy of the calculation by DFT mathematics. The 6-31G basis set was chosen as a larger basis set gave a better approximation to the atomic orbitals as they place fewer restrictions on the wavefunction while the split basis sets allowed for size changes during bonding.<sup>5</sup>

==Exercise 1: Reaction of Butadiene and Ethene==
===Reaction Scheme===
[[File:Reaction_Scheme_Ex1_zwl115.PNG]]
===Jmol Files===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_PDT_OPT_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

===MO Diagram===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! MO diagram for the formation of the Butadiene/Ethene transition state !! Ethene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of butadiene||rowspan="2"|[[File:MO_Diagram_Ex_1_2_zwl115.PNG|centre|frame]] || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Ethene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Butadiene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Ethene
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! MO 1 !! MO 2 !! MO 3 !! MO 4
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

Referring to the MO diagram above, the HOMO of butadiene is higher in energy than that of ethene, indicating that this is a normal electron demand cycloaddition. Bonding MOs (MOs 1 and 2) of the transition state formed from the MOs of the reactants are much higher in energy than what is expected for a product. Similarly, the anti-bonding MOs of the transition state are lower in energy than the corresponding MOs of the product. This is due to the fact that the transition state lies at the maximum of the lowest energy pathway and the overlap of orbitals are not as strong as what would be seen in the products of the reaction. This leads to an overall destabilisation of the structure as the electrons are occupying MOs which are higher in energy than that of the reactants.

===Symmetry===

[[File:WH_analysis__2_EX1_zwl115.PNG|frame|100px|Figure 1. Woodward-Hoffmann analysis of cycloaddition of butadiene and ethene.]]

For a thermal pericyclic reaction, whether a reaction is 'allowed' or 'forbidden' depends on the Woodward-Hoffmann rules which states that the total number of (4q+2)<sub>s</sub> and (4r)<sub>a</sub> components must be odd.<sup>6</sup> The suffix 's' represents suprafacial where the new bonds are formed on the same side at both ends of the component. The suffix 'a' represents antarafacial where the new bonds formed are on opposite sides of both ends of the component. As seen from Figure 1, when both components are suprafacial, it would allow for good orbital overlap and the Woodward-Hoffmann rules are obeyed. This is in agreement with the results obtained for the combination of the Frontier Orbitals of butadiene and ethene in the MO diagram. Reactions are only allowed when the symmetry of the FO of butadiene is the same as that for the FO of ethene as this would lead to a non-zero orbital overlap. Conversely, an overlap between a symmetric FO and an anti-symmetric FO would lead to an orbital overlap integral of 0 and hence, no reaction will occur.

===Bond Length Analysis===

[[File:Bond_lengths_Ex1.PNG|centre|frame| Figure 2: Reaction Scheme showing the bond lengths of the reactants, transition state and the products]]
The C-C bond lengths for the reactants, transition state and the products are summarised in the Figure 2. Butadiene has shorter C=C terminal bonds of 1.34 Å and a longer C-C internal bond of 1.47 Å while ethene has a bond length of 1.33 Å. The shorter bond lengths observed in butadiene are due to the overlap between sp<sup>2</sup> C atoms which have a typical value of 1.34 Å<sup>7</sup> while the longer C-C bonds observed are due to the overlap between sp<sup>3</sup> C atoms which have a typical value of 1.54 Å.<sup>7</sup> At the transition state, the C=C terminal bonds of butadiene and the C=C bond in ethene lengthen to 1.38 Å, moving towards the value of a bond length observed between sp<sup>3</sup> C atoms. This indicates that the bond order has decreased from 2 to a value between 1 and 2. In contrast, the internal bond shortens to 1.41 Å, moving towards the value of a bond length observed between sp<sup>2</sup> C atoms and the bond order has increased from 1 to a value between 1 and 2, similar to the bond lengths of the terminal bonds. Finally in the products, the bond lengths continue to change in the same way. C5-C6 which was previously the internal bond of the butadiene has the shortest bond length of 1.34 Å due to the overlap between sp<sup>2</sup> C atoms. C1-C2, C2-C3 and C3-C4 have very similar bond lengths of 1.53-1.54 Å which reflects the overlap between sp<sup>3</sup> C atoms. C1-C6 and C4-C5 which were previously the terminal bonds of the butadiene have a bond length of 1.50 Å which is slightly shorter than the other single bonds in the molecule. This is due to the sp<sup>2</sup>-sp<sup>3</sup> overlap of the C atoms. The greater s character of the sp<sup>2</sup> C atom results in a stronger and shorter sigma bond. The length of the partially formed C-C bonds in the transition state is 2.11 Å which is significantly greater than the Van Der Waals radius of C (1.70 Å).<sup>8</sup> This indicates that at the transition state, no new C-C bonds were formed.

===Reaction path towards the products from the transition state===

[[File:Vibration_TS_Ex1_zwl115.gif|centre|frame| Figure 3. Illustration of vibration of reaction path at the Transition state]]
As seen from the illustration showing the vibration corresponding to the transition state, the formation of the 2 bonds is synchronous. The ends of the butadiene and ethene fragments move towards each other in a symmetric fashion showing a concerted mechanism.

==Link to Exercise 2==
https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_States_and_Reactivity_Exercise2_ZWL115

==Link to Exercise 3==
https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_States_and_Reactivity_Exercise3_ZWL115

==References==
1. Potential Energy Surface. Encyclopedia of Human thermodynamics.

2. Potential Energy Surfaces. C, David Sherrill. School of Chemistry and Biochemistry Georgia Institute of Technology.

3. Computational Quantum Chemistry. C, David Sherrill.

4. Introduction to Computational Quantum Chemistry: Theory. A, Gilbert. The Australian National University.

5. Introduction to Computational Chemistry. V H¨anninen. University of Helsinki

6. Woodward, R. B.; Hoffmann, R. J. Am. Chem. Soc. 1965, 87(2), 395-397.

7. Bond Length. Wikipedia.

8. Van der Waals radius. Wikipedia.

Rep:Transition States and Reactivity ZWL115

2018-02-28T01:35:41Z

Zwl115: /* Link to Exercise 2 */

==Introduction==

===What is a potential energy surface?===

A potential energy surface (PES) describes the potential energy of a chemical system in terms of certain parameters such as time and extent of reactions. Each geometry of the atoms in a system has its own unique potential energy due to the varying distances of the different atoms. Two atoms which are very far apart will have no interactions while 2 atoms which are very close together will have strong repulsive forces between them. This results in the creation of a smooth energy landscape such as the one shown in Figure 1. In Figure 1, the vertical coordinate gives the potential energy which varies with the 2 horizontal coordinates which are the bond lengths of atoms AB and atoms BC

[[File:PES_zwl115.jpg|centre|frame|Figure 1. Example of a PES<sup>1</sup>]]

===What is a transition state?===

Minima in a PES are assiociated with the structures of the reactants, products or intermediates of a reaction system. The reaction path is the lowest energy pathway between the reactant minimum and the product minimum which is denoted as a red line in Figure 1. The highest point on the reaction path corresponds to the transition state. A minimum and a transition state are both stationary points as they have zero gradient on the PES. For a stationary point, the Hessian Index, which is the number of negative eigenvalues of a force constant matrix, corresponds to the number of internal degrees of freedom along which that point is a potential energy maximum<sup>2</sup>. The Hessian Index is also equal to the number of imaginary vibrational frequencies. A minimum and a transition state can be distinguished via this Hessian Index. A minimum will have only positive eigenvalues of the Hessian and have an Hessian Index of 0. Hence, there will be no imaginary frequencies. However, since a transition state is the maximum of the lowest energy pathway, it will have a single negative Hessian eigenvalue and have a Hessian Index of 0. Hence, it will have a single imaginary vibrational frequency.

===Quantum Chemical methods used===
The semi-empirical PM6 method was used for initial calculations, followed by the more accurate DFT (Density Functional Theory) method B3LYP. The PM6 method was used to speed up initial calculations due to the method replacing some of the two-electron integrals, the Coulomb and the exchange integrals (which are difficult to calculate), used in the Hartree Fock, with empirical parameters.<sup>3</sup> The DFT method is a computational method that derives the properties of a molecular system based on the determination of the electron density of the molecule.<sup>4</sup> Unlike a wavefunction, which becomes increasingly complex as the number of electrons increase, the determination of electron density is independent of the number of electrons. The B3LYP method is a hybrid method which utilises the useful features from <i>ab initio</i> methods and improves the accuracy of the calculation by DFT mathematics. The 6-31G basis set was chosen as a larger basis set gave a better approximation to the atomic orbitals as they place fewer restrictions on the wavefunction while the split basis sets allowed for size changes during bonding.<sup>5</sup>

==Exercise 1: Reaction of Butadiene and Ethene==
===Reaction Scheme===
[[File:Reaction_Scheme_Ex1_zwl115.PNG]]
===Jmol Files===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_PDT_OPT_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

===MO Diagram===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! MO diagram for the formation of the Butadiene/Ethene transition state !! Ethene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of butadiene||rowspan="2"|[[File:MO_Diagram_Ex_1_2_zwl115.PNG|centre|frame]] || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Ethene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Butadiene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Ethene
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! MO 1 !! MO 2 !! MO 3 !! MO 4
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

Referring to the MO diagram above, the HOMO of butadiene is higher in energy than that of ethene, indicating that this is a normal electron demand cycloaddition. Bonding MOs (MOs 1 and 2) of the transition state formed from the MOs of the reactants are much higher in energy than what is expected for a product. Similarly, the anti-bonding MOs of the transition state are lower in energy than the corresponding MOs of the product. This is due to the fact that the transition state lies at the maximum of the lowest energy pathway and the overlap of orbitals are not as strong as what would be seen in the products of the reaction. This leads to an overall destabilisation of the structure as the electrons are occupying MOs which are higher in energy than that of the reactants.

===Symmetry===

[[File:WH_analysis__2_EX1_zwl115.PNG|frame|100px|Figure 1. Woodward-Hoffmann analysis of cycloaddition of butadiene and ethene.]]

For a thermal pericyclic reaction, whether a reaction is 'allowed' or 'forbidden' depends on the Woodward-Hoffmann rules which states that the total number of (4q+2)<sub>s</sub> and (4r)<sub>a</sub> components must be odd.<sup>6</sup> The suffix 's' represents suprafacial where the new bonds are formed on the same side at both ends of the component. The suffix 'a' represents antarafacial where the new bonds formed are on opposite sides of both ends of the component. As seen from Figure 1, when both components are suprafacial, it would allow for good orbital overlap and the Woodward-Hoffmann rules are obeyed. This is in agreement with the results obtained for the combination of the Frontier Orbitals of butadiene and ethene in the MO diagram. Reactions are only allowed when the symmetry of the FO of butadiene is the same as that for the FO of ethene as this would lead to a non-zero orbital overlap. Conversely, an overlap between a symmetric FO and an anti-symmetric FO would lead to an orbital overlap integral of 0 and hence, no reaction will occur.

===Bond Length Analysis===

[[File:Bond_lengths_Ex1.PNG|centre|frame| Figure 2: Reaction Scheme showing the bond lengths of the reactants, transition state and the products]]
The C-C bond lengths for the reactants, transition state and the products are summarised in the Figure 2. Butadiene has shorter C=C terminal bonds of 1.34 Å and a longer C-C internal bond of 1.47 Å while ethene has a bond length of 1.33 Å. The shorter bond lengths observed in butadiene are due to the overlap between sp<sup>2</sup> C atoms which have a typical value of 1.34 Å<sup>7</sup> while the longer C-C bonds observed are due to the overlap between sp<sup>3</sup> C atoms which have a typical value of 1.54 Å.<sup>7</sup> At the transition state, the C=C terminal bonds of butadiene and the C=C bond in ethene lengthen to 1.38 Å, moving towards the value of a bond length observed between sp<sup>3</sup> C atoms. This indicates that the bond order has decreased from 2 to a value between 1 and 2. In contrast, the internal bond shortens to 1.41 Å, moving towards the value of a bond length observed between sp<sup>2</sup> C atoms and the bond order has increased from 1 to a value between 1 and 2, similar to the bond lengths of the terminal bonds. Finally in the products, the bond lengths continue to change in the same way. C5-C6 which was previously the internal bond of the butadiene has the shortest bond length of 1.34 Å due to the overlap between sp<sup>2</sup> C atoms. C1-C2, C2-C3 and C3-C4 have very similar bond lengths of 1.53-1.54 Å which reflects the overlap between sp<sup>3</sup> C atoms. C1-C6 and C4-C5 which were previously the terminal bonds of the butadiene have a bond length of 1.50 Å which is slightly shorter than the other single bonds in the molecule. This is due to the sp<sup>2</sup>-sp<sup>3</sup> overlap of the C atoms. The greater s character of the sp<sup>2</sup> C atom results in a stronger and shorter sigma bond. The length of the partially formed C-C bonds in the transition state is 2.11 Å which is significantly greater than the Van Der Waals radius of C (1.70 Å).<sup>8</sup> This indicates that at the transition state, no new C-C bonds were formed.

===Reaction path towards the products from the transition state===

[[File:Vibration_TS_Ex1_zwl115.gif|centre|frame| Figure 3. Illustration of vibration of reaction path at the Transition state]]
As seen from the illustration showing the vibration corresponding to the transition state, the formation of the 2 bonds is synchronous. The ends of the butadiene and ethene fragments move towards each other in a symmetric fashion showing a concerted mechanism.

==Link to Exercise 2==
https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_States_and_Reactivity_Exercise2_ZWL115

==Link to Exercise 3==

==References==
1. Potential Energy Surface. Encyclopedia of Human thermodynamics.

2. Potential Energy Surfaces. C, David Sherrill. School of Chemistry and Biochemistry Georgia Institute of Technology.

3. Computational Quantum Chemistry. C, David Sherrill.

4. Introduction to Computational Quantum Chemistry: Theory. A, Gilbert. The Australian National University.

5. Introduction to Computational Chemistry. V H¨anninen. University of Helsinki

6. Woodward, R. B.; Hoffmann, R. J. Am. Chem. Soc. 1965, 87(2), 395-397.

7. Bond Length. Wikipedia.

8. Van der Waals radius. Wikipedia.

Rep:Transition States and Reactivity ZWL115

2018-02-28T01:34:48Z

Zwl115: /* References */

==Introduction==

===What is a potential energy surface?===

A potential energy surface (PES) describes the potential energy of a chemical system in terms of certain parameters such as time and extent of reactions. Each geometry of the atoms in a system has its own unique potential energy due to the varying distances of the different atoms. Two atoms which are very far apart will have no interactions while 2 atoms which are very close together will have strong repulsive forces between them. This results in the creation of a smooth energy landscape such as the one shown in Figure 1. In Figure 1, the vertical coordinate gives the potential energy which varies with the 2 horizontal coordinates which are the bond lengths of atoms AB and atoms BC

[[File:PES_zwl115.jpg|centre|frame|Figure 1. Example of a PES<sup>1</sup>]]

===What is a transition state?===

Minima in a PES are assiociated with the structures of the reactants, products or intermediates of a reaction system. The reaction path is the lowest energy pathway between the reactant minimum and the product minimum which is denoted as a red line in Figure 1. The highest point on the reaction path corresponds to the transition state. A minimum and a transition state are both stationary points as they have zero gradient on the PES. For a stationary point, the Hessian Index, which is the number of negative eigenvalues of a force constant matrix, corresponds to the number of internal degrees of freedom along which that point is a potential energy maximum<sup>2</sup>. The Hessian Index is also equal to the number of imaginary vibrational frequencies. A minimum and a transition state can be distinguished via this Hessian Index. A minimum will have only positive eigenvalues of the Hessian and have an Hessian Index of 0. Hence, there will be no imaginary frequencies. However, since a transition state is the maximum of the lowest energy pathway, it will have a single negative Hessian eigenvalue and have a Hessian Index of 0. Hence, it will have a single imaginary vibrational frequency.

===Quantum Chemical methods used===
The semi-empirical PM6 method was used for initial calculations, followed by the more accurate DFT (Density Functional Theory) method B3LYP. The PM6 method was used to speed up initial calculations due to the method replacing some of the two-electron integrals, the Coulomb and the exchange integrals (which are difficult to calculate), used in the Hartree Fock, with empirical parameters.<sup>3</sup> The DFT method is a computational method that derives the properties of a molecular system based on the determination of the electron density of the molecule.<sup>4</sup> Unlike a wavefunction, which becomes increasingly complex as the number of electrons increase, the determination of electron density is independent of the number of electrons. The B3LYP method is a hybrid method which utilises the useful features from <i>ab initio</i> methods and improves the accuracy of the calculation by DFT mathematics. The 6-31G basis set was chosen as a larger basis set gave a better approximation to the atomic orbitals as they place fewer restrictions on the wavefunction while the split basis sets allowed for size changes during bonding.<sup>5</sup>

==Exercise 1: Reaction of Butadiene and Ethene==
===Reaction Scheme===
[[File:Reaction_Scheme_Ex1_zwl115.PNG]]
===Jmol Files===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_PDT_OPT_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

===MO Diagram===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! MO diagram for the formation of the Butadiene/Ethene transition state !! Ethene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of butadiene||rowspan="2"|[[File:MO_Diagram_Ex_1_2_zwl115.PNG|centre|frame]] || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Ethene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Butadiene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Ethene
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! MO 1 !! MO 2 !! MO 3 !! MO 4
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

Referring to the MO diagram above, the HOMO of butadiene is higher in energy than that of ethene, indicating that this is a normal electron demand cycloaddition. Bonding MOs (MOs 1 and 2) of the transition state formed from the MOs of the reactants are much higher in energy than what is expected for a product. Similarly, the anti-bonding MOs of the transition state are lower in energy than the corresponding MOs of the product. This is due to the fact that the transition state lies at the maximum of the lowest energy pathway and the overlap of orbitals are not as strong as what would be seen in the products of the reaction. This leads to an overall destabilisation of the structure as the electrons are occupying MOs which are higher in energy than that of the reactants.

===Symmetry===

[[File:WH_analysis__2_EX1_zwl115.PNG|frame|100px|Figure 1. Woodward-Hoffmann analysis of cycloaddition of butadiene and ethene.]]

For a thermal pericyclic reaction, whether a reaction is 'allowed' or 'forbidden' depends on the Woodward-Hoffmann rules which states that the total number of (4q+2)<sub>s</sub> and (4r)<sub>a</sub> components must be odd.<sup>6</sup> The suffix 's' represents suprafacial where the new bonds are formed on the same side at both ends of the component. The suffix 'a' represents antarafacial where the new bonds formed are on opposite sides of both ends of the component. As seen from Figure 1, when both components are suprafacial, it would allow for good orbital overlap and the Woodward-Hoffmann rules are obeyed. This is in agreement with the results obtained for the combination of the Frontier Orbitals of butadiene and ethene in the MO diagram. Reactions are only allowed when the symmetry of the FO of butadiene is the same as that for the FO of ethene as this would lead to a non-zero orbital overlap. Conversely, an overlap between a symmetric FO and an anti-symmetric FO would lead to an orbital overlap integral of 0 and hence, no reaction will occur.

===Bond Length Analysis===

[[File:Bond_lengths_Ex1.PNG|centre|frame| Figure 2: Reaction Scheme showing the bond lengths of the reactants, transition state and the products]]
The C-C bond lengths for the reactants, transition state and the products are summarised in the Figure 2. Butadiene has shorter C=C terminal bonds of 1.34 Å and a longer C-C internal bond of 1.47 Å while ethene has a bond length of 1.33 Å. The shorter bond lengths observed in butadiene are due to the overlap between sp<sup>2</sup> C atoms which have a typical value of 1.34 Å<sup>7</sup> while the longer C-C bonds observed are due to the overlap between sp<sup>3</sup> C atoms which have a typical value of 1.54 Å.<sup>7</sup> At the transition state, the C=C terminal bonds of butadiene and the C=C bond in ethene lengthen to 1.38 Å, moving towards the value of a bond length observed between sp<sup>3</sup> C atoms. This indicates that the bond order has decreased from 2 to a value between 1 and 2. In contrast, the internal bond shortens to 1.41 Å, moving towards the value of a bond length observed between sp<sup>2</sup> C atoms and the bond order has increased from 1 to a value between 1 and 2, similar to the bond lengths of the terminal bonds. Finally in the products, the bond lengths continue to change in the same way. C5-C6 which was previously the internal bond of the butadiene has the shortest bond length of 1.34 Å due to the overlap between sp<sup>2</sup> C atoms. C1-C2, C2-C3 and C3-C4 have very similar bond lengths of 1.53-1.54 Å which reflects the overlap between sp<sup>3</sup> C atoms. C1-C6 and C4-C5 which were previously the terminal bonds of the butadiene have a bond length of 1.50 Å which is slightly shorter than the other single bonds in the molecule. This is due to the sp<sup>2</sup>-sp<sup>3</sup> overlap of the C atoms. The greater s character of the sp<sup>2</sup> C atom results in a stronger and shorter sigma bond. The length of the partially formed C-C bonds in the transition state is 2.11 Å which is significantly greater than the Van Der Waals radius of C (1.70 Å).<sup>8</sup> This indicates that at the transition state, no new C-C bonds were formed.

===Reaction path towards the products from the transition state===

[[File:Vibration_TS_Ex1_zwl115.gif|centre|frame| Figure 3. Illustration of vibration of reaction path at the Transition state]]
As seen from the illustration showing the vibration corresponding to the transition state, the formation of the 2 bonds is synchronous. The ends of the butadiene and ethene fragments move towards each other in a symmetric fashion showing a concerted mechanism.

==Link to Exercise 2==
==Link to Exercise 3==

==References==
1. Potential Energy Surface. Encyclopedia of Human thermodynamics.

2. Potential Energy Surfaces. C, David Sherrill. School of Chemistry and Biochemistry Georgia Institute of Technology.

3. Computational Quantum Chemistry. C, David Sherrill.

4. Introduction to Computational Quantum Chemistry: Theory. A, Gilbert. The Australian National University.

5. Introduction to Computational Chemistry. V H¨anninen. University of Helsinki

6. Woodward, R. B.; Hoffmann, R. J. Am. Chem. Soc. 1965, 87(2), 395-397.

7. Bond Length. Wikipedia.

8. Van der Waals radius. Wikipedia.

Rep:Transition States and Reactivity ZWL115

2018-02-28T01:34:19Z

Zwl115: /* Bond Length Analysis */

==Introduction==

===What is a potential energy surface?===

A potential energy surface (PES) describes the potential energy of a chemical system in terms of certain parameters such as time and extent of reactions. Each geometry of the atoms in a system has its own unique potential energy due to the varying distances of the different atoms. Two atoms which are very far apart will have no interactions while 2 atoms which are very close together will have strong repulsive forces between them. This results in the creation of a smooth energy landscape such as the one shown in Figure 1. In Figure 1, the vertical coordinate gives the potential energy which varies with the 2 horizontal coordinates which are the bond lengths of atoms AB and atoms BC

[[File:PES_zwl115.jpg|centre|frame|Figure 1. Example of a PES<sup>1</sup>]]

===What is a transition state?===

Minima in a PES are assiociated with the structures of the reactants, products or intermediates of a reaction system. The reaction path is the lowest energy pathway between the reactant minimum and the product minimum which is denoted as a red line in Figure 1. The highest point on the reaction path corresponds to the transition state. A minimum and a transition state are both stationary points as they have zero gradient on the PES. For a stationary point, the Hessian Index, which is the number of negative eigenvalues of a force constant matrix, corresponds to the number of internal degrees of freedom along which that point is a potential energy maximum<sup>2</sup>. The Hessian Index is also equal to the number of imaginary vibrational frequencies. A minimum and a transition state can be distinguished via this Hessian Index. A minimum will have only positive eigenvalues of the Hessian and have an Hessian Index of 0. Hence, there will be no imaginary frequencies. However, since a transition state is the maximum of the lowest energy pathway, it will have a single negative Hessian eigenvalue and have a Hessian Index of 0. Hence, it will have a single imaginary vibrational frequency.

===Quantum Chemical methods used===
The semi-empirical PM6 method was used for initial calculations, followed by the more accurate DFT (Density Functional Theory) method B3LYP. The PM6 method was used to speed up initial calculations due to the method replacing some of the two-electron integrals, the Coulomb and the exchange integrals (which are difficult to calculate), used in the Hartree Fock, with empirical parameters.<sup>3</sup> The DFT method is a computational method that derives the properties of a molecular system based on the determination of the electron density of the molecule.<sup>4</sup> Unlike a wavefunction, which becomes increasingly complex as the number of electrons increase, the determination of electron density is independent of the number of electrons. The B3LYP method is a hybrid method which utilises the useful features from <i>ab initio</i> methods and improves the accuracy of the calculation by DFT mathematics. The 6-31G basis set was chosen as a larger basis set gave a better approximation to the atomic orbitals as they place fewer restrictions on the wavefunction while the split basis sets allowed for size changes during bonding.<sup>5</sup>

==Exercise 1: Reaction of Butadiene and Ethene==
===Reaction Scheme===
[[File:Reaction_Scheme_Ex1_zwl115.PNG]]
===Jmol Files===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_PDT_OPT_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

===MO Diagram===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! MO diagram for the formation of the Butadiene/Ethene transition state !! Ethene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of butadiene||rowspan="2"|[[File:MO_Diagram_Ex_1_2_zwl115.PNG|centre|frame]] || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Ethene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Butadiene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Ethene
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! MO 1 !! MO 2 !! MO 3 !! MO 4
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

Referring to the MO diagram above, the HOMO of butadiene is higher in energy than that of ethene, indicating that this is a normal electron demand cycloaddition. Bonding MOs (MOs 1 and 2) of the transition state formed from the MOs of the reactants are much higher in energy than what is expected for a product. Similarly, the anti-bonding MOs of the transition state are lower in energy than the corresponding MOs of the product. This is due to the fact that the transition state lies at the maximum of the lowest energy pathway and the overlap of orbitals are not as strong as what would be seen in the products of the reaction. This leads to an overall destabilisation of the structure as the electrons are occupying MOs which are higher in energy than that of the reactants.

===Symmetry===

[[File:WH_analysis__2_EX1_zwl115.PNG|frame|100px|Figure 1. Woodward-Hoffmann analysis of cycloaddition of butadiene and ethene.]]

For a thermal pericyclic reaction, whether a reaction is 'allowed' or 'forbidden' depends on the Woodward-Hoffmann rules which states that the total number of (4q+2)<sub>s</sub> and (4r)<sub>a</sub> components must be odd.<sup>6</sup> The suffix 's' represents suprafacial where the new bonds are formed on the same side at both ends of the component. The suffix 'a' represents antarafacial where the new bonds formed are on opposite sides of both ends of the component. As seen from Figure 1, when both components are suprafacial, it would allow for good orbital overlap and the Woodward-Hoffmann rules are obeyed. This is in agreement with the results obtained for the combination of the Frontier Orbitals of butadiene and ethene in the MO diagram. Reactions are only allowed when the symmetry of the FO of butadiene is the same as that for the FO of ethene as this would lead to a non-zero orbital overlap. Conversely, an overlap between a symmetric FO and an anti-symmetric FO would lead to an orbital overlap integral of 0 and hence, no reaction will occur.

===Bond Length Analysis===

[[File:Bond_lengths_Ex1.PNG|centre|frame| Figure 2: Reaction Scheme showing the bond lengths of the reactants, transition state and the products]]
The C-C bond lengths for the reactants, transition state and the products are summarised in the Figure 2. Butadiene has shorter C=C terminal bonds of 1.34 Å and a longer C-C internal bond of 1.47 Å while ethene has a bond length of 1.33 Å. The shorter bond lengths observed in butadiene are due to the overlap between sp<sup>2</sup> C atoms which have a typical value of 1.34 Å<sup>7</sup> while the longer C-C bonds observed are due to the overlap between sp<sup>3</sup> C atoms which have a typical value of 1.54 Å.<sup>7</sup> At the transition state, the C=C terminal bonds of butadiene and the C=C bond in ethene lengthen to 1.38 Å, moving towards the value of a bond length observed between sp<sup>3</sup> C atoms. This indicates that the bond order has decreased from 2 to a value between 1 and 2. In contrast, the internal bond shortens to 1.41 Å, moving towards the value of a bond length observed between sp<sup>2</sup> C atoms and the bond order has increased from 1 to a value between 1 and 2, similar to the bond lengths of the terminal bonds. Finally in the products, the bond lengths continue to change in the same way. C5-C6 which was previously the internal bond of the butadiene has the shortest bond length of 1.34 Å due to the overlap between sp<sup>2</sup> C atoms. C1-C2, C2-C3 and C3-C4 have very similar bond lengths of 1.53-1.54 Å which reflects the overlap between sp<sup>3</sup> C atoms. C1-C6 and C4-C5 which were previously the terminal bonds of the butadiene have a bond length of 1.50 Å which is slightly shorter than the other single bonds in the molecule. This is due to the sp<sup>2</sup>-sp<sup>3</sup> overlap of the C atoms. The greater s character of the sp<sup>2</sup> C atom results in a stronger and shorter sigma bond. The length of the partially formed C-C bonds in the transition state is 2.11 Å which is significantly greater than the Van Der Waals radius of C (1.70 Å).<sup>8</sup> This indicates that at the transition state, no new C-C bonds were formed.

===Reaction path towards the products from the transition state===

[[File:Vibration_TS_Ex1_zwl115.gif|centre|frame| Figure 3. Illustration of vibration of reaction path at the Transition state]]
As seen from the illustration showing the vibration corresponding to the transition state, the formation of the 2 bonds is synchronous. The ends of the butadiene and ethene fragments move towards each other in a symmetric fashion showing a concerted mechanism.

==Link to Exercise 2==
==Link to Exercise 3==

==References==
1. Potential Energy Surface. Encyclopedia of Human thermodynamics.
2. Potential Energy Surfaces. C, David Sherrill. School of Chemistry and Biochemistry Georgia Institute of Technology.
3. Computational Quantum Chemistry. C, David Sherrill.
4. Introduction to Computational Quantum Chemistry: Theory. A, Gilbert. The Australian National University.
5. Introduction to Computational Chemistry. V H¨anninen. University of Helsinki
6. Woodward, R. B.; Hoffmann, R. J. Am. Chem. Soc. 1965, 87(2), 395-397.
7. Bond Length. Wikipedia.
8. Van der Waals radius. Wikipedia.

Rep:Transition States and Reactivity ZWL115

2018-02-28T01:32:53Z

Zwl115: /* Symmetry */

==Introduction==

===What is a potential energy surface?===

A potential energy surface (PES) describes the potential energy of a chemical system in terms of certain parameters such as time and extent of reactions. Each geometry of the atoms in a system has its own unique potential energy due to the varying distances of the different atoms. Two atoms which are very far apart will have no interactions while 2 atoms which are very close together will have strong repulsive forces between them. This results in the creation of a smooth energy landscape such as the one shown in Figure 1. In Figure 1, the vertical coordinate gives the potential energy which varies with the 2 horizontal coordinates which are the bond lengths of atoms AB and atoms BC

[[File:PES_zwl115.jpg|centre|frame|Figure 1. Example of a PES<sup>1</sup>]]

===What is a transition state?===

Minima in a PES are assiociated with the structures of the reactants, products or intermediates of a reaction system. The reaction path is the lowest energy pathway between the reactant minimum and the product minimum which is denoted as a red line in Figure 1. The highest point on the reaction path corresponds to the transition state. A minimum and a transition state are both stationary points as they have zero gradient on the PES. For a stationary point, the Hessian Index, which is the number of negative eigenvalues of a force constant matrix, corresponds to the number of internal degrees of freedom along which that point is a potential energy maximum<sup>2</sup>. The Hessian Index is also equal to the number of imaginary vibrational frequencies. A minimum and a transition state can be distinguished via this Hessian Index. A minimum will have only positive eigenvalues of the Hessian and have an Hessian Index of 0. Hence, there will be no imaginary frequencies. However, since a transition state is the maximum of the lowest energy pathway, it will have a single negative Hessian eigenvalue and have a Hessian Index of 0. Hence, it will have a single imaginary vibrational frequency.

===Quantum Chemical methods used===
The semi-empirical PM6 method was used for initial calculations, followed by the more accurate DFT (Density Functional Theory) method B3LYP. The PM6 method was used to speed up initial calculations due to the method replacing some of the two-electron integrals, the Coulomb and the exchange integrals (which are difficult to calculate), used in the Hartree Fock, with empirical parameters.<sup>3</sup> The DFT method is a computational method that derives the properties of a molecular system based on the determination of the electron density of the molecule.<sup>4</sup> Unlike a wavefunction, which becomes increasingly complex as the number of electrons increase, the determination of electron density is independent of the number of electrons. The B3LYP method is a hybrid method which utilises the useful features from <i>ab initio</i> methods and improves the accuracy of the calculation by DFT mathematics. The 6-31G basis set was chosen as a larger basis set gave a better approximation to the atomic orbitals as they place fewer restrictions on the wavefunction while the split basis sets allowed for size changes during bonding.<sup>5</sup>

==Exercise 1: Reaction of Butadiene and Ethene==
===Reaction Scheme===
[[File:Reaction_Scheme_Ex1_zwl115.PNG]]
===Jmol Files===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_PDT_OPT_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

===MO Diagram===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! MO diagram for the formation of the Butadiene/Ethene transition state !! Ethene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of butadiene||rowspan="2"|[[File:MO_Diagram_Ex_1_2_zwl115.PNG|centre|frame]] || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Ethene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Butadiene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Ethene
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! MO 1 !! MO 2 !! MO 3 !! MO 4
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

Referring to the MO diagram above, the HOMO of butadiene is higher in energy than that of ethene, indicating that this is a normal electron demand cycloaddition. Bonding MOs (MOs 1 and 2) of the transition state formed from the MOs of the reactants are much higher in energy than what is expected for a product. Similarly, the anti-bonding MOs of the transition state are lower in energy than the corresponding MOs of the product. This is due to the fact that the transition state lies at the maximum of the lowest energy pathway and the overlap of orbitals are not as strong as what would be seen in the products of the reaction. This leads to an overall destabilisation of the structure as the electrons are occupying MOs which are higher in energy than that of the reactants.

===Symmetry===

[[File:WH_analysis__2_EX1_zwl115.PNG|frame|100px|Figure 1. Woodward-Hoffmann analysis of cycloaddition of butadiene and ethene.]]

For a thermal pericyclic reaction, whether a reaction is 'allowed' or 'forbidden' depends on the Woodward-Hoffmann rules which states that the total number of (4q+2)<sub>s</sub> and (4r)<sub>a</sub> components must be odd.<sup>6</sup> The suffix 's' represents suprafacial where the new bonds are formed on the same side at both ends of the component. The suffix 'a' represents antarafacial where the new bonds formed are on opposite sides of both ends of the component. As seen from Figure 1, when both components are suprafacial, it would allow for good orbital overlap and the Woodward-Hoffmann rules are obeyed. This is in agreement with the results obtained for the combination of the Frontier Orbitals of butadiene and ethene in the MO diagram. Reactions are only allowed when the symmetry of the FO of butadiene is the same as that for the FO of ethene as this would lead to a non-zero orbital overlap. Conversely, an overlap between a symmetric FO and an anti-symmetric FO would lead to an orbital overlap integral of 0 and hence, no reaction will occur.

===Bond Length Analysis===

[[File:Bond_lengths_Ex1.PNG|centre|frame| Figure 2: Reaction Scheme showing the bond lengths of the reactants, transition state and the products]]
The C-C bond lengths for the reactants, transition state and the products are summarised in the Figure 2. Butadiene has shorter C=C terminal bonds of 1.34 Å and a longer C-C internal bond of 1.47 Å while ethene has a bond length of 1.33 Å. The shorter bond lengths observed in butadiene are due to the overlap between sp<sup>2</sup> C atoms which have a typical value of 1.34 Å while the longer C-C bonds observed are due to the overlap between sp<sup>3</sup> C atoms which have a typical value of 1.54 Å. At the transition state, the C=C terminal bonds of butadiene and the C=C bond in ethene lengthen to 1.38 Å, moving towards the value of a bond length observed between sp<sup>3</sup> C atoms. This indicates that the bond order has decreased from 2 to a value between 1 and 2. In contrast, the internal bond shortens to 1.41 Å, moving towards the value of a bond length observed between sp<sup>2</sup> C atoms and the bond order has increased from 1 to a value between 1 and 2, similar to the bond lengths of the terminal bonds. Finally in the products, the bond lengths continue to change in the same way. C5-C6 which was previously the internal bond of the butadiene has the shortest bond length of 1.34 Å due to the overlap between sp<sup>2</sup> C atoms. C1-C2, C2-C3 and C3-C4 have very similar bond lengths of 1.53-1.54 Å which reflects the overlap between sp<sup>3</sup> C atoms. C1-C6 and C4-C5 which were previously the terminal bonds of the butadiene have a bond length of 1.50 Å which is slightly shorter than the other single bonds in the molecule. This is due to the sp<sup>2</sup>-sp<sup>3</sup> overlap of the C atoms. The greater s character of the sp<sup>2</sup> C atom results in a stronger and shorter sigma bond. The length of the partially formed C-C bonds in the transition state is 2.11 Å which is significantly greater than the Van Der Waals radius of C (1.70 Å). This indicates that at the transition state, no new C-C bonds were formed.

===Reaction path towards the products from the transition state===

[[File:Vibration_TS_Ex1_zwl115.gif|centre|frame| Figure 3. Illustration of vibration of reaction path at the Transition state]]
As seen from the illustration showing the vibration corresponding to the transition state, the formation of the 2 bonds is synchronous. The ends of the butadiene and ethene fragments move towards each other in a symmetric fashion showing a concerted mechanism.

==Link to Exercise 2==
==Link to Exercise 3==

==References==
1. Potential Energy Surface. Encyclopedia of Human thermodynamics.
2. Potential Energy Surfaces. C, David Sherrill. School of Chemistry and Biochemistry Georgia Institute of Technology.
3. Computational Quantum Chemistry. C, David Sherrill.
4. Introduction to Computational Quantum Chemistry: Theory. A, Gilbert. The Australian National University.
5. Introduction to Computational Chemistry. V H¨anninen. University of Helsinki
6. Woodward, R. B.; Hoffmann, R. J. Am. Chem. Soc. 1965, 87(2), 395-397.
7. Bond Length. Wikipedia.
8. Van der Waals radius. Wikipedia.

Rep:Transition States and Reactivity ZWL115

2018-02-28T01:32:12Z

Zwl115: /* Symmetry */

==Introduction==

===What is a potential energy surface?===

A potential energy surface (PES) describes the potential energy of a chemical system in terms of certain parameters such as time and extent of reactions. Each geometry of the atoms in a system has its own unique potential energy due to the varying distances of the different atoms. Two atoms which are very far apart will have no interactions while 2 atoms which are very close together will have strong repulsive forces between them. This results in the creation of a smooth energy landscape such as the one shown in Figure 1. In Figure 1, the vertical coordinate gives the potential energy which varies with the 2 horizontal coordinates which are the bond lengths of atoms AB and atoms BC

[[File:PES_zwl115.jpg|centre|frame|Figure 1. Example of a PES<sup>1</sup>]]

===What is a transition state?===

Minima in a PES are assiociated with the structures of the reactants, products or intermediates of a reaction system. The reaction path is the lowest energy pathway between the reactant minimum and the product minimum which is denoted as a red line in Figure 1. The highest point on the reaction path corresponds to the transition state. A minimum and a transition state are both stationary points as they have zero gradient on the PES. For a stationary point, the Hessian Index, which is the number of negative eigenvalues of a force constant matrix, corresponds to the number of internal degrees of freedom along which that point is a potential energy maximum<sup>2</sup>. The Hessian Index is also equal to the number of imaginary vibrational frequencies. A minimum and a transition state can be distinguished via this Hessian Index. A minimum will have only positive eigenvalues of the Hessian and have an Hessian Index of 0. Hence, there will be no imaginary frequencies. However, since a transition state is the maximum of the lowest energy pathway, it will have a single negative Hessian eigenvalue and have a Hessian Index of 0. Hence, it will have a single imaginary vibrational frequency.

===Quantum Chemical methods used===
The semi-empirical PM6 method was used for initial calculations, followed by the more accurate DFT (Density Functional Theory) method B3LYP. The PM6 method was used to speed up initial calculations due to the method replacing some of the two-electron integrals, the Coulomb and the exchange integrals (which are difficult to calculate), used in the Hartree Fock, with empirical parameters.<sup>3</sup> The DFT method is a computational method that derives the properties of a molecular system based on the determination of the electron density of the molecule.<sup>4</sup> Unlike a wavefunction, which becomes increasingly complex as the number of electrons increase, the determination of electron density is independent of the number of electrons. The B3LYP method is a hybrid method which utilises the useful features from <i>ab initio</i> methods and improves the accuracy of the calculation by DFT mathematics. The 6-31G basis set was chosen as a larger basis set gave a better approximation to the atomic orbitals as they place fewer restrictions on the wavefunction while the split basis sets allowed for size changes during bonding.<sup>5</sup>

==Exercise 1: Reaction of Butadiene and Ethene==
===Reaction Scheme===
[[File:Reaction_Scheme_Ex1_zwl115.PNG]]
===Jmol Files===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_PDT_OPT_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

===MO Diagram===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! MO diagram for the formation of the Butadiene/Ethene transition state !! Ethene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of butadiene||rowspan="2"|[[File:MO_Diagram_Ex_1_2_zwl115.PNG|centre|frame]] || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Ethene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Butadiene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Ethene
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! MO 1 !! MO 2 !! MO 3 !! MO 4
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

Referring to the MO diagram above, the HOMO of butadiene is higher in energy than that of ethene, indicating that this is a normal electron demand cycloaddition. Bonding MOs (MOs 1 and 2) of the transition state formed from the MOs of the reactants are much higher in energy than what is expected for a product. Similarly, the anti-bonding MOs of the transition state are lower in energy than the corresponding MOs of the product. This is due to the fact that the transition state lies at the maximum of the lowest energy pathway and the overlap of orbitals are not as strong as what would be seen in the products of the reaction. This leads to an overall destabilisation of the structure as the electrons are occupying MOs which are higher in energy than that of the reactants.

===Symmetry===

[[File:WH_analysis__2_EX1_zwl115.PNG|frame|100px|Figure 1. Woodward-Hoffmann analysis of cycloaddition of butadiene and ethene.]]

For a thermal pericyclic reaction, whether a reaction is 'allowed' or 'forbidden' depends on the Woodward-Hoffmann rules which states that the total number of (4q+2)<sub>s</sub> and (4r)<sub>a</sub> components must be odd.<sup>5</sup> The suffix 's' represents suprafacial where the new bonds are formed on the same side at both ends of the component. The suffix 'a' represents antarafacial where the new bonds formed are on opposite sides of both ends of the component. As seen from Figure 1, when both components are suprafacial, it would allow for good orbital overlap and the Woodward-Hoffmann rules are obeyed. This is in agreement with the results obtained for the combination of the Frontier Orbitals of butadiene and ethene in the MO diagram. Reactions are only allowed when the symmetry of the FO of butadiene is the same as that for the FO of ethene as this would lead to a non-zero orbital overlap. Conversely, an overlap between a symmetric FO and an anti-symmetric FO would lead to an orbital overlap integral of 0 and hence, no reaction will occur.

===Bond Length Analysis===

[[File:Bond_lengths_Ex1.PNG|centre|frame| Figure 2: Reaction Scheme showing the bond lengths of the reactants, transition state and the products]]
The C-C bond lengths for the reactants, transition state and the products are summarised in the Figure 2. Butadiene has shorter C=C terminal bonds of 1.34 Å and a longer C-C internal bond of 1.47 Å while ethene has a bond length of 1.33 Å. The shorter bond lengths observed in butadiene are due to the overlap between sp<sup>2</sup> C atoms which have a typical value of 1.34 Å while the longer C-C bonds observed are due to the overlap between sp<sup>3</sup> C atoms which have a typical value of 1.54 Å. At the transition state, the C=C terminal bonds of butadiene and the C=C bond in ethene lengthen to 1.38 Å, moving towards the value of a bond length observed between sp<sup>3</sup> C atoms. This indicates that the bond order has decreased from 2 to a value between 1 and 2. In contrast, the internal bond shortens to 1.41 Å, moving towards the value of a bond length observed between sp<sup>2</sup> C atoms and the bond order has increased from 1 to a value between 1 and 2, similar to the bond lengths of the terminal bonds. Finally in the products, the bond lengths continue to change in the same way. C5-C6 which was previously the internal bond of the butadiene has the shortest bond length of 1.34 Å due to the overlap between sp<sup>2</sup> C atoms. C1-C2, C2-C3 and C3-C4 have very similar bond lengths of 1.53-1.54 Å which reflects the overlap between sp<sup>3</sup> C atoms. C1-C6 and C4-C5 which were previously the terminal bonds of the butadiene have a bond length of 1.50 Å which is slightly shorter than the other single bonds in the molecule. This is due to the sp<sup>2</sup>-sp<sup>3</sup> overlap of the C atoms. The greater s character of the sp<sup>2</sup> C atom results in a stronger and shorter sigma bond. The length of the partially formed C-C bonds in the transition state is 2.11 Å which is significantly greater than the Van Der Waals radius of C (1.70 Å). This indicates that at the transition state, no new C-C bonds were formed.

===Reaction path towards the products from the transition state===

[[File:Vibration_TS_Ex1_zwl115.gif|centre|frame| Figure 3. Illustration of vibration of reaction path at the Transition state]]
As seen from the illustration showing the vibration corresponding to the transition state, the formation of the 2 bonds is synchronous. The ends of the butadiene and ethene fragments move towards each other in a symmetric fashion showing a concerted mechanism.

==Link to Exercise 2==
==Link to Exercise 3==

==References==
1. Potential Energy Surface. Encyclopedia of Human thermodynamics.
2. Potential Energy Surfaces. C, David Sherrill. School of Chemistry and Biochemistry Georgia Institute of Technology.
3. Computational Quantum Chemistry. C, David Sherrill.
4. Introduction to Computational Quantum Chemistry: Theory. A, Gilbert. The Australian National University.
5. Introduction to Computational Chemistry. V H¨anninen. University of Helsinki
6. Woodward, R. B.; Hoffmann, R. J. Am. Chem. Soc. 1965, 87(2), 395-397.
7. Bond Length. Wikipedia.
8. Van der Waals radius. Wikipedia.

Rep:Transition States and Reactivity ZWL115

2018-02-28T01:31:20Z

Zwl115: /* References */

==Introduction==

===What is a potential energy surface?===

A potential energy surface (PES) describes the potential energy of a chemical system in terms of certain parameters such as time and extent of reactions. Each geometry of the atoms in a system has its own unique potential energy due to the varying distances of the different atoms. Two atoms which are very far apart will have no interactions while 2 atoms which are very close together will have strong repulsive forces between them. This results in the creation of a smooth energy landscape such as the one shown in Figure 1. In Figure 1, the vertical coordinate gives the potential energy which varies with the 2 horizontal coordinates which are the bond lengths of atoms AB and atoms BC

[[File:PES_zwl115.jpg|centre|frame|Figure 1. Example of a PES<sup>1</sup>]]

===What is a transition state?===

Minima in a PES are assiociated with the structures of the reactants, products or intermediates of a reaction system. The reaction path is the lowest energy pathway between the reactant minimum and the product minimum which is denoted as a red line in Figure 1. The highest point on the reaction path corresponds to the transition state. A minimum and a transition state are both stationary points as they have zero gradient on the PES. For a stationary point, the Hessian Index, which is the number of negative eigenvalues of a force constant matrix, corresponds to the number of internal degrees of freedom along which that point is a potential energy maximum<sup>2</sup>. The Hessian Index is also equal to the number of imaginary vibrational frequencies. A minimum and a transition state can be distinguished via this Hessian Index. A minimum will have only positive eigenvalues of the Hessian and have an Hessian Index of 0. Hence, there will be no imaginary frequencies. However, since a transition state is the maximum of the lowest energy pathway, it will have a single negative Hessian eigenvalue and have a Hessian Index of 0. Hence, it will have a single imaginary vibrational frequency.

===Quantum Chemical methods used===
The semi-empirical PM6 method was used for initial calculations, followed by the more accurate DFT (Density Functional Theory) method B3LYP. The PM6 method was used to speed up initial calculations due to the method replacing some of the two-electron integrals, the Coulomb and the exchange integrals (which are difficult to calculate), used in the Hartree Fock, with empirical parameters.<sup>3</sup> The DFT method is a computational method that derives the properties of a molecular system based on the determination of the electron density of the molecule.<sup>4</sup> Unlike a wavefunction, which becomes increasingly complex as the number of electrons increase, the determination of electron density is independent of the number of electrons. The B3LYP method is a hybrid method which utilises the useful features from <i>ab initio</i> methods and improves the accuracy of the calculation by DFT mathematics. The 6-31G basis set was chosen as a larger basis set gave a better approximation to the atomic orbitals as they place fewer restrictions on the wavefunction while the split basis sets allowed for size changes during bonding.<sup>5</sup>

==Exercise 1: Reaction of Butadiene and Ethene==
===Reaction Scheme===
[[File:Reaction_Scheme_Ex1_zwl115.PNG]]
===Jmol Files===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_PDT_OPT_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

===MO Diagram===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! MO diagram for the formation of the Butadiene/Ethene transition state !! Ethene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of butadiene||rowspan="2"|[[File:MO_Diagram_Ex_1_2_zwl115.PNG|centre|frame]] || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Ethene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Butadiene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Ethene
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! MO 1 !! MO 2 !! MO 3 !! MO 4
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

Referring to the MO diagram above, the HOMO of butadiene is higher in energy than that of ethene, indicating that this is a normal electron demand cycloaddition. Bonding MOs (MOs 1 and 2) of the transition state formed from the MOs of the reactants are much higher in energy than what is expected for a product. Similarly, the anti-bonding MOs of the transition state are lower in energy than the corresponding MOs of the product. This is due to the fact that the transition state lies at the maximum of the lowest energy pathway and the overlap of orbitals are not as strong as what would be seen in the products of the reaction. This leads to an overall destabilisation of the structure as the electrons are occupying MOs which are higher in energy than that of the reactants.

===Symmetry===

[[File:WH_analysis__2_EX1_zwl115.PNG|frame|100px|Figure 1. Woodward-Hoffmann analysis of cycloaddition of butadiene and ethene.]]

For a thermal pericyclic reaction, whether a reaction is 'allowed' or 'forbidden' depends on the Woodward-Hoffmann rules which states that the total number of (4q+2)<sub>s</sub> and (4r)<sub>a</sub> components must be odd. The suffix 's' represents suprafacial where the new bonds are formed on the same side at both ends of the component. The suffix 'a' represents antarafacial where the new bonds formed are on opposite sides of both ends of the component. As seen from Figure 1, when both components are suprafacial, it would allow for good orbital overlap and the Woodward-Hoffmann rules are obeyed. This is in agreement with the results obtained for the combination of the Frontier Orbitals of butadiene and ethene in the MO diagram. Reactions are only allowed when the symmetry of the FO of butadiene is the same as that for the FO of ethene as this would lead to a non-zero orbital overlap. Conversely, an overlap between a symmetric FO and an anti-symmetric FO would lead to an orbital overlap integral of 0 and hence, no reaction will occur.

===Bond Length Analysis===

[[File:Bond_lengths_Ex1.PNG|centre|frame| Figure 2: Reaction Scheme showing the bond lengths of the reactants, transition state and the products]]
The C-C bond lengths for the reactants, transition state and the products are summarised in the Figure 2. Butadiene has shorter C=C terminal bonds of 1.34 Å and a longer C-C internal bond of 1.47 Å while ethene has a bond length of 1.33 Å. The shorter bond lengths observed in butadiene are due to the overlap between sp<sup>2</sup> C atoms which have a typical value of 1.34 Å while the longer C-C bonds observed are due to the overlap between sp<sup>3</sup> C atoms which have a typical value of 1.54 Å. At the transition state, the C=C terminal bonds of butadiene and the C=C bond in ethene lengthen to 1.38 Å, moving towards the value of a bond length observed between sp<sup>3</sup> C atoms. This indicates that the bond order has decreased from 2 to a value between 1 and 2. In contrast, the internal bond shortens to 1.41 Å, moving towards the value of a bond length observed between sp<sup>2</sup> C atoms and the bond order has increased from 1 to a value between 1 and 2, similar to the bond lengths of the terminal bonds. Finally in the products, the bond lengths continue to change in the same way. C5-C6 which was previously the internal bond of the butadiene has the shortest bond length of 1.34 Å due to the overlap between sp<sup>2</sup> C atoms. C1-C2, C2-C3 and C3-C4 have very similar bond lengths of 1.53-1.54 Å which reflects the overlap between sp<sup>3</sup> C atoms. C1-C6 and C4-C5 which were previously the terminal bonds of the butadiene have a bond length of 1.50 Å which is slightly shorter than the other single bonds in the molecule. This is due to the sp<sup>2</sup>-sp<sup>3</sup> overlap of the C atoms. The greater s character of the sp<sup>2</sup> C atom results in a stronger and shorter sigma bond. The length of the partially formed C-C bonds in the transition state is 2.11 Å which is significantly greater than the Van Der Waals radius of C (1.70 Å). This indicates that at the transition state, no new C-C bonds were formed.

===Reaction path towards the products from the transition state===

[[File:Vibration_TS_Ex1_zwl115.gif|centre|frame| Figure 3. Illustration of vibration of reaction path at the Transition state]]
As seen from the illustration showing the vibration corresponding to the transition state, the formation of the 2 bonds is synchronous. The ends of the butadiene and ethene fragments move towards each other in a symmetric fashion showing a concerted mechanism.

==Link to Exercise 2==
==Link to Exercise 3==

==References==
1. Potential Energy Surface. Encyclopedia of Human thermodynamics.
2. Potential Energy Surfaces. C, David Sherrill. School of Chemistry and Biochemistry Georgia Institute of Technology.
3. Computational Quantum Chemistry. C, David Sherrill.
4. Introduction to Computational Quantum Chemistry: Theory. A, Gilbert. The Australian National University.
5. Introduction to Computational Chemistry. V H¨anninen. University of Helsinki
6. Woodward, R. B.; Hoffmann, R. J. Am. Chem. Soc. 1965, 87(2), 395-397.
7. Bond Length. Wikipedia.
8. Van der Waals radius. Wikipedia.

Rep:Transition States and Reactivity ZWL115

2018-02-28T01:26:05Z

Zwl115: /* Reaction path towards the products from the transition state */

==Introduction==

===What is a potential energy surface?===

A potential energy surface (PES) describes the potential energy of a chemical system in terms of certain parameters such as time and extent of reactions. Each geometry of the atoms in a system has its own unique potential energy due to the varying distances of the different atoms. Two atoms which are very far apart will have no interactions while 2 atoms which are very close together will have strong repulsive forces between them. This results in the creation of a smooth energy landscape such as the one shown in Figure 1. In Figure 1, the vertical coordinate gives the potential energy which varies with the 2 horizontal coordinates which are the bond lengths of atoms AB and atoms BC

[[File:PES_zwl115.jpg|centre|frame|Figure 1. Example of a PES<sup>1</sup>]]

===What is a transition state?===

Minima in a PES are assiociated with the structures of the reactants, products or intermediates of a reaction system. The reaction path is the lowest energy pathway between the reactant minimum and the product minimum which is denoted as a red line in Figure 1. The highest point on the reaction path corresponds to the transition state. A minimum and a transition state are both stationary points as they have zero gradient on the PES. For a stationary point, the Hessian Index, which is the number of negative eigenvalues of a force constant matrix, corresponds to the number of internal degrees of freedom along which that point is a potential energy maximum<sup>2</sup>. The Hessian Index is also equal to the number of imaginary vibrational frequencies. A minimum and a transition state can be distinguished via this Hessian Index. A minimum will have only positive eigenvalues of the Hessian and have an Hessian Index of 0. Hence, there will be no imaginary frequencies. However, since a transition state is the maximum of the lowest energy pathway, it will have a single negative Hessian eigenvalue and have a Hessian Index of 0. Hence, it will have a single imaginary vibrational frequency.

===Quantum Chemical methods used===
The semi-empirical PM6 method was used for initial calculations, followed by the more accurate DFT (Density Functional Theory) method B3LYP. The PM6 method was used to speed up initial calculations due to the method replacing some of the two-electron integrals, the Coulomb and the exchange integrals (which are difficult to calculate), used in the Hartree Fock, with empirical parameters.<sup>3</sup> The DFT method is a computational method that derives the properties of a molecular system based on the determination of the electron density of the molecule.<sup>4</sup> Unlike a wavefunction, which becomes increasingly complex as the number of electrons increase, the determination of electron density is independent of the number of electrons. The B3LYP method is a hybrid method which utilises the useful features from <i>ab initio</i> methods and improves the accuracy of the calculation by DFT mathematics. The 6-31G basis set was chosen as a larger basis set gave a better approximation to the atomic orbitals as they place fewer restrictions on the wavefunction while the split basis sets allowed for size changes during bonding.<sup>5</sup>

==Exercise 1: Reaction of Butadiene and Ethene==
===Reaction Scheme===
[[File:Reaction_Scheme_Ex1_zwl115.PNG]]
===Jmol Files===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_PDT_OPT_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

===MO Diagram===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! MO diagram for the formation of the Butadiene/Ethene transition state !! Ethene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of butadiene||rowspan="2"|[[File:MO_Diagram_Ex_1_2_zwl115.PNG|centre|frame]] || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Ethene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Butadiene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Ethene
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! MO 1 !! MO 2 !! MO 3 !! MO 4
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

Referring to the MO diagram above, the HOMO of butadiene is higher in energy than that of ethene, indicating that this is a normal electron demand cycloaddition. Bonding MOs (MOs 1 and 2) of the transition state formed from the MOs of the reactants are much higher in energy than what is expected for a product. Similarly, the anti-bonding MOs of the transition state are lower in energy than the corresponding MOs of the product. This is due to the fact that the transition state lies at the maximum of the lowest energy pathway and the overlap of orbitals are not as strong as what would be seen in the products of the reaction. This leads to an overall destabilisation of the structure as the electrons are occupying MOs which are higher in energy than that of the reactants.

===Symmetry===

[[File:WH_analysis__2_EX1_zwl115.PNG|frame|100px|Figure 1. Woodward-Hoffmann analysis of cycloaddition of butadiene and ethene.]]

For a thermal pericyclic reaction, whether a reaction is 'allowed' or 'forbidden' depends on the Woodward-Hoffmann rules which states that the total number of (4q+2)<sub>s</sub> and (4r)<sub>a</sub> components must be odd. The suffix 's' represents suprafacial where the new bonds are formed on the same side at both ends of the component. The suffix 'a' represents antarafacial where the new bonds formed are on opposite sides of both ends of the component. As seen from Figure 1, when both components are suprafacial, it would allow for good orbital overlap and the Woodward-Hoffmann rules are obeyed. This is in agreement with the results obtained for the combination of the Frontier Orbitals of butadiene and ethene in the MO diagram. Reactions are only allowed when the symmetry of the FO of butadiene is the same as that for the FO of ethene as this would lead to a non-zero orbital overlap. Conversely, an overlap between a symmetric FO and an anti-symmetric FO would lead to an orbital overlap integral of 0 and hence, no reaction will occur.

===Bond Length Analysis===

[[File:Bond_lengths_Ex1.PNG|centre|frame| Figure 2: Reaction Scheme showing the bond lengths of the reactants, transition state and the products]]
The C-C bond lengths for the reactants, transition state and the products are summarised in the Figure 2. Butadiene has shorter C=C terminal bonds of 1.34 Å and a longer C-C internal bond of 1.47 Å while ethene has a bond length of 1.33 Å. The shorter bond lengths observed in butadiene are due to the overlap between sp<sup>2</sup> C atoms which have a typical value of 1.34 Å while the longer C-C bonds observed are due to the overlap between sp<sup>3</sup> C atoms which have a typical value of 1.54 Å. At the transition state, the C=C terminal bonds of butadiene and the C=C bond in ethene lengthen to 1.38 Å, moving towards the value of a bond length observed between sp<sup>3</sup> C atoms. This indicates that the bond order has decreased from 2 to a value between 1 and 2. In contrast, the internal bond shortens to 1.41 Å, moving towards the value of a bond length observed between sp<sup>2</sup> C atoms and the bond order has increased from 1 to a value between 1 and 2, similar to the bond lengths of the terminal bonds. Finally in the products, the bond lengths continue to change in the same way. C5-C6 which was previously the internal bond of the butadiene has the shortest bond length of 1.34 Å due to the overlap between sp<sup>2</sup> C atoms. C1-C2, C2-C3 and C3-C4 have very similar bond lengths of 1.53-1.54 Å which reflects the overlap between sp<sup>3</sup> C atoms. C1-C6 and C4-C5 which were previously the terminal bonds of the butadiene have a bond length of 1.50 Å which is slightly shorter than the other single bonds in the molecule. This is due to the sp<sup>2</sup>-sp<sup>3</sup> overlap of the C atoms. The greater s character of the sp<sup>2</sup> C atom results in a stronger and shorter sigma bond. The length of the partially formed C-C bonds in the transition state is 2.11 Å which is significantly greater than the Van Der Waals radius of C (1.70 Å). This indicates that at the transition state, no new C-C bonds were formed.

===Reaction path towards the products from the transition state===

[[File:Vibration_TS_Ex1_zwl115.gif|centre|frame| Figure 3. Illustration of vibration of reaction path at the Transition state]]
As seen from the illustration showing the vibration corresponding to the transition state, the formation of the 2 bonds is synchronous. The ends of the butadiene and ethene fragments move towards each other in a symmetric fashion showing a concerted mechanism.

==Link to Exercise 2==
==Link to Exercise 3==
==References==
1.

Rep:Transition States and Reactivity ZWL115

2018-02-28T00:55:55Z

Zwl115: /* References */

==Introduction==

===What is a potential energy surface?===

A potential energy surface (PES) describes the potential energy of a chemical system in terms of certain parameters such as time and extent of reactions. Each geometry of the atoms in a system has its own unique potential energy due to the varying distances of the different atoms. Two atoms which are very far apart will have no interactions while 2 atoms which are very close together will have strong repulsive forces between them. This results in the creation of a smooth energy landscape such as the one shown in Figure 1. In Figure 1, the vertical coordinate gives the potential energy which varies with the 2 horizontal coordinates which are the bond lengths of atoms AB and atoms BC

[[File:PES_zwl115.jpg|centre|frame|Figure 1. Example of a PES<sup>1</sup>]]

===What is a transition state?===

Minima in a PES are assiociated with the structures of the reactants, products or intermediates of a reaction system. The reaction path is the lowest energy pathway between the reactant minimum and the product minimum which is denoted as a red line in Figure 1. The highest point on the reaction path corresponds to the transition state. A minimum and a transition state are both stationary points as they have zero gradient on the PES. For a stationary point, the Hessian Index, which is the number of negative eigenvalues of a force constant matrix, corresponds to the number of internal degrees of freedom along which that point is a potential energy maximum<sup>2</sup>. The Hessian Index is also equal to the number of imaginary vibrational frequencies. A minimum and a transition state can be distinguished via this Hessian Index. A minimum will have only positive eigenvalues of the Hessian and have an Hessian Index of 0. Hence, there will be no imaginary frequencies. However, since a transition state is the maximum of the lowest energy pathway, it will have a single negative Hessian eigenvalue and have a Hessian Index of 0. Hence, it will have a single imaginary vibrational frequency.

===Quantum Chemical methods used===
The semi-empirical PM6 method was used for initial calculations, followed by the more accurate DFT (Density Functional Theory) method B3LYP. The PM6 method was used to speed up initial calculations due to the method replacing some of the two-electron integrals, the Coulomb and the exchange integrals (which are difficult to calculate), used in the Hartree Fock, with empirical parameters.<sup>3</sup> The DFT method is a computational method that derives the properties of a molecular system based on the determination of the electron density of the molecule.<sup>4</sup> Unlike a wavefunction, which becomes increasingly complex as the number of electrons increase, the determination of electron density is independent of the number of electrons. The B3LYP method is a hybrid method which utilises the useful features from <i>ab initio</i> methods and improves the accuracy of the calculation by DFT mathematics. The 6-31G basis set was chosen as a larger basis set gave a better approximation to the atomic orbitals as they place fewer restrictions on the wavefunction while the split basis sets allowed for size changes during bonding.<sup>5</sup>

==Exercise 1: Reaction of Butadiene and Ethene==
===Reaction Scheme===
[[File:Reaction_Scheme_Ex1_zwl115.PNG]]
===Jmol Files===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_PDT_OPT_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

===MO Diagram===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! MO diagram for the formation of the Butadiene/Ethene transition state !! Ethene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of butadiene||rowspan="2"|[[File:MO_Diagram_Ex_1_2_zwl115.PNG|centre|frame]] || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Ethene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Butadiene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Ethene
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! MO 1 !! MO 2 !! MO 3 !! MO 4
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

Referring to the MO diagram above, the HOMO of butadiene is higher in energy than that of ethene, indicating that this is a normal electron demand cycloaddition. Bonding MOs (MOs 1 and 2) of the transition state formed from the MOs of the reactants are much higher in energy than what is expected for a product. Similarly, the anti-bonding MOs of the transition state are lower in energy than the corresponding MOs of the product. This is due to the fact that the transition state lies at the maximum of the lowest energy pathway and the overlap of orbitals are not as strong as what would be seen in the products of the reaction. This leads to an overall destabilisation of the structure as the electrons are occupying MOs which are higher in energy than that of the reactants.

===Symmetry===

[[File:WH_analysis__2_EX1_zwl115.PNG|frame|100px|Figure 1. Woodward-Hoffmann analysis of cycloaddition of butadiene and ethene.]]

For a thermal pericyclic reaction, whether a reaction is 'allowed' or 'forbidden' depends on the Woodward-Hoffmann rules which states that the total number of (4q+2)<sub>s</sub> and (4r)<sub>a</sub> components must be odd. The suffix 's' represents suprafacial where the new bonds are formed on the same side at both ends of the component. The suffix 'a' represents antarafacial where the new bonds formed are on opposite sides of both ends of the component. As seen from Figure 1, when both components are suprafacial, it would allow for good orbital overlap and the Woodward-Hoffmann rules are obeyed. This is in agreement with the results obtained for the combination of the Frontier Orbitals of butadiene and ethene in the MO diagram. Reactions are only allowed when the symmetry of the FO of butadiene is the same as that for the FO of ethene as this would lead to a non-zero orbital overlap. Conversely, an overlap between a symmetric FO and an anti-symmetric FO would lead to an orbital overlap integral of 0 and hence, no reaction will occur.

===Bond Length Analysis===

[[File:Bond_lengths_Ex1.PNG|centre|frame| Figure 2: Reaction Scheme showing the bond lengths of the reactants, transition state and the products]]
The C-C bond lengths for the reactants, transition state and the products are summarised in the Figure 2. Butadiene has shorter C=C terminal bonds of 1.34 Å and a longer C-C internal bond of 1.47 Å while ethene has a bond length of 1.33 Å. The shorter bond lengths observed in butadiene are due to the overlap between sp<sup>2</sup> C atoms which have a typical value of 1.34 Å while the longer C-C bonds observed are due to the overlap between sp<sup>3</sup> C atoms which have a typical value of 1.54 Å. At the transition state, the C=C terminal bonds of butadiene and the C=C bond in ethene lengthen to 1.38 Å, moving towards the value of a bond length observed between sp<sup>3</sup> C atoms. This indicates that the bond order has decreased from 2 to a value between 1 and 2. In contrast, the internal bond shortens to 1.41 Å, moving towards the value of a bond length observed between sp<sup>2</sup> C atoms and the bond order has increased from 1 to a value between 1 and 2, similar to the bond lengths of the terminal bonds. Finally in the products, the bond lengths continue to change in the same way. C5-C6 which was previously the internal bond of the butadiene has the shortest bond length of 1.34 Å due to the overlap between sp<sup>2</sup> C atoms. C1-C2, C2-C3 and C3-C4 have very similar bond lengths of 1.53-1.54 Å which reflects the overlap between sp<sup>3</sup> C atoms. C1-C6 and C4-C5 which were previously the terminal bonds of the butadiene have a bond length of 1.50 Å which is slightly shorter than the other single bonds in the molecule. This is due to the sp<sup>2</sup>-sp<sup>3</sup> overlap of the C atoms. The greater s character of the sp<sup>2</sup> C atom results in a stronger and shorter sigma bond. The length of the partially formed C-C bonds in the transition state is 2.11 Å which is significantly greater than the Van Der Waals radius of C (1.70 Å). This indicates that at the transition state, no new C-C bonds were formed.

===Reaction path towards the products from the transition state===

[[File:Vibration_TS_Ex1_zwl115.gif|centre|frame| Figure 3. Illustration of vibration of reaction path at the Transition state]]
As seen from the illustration showing the vibration corresponding to the transition state, the formation of the 2 bonds is synchronous. The ends of the butadiene and ethene fragments move towards each other in a symmetric fashion showing a concerted mechanism.

****References for Van Der Waals radius****

==Link to Exercise 2==
==Link to Exercise 3==
==References==
1.

Rep:Transition States and Reactivity ZWL115

2018-02-28T00:52:10Z

Zwl115: /* Exercise 3 */

==Introduction==

===What is a potential energy surface?===

A potential energy surface (PES) describes the potential energy of a chemical system in terms of certain parameters such as time and extent of reactions. Each geometry of the atoms in a system has its own unique potential energy due to the varying distances of the different atoms. Two atoms which are very far apart will have no interactions while 2 atoms which are very close together will have strong repulsive forces between them. This results in the creation of a smooth energy landscape such as the one shown in Figure 1. In Figure 1, the vertical coordinate gives the potential energy which varies with the 2 horizontal coordinates which are the bond lengths of atoms AB and atoms BC

[[File:PES_zwl115.jpg|centre|frame|Figure 1. Example of a PES<sup>1</sup>]]

===What is a transition state?===

Minima in a PES are assiociated with the structures of the reactants, products or intermediates of a reaction system. The reaction path is the lowest energy pathway between the reactant minimum and the product minimum which is denoted as a red line in Figure 1. The highest point on the reaction path corresponds to the transition state. A minimum and a transition state are both stationary points as they have zero gradient on the PES. For a stationary point, the Hessian Index, which is the number of negative eigenvalues of a force constant matrix, corresponds to the number of internal degrees of freedom along which that point is a potential energy maximum<sup>2</sup>. The Hessian Index is also equal to the number of imaginary vibrational frequencies. A minimum and a transition state can be distinguished via this Hessian Index. A minimum will have only positive eigenvalues of the Hessian and have an Hessian Index of 0. Hence, there will be no imaginary frequencies. However, since a transition state is the maximum of the lowest energy pathway, it will have a single negative Hessian eigenvalue and have a Hessian Index of 0. Hence, it will have a single imaginary vibrational frequency.

===Quantum Chemical methods used===
The semi-empirical PM6 method was used for initial calculations, followed by the more accurate DFT (Density Functional Theory) method B3LYP. The PM6 method was used to speed up initial calculations due to the method replacing some of the two-electron integrals, the Coulomb and the exchange integrals (which are difficult to calculate), used in the Hartree Fock, with empirical parameters.<sup>3</sup> The DFT method is a computational method that derives the properties of a molecular system based on the determination of the electron density of the molecule.<sup>4</sup> Unlike a wavefunction, which becomes increasingly complex as the number of electrons increase, the determination of electron density is independent of the number of electrons. The B3LYP method is a hybrid method which utilises the useful features from <i>ab initio</i> methods and improves the accuracy of the calculation by DFT mathematics. The 6-31G basis set was chosen as a larger basis set gave a better approximation to the atomic orbitals as they place fewer restrictions on the wavefunction while the split basis sets allowed for size changes during bonding.<sup>5</sup>

==Exercise 1: Reaction of Butadiene and Ethene==
===Reaction Scheme===
[[File:Reaction_Scheme_Ex1_zwl115.PNG]]
===Jmol Files===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_PDT_OPT_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

===MO Diagram===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! MO diagram for the formation of the Butadiene/Ethene transition state !! Ethene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of butadiene||rowspan="2"|[[File:MO_Diagram_Ex_1_2_zwl115.PNG|centre|frame]] || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Ethene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Butadiene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Ethene
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! MO 1 !! MO 2 !! MO 3 !! MO 4
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

Referring to the MO diagram above, the HOMO of butadiene is higher in energy than that of ethene, indicating that this is a normal electron demand cycloaddition. Bonding MOs (MOs 1 and 2) of the transition state formed from the MOs of the reactants are much higher in energy than what is expected for a product. Similarly, the anti-bonding MOs of the transition state are lower in energy than the corresponding MOs of the product. This is due to the fact that the transition state lies at the maximum of the lowest energy pathway and the overlap of orbitals are not as strong as what would be seen in the products of the reaction. This leads to an overall destabilisation of the structure as the electrons are occupying MOs which are higher in energy than that of the reactants.

===Symmetry===

[[File:WH_analysis__2_EX1_zwl115.PNG|frame|100px|Figure 1. Woodward-Hoffmann analysis of cycloaddition of butadiene and ethene.]]

For a thermal pericyclic reaction, whether a reaction is 'allowed' or 'forbidden' depends on the Woodward-Hoffmann rules which states that the total number of (4q+2)<sub>s</sub> and (4r)<sub>a</sub> components must be odd. The suffix 's' represents suprafacial where the new bonds are formed on the same side at both ends of the component. The suffix 'a' represents antarafacial where the new bonds formed are on opposite sides of both ends of the component. As seen from Figure 1, when both components are suprafacial, it would allow for good orbital overlap and the Woodward-Hoffmann rules are obeyed. This is in agreement with the results obtained for the combination of the Frontier Orbitals of butadiene and ethene in the MO diagram. Reactions are only allowed when the symmetry of the FO of butadiene is the same as that for the FO of ethene as this would lead to a non-zero orbital overlap. Conversely, an overlap between a symmetric FO and an anti-symmetric FO would lead to an orbital overlap integral of 0 and hence, no reaction will occur.

===Bond Length Analysis===

[[File:Bond_lengths_Ex1.PNG|centre|frame| Figure 2: Reaction Scheme showing the bond lengths of the reactants, transition state and the products]]
The C-C bond lengths for the reactants, transition state and the products are summarised in the Figure 2. Butadiene has shorter C=C terminal bonds of 1.34 Å and a longer C-C internal bond of 1.47 Å while ethene has a bond length of 1.33 Å. The shorter bond lengths observed in butadiene are due to the overlap between sp<sup>2</sup> C atoms which have a typical value of 1.34 Å while the longer C-C bonds observed are due to the overlap between sp<sup>3</sup> C atoms which have a typical value of 1.54 Å. At the transition state, the C=C terminal bonds of butadiene and the C=C bond in ethene lengthen to 1.38 Å, moving towards the value of a bond length observed between sp<sup>3</sup> C atoms. This indicates that the bond order has decreased from 2 to a value between 1 and 2. In contrast, the internal bond shortens to 1.41 Å, moving towards the value of a bond length observed between sp<sup>2</sup> C atoms and the bond order has increased from 1 to a value between 1 and 2, similar to the bond lengths of the terminal bonds. Finally in the products, the bond lengths continue to change in the same way. C5-C6 which was previously the internal bond of the butadiene has the shortest bond length of 1.34 Å due to the overlap between sp<sup>2</sup> C atoms. C1-C2, C2-C3 and C3-C4 have very similar bond lengths of 1.53-1.54 Å which reflects the overlap between sp<sup>3</sup> C atoms. C1-C6 and C4-C5 which were previously the terminal bonds of the butadiene have a bond length of 1.50 Å which is slightly shorter than the other single bonds in the molecule. This is due to the sp<sup>2</sup>-sp<sup>3</sup> overlap of the C atoms. The greater s character of the sp<sup>2</sup> C atom results in a stronger and shorter sigma bond. The length of the partially formed C-C bonds in the transition state is 2.11 Å which is significantly greater than the Van Der Waals radius of C (1.70 Å). This indicates that at the transition state, no new C-C bonds were formed.

===Reaction path towards the products from the transition state===

[[File:Vibration_TS_Ex1_zwl115.gif|centre|frame| Figure 3. Illustration of vibration of reaction path at the Transition state]]
As seen from the illustration showing the vibration corresponding to the transition state, the formation of the 2 bonds is synchronous. The ends of the butadiene and ethene fragments move towards each other in a symmetric fashion showing a concerted mechanism.

****References for Van Der Waals radius****

==Link to Exercise 2==
==Link to Exercise 3==
==References==

Rep:Transition States and Reactivity ZWL115

2018-02-28T00:50:09Z

Zwl115: /* Introduction */

==Introduction==

===What is a potential energy surface?===

A potential energy surface (PES) describes the potential energy of a chemical system in terms of certain parameters such as time and extent of reactions. Each geometry of the atoms in a system has its own unique potential energy due to the varying distances of the different atoms. Two atoms which are very far apart will have no interactions while 2 atoms which are very close together will have strong repulsive forces between them. This results in the creation of a smooth energy landscape such as the one shown in Figure 1. In Figure 1, the vertical coordinate gives the potential energy which varies with the 2 horizontal coordinates which are the bond lengths of atoms AB and atoms BC

[[File:PES_zwl115.jpg|centre|frame|Figure 1. Example of a PES<sup>1</sup>]]

===What is a transition state?===

Minima in a PES are assiociated with the structures of the reactants, products or intermediates of a reaction system. The reaction path is the lowest energy pathway between the reactant minimum and the product minimum which is denoted as a red line in Figure 1. The highest point on the reaction path corresponds to the transition state. A minimum and a transition state are both stationary points as they have zero gradient on the PES. For a stationary point, the Hessian Index, which is the number of negative eigenvalues of a force constant matrix, corresponds to the number of internal degrees of freedom along which that point is a potential energy maximum<sup>2</sup>. The Hessian Index is also equal to the number of imaginary vibrational frequencies. A minimum and a transition state can be distinguished via this Hessian Index. A minimum will have only positive eigenvalues of the Hessian and have an Hessian Index of 0. Hence, there will be no imaginary frequencies. However, since a transition state is the maximum of the lowest energy pathway, it will have a single negative Hessian eigenvalue and have a Hessian Index of 0. Hence, it will have a single imaginary vibrational frequency.

===Quantum Chemical methods used===
The semi-empirical PM6 method was used for initial calculations, followed by the more accurate DFT (Density Functional Theory) method B3LYP. The PM6 method was used to speed up initial calculations due to the method replacing some of the two-electron integrals, the Coulomb and the exchange integrals (which are difficult to calculate), used in the Hartree Fock, with empirical parameters.<sup>3</sup> The DFT method is a computational method that derives the properties of a molecular system based on the determination of the electron density of the molecule.<sup>4</sup> Unlike a wavefunction, which becomes increasingly complex as the number of electrons increase, the determination of electron density is independent of the number of electrons. The B3LYP method is a hybrid method which utilises the useful features from <i>ab initio</i> methods and improves the accuracy of the calculation by DFT mathematics. The 6-31G basis set was chosen as a larger basis set gave a better approximation to the atomic orbitals as they place fewer restrictions on the wavefunction while the split basis sets allowed for size changes during bonding.<sup>5</sup>

==Exercise 1: Reaction of Butadiene and Ethene==
===Reaction Scheme===
[[File:Reaction_Scheme_Ex1_zwl115.PNG]]
===Jmol Files===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_PDT_OPT_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

===MO Diagram===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! MO diagram for the formation of the Butadiene/Ethene transition state !! Ethene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of butadiene||rowspan="2"|[[File:MO_Diagram_Ex_1_2_zwl115.PNG|centre|frame]] || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Ethene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_FRAG_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Butadiene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Ethene
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! MO 1 !! MO 2 !! MO 3 !! MO 4
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE_OPT_POSTFREEZE_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

Referring to the MO diagram above, the HOMO of butadiene is higher in energy than that of ethene, indicating that this is a normal electron demand cycloaddition. Bonding MOs (MOs 1 and 2) of the transition state formed from the MOs of the reactants are much higher in energy than what is expected for a product. Similarly, the anti-bonding MOs of the transition state are lower in energy than the corresponding MOs of the product. This is due to the fact that the transition state lies at the maximum of the lowest energy pathway and the overlap of orbitals are not as strong as what would be seen in the products of the reaction. This leads to an overall destabilisation of the structure as the electrons are occupying MOs which are higher in energy than that of the reactants.

===Symmetry===

[[File:WH_analysis__2_EX1_zwl115.PNG|frame|100px|Figure 1. Woodward-Hoffmann analysis of cycloaddition of butadiene and ethene.]]

For a thermal pericyclic reaction, whether a reaction is 'allowed' or 'forbidden' depends on the Woodward-Hoffmann rules which states that the total number of (4q+2)<sub>s</sub> and (4r)<sub>a</sub> components must be odd. The suffix 's' represents suprafacial where the new bonds are formed on the same side at both ends of the component. The suffix 'a' represents antarafacial where the new bonds formed are on opposite sides of both ends of the component. As seen from Figure 1, when both components are suprafacial, it would allow for good orbital overlap and the Woodward-Hoffmann rules are obeyed. This is in agreement with the results obtained for the combination of the Frontier Orbitals of butadiene and ethene in the MO diagram. Reactions are only allowed when the symmetry of the FO of butadiene is the same as that for the FO of ethene as this would lead to a non-zero orbital overlap. Conversely, an overlap between a symmetric FO and an anti-symmetric FO would lead to an orbital overlap integral of 0 and hence, no reaction will occur.

===Bond Length Analysis===

[[File:Bond_lengths_Ex1.PNG|centre|frame| Figure 2: Reaction Scheme showing the bond lengths of the reactants, transition state and the products]]
The C-C bond lengths for the reactants, transition state and the products are summarised in the Figure 2. Butadiene has shorter C=C terminal bonds of 1.34 Å and a longer C-C internal bond of 1.47 Å while ethene has a bond length of 1.33 Å. The shorter bond lengths observed in butadiene are due to the overlap between sp<sup>2</sup> C atoms which have a typical value of 1.34 Å while the longer C-C bonds observed are due to the overlap between sp<sup>3</sup> C atoms which have a typical value of 1.54 Å. At the transition state, the C=C terminal bonds of butadiene and the C=C bond in ethene lengthen to 1.38 Å, moving towards the value of a bond length observed between sp<sup>3</sup> C atoms. This indicates that the bond order has decreased from 2 to a value between 1 and 2. In contrast, the internal bond shortens to 1.41 Å, moving towards the value of a bond length observed between sp<sup>2</sup> C atoms and the bond order has increased from 1 to a value between 1 and 2, similar to the bond lengths of the terminal bonds. Finally in the products, the bond lengths continue to change in the same way. C5-C6 which was previously the internal bond of the butadiene has the shortest bond length of 1.34 Å due to the overlap between sp<sup>2</sup> C atoms. C1-C2, C2-C3 and C3-C4 have very similar bond lengths of 1.53-1.54 Å which reflects the overlap between sp<sup>3</sup> C atoms. C1-C6 and C4-C5 which were previously the terminal bonds of the butadiene have a bond length of 1.50 Å which is slightly shorter than the other single bonds in the molecule. This is due to the sp<sup>2</sup>-sp<sup>3</sup> overlap of the C atoms. The greater s character of the sp<sup>2</sup> C atom results in a stronger and shorter sigma bond. The length of the partially formed C-C bonds in the transition state is 2.11 Å which is significantly greater than the Van Der Waals radius of C (1.70 Å). This indicates that at the transition state, no new C-C bonds were formed.

===Reaction path towards the products from the transition state===

[[File:Vibration_TS_Ex1_zwl115.gif|centre|frame| Figure 3. Illustration of vibration of reaction path at the Transition state]]
As seen from the illustration showing the vibration corresponding to the transition state, the formation of the 2 bonds is synchronous. The ends of the butadiene and ethene fragments move towards each other in a symmetric fashion showing a concerted mechanism.

****References for Van Der Waals radius****

==Exercise 3==
https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_States_and_Reactivity_Exercise2_ZWL115#MO_diagrams_for_the_formation_of_the_Cyclohexadienediene.2F1.2C3-Dioxole_transition_states
https://wiki.ch.ic.ac.uk/wiki/index.php?title=Transition_States_and_Reactivity_Exercise3_ZWL115&action=submit

File:PES zwl115.jpg

2018-02-27T22:47:33Z

Zwl115:

Rep:Transition States and Reactivity Exercise3 ZWL115

2018-02-27T22:14:51Z

Zwl115:

==Exercise 3==

===Reaction Scheme===

O-Xylylene can react with SO<sub>2</sub> via 2 different Diels-Alder cycloadditions and a chelotropic pathway. These pathways are illustrated in Figure. XX.
[[File:Reaction_scheme_ex3_zwl115.PNG|left|frame| Figure XX. Reaction scheme showing the Exo, Endo Diels-Alder cycloadditions and the Chelotropic reaction mechanisms possible.]]

{| class="wikitable"
|-
! Reactants
! Transition States
! Products
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> SO2_OPT_PM6_2_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> SO<sub>2</sub>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_ENDO_TS_FREQ_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 50; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_PDT_ENDO_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> XYLYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Xylylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_EXO_TS_FREQ1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 72; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_PDT_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
|-
|
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 48; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>C_TS_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Chelotropic
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>C_PDT_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Chelotropic
|}

===Reaction Coordinate===
{| class="wikitable"
|+IRC pathways
|-
! Endo
! Exo
! Chelotropic
|-
| [[File:DA_endo_TS_freq_IRC_PM6_zwl115.gif|500px]]
| [[File:DA_exo_TS_freq_IRC_PM6_zwl115.gif|500px]]
| [[File:C_TS_freq_IRC_PM6_zwl115.gif|500px]]
|}

The instability of Xylylene can be rationalised using Hückel's Molecular Orbital Theory. According to the theory, a compound is stable when all of its bonding orbitals are filled and no electrons fill the anti-bonding orbitals. This is especially true in aromatic compounds, where 2 electrons fill the lowest energy molecular orbital and 4 electrons fill the subsequent degenerate pair of orbitals (the number of pairs of orbitals is denoted by the by <i>n</i>). This gives rise to Hückel's rule where aromatic compounds have 4n+2 π electrons which are in a conjugated ring system while compounds with 4n π electrons show anti-aromatic behaviour and are highly unstable. O-Xylylene only has 4π electrons in the ring resulting in anti-aromatic instability due to filling of the anti-bonding orbitals. During the course of the reactions, the 6-membered ring of Xylylene becomes a stabilised benzene ring in all 3 pathways as seen in the IRCs. The benzene ring has 6π electrons in a conjugated ring system which obeys Hückel's rule (where <i>n</i> = 1), making it aromatic. Hence the resulting products are more stabilised and the reactions occur favourably.

===Gibbs Free Energies===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
!
! Xylylene
! Sulfur Dioxide
! Exo Transition State
! Endo Transition State
! Chelotropic Transition State
! Exo Product
! Endo Product
! Chelotropic Product
|-
| '''Energy/Hartrees'''
| -0.119269
| 0.178119
| 0.092077
| 0.090559
| 0.099062
| 0.021452
| 0.021697
| -0.000018
|-
| '''Energy/kJmol<sup>-1</sup>'''
| -313.141
| 467.651
| 241.748
| 237.762
| 260.087
| 56.3222
| 56.9654
| -0.04726
|}

===Energy Profile Diagram===
[[File:Energy_profile_diagram_ex3_1_zwl115.PNG|centre|frame|Figure xx. Energy Profile Diagram showing the 3 different reaction pathways for the reaction between Xylylene and SO<sub>2</sub>]]

==Diels-Alder reaction with second cis-butadiene fragment==

===Reaction Scheme===
[[File:Reaction_scheme_ex3_part_2_zwl115.PNG|centre|frame| Figure XX. Reaction scheme showing the Exo and Endo Diels-Alder cycloadditions mechanisms possible.]]

===Jmol Files===
{| class="wikitable"
|-
! Reactants
! Transition States
! Products
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> SO2_OPT_PM6_2_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> SO<sub>2</sub>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_DA_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 50; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_PDT_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> XYLYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Xylylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_DA_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 72; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_PDT_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
|}

===Reaction Profile Diagram===
[[File:Energy_profile_diagram_ex3_part_2_zwl115.PNG|centre|frame|Figure XX. Energy Profile diagram showing the thermodynamics of the 2 Diels-Alder cycloaddition pathways]]
The Endo and Exo Diels-Alder reactions for this cis-butadiene fragment is thermodynamically and kinetically unfavourable. Comparing Figures XX and XX, the activation energies for both the exo and endo Diels-Alder cycloadditions at this site are much greater than those of the terminal butadiene fragment. Furthermore, the products of the reactions for the non-terminal cis-butadiene fragment are much higher in energy than those for the terminal cis butadiene fragment. The overall reaction for both endo and exo pathways are endothermic in this case. The kinetic and thermodynamic consequences can be rationalised by the greater steric clash present in the transition state and the products when SO<sub>2</sub> reacts with the non-terminal cis-butadiene fragment which are absent with the terminal cis-butadiene fragment.

File:Energy profile diagram ex3 1 zwl115.PNG

2018-02-27T22:14:18Z

Zwl115:

Rep:Transition States and Reactivity Exercise3 ZWL115

2018-02-27T22:06:25Z

Zwl115: /* Exercise 3 */

==Exercise 3==

===Reaction Scheme===

O-Xylylene can react with SO<sub>2</sub> via 2 different Diels-Alder cycloadditions and a chelotropic pathway. These pathways are illustrated in Figure. XX.
[[File:Reaction_scheme_ex3_zwl115.PNG|frame| Figure XX. Reaction scheme showing the Exo, Endo Diels-Alder cycloadditions and the Chelotropic reaction mechanisms possible.]]

{| class="wikitable"
|-
! Reactants
! Transition States
! Products
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> SO2_OPT_PM6_2_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> SO<sub>2</sub>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_ENDO_TS_FREQ_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 50; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_PDT_ENDO_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> XYLYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Xylylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_EXO_TS_FREQ1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 72; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_PDT_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
|-
|
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 48; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>C_TS_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Chelotropic
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>C_PDT_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Chelotropic
|}

===Reaction Coordinate===
{| class="wikitable"
|+IRC pathways
|-
! Endo
! Exo
! Chelotropic
|-
| [[File:DA_endo_TS_freq_IRC_PM6_zwl115.gif|500px]]
| [[File:DA_exo_TS_freq_IRC_PM6_zwl115.gif|500px]]
| [[File:C_TS_freq_IRC_PM6_zwl115.gif|500px]]
|}

The instability of Xylylene can be rationalised using Hückel's Molecular Orbital Theory. According to the theory, a compound is stable when all of its bonding orbitals are filled and no electrons fill the anti-bonding orbitals. This is especially true in aromatic compounds, where 2 electrons fill the lowest energy molecular orbital and 4 electrons fill the subsequent degenerate pair of orbitals (the number of pairs of orbitals is denoted by the by <i>n</i>). This gives rise to Hückel's rule where aromatic compounds have 4n+2 π electrons which are in a conjugated ring system while compounds with 4n π electrons show anti-aromatic behaviour and are highly unstable. O-Xylylene only has 4π electrons in the ring resulting in anti-aromatic instability due to filling of the anti-bonding orbitals. During the course of the reactions, the 6-membered ring of Xylylene becomes a stabilised benzene ring in all 3 pathways as seen in the IRCs. The benzene ring has 6π electrons in a conjugated ring system which obeys Hückel's rule (where <i>n</i> = 1), making it aromatic. Hence the resulting products are more stabilised and the reactions occur favourably.

===Gibbs Free Energies===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
!
! Xylylene
! Sulfur Dioxide
! Exo Transition State
! Endo Transition State
! Chelotropic Transition State
! Exo Product
! Endo Product
! Chelotropic Product
|-
| '''Energy/Hartrees'''
| -0.119269
| 0.178119
| 0.092077
| 0.090559
| 0.099062
| 0.021452
| 0.021697
| -0.000018
|-
| '''Energy/kJmol<sup>-1</sup>'''
| -313.141
| 467.651
| 241.748
| 237.762
| 260.087
| 56.3222
| 56.9654
| -0.04726
|}

===Energy Profile Diagram===
[[File:Energy profile diagram ex3 zwl115.PNG|frame|Figure xx. Energy Profile Diagram showing the 3 different reaction pathways for the reaction between Xylylene and SO<sub>2</sub>]]

==Diels-Alder reaction with second cis-butadiene fragment==

===Reaction Scheme===
[[File:Reaction_scheme_ex3_part_2_zwl115.PNG|centre|frame| Figure XX. Reaction scheme showing the Exo and Endo Diels-Alder cycloadditions mechanisms possible.]]

===Jmol Files===
{| class="wikitable"
|-
! Reactants
! Transition States
! Products
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> SO2_OPT_PM6_2_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> SO<sub>2</sub>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_DA_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 50; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_PDT_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> XYLYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Xylylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_DA_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 72; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_PDT_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
|}

===Reaction Profile Diagram===
[[File:Energy_profile_diagram_ex3_part_2_zwl115.PNG|centre|frame|Figure XX. Energy Profile diagram showing the thermodynamics of the 2 Diels-Alder cycloaddition pathways]]
The Endo and Exo Diels-Alder reactions for this cis-butadiene fragment is thermodynamically and kinetically unfavourable. Comparing Figures XX and XX, the activation energies for both the exo and endo Diels-Alder cycloadditions at this site are much greater than those of the terminal butadiene fragment. Furthermore, the products of the reactions for the non-terminal cis-butadiene fragment are much higher in energy than those for the terminal cis butadiene fragment. The overall reaction for both endo and exo pathways are endothermic in this case. The kinetic and thermodynamic consequences can be rationalised by the greater steric clash present in the transition state and the products when SO<sub>2</sub> reacts with the non-terminal cis-butadiene fragment which are absent with the terminal cis-butadiene fragment.

File:Energy profile diagram ex3 part 2 zwl115.PNG

2018-02-27T22:05:41Z

Zwl115: Zwl115 uploaded a new version of File:Energy profile diagram ex3 part 2 zwl115.PNG

File:Energy profile diagram ex3 zwl115.PNG

2018-02-27T22:04:28Z

Zwl115: Zwl115 uploaded a new version of File:Energy profile diagram ex3 zwl115.PNG

File:Energy profile diagram ex3 zwl115.PNG

2018-02-27T22:03:07Z

Zwl115: Zwl115 uploaded a new version of File:Energy profile diagram ex3 zwl115.PNG

File:Energy profile diagram ex3 zwl115.PNG

2018-02-27T22:00:14Z

Zwl115: Zwl115 uploaded a new version of File:Energy profile diagram ex3 zwl115.PNG

File:Energy profile diagram ex3 zwl115.PNG

2018-02-27T21:58:40Z

Zwl115: Zwl115 uploaded a new version of File:Energy profile diagram ex3 zwl115.PNG

Rep:Transition States and Reactivity Exercise3 ZWL115

2018-02-27T21:56:24Z

Zwl115: /* Diels-Alder reaction with second cis-butadiene fragment */

==Exercise 3==

===Reaction Scheme===

O-Xylylene can react with SO<sub>2</sub> via 2 different Diels-Alder cycloadditions and a chelotropic pathway. These pathways are illustrated in Figure. XX.
[[File:Reaction_scheme_ex3_zwl115.PNG|centre|frame| Figure XX. Reaction scheme showing the Exo, Endo Diels-Alder cycloadditions and the Chelotropic reaction mechanisms possible.]]

{| class="wikitable"
|-
! Reactants
! Transition States
! Products
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> SO2_OPT_PM6_2_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> SO<sub>2</sub>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_ENDO_TS_FREQ_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 50; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_PDT_ENDO_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> XYLYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Xylylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_EXO_TS_FREQ1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 72; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_PDT_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
|-
|
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 48; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>C_TS_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Chelotropic
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>C_PDT_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Chelotropic
|}

===Reaction Coordinate===
{| class="wikitable"
|+IRC pathways
|-
! Endo
! Exo
! Chelotropic
|-
| [[File:DA_endo_TS_freq_IRC_PM6_zwl115.gif|500px]]
| [[File:DA_exo_TS_freq_IRC_PM6_zwl115.gif|500px]]
| [[File:C_TS_freq_IRC_PM6_zwl115.gif|500px]]
|}

The instability of Xylylene can be rationalised using Hückel's Molecular Orbital Theory. According to the theory, a compound is stable when all of its bonding orbitals are filled and no electrons fill the anti-bonding orbitals. This is especially true in aromatic compounds, where 2 electrons fill the lowest energy molecular orbital and 4 electrons fill the subsequent degenerate pair of orbitals (the number of pairs of orbitals is denoted by the by <i>n</i>). This gives rise to Hückel's rule where aromatic compounds have 4n+2 π electrons which are in a conjugated ring system while compounds with 4n π electrons show anti-aromatic behaviour and are highly unstable. O-Xylylene only has 4π electrons in the ring resulting in anti-aromatic instability due to filling of the anti-bonding orbitals. During the course of the reactions, the 6-membered ring of Xylylene becomes a stabilised benzene ring in all 3 pathways as seen in the IRCs. The benzene ring has 6π electrons in a conjugated ring system which obeys Hückel's rule (where <i>n</i> = 1), making it aromatic. Hence the resulting products are more stabilised and the reactions occur favourably.

===Gibbs Free Energies===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
!
! Xylylene
! Sulfur Dioxide
! Exo Transition State
! Endo Transition State
! Chelotropic Transition State
! Exo Product
! Endo Product
! Chelotropic Product
|-
| '''Energy/Hartrees'''
| -0.119269
| 0.178119
| 0.092077
| 0.090559
| 0.099062
| 0.021452
| 0.021697
| -0.000018
|-
| '''Energy/kJmol<sup>-1</sup>'''
| -313.141
| 467.651
| 241.748
| 237.762
| 260.087
| 56.3222
| 56.9654
| -0.04726
|}

===Energy Profile Diagram===
[[File:Energy profile diagram ex3 zwl115.PNG|frame|centre|Figure xx. Energy Profile Diagram showing the 3 different reaction pathways for the reaction between Xylylene and SO<sub>2</sub>]]

==Diels-Alder reaction with second cis-butadiene fragment==

===Reaction Scheme===
[[File:Reaction_scheme_ex3_part_2_zwl115.PNG|centre|frame| Figure XX. Reaction scheme showing the Exo and Endo Diels-Alder cycloadditions mechanisms possible.]]

===Jmol Files===
{| class="wikitable"
|-
! Reactants
! Transition States
! Products
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> SO2_OPT_PM6_2_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> SO<sub>2</sub>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_DA_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 50; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_PDT_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> XYLYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Xylylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_DA_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 72; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_PDT_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
|}

===Reaction Profile Diagram===
[[File:Energy_profile_diagram_ex3_part_2_zwl115.PNG|centre|frame|Figure XX. Energy Profile diagram showing the thermodynamics of the 2 Diels-Alder cycloaddition pathways]]
The Endo and Exo Diels-Alder reactions for this cis-butadiene fragment is thermodynamically and kinetically unfavourable. Comparing Figures XX and XX, the activation energies for both the exo and endo Diels-Alder cycloadditions at this site are much greater than those of the terminal butadiene fragment. Furthermore, the products of the reactions for the non-terminal cis-butadiene fragment are much higher in energy than those for the terminal cis butadiene fragment. The overall reaction for both endo and exo pathways are endothermic in this case. The kinetic and thermodynamic consequences can be rationalised by the greater steric clash present in the transition state and the products when SO<sub>2</sub> reacts with the non-terminal cis-butadiene fragment which are absent with the terminal cis-butadiene fragment.

File:Energy profile diagram ex3 part 2 zwl115.PNG

2018-02-27T21:38:19Z

Zwl115:

File:Reaction scheme ex3 part 2 zwl115.PNG

2018-02-27T20:46:06Z

Zwl115:

Rep:Transition States and Reactivity Exercise3 ZWL115

2018-02-27T20:45:10Z

Zwl115: /* Exercise 3 */

==Exercise 3==

===Reaction Scheme===

O-Xylylene can react with SO<sub>2</sub> via 2 different Diels-Alder cycloadditions and a chelotropic pathway. These pathways are illustrated in Figure. XX.
[[File:Reaction_scheme_ex3_zwl115.PNG|centre|frame| Figure XX. Reaction scheme showing the Exo, Endo Diels-Alder cycloadditions and the Chelotropic reaction mechanisms possible.]]

{| class="wikitable"
|-
! Reactants
! Transition States
! Products
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> SO2_OPT_PM6_2_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> SO<sub>2</sub>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_ENDO_TS_FREQ_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 50; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_PDT_ENDO_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> XYLYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Xylylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_EXO_TS_FREQ1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 72; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_PDT_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
|-
|
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 48; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>C_TS_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Chelotropic
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>C_PDT_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Chelotropic
|}

===Reaction Coordinate===
{| class="wikitable"
|+IRC pathways
|-
! Endo
! Exo
! Chelotropic
|-
| [[File:DA_endo_TS_freq_IRC_PM6_zwl115.gif|500px]]
| [[File:DA_exo_TS_freq_IRC_PM6_zwl115.gif|500px]]
| [[File:C_TS_freq_IRC_PM6_zwl115.gif|500px]]
|}

The instability of Xylylene can be rationalised using Hückel's Molecular Orbital Theory. According to the theory, a compound is stable when all of its bonding orbitals are filled and no electrons fill the anti-bonding orbitals. This is especially true in aromatic compounds, where 2 electrons fill the lowest energy molecular orbital and 4 electrons fill the subsequent degenerate pair of orbitals (the number of pairs of orbitals is denoted by the by <i>n</i>). This gives rise to Hückel's rule where aromatic compounds have 4n+2 π electrons which are in a conjugated ring system while compounds with 4n π electrons show anti-aromatic behaviour and are highly unstable. O-Xylylene only has 4π electrons in the ring resulting in anti-aromatic instability due to filling of the anti-bonding orbitals. During the course of the reactions, the 6-membered ring of Xylylene becomes a stabilised benzene ring in all 3 pathways as seen in the IRCs. The benzene ring has 6π electrons in a conjugated ring system which obeys Hückel's rule (where <i>n</i> = 1), making it aromatic. Hence the resulting products are more stabilised and the reactions occur favourably.

===Gibbs Free Energies===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
!
! Xylylene
! Sulfur Dioxide
! Exo Transition State
! Endo Transition State
! Chelotropic Transition State
! Exo Product
! Endo Product
! Chelotropic Product
|-
| '''Energy/Hartrees'''
| -0.119269
| 0.178119
| 0.092077
| 0.090559
| 0.099062
| 0.021452
| 0.021697
| -0.000018
|-
| '''Energy/kJmol<sup>-1</sup>'''
| -313.141
| 467.651
| 241.748
| 237.762
| 260.087
| 56.3222
| 56.9654
| -0.04726
|}

===Energy Profile Diagram===
[[File:Energy profile diagram ex3 zwl115.PNG|frame|centre|Figure xx. Energy Profile Diagram showing the 3 different reaction pathways for the reaction between Xylylene and SO<sub>2</sub>]]

==Diels-Alder reaction with second cis-butadiene fragment==
{| class="wikitable"
|-
! Reactants
! Transition States
! Products
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> SO2_OPT_PM6_2_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> SO<sub>2</sub>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_DA_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 50; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_PDT_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> XYLYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Xylylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_DA_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 72; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_PDT_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
|}

File:Reaction scheme ex3 zwl115.PNG

2018-02-27T20:42:31Z

Zwl115:

Rep:Transition States and Reactivity Exercise3 ZWL115

2018-02-27T18:29:36Z

Zwl115: /* Stability of Xylylene */

==Exercise 3==

{| class="wikitable"
|-
! Reactants
! Transition States
! Products
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> SO2_OPT_PM6_2_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> SO<sub>2</sub>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_ENDO_TS_FREQ_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 50; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_PDT_ENDO_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> XYLYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Xylylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_EXO_TS_FREQ1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 72; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_PDT_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
|-
|
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 48; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>C_TS_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Chelotropic
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>C_PDT_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Chelotropic
|}

===Reaction Coordinate===
{| class="wikitable"
|+IRC pathways
|-
! Endo
! Exo
! Chelotropic
|-
| [[File:DA_endo_TS_freq_IRC_PM6_zwl115.gif|500px]]
| [[File:DA_exo_TS_freq_IRC_PM6_zwl115.gif|500px]]
| [[File:C_TS_freq_IRC_PM6_zwl115.gif|500px]]
|}

The instability of Xylylene can be rationalised using Hückel's Molecular Orbital Theory. According to the theory, a compound is stable when all of its bonding orbitals are filled and no electrons fill the anti-bonding orbitals. This is especially true in aromatic compounds, where 2 electrons fill the lowest energy molecular orbital and 4 electrons fill the subsequent degenerate pair of orbitals (the number of pairs of orbitals is denoted by the by <i>n</i>). This gives rise to Hückel's rule where aromatic compounds have 4n+2 π electrons which are in a conjugated ring system while compounds with 4n π electrons show anti-aromatic behaviour and are highly unstable. O-Xylylene only has 4π electrons in the ring resulting in anti-aromatic instability due to filling of the anti-bonding orbitals. During the course of the reactions, the 6-membered ring of Xylylene becomes a stabilised benzene ring in all 3 pathways as seen in the IRCs. The benzene ring has 6π electrons in a conjugated ring system which obeys Hückel's rule (where <i>n</i> = 1), making it aromatic. Hence the resulting products are more stabilised and the reactions occur favourably.

===Gibbs Free Energies===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
!
! Xylylene
! Sulfur Dioxide
! Exo Transition State
! Endo Transition State
! Chelotropic Transition State
! Exo Product
! Endo Product
! Chelotropic Product
|-
| '''Energy/Hartrees'''
| -0.119269
| 0.178119
| 0.092077
| 0.090559
| 0.099062
| 0.021452
| 0.021697
| -0.000018
|-
| '''Energy/kJmol<sup>-1</sup>'''
| -313.141
| 467.651
| 241.748
| 237.762
| 260.087
| 56.3222
| 56.9654
| -0.04726
|}

===Energy Profile Diagram===
[[File:Energy profile diagram ex3 zwl115.PNG|frame|centre|Figure xx. Energy Profile Diagram showing the 3 different reaction pathways for the reaction between Xylylene and SO<sub>2</sub>]]

==Diels-Alder reaction with second cis-butadiene fragment==
{| class="wikitable"
|-
! Reactants
! Transition States
! Products
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> SO2_OPT_PM6_2_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> SO<sub>2</sub>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_DA_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 50; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_PDT_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> XYLYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Xylylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_DA_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 72; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_PDT_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
|}

Rep:Transition States and Reactivity Exercise3 ZWL115

2018-02-27T18:24:54Z

Zwl115: /* Reaction Coordinate */

==Exercise 3==

{| class="wikitable"
|-
! Reactants
! Transition States
! Products
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> SO2_OPT_PM6_2_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> SO<sub>2</sub>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_ENDO_TS_FREQ_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 50; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_PDT_ENDO_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> XYLYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Xylylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_EXO_TS_FREQ1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 72; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_PDT_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
|-
|
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 48; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>C_TS_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Chelotropic
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>C_PDT_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Chelotropic
|}

===Reaction Coordinate===
{| class="wikitable"
|+IRC pathways
|-
! Endo
! Exo
! Chelotropic
|-
| [[File:DA_endo_TS_freq_IRC_PM6_zwl115.gif|500px]]
| [[File:DA_exo_TS_freq_IRC_PM6_zwl115.gif|500px]]
| [[File:C_TS_freq_IRC_PM6_zwl115.gif|500px]]
|}

The instability of Xylylene can be rationalised using Hückel's Molecular Orbital Theory. According to the theory, a compound is stable when all of its bonding orbitals are filled and no electrons fill the anti-bonding orbitals. This is especially true in aromatic compounds, where 2 electrons fill the lowest energy molecular orbital and 4 electrons fill the subsequent degenerate pair of orbitals (the number of pairs of orbitals is denoted by the by <i>n</i>). This gives rise to Hückel's rule where aromatic compounds have 4n+2 π electrons which are in a conjugated ring system while compounds with 4n π electrons show anti-aromatic behaviour and are highly unstable. O-Xylylene only has 4π electrons in the ring resulting in anti-aromatic instability due to filling of the anti-bonding orbitals. During the course of the reactions, the 6-membered ring of Xylylene becomes a stabilised benzene ring in all 3 pathways as seen in the IRCs. The benzene ring has 6π electrons in a conjugated ring system which obeys Hückel's rule (where <i>n</i> = 1), making it aromatic. Hence the resulting products are more stabilised and the reactions occur favourably.

===Gibbs Free Energies===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
!
! Xylylene
! Sulfur Dioxide
! Exo Transition State
! Endo Transition State
! Chelotropic Transition State
! Exo Product
! Endo Product
! Chelotropic Product
|-
| '''Energy/Hartrees'''
| -0.119269
| 0.178119
| 0.092077
| 0.090559
| 0.099062
| 0.021452
| 0.021697
| -0.000018
|-
| '''Energy/kJmol<sup>-1</sup>'''
| -313.141
| 467.651
| 241.748
| 237.762
| 260.087
| 56.3222
| 56.9654
| -0.04726
|}

===Energy Profile Diagram===
[[File:Energy profile diagram ex3 zwl115.PNG|frame|centre|Figure xx. Energy Profile Diagram showing the 3 different reaction pathways for the reaction between Xylylene and SO<sub>2</sub>]]

===Stability of Xylylene===

==Diels-Alder reaction with second cis-butadiene fragment==
{| class="wikitable"
|-
! Reactants
! Transition States
! Products
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> SO2_OPT_PM6_2_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> SO<sub>2</sub>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_DA_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 50; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_PDT_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> XYLYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Xylylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_DA_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 72; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_PDT_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
|}

Rep:Transition States and Reactivity Exercise3 ZWL115

2018-02-27T18:21:06Z

Zwl115: /* Reaction Coordinate */

==Exercise 3==

{| class="wikitable"
|-
! Reactants
! Transition States
! Products
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> SO2_OPT_PM6_2_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> SO<sub>2</sub>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_ENDO_TS_FREQ_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 50; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_PDT_ENDO_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> XYLYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Xylylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_EXO_TS_FREQ1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 72; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_PDT_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
|-
|
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 48; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>C_TS_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Chelotropic
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>C_PDT_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Chelotropic
|}

===Reaction Coordinate===
{| class="wikitable"
|+IRC pathways
|-
! Endo
! Exo
! Chelotropic
|-
| [[File:DA_endo_TS_freq_IRC_PM6_zwl115.gif|500px]]
| [[File:DA_exo_TS_freq_IRC_PM6_zwl115.gif|500px]]
| [[File:C_TS_freq_IRC_PM6_zwl115.gif|500px]]
|}

The instability of Xylylene can be rationalised using Hückel's Molecular Orbital Theory. According to the theory, a compound is stable when all of its bonding orbitals are filled and no electrons fill the anti-bonding orbitals. This is especially true in aromatic compounds, where 2 electrons fill the lowest energy molecular orbital and 4 electrons fill the subsequent degenerate pair of orbitals (the number of pairs of orbitals is denoted by the by <i>n</i>). This gives rise to Hückel's rule where aromatic compounds have 4n+2 π electrons which are in a conjugated ring system. O-Xylylene only has 4π electrons in the ring resulting in anti-aromatic instability due to filling of the anti-bonding orbitals. During the course of the reactions, the 6-membered ring of Xylylene becomes a stabilised benzene ring in all 3 pathways as seen in the IRCs. The benzene ring has 6π electrons in a conjugated ring system which obeys Hückel's rule (where <i>n</i> = 1), making it aromatic. Hence the resulting products are more stabilised.

===Gibbs Free Energies===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
!
! Xylylene
! Sulfur Dioxide
! Exo Transition State
! Endo Transition State
! Chelotropic Transition State
! Exo Product
! Endo Product
! Chelotropic Product
|-
| '''Energy/Hartrees'''
| -0.119269
| 0.178119
| 0.092077
| 0.090559
| 0.099062
| 0.021452
| 0.021697
| -0.000018
|-
| '''Energy/kJmol<sup>-1</sup>'''
| -313.141
| 467.651
| 241.748
| 237.762
| 260.087
| 56.3222
| 56.9654
| -0.04726
|}

===Energy Profile Diagram===
[[File:Energy profile diagram ex3 zwl115.PNG|frame|centre|Figure xx. Energy Profile Diagram showing the 3 different reaction pathways for the reaction between Xylylene and SO<sub>2</sub>]]

===Stability of Xylylene===

==Diels-Alder reaction with second cis-butadiene fragment==
{| class="wikitable"
|-
! Reactants
! Transition States
! Products
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> SO2_OPT_PM6_2_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> SO<sub>2</sub>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_DA_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 50; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_PDT_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> XYLYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Xylylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_DA_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 72; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_PDT_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
|}

Rep:Transition States and Reactivity Exercise3 ZWL115

2018-02-24T17:48:48Z

Zwl115: /* Diels-Alder reaction with second cis-butadiene fragment */

==Exercise 3==

{| class="wikitable"
|-
! Reactants
! Transition States
! Products
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> SO2_OPT_PM6_2_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> SO<sub>2</sub>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_ENDO_TS_FREQ_1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 50; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_PDT_ENDO_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> XYLYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Xylylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_EXO_TS_FREQ1_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 72; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA_PDT_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
|-
|
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 48; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>C_TS_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Chelotropic
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>C_PDT_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Chelotropic
|}

===Reaction Coordinate===
{| class="wikitable"
|+IRC pathways
|-
! Endo
! Exo
! Chelotropic
|-
| [[File:DA_endo_TS_freq_IRC_PM6_zwl115.gif|500px]]
| [[File:DA_exo_TS_freq_IRC_PM6_zwl115.gif|500px]]
| [[File:C_TS_freq_IRC_PM6_zwl115.gif|500px]]
|}

===Gibbs Free Energies===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
!
! Xylylene
! Sulfur Dioxide
! Exo Transition State
! Endo Transition State
! Chelotropic Transition State
! Exo Product
! Endo Product
! Chelotropic Product
|-
| '''Energy/Hartrees'''
| -0.119269
| 0.178119
| 0.092077
| 0.090559
| 0.099062
| 0.021452
| 0.021697
| -0.000018
|-
| '''Energy/kJmol<sup>-1</sup>'''
| -313.141
| 467.651
| 241.748
| 237.762
| 260.087
| 56.3222
| 56.9654
| -0.04726
|}

===Energy Profile Diagram===
[[File:Energy profile diagram ex3 zwl115.PNG|frame|centre|Figure xx. Energy Profile Diagram showing the 3 different reaction pathways for the reaction between Xylylene and SO<sub>2</sub>]]

===Stability of Xylylene===

==Diels-Alder reaction with second cis-butadiene fragment==
{| class="wikitable"
|-
! Reactants
! Transition States
! Products
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> SO2_OPT_PM6_2_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> SO<sub>2</sub>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_DA_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 50; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_PDT_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Endo
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents> XYLYLENE_OPT_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Xylylene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_DA_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 72; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_PDT_FREQ_PM6_zwl115.LOG</uploadedFileContents>
</jmolApplet>
</jmol> Exo
|}