ChemWiki - User contributions [en]

Rep:MOD:spk15TSEx2

2018-01-30T12:19:14Z

Spk15: /* MO Analysis of Reaction */

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

===Reaction Scheme===
Cyclohexadiene reacts with Dioxole in a concerted, suprafacial [4+2] cycloaddition according to the mechanism shown below in Figure 5 to form two products- the exo and endo products.
[[File:Spk15 ex2Reaction Scheme3.png|thumb|frame|centre|600px|Figure 5: Mechanism of reaction between cyclohexadiene and 1,3-dioxole]]

===Jmol Files===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Reactants !! Transition States !! Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXADIENE2_631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Cyclohexadiene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS FREQ 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Exo TS|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO PDT FREQ 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Exo product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIOXOLE2 631GD.LOG </uploadedFileContents>
</jmolApplet>
</jmol><br>Dioxole || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDOTS FREQ 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Endo TS|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO PDT FREQ 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Endo product
|-
|}

===Single Point Energy Calculation===
In order to determine if the reaction between cyclohexadiene and 1,3-dioxole proceeded via normal or inverse electron demand, the relative levels of the HOMO and LUMO of the reactants were compared by performing a single point energy calculation. This allowed the reactants to be studied on the same potential energy surface and the energies of their MOs to be compared more accurately. In this reaction, the HOMO of 1,3-dioxole, the dienophile, was found to be higher than the HOMO of cyclohexadiene, the diene, as shown below. This indicates the reaction proceeds via inverse electron demand.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Cyclohexadiene !! Relative Energies of the HOMO and LUMO of the Reactants !! 1,3-Dioxole
|-
|<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>REACTANTS ENDO SP.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Cyclohexadiene||rowspan="2"|[[File:Individual Reactant MOs.PNG]] || <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>REACTANTS ENDO SP.LOG</uploadedFileContents>
</jmolApplet>
</jmol> 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>REACTANTS ENDO SP.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Cyclohexadiene|| <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>REACTANTS ENDO SP.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of 1,3-Dioxole
|}

===MO Analysis of Reaction===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|+ Occupied and Unoccupied Orbitals of the TS
! !! Occupied Orbital !! HOMO !! LUMO !! Unoccupied Orbital
|-
| colspan="1"|Exo || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS FREQ 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS FREQ 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS FREQ 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS FREQ 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| colspan="1"|Endo || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDOTS FREQ 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDOTS FREQ 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDOTS FREQ 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDOTS FREQ 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Cyclohexadiene !! MO diagram for the formation of the Cyclohexadienediene/1,3-Dioxole transition state !! 1,3-Dioxole
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXADIENE2 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Cyclohexadiene||rowspan="2"|[[File:Spk15 ex2MOdiagram.png|thumb|centre|700px]] || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIOXOLE2 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of 1,3-Dioxole
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXADIENE2 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Cyclohexadiene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIOXOLE2 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of 1,3-Dioxole
|}

In this inverse electron demand [4+2] cycloaddition reaction, the 1,3-dioxole acts as a electron rich dienophile since the oxygen atoms can donate their lone pair of electrons into the pi system of the double bond. Hence, the HOMO of the 1,3-dioxole is raised higher than the HOMO of the dienophile and is high enough in energy to interact with the LUMO of the diene (cylohexadiene). MO1 and MO4 are a bonding/antibonding pair formed from the overlap of the HOMO of cyclohexadiene and the LUMO of the 1,3-dioxole. MO2 and MO3 are another bonding/antibonding pair formed from the overlap of the HOMO of the 1,3-dioxole and the LUMO of cyclohexadiene.<sup>6</sup>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|+ Comparing a normal and inverse electron demand [4+2] cycloaddition
! Normal
! Inverse
|-
| [[File:Spk15 normal.PNG|thumb|500px]]
| [[File:Spk15 inverse.PNG|thumb|500px]]
|}

===Reaction Dynamics===
The Gibbs Free energies of the reactants, products and transition states were tabulated at the PM6 and B3LYP level, and are shown in Figure 6 below.
[[File:Spk15 absoluteenergies.PNG|centre|frame|Figure 6: Absolute Energies of reactants, transition states and products]]

<br>The reaction energy and reaction barrier were calculated according to the equations shown below:
<div style="text-align: center;">Reaction Energy = Energy of Products - Energy of Reactants</div>
<br> <div style="text-align: center;">Reaction Barrier = Energy of Transition State - Energy of Reactants</div>

[[File:Spk15 ex2reactionprofile3.png|thumb|frame|centre|600px|Figure 7: Reaction profile diagram]]
<br>According to the reaction profile (Figure 7), the endo product is both kinetically and thermodynamically favoured. The endo activation energy is lower than the exo activation energy which means that the reactants will form the endo transition state faster than the exo transition state. The endo transition state is lower in energy than the exo transition state since there are secondary orbital interactions between the butadiene pi orbitals and the p orbitals of the oxygen atoms which is discussed more below. This lowers the energy of the endo transition state. The endo Diels-Alder product is also lower in energy than the exo product which indicates that the endo product is more stable and hence thermodynamically favoured. The endo product is lower in energy as there is greater steric clash in the exo product between the CH<sub>2</sub> hydrogens and the oxygen atoms as shown in Figure 8 below.<sup>7</sup> On the other hand, in the endo product with the dioxole in an axial position, there is much less steric clash between the CH<sub>2</sub> hydrogens and the other hydrogen atoms since hydrogen has a much smaller VDW radius than oxygen. Furthermore, the endo product is more thermodynamically preferred as the former 1,3-Dioxole component is anti to the carbon bridge group rather than gauche in the exo product. There is reduced steric hindrance in the molecule as the two larger groups are anti to one another. This is shown in Figure 9.
[[File:Spk15 endoexostericclash.png|thumb|frame|centre|600px|Figure 8: Steric clash in exo and endo products]][[File:Screen Shot 2018-01-27 at 18.12.33.png|thumb|centre|600px|Figure 9: Newman projection of endo and exo products viewed along the bolded line]]

===Secondary Orbital Interactions===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! HOMO of Exo TS !! HOMO of Endo TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS FREQ 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDOTS TS631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<br>In both the endo and exo transition states, there are primary orbital interactions between the pi orbitals of cyclohexadiene and dioxole which result in the formation of the new sigma bonds. In the endo transition state, there are additional secondary orbital interactions between the p-orbitals of the cyclohexadiene and the non-bonding p-orbitals of the oxygen atoms in dioxole, this stabilises the transition state and results in the endo transition state forming faster, and making the endo product more kinetically favourable.<sup>8</sup> This is shown more clearly in Figure 10 below.
[[File: Spk15secondaryorbitalinteractions.png|thumb|frame|centre|600px|Figure 10: Possibility of secondary orbital interactions]]

Rep:MOD:spk15TSEx3

2018-01-29T15:32:13Z

Spk15: /* IRC Pathway */

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

===Reaction Scheme===

O-Xylylene can react with SO<sub>2</sub> via 2 different pathways- Diels-Alder reaction or Cheletropic reaction shown in Figure 11 . The Diels-Alder reaction produces a mixture of endo and exo products while the Cheletropic reaction only produces a single exo product due to the endo pathway being very kinetically unfavoured.

[[File:Spk15 ex3Reaction Scheme.png|thumb|700px|centre|frame|Figure 11: Mechanism for the reaction of O-xylylene with SO<sub>2</sub>]]

===Jmol Files===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Reactants !! Transition States !! Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 50; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>O-XYLYLENE PM6.LOG </uploadedFileContents>
</jmolApplet>
</jmol><br>O-Xylylene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA EXOTS TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Diels-Alder Exo TS|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 96; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA EXO PDT.LOG </uploadedFileContents>
</jmolApplet>
</jmol><br>Diels-Alder Exo product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 9; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>SO2 PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>SO<sub>2</sub>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Diels-Alder Endo TS|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 52; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA ENDO PDT.LOG </uploadedFileContents>
</jmolApplet>
</jmol><br>Diels-Alder Endo product
|-
||| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CT EXOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Cheletropic TS|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CT EXO PDT.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Cheletropic product
|-
|}

===IRC Pathway===

{| class="wikitable" border="1"
|+
! Endo TS !! Exo TS !! Cheletropic
|-
| [[File:DA endoIRCpathway.gif|500px]] || [[File:DA exoIRCpathway.gif|500px]] || [[File:Cheletropicpathway.gif|500px]]
|}
<br>According to Huckel's Molecular Orbital Theory, a compound is particularly stable if all of its bonding molecular orbitals are filled with pair electrons. This is true of aromatic compounds, which display extremely high stability. With aromatic compounds, 2 electrons fill the lowest energy MO, and 4 electrons fill each subsequent energy level (the number of subsequent energy levels is denoted n), leaving all bonding orbitals filled and no anti-bonding orbitals occipied. This gives the Huckel Rule that compounds with a total of [4n+2] π electrons have higher stability and compounds with [4n] π electrons display anti-aromatic behaviour and have a lower stability since their anti-bonding orbitals are now filled.<sup>10</sup> The initial O-xylylene molecule has 8π electrons delocalised across the 4 conjugated double bonds. Hence, the molecule is anti-aromatic and highly unstable. Throughout the course of the reaction, the 6-membered ring in O-xylylene forms a benzene ring. Benzene has 6 π electrons and is aromatic and stabilised. Hence, this reaction proceeds favourably to form an aromatic product. This also explains why o-xylylene is so reactive as it is anti-aromatic and highly unstable.

===Reaction Dynamics===
Similar to exercise 2, the Gibbs Free energies were calculated at both the PM6 and B3LYP level for the reactants, products and transition states and are shown in Figure 12. The activation energy (reaction barrier) and reaction energies were also calculated using the same formula as in exercise 2. They are shown in Figure 13.
[[File:Spk15 ex3absoluteenergies.PNG|centre|frame|Figure 12: Absolute energies at PM6 and B3LYP(6-31G) level]]<br>[[File:Spk15 activationreactionenergies.PNG|centre|frame|Figure 13: Activation and reaction energies]]

[[File:Spk15 reactionprofileex3.png|thumb|700px|centre|frame|Figure 14: Reaction profile Diagram]]

===Alternative Diels-Alder Reaction===
SO<sub>2</sub> can also react with the second cis-butadiene fragment in O-Xylylene according to the reaction scheme shown in Figure 15.

[[File:Spk15 dielsalder2reactionscheme.png|thumb|centre|600px|Figure 15: Mechanism for the alternative Diels-Alder reaction]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Transition States !! Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 50; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA2 EXOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Endo TS|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA2 ENDOPRODUCT.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Endo product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 9; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIELSALDER2 EXOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Exo TS|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIELSALDER2 EXOPRODUCT.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Exo product
|-
|}

<br>Due to the this second cir-butadiene fragment being much more sterically hindered, there is a much larger activation energy to reach this transition state. Furthermore, the product formed is higher in energy than the reactants, making the endothermic reaction very thermodynamically unfavourable.

[[File:Spk15 dielsalder2reactionprofile.png|thumb|centre|600px|Reaction profile diagram for the alternative Diels-Alder reaction]]

Rep:MOD:spk15TS

2018-01-29T15:31:47Z

Spk15: /* References */

==Introduction==

===What is a potential energy surface?===
The potential energy surface (PES) describes how the energy of a system in a particular state changes with the structure of the molecule. A simple representation of the potential energy surface is shown in Figure 1, in which the potential energy of the system is given by the vertical coordinates and two geometric variables are given by the horizontal coordinates. Although most molecules have more than two geometric variables, most of the key features of a PES can be represented in such a landscape.

[[File:Model PES.gif|frame|centre|Figure 1: Model PES<sup>1</sup>]]

===What are a minimum and transition state?===
A minimum in the potential energy surface represents the equilibrium structure of the reactants, products or intermediates. The lowest energy pathway between the reactant minimum and the product minimum is the reaction path. The highest point on the lowest energy reaction path is the transition state (TS) for the reaction. A TS is a maximum in one direction (the direction connecting reactant and product along the reaction path) but is a minimum in all other directions perpendicular to the reaction path, making it first-order saddle point. The potential energy surface around a transition state is shown more clearly in Figure 2, where the point A is a maximum along the θ direction but a minimum in the R direction.<sup>2</sup>

[[File:Spk15 transitionstatePES.PNG|thumb|centre|frame|Figure 2: Potential energy surface around a transition state]]

===How do energy derivatives vary between minimum and transition states?===
The first and second derivatives of the energy (E) with respect to geometrical parameters (x) can be used to confirm the character of minima and TSs. The matrix of the first derivative is given by the gradient of the PES. Both a minimum and TS are characterised by having a zero gradient on the PES. Since the negative of the gradient is the vector of forces on the atoms in the molecule, the minimum and TSs both have zero forces acting on them and are also termed stationary points.<br>What distinguishes a minimum and a transition state is the curvature of the potential energy surface around the stationary point which is given by the force constant (second derivative) matrix.The matrix of second derivatives of the energy is known as the Hessian. The eigenvectors of the Hessian correspond to the normal modes of vibration (plus 5 or 6 modes for translation and rotation). For a structure to be classified as a minimum, the gradient must be zero and all the eigenvalues of the Hessian must be positive. Using the model for a diatomic molecule, the vibrational freqency is given by <br>[[File:Spk15 ex1equation.PNG|frame|centre]]<div style="text-align: center;">where k is the second derivative of E with respect to x.</div> <br>Therefore, if the Hessian matrix and subsequently second derivative of E is positive, the vibrational frequencies must all be positive at a minimum. For a TS, the PES is a maximum along the reaction path and a minimum in all other perpendicular directions. Therefore, a TS is characterised by a negative second derivative of E with respect to x in one dimension, and thus one negative Hessian eigenvalue. Since the minimum has a positive second derivative along all dimensions, the curvature at a minimum is positive. The transition state is the maximum point along the reaction path and therefore has negative curvature along the reaction path.<sup>3</sup>

==Exercise 1: Reaction of Butadiene with Ethylene==

===Reaction Scheme===
Butadiene reacts with Ethylene in a concerted, suprafacial [4+2] cycloaddition according to the mechanism shown in Figure 3.
[[File:Spk15 Reaction Scheme mechanism2.PNG|centre|frame|Figure 3: Mechanism of the reaction of butadiene with ethylene]]

===Trans-butadiene===
For this [4=2] cycloaddition, butadiene has to be in a cis conformation. However, butadiene usually exists as a more stable trans-isomer. (96% of the time butadiene is in the trans conformation).<sup>4</sup> The reaction energy for the conversion from trans to cis-butadiene is +4.16 kj/mol<sup>-1</sup> at the PM6 level.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Trans-butadiene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 12; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRANSBUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! Ethylene !! TS !! Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26; mo 12; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE2 MIN PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE MIN PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 16; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TS TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 48; mo 16; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>PRODUCT2 MIN PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-

===MO Analysis of reaction===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! MO diagram for the formation of the Butadiene/Ethylene transition state !! Ethylene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE2 MIN PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Butadiene||rowspan="2"|[[File:SPK15 EX1MO diagram2.png|thumb|centre|700px]] || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE MIN PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Ethylene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE2 MIN PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Butadiene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE MIN PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Ethylene
|}

In this normal electron demand [4+2] Diels-Alder reaction, the diene (butadiene) is more electron rich than the dienophile (ethylene) since it has more pi electrons due to one more double bond. Hence, butadiene has orbitals that are higher in energy than the orbitals of ethylene. The major interaction is between the antisymmetric LUMO of ethylene and HOMO of butadiene since they are closest in energy. The bonding interaction between these two frontier molecular orbitals produces MO1. The transition state HOMO, MO2 is the bonding interaction between the symmetric LUMO of butadiene and HOMO of ethylene. MO3 is the antibonding pair of MO2, formed from the antibonding interaction between the LUMO of butadiene and HOMO of ethylene. It is only slightly higher in energy than the LUMO of butadiene, indicating it is only destabilised by a small amount. Finally, MO4 is formed by the bonding interaction between the asymmetric highest energy frontier orbital of butadiene and the asymmetric LUMO of ethylene. Due to the close energy of all the frontier molecular orbitals, there is some orbital mixing between the orbital formed by the HOMO of butadiene and LUMO of ethylene and this high energy butadiene orbital.<sup>5</sup>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|+ MOs 1-4 of the transition state
! [[File:Spk15 ex1 MO1.PNG]] !! [[File:Spk15 ex1 MO2.PNG]] !! [[File:Spk15 ex1 MO3.PNG]] !!
[[File:Spk15 exercise1 Mo4.PNG]]
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 16; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TS TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 17; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TS TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 18; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TS TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 19; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TS TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

===Woodward-Hoffmann Rules and Orbital Symmetry===
A reaction is 'allowed' thermally when the total number of [4q+2]<sub>s</sub> + [4r]<sub>a</sub> components is odd. In this reaction, the orbitals interact with orbitals of the same symmetry (symmetric with symmetric or asymmetric with asymmetric) so all the components are suprafacial since the new bonds form on the same face at both ends of the component.
[[File:Woodward Hoffmann.png|frame|centre|In this reaction, there is 1 [4q+2]<sub>s</sub> component and 0 [4r]<sub>a</sub> components so the reaction is allowed]]

<div style="text-align: center;"><u>Orbital overlap integral</u></div>
<div style="text-align: center;">Symmetric-Antisymmetric: Zero</div>
<div style="text-align: center;">Symmetric-Symmetric: Non-zero</div>
<div style="text-align: center;">Antisymmetric-Antisymmetric: Non-Zero</div>

===Bond length analysis of the reaction===

[[File:Spk15 bondlengths2.PNG|frame|centre|Bond lengths for reactants, transition state and product]]
[[File:Spk15 IRCplot.png|frame|centre|Changes in bond length throughout the reaction]]

<br>As the reaction proceeds, the carbon centres change from sp<sup>3</sup> to sp<sup>2</sup> hybridised or vice versa. The carbon-numbering is shown in Figure 4.
[[File:Spk15 carbonnumbering.PNG|frame|centre|Figure 4: Carbon-numbering]]

The largest change in bond length is between C1-C2 and C3-C4 where the new sigma bonds are formed. The bond lengths decrease from 3.41A (too far for any bonding interaction so implies different molecules) to 1.54A, which is typical of a sp<sup>3</sup>-sp<sup>3</sup> single bond. At the same time, the C5-C6 bond length decreases from 1.47A(sp<sup>2</sup>-sp<sup>2</sup>) to 1.34A (which is the typical bond length of a C=C). The C1-C6 and C4-C5 double bonds increase in length from 1.34A to 1.50A. 1.50A is exactly the typical sp<sup>3</sup>-sp<sup>2</sup> bond length and shows the change from a double to single bond. In the TS, the partly formed C-C bonds have a bond length of 2.11A, which is in between the combined VDW radius of the 2 C atoms (1.70A x 2 = 3.40A) and the typical sp<sup>3</sup>-sp<sup>3</sup> single bond length (1.54A).

===Vibration corresponding to the reaction path at the transition state===

[[File:TSvibration.gif|frame|centre|Vibration corresponding to the imaginary frequency of the transition state]]

The formation of the two bonds is synchronous. The movement of the bonds at the transition state show that C2 approaches C1 at the same time as C3 approaches C4, and the two sigma bonds form simultaneously. This implies that the bonds form at the same time, and possibly but not necessarily at the same rate.

==Link to Exercise 2==
https://wiki.ch.ic.ac.uk/wiki/index.php?title=MOD:spk15TSEx2

==Link to Exercise 3==
https://wiki.ch.ic.ac.uk/wiki/index.php?title=MOD:spk15TSEx3

==Conclusion==

The focus of this computational lab was on locating transition structures for a series of reactions and abstracting information about the reaction.Two electronic structure methods were employed: the semi-empirical method PM6 and the Density Functional Theory (DFT) method B3LYP to optimise the structures while IRCs were run on the transition state to confirm they connected the reactants and products along the lowest energy pathway. The symmetry requirements according to the Woodward-Hoffmann Rules for cycloadditions were explored along with the 2 types of Diels-Alder reaction- normal electron demand and inverse electron demand. The relative energy levels of the frontier molecular orbitals were examined and the HOMO of the dienophile was found to be higher than that of diene in an inverse electron demand reaction while the opposite was true for a normal electron demand reaction. However, this was found not to affect the relative energy levels of the transition state. The thermochemistry of the reactions was also studied and it was found that secondary orbital interactions could lower the energy of transition states, making a product more kinetically favourable. In a reversible reaction, steric hindrance can also determine the relative thermodynamic stability of a product.

==References==
1. Potential Energy Surface - Chemistry LibreTexts.
<br>2. Schlegel, H. B. (2011). Geometry optimization, 1(October), 790–809.
<br>3. Ot, W. J. (1990). Computational quantum chemistry. Journal of Molecular Structure: THEOCHEM (Vol. 207).
<br>4. Butadiene: A Molecular Mechanics Study.
<br>5. Fleming, Ian (1978). Frontier Orbitals and Organic Chemical Reactions.
<br>6. Progress in Heterocyclic Chemistry, Volume 28, 1st Edition.
<br>7. Ho, G. M., Huang, C. J., Li, E. Y. T., Hsu, S. K., Wu, T., Zulueta, M. M. L., … Hung, S. C. (2016). Unconventional exo selectivity in thermal normal-electron-demand Diels-Alder reactions. Scientific Reports, 6(October), 1–10.
<br>8. Secondary orbital interactions determining regioselectivity in the Diels-Alder reaction.
Peter V. Alston, Raphael M. Ottenbrite, and Theodore Cohen, The Journal of Organic Chemistry 1978 43 (10), 1864-1867
<br>9. Wiley, 1985. Advanced Organic Chemistry: Reactions, Mechanisms, and Structure.
<br>10. Aromaticity and the Hückel 4n + 2 Rule - Chemistry LibreTexts.

Rep:MOD:spk15TS

2018-01-29T15:30:01Z

Spk15: /* References */

Rep:MOD:spk15TSEx3

2018-01-29T15:29:07Z

Spk15: /* Reaction Dynamics */

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

===Reaction Scheme===

O-Xylylene can react with SO<sub>2</sub> via 2 different pathways- Diels-Alder reaction or Cheletropic reaction shown in Figure 11 . The Diels-Alder reaction produces a mixture of endo and exo products while the Cheletropic reaction only produces a single exo product due to the endo pathway being very kinetically unfavoured.

[[File:Spk15 ex3Reaction Scheme.png|thumb|700px|centre|frame|Figure 11: Mechanism for the reaction of O-xylylene with SO<sub>2</sub>]]

===Jmol Files===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Reactants !! Transition States !! Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 50; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>O-XYLYLENE PM6.LOG </uploadedFileContents>
</jmolApplet>
</jmol><br>O-Xylylene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA EXOTS TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Diels-Alder Exo TS|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 96; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA EXO PDT.LOG </uploadedFileContents>
</jmolApplet>
</jmol><br>Diels-Alder Exo product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 9; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>SO2 PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>SO<sub>2</sub>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Diels-Alder Endo TS|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 52; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA ENDO PDT.LOG </uploadedFileContents>
</jmolApplet>
</jmol><br>Diels-Alder Endo product
|-
||| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CT EXOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Cheletropic TS|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CT EXO PDT.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Cheletropic product
|-
|}

===IRC Pathway===

{| class="wikitable" border="1"
|+
! Endo TS !! Exo TS !! Cheletropic
|-
| [[File:DA endoIRCpathway.gif|500px]] || [[File:DA exoIRCpathway.gif|500px]] || [[File:Cheletropicpathway.gif|500px]]
|}
<br>According to Huckel's Molecular Orbital Theory, a compound is particularly stable if all of its bonding molecular orbitals are filled with pair electrons. This is true of aromatic compounds, which display extremely high stability. With aromatic compounds, 2 electrons fill the lowest energy MO, and 4 electrons fill each subsequent energy level (the number of subsequent energy levels is denoted n), leaving all bonding orbitals filled and no anti-bonding orbitals occipied. This gives the Huckel Rule that compounds with a total of [4n+2] π electrons have higher stability and compounds with [4n] π electrons display anti-aromatic behaviour and have a lower stability since their anti-bonding orbitals are now filled. The initial O-xylylene molecule has 8π electrons delocalised across the 4 conjugated double bonds. Hence, the molecule is anti-aromatic and highly unstable. Throughout the course of the reaction, the 6-membered ring in O-xylylene forms a benzene ring. Benzene has 6 π electrons and is aromatic and stabilised. Hence, this reaction proceeds favourably to form an aromatic product. This also explains why o-xylylene is so reactive as it is anti-aromatic and highly unstable.

===Reaction Dynamics===
Similar to exercise 2, the Gibbs Free energies were calculated at both the PM6 and B3LYP level for the reactants, products and transition states and are shown in Figure 12. The activation energy (reaction barrier) and reaction energies were also calculated using the same formula as in exercise 2. They are shown in Figure 13.
[[File:Spk15 ex3absoluteenergies.PNG|centre|frame|Figure 12: Absolute energies at PM6 and B3LYP(6-31G) level]]<br>[[File:Spk15 activationreactionenergies.PNG|centre|frame|Figure 13: Activation and reaction energies]]

[[File:Spk15 reactionprofileex3.png|thumb|700px|centre|frame|Figure 14: Reaction profile Diagram]]

===Alternative Diels-Alder Reaction===
SO<sub>2</sub> can also react with the second cis-butadiene fragment in O-Xylylene according to the reaction scheme shown in Figure 15.

[[File:Spk15 dielsalder2reactionscheme.png|thumb|centre|600px|Figure 15: Mechanism for the alternative Diels-Alder reaction]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Transition States !! Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 50; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA2 EXOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Endo TS|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA2 ENDOPRODUCT.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Endo product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 9; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIELSALDER2 EXOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Exo TS|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIELSALDER2 EXOPRODUCT.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Exo product
|-
|}

<br>Due to the this second cir-butadiene fragment being much more sterically hindered, there is a much larger activation energy to reach this transition state. Furthermore, the product formed is higher in energy than the reactants, making the endothermic reaction very thermodynamically unfavourable.

[[File:Spk15 dielsalder2reactionprofile.png|thumb|centre|600px|Reaction profile diagram for the alternative Diels-Alder reaction]]

Rep:MOD:spk15TSEx3

2018-01-29T15:28:41Z

Spk15: /* IRC Pathway */

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

===Reaction Scheme===

O-Xylylene can react with SO<sub>2</sub> via 2 different pathways- Diels-Alder reaction or Cheletropic reaction shown in Figure 11 . The Diels-Alder reaction produces a mixture of endo and exo products while the Cheletropic reaction only produces a single exo product due to the endo pathway being very kinetically unfavoured.

[[File:Spk15 ex3Reaction Scheme.png|thumb|700px|centre|frame|Figure 11: Mechanism for the reaction of O-xylylene with SO<sub>2</sub>]]

===Jmol Files===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Reactants !! Transition States !! Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 50; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>O-XYLYLENE PM6.LOG </uploadedFileContents>
</jmolApplet>
</jmol><br>O-Xylylene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA EXOTS TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Diels-Alder Exo TS|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 96; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA EXO PDT.LOG </uploadedFileContents>
</jmolApplet>
</jmol><br>Diels-Alder Exo product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 9; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>SO2 PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>SO<sub>2</sub>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Diels-Alder Endo TS|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 52; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA ENDO PDT.LOG </uploadedFileContents>
</jmolApplet>
</jmol><br>Diels-Alder Endo product
|-
||| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CT EXOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Cheletropic TS|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CT EXO PDT.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Cheletropic product
|-
|}

===IRC Pathway===

{| class="wikitable" border="1"
|+
! Endo TS !! Exo TS !! Cheletropic
|-
| [[File:DA endoIRCpathway.gif|500px]] || [[File:DA exoIRCpathway.gif|500px]] || [[File:Cheletropicpathway.gif|500px]]
|}
<br>According to Huckel's Molecular Orbital Theory, a compound is particularly stable if all of its bonding molecular orbitals are filled with pair electrons. This is true of aromatic compounds, which display extremely high stability. With aromatic compounds, 2 electrons fill the lowest energy MO, and 4 electrons fill each subsequent energy level (the number of subsequent energy levels is denoted n), leaving all bonding orbitals filled and no anti-bonding orbitals occipied. This gives the Huckel Rule that compounds with a total of [4n+2] π electrons have higher stability and compounds with [4n] π electrons display anti-aromatic behaviour and have a lower stability since their anti-bonding orbitals are now filled. The initial O-xylylene molecule has 8π electrons delocalised across the 4 conjugated double bonds. Hence, the molecule is anti-aromatic and highly unstable. Throughout the course of the reaction, the 6-membered ring in O-xylylene forms a benzene ring. Benzene has 6 π electrons and is aromatic and stabilised. Hence, this reaction proceeds favourably to form an aromatic product. This also explains why o-xylylene is so reactive as it is anti-aromatic and highly unstable.

===Reaction Dynamics===
Similar to exercise 2, the Gibbs Free energies were calculated at both the PM6 and B3LYP level for the reactants, products and transition states and are shown in Figure 12. The activation energy (reaction barrier) and reaction energies were also calculated using the same formula as in exercise 2. They are shown in Figure 13.
[[File:Spk15 ex3absoluteenergies.PNG|centre|frame|Figure 12: Absolute energies at PM6 and B3LYP(6-31G) level]]<br>[[File:Spk15 activationreactionenergies.PNG|centre|frame|Figure 13: Activation and reaction energies]]

[[File:Spk15 reactionprofileex3.png|thumb|700px|centre|frame|Figure 14: Reaction profile Diagram]]

===Alternative Diels-Alder Reaction===
SO<sub>2</sub> can also react with the second cis-butadiene fragment in O-Xylylene according to the reaction scheme shown in Figure 15.

[[File:Spk15 dielsalder2reactionscheme.png|thumb|centre|600px|Figure 15: Mechanism for the alternative Diels-Alder reaction]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Transition States !! Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 50; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA2 EXOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Endo TS|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DA2 ENDOPRODUCT.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Endo product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 9; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIELSALDER2 EXOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Exo TS|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 29; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIELSALDER2 EXOPRODUCT.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Exo product
|-
|}

<br>Due to the this second cir-butadiene fragment being much more sterically hindered, there is a much larger activation energy to reach this transition state. Furthermore, the product formed is higher in energy than the reactants, making the endothermic reaction very thermodynamically unfavourable.

[[File:Spk15 dielsalder2reactionprofile.png|thumb|centre|600px|Reaction profile diagram for the alternative Diels-Alder reaction]]

Rep:MOD:spk15TSEx3

2018-01-29T15:20:49Z

2018-01-29T14:54:40Z

Spk15: /* Bond length analysis of the reaction */

==Introduction==

===What is a potential energy surface?===
The potential energy surface (PES) describes how the energy of a system in a particular state changes with the structure of the molecule. A simple representation of the potential energy surface is shown in Figure 1, in which the potential energy of the system is given by the vertical coordinates and two geometric variables are given by the horizontal coordinates. Although most molecules have more than two geometric variables, most of the key features of a PES can be represented in such a landscape.

[[File:Model PES.gif|frame|centre|Figure 1: Model PES<sup>1</sup>]]

===What are a minimum and transition state?===
A minimum in the potential energy surface represents the equilibrium structure of the reactants, products or intermediates. The lowest energy pathway between the reactant minimum and the product minimum is the reaction path. The highest point on the lowest energy reaction path is the transition state (TS) for the reaction. A TS is a maximum in one direction (the direction connecting reactant and product along the reaction path) but is a minimum in all other directions perpendicular to the reaction path, making it first-order saddle point. The potential energy surface around a transition state is shown more clearly in Figure 2, where the point A is a maximum along the θ direction but a minimum in the R direction.<sup>2</sup>

[[File:Spk15 transitionstatePES.PNG|thumb|centre|frame|Figure 2: Potential energy surface around a transition state]]

===How do energy derivatives vary between minimum and transition states?===
The first and second derivatives of the energy (E) with respect to geometrical parameters (x) can be used to confirm the character of minima and TSs. The matrix of the first derivative is given by the gradient of the PES. Both a minimum and TS are characterised by having a zero gradient on the PES. Since the negative of the gradient is the vector of forces on the atoms in the molecule, the minimum and TSs both have zero forces acting on them and are also termed stationary points.<br>What distinguishes a minimum and a transition state is the curvature of the potential energy surface around the stationary point which is given by the force constant (second derivative) matrix.The matrix of second derivatives of the energy is known as the Hessian. The eigenvectors of the Hessian correspond to the normal modes of vibration (plus 5 or 6 modes for translation and rotation). For a structure to be classified as a minimum, the gradient must be zero and all the eigenvalues of the Hessian must be positive. Using the model for a diatomic molecule, the vibrational freqency is given by <br>[[File:Spk15 ex1equation.PNG|frame|centre]]<div style="text-align: center;">where k is the second derivative of E with respect to x.</div> <br>Therefore, if the Hessian matrix and subsequently second derivative of E is positive, the vibrational frequencies must all be positive at a minimum. For a TS, the PES is a maximum along the reaction path and a minimum in all other perpendicular directions. Therefore, a TS is characterised by a negative second derivative of E with respect to x in one dimension, and thus one negative Hessian eigenvalue. Since the minimum has a positive second derivative along all dimensions, the curvature at a minimum is positive. The transition state is the maximum point along the reaction path and therefore has negative curvature along the reaction path.<sup>3</sup>

==Exercise 1: Reaction of Butadiene with Ethylene==

===Reaction Scheme===
Butadiene reacts with Ethylene in a concerted, suprafacial [4+2] cycloaddition according to the mechanism shown in Figure 3.
[[File:Spk15 Reaction Scheme mechanism2.PNG|centre|frame|Figure 3: Mechanism of the reaction of butadiene with ethylene]]

===Trans-butadiene===
For this [4=2] cycloaddition, butadiene has to be in a cis conformation. However, butadiene usually exists as a more stable trans-isomer. (96% of the time butadiene is in the trans conformation).<sup>4</sup> The reaction energy for the conversion from trans to cis-butadiene is +4.16 kj/mol<sup>-1</sup> at the PM6 level.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Trans-butadiene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 12; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRANSBUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! Ethylene !! TS !! Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26; mo 12; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE2 MIN PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE MIN PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 16; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TS TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 48; mo 16; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>PRODUCT2 MIN PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-

===MO Analysis of reaction===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! MO diagram for the formation of the Butadiene/Ethylene transition state !! Ethylene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE2 MIN PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Butadiene||rowspan="2"|[[File:SPK15 EX1MO diagram2.png|thumb|centre|700px]] || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE MIN PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Ethylene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE2 MIN PM6.LOG</uploadedFileContents>
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</jmol> HOMO of Butadiene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE MIN PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Ethylene
|}

In this normal electron demand [4+2] Diels-Alder reaction, the diene (butadiene) is more electron rich than the dienophile (ethylene) since it has more pi electrons due to one more double bond. Hence, butadiene has orbitals that are higher in energy than the orbitals of ethylene. The major interaction is between the antisymmetric LUMO of ethylene and HOMO of butadiene since they are closest in energy. The bonding interaction between these two frontier molecular orbitals produces MO1. The transition state HOMO, MO2 is the bonding interaction between the symmetric LUMO of butadiene and HOMO of ethylene. MO3 is the antibonding pair of MO2, formed from the antibonding interaction between the LUMO of butadiene and HOMO of ethylene. It is only slightly higher in energy than the LUMO of butadiene, indicating it is only destabilised by a small amount. Finally, MO4 is formed by the bonding interaction between the asymmetric highest energy frontier orbital of butadiene and the asymmetric LUMO of ethylene. Due to the close energy of all the frontier molecular orbitals, there is some orbital mixing between the orbital formed by the HOMO of butadiene and LUMO of ethylene and this high energy butadiene orbital.<sup>5</sup>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|+ MOs 1-4 of the transition state
! [[File:Spk15 ex1 MO1.PNG]] !! [[File:Spk15 ex1 MO2.PNG]] !! [[File:Spk15 ex1 MO3.PNG]] !!
[[File:Spk15 exercise1 Mo4.PNG]]
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 16; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TS TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 17; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TS TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
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<script>frame 38; mo 18; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TS TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 19; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TS TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

===Woodward-Hoffmann Rules and Orbital Symmetry===
A reaction is 'allowed' thermally when the total number of [4q+2]<sub>s</sub> + [4r]<sub>a</sub> components is odd. In this reaction, the orbitals interact with orbitals of the same symmetry (symmetric with symmetric or asymmetric with asymmetric) so all the components are suprafacial since the new bonds form on the same face at both ends of the component.
[[File:Woodward Hoffmann.png|frame|centre|In this reaction, there is 1 [4q+2]<sub>s</sub> component and 0 [4r]<sub>a</sub> components so the reaction is allowed]]

<div style="text-align: center;"><u>Orbital overlap integral</u></div>
<div style="text-align: center;">Symmetric-Antisymmetric: Zero</div>
<div style="text-align: center;">Symmetric-Symmetric: Non-zero</div>
<div style="text-align: center;">Antisymmetric-Antisymmetric: Non-Zero</div>

===Bond length analysis of the reaction===

[[File:Spk15 bondlengths2.PNG|frame|centre|Bond lengths for reactants, transition state and product]]
[[File:Spk15 IRCplot.png|frame|centre|Changes in bond length throughout the reaction]]

<br>As the reaction proceeds, the carbon centres change from sp<sup>3</sup> to sp<sup>2</sup> hybridised or vice versa. The typical bond lengths based on the hybridisation of the carbon centre is shown below in Figure 4. The carbon-numbering is shown in Figure 5.

[[File:Typical_bond_lengths.PNG|frame|left|Figure 4: Typical carbon-carbon bond lengths]][[File:Spk15 carbonnumbering.PNG|frame|right|Figure 5: Carbon-numbering]]
The largest change in bond length is between C1-C2 and C3-C4 where the new sigma bonds are formed. The bond lengths decrease from 3.41A (too far for any bonding interaction so implies different molecules) to 1.54A, which is typical of a sp<sup>3</sup>-sp<sup>3</sup> single bond. At the same time, the C5-C6 bond length decreases from 1.47A to 1.34A (which is the typical bond length of a C=C). The C1-C6 and C4-C5 double bonds increase in length from 1.34A to 1.50A. This is exactly the typical sp<sup>3</sup>-sp<sup>2</sup> bond length and shows the change from a double to single bond. In the TS, the partly formed C-C bonds have a bond length of 2.11A, which is in between the combined VDW radius of the 2 C atoms (1.70A x 2 = 3.40A) and the typical sp<sup>3</sup>-sp<sup>3</sup> single bond length (1.54A).

===Vibration corresponding to the reaction path at the transition state===

[[File:TSvibration.gif|frame|centre|Vibration corresponding to the imaginary frequency of the transition state]]

The formation of the two bonds is synchronous. The movement of the bonds at the transition state show that C2 approaches C1 at the same time as C3 approaches C4, and the two sigma bonds form simultaneously. This implies that the bonds form at the same time, and possibly but not necessarily at the same rate.

==Link to Exercise 2==
https://wiki.ch.ic.ac.uk/wiki/index.php?title=MOD:spk15TSEx2

==Link to Exercise 3==
https://wiki.ch.ic.ac.uk/wiki/index.php?title=MOD:spk15TSEx3

==Conclusion==

The focus of this computational lab was on locating transition structures for a series of reactions and abstracting information about the reaction.Two electronic structure methods were employed: the semi-empirical method PM6 and the Density Functional Theory (DFT) method B3LYP to optimise the structures while IRCs were run on the transition state to confirm they connected the reactants and products along the lowest energy pathway. The symmetry requirements according to the Woodward-Hoffmann Rules for cycloadditions were explored along with the 2 types of Diels-Alder reaction- normal electron demand and inverse electron demand. The relative energy levels of the frontier molecular orbitals were examined and the HOMO of the dienophile was found to be higher than that of diene in an inverse electron demand reaction while the opposite was true for a normal electron demand reaction. However, this was found not to affect the relative energy levels of the transition state. The thermochemistry of the reactions was also studied and it was found that secondary orbital interactions could lower the energy of transition states, making a product more kinetically favourable. In a reversible reaction, steric hindrance can also determine the relative thermodynamic stability of a product.

==References==
1. Potential Energy Surface - Chemistry LibreTexts.
<br>2. Schlegel, H. B. (2011). Geometry optimization, 1(October), 790–809.
<br>3. Ot, W. J. (1990). Computational quantum chemistry. Journal of Molecular Structure: THEOCHEM (Vol. 207).
<br>4. Butadiene: A Molecular Mechanics Study.
<br>5. Fleming, Ian (1978). Frontier Orbitals and Organic Chemical Reactions.
<br>6. Progress in Heterocyclic Chemistry, Volume 28, 1st Edition.
<br>7. Ho, G. M., Huang, C. J., Li, E. Y. T., Hsu, S. K., Wu, T., Zulueta, M. M. L., … Hung, S. C. (2016). Unconventional exo selectivity in thermal normal-electron-demand Diels-Alder reactions. Scientific Reports, 6(October), 1–10.
<br>8. Secondary orbital interactions determining regioselectivity in the Diels-Alder reaction. Peter V. Alston, Raphael M. Ottenbrite, and Theodore Cohen, The Journal of Organic Chemistry 1978 43 (10), 1864-1867
<br>9. Wiley, 1985. Advanced Organic Chemistry: Reactions, Mechanisms, and Structure.

2018-01-28T18:42:21Z

Spk15: /* Introduction */

==Introduction==

===What is a potential energy surface?===
The potential energy surface (PES) describes how the energy of a system in a particular state changes with the structure of the molecule. A simple representation of the potential energy surface is shown in Figure 1, in which the potential energy of the system is given by the vertical coordinates and two geometric variables are given by the horizontal coordinates. Although most molecules have more than two geometric variables, most of the key features of a PES can be represented in such a landscape.

[[File:Model PES.gif|frame|centre|Figure 1: Model PES ]]

===What are a minimum and transition state?===
A minimum in the potential energy surface represents the equilibrium structure of the reactants, products or intermediates. The lowest energy pathway between the reactant minimum and the product minimum is the reaction path. The highest point on the lowest energy reaction path is the transition state (TS) for the reaction. A TS is a maximum in one direction (the direction connecting reactant and product along the reaction path) but is a minimum in all other directions perpendicular to the reaction path, making it first-order saddle point. The potential energy surface around a transition state is shown more clearly in Figure 2, where the point A is a maximum along the θ direction but a minimum in the R direction.

[[File:Spk15 transitionstatePES.PNG|thumb|centre|frame|Figure 2: Potential energy surface around a transition state]]

===How do energy derivatives vary between minimum and transition states?===
The first and second derivatives of the energy (E) with respect to geometrical parameters (x) can be used to confirm the character of minima and TSs. The matrix of the first derivative is given by the gradient of the PES. Both a minimum and TS are characterised by having a zero gradient on the PES. Since the negative of the gradient is the vector of forces on the atoms in the molecule, the minimum and TSs both have zero forces acting on them and are also termed stationary points.<br>What distinguishes a minimum and a transition state is the curvature of the potential energy surface around the stationary point which is given by the force constant (second derivative) matrix.The matrix of second derivatives of the energy is known as the Hessian. The eigenvectors of the Hessian correspond to the normal modes of vibration (plus 5 or 6 modes for translation and rotation). For a structure to be classified as a minimum, the gradient must be zero and all the eigenvalues of the Hessian must be positive. Using the model for a diatomic molecule, the vibrational freqency is given by <br>[[File:Spk15 ex1equation.PNG|frame|centre]]<div style="text-align: center;">where k is the second derivative of E with respect to x.</div> <br>Therefore, if the Hessian matrix and subsequently second derivative of E is positive, the vibrational frequencies must all be positive at a minimum. For a TS, the PES is a maximum along the reaction path and a minimum in all other perpendicular directions. Therefore, a TS is characterised by a negative second derivative of E with respect to x in one dimension, and thus one negative Hessian eigenvalue. Since the minimum has a positive second derivative along all dimensions, the curvature at a minimum is positive. The transition state is the maximum point along the reaction path and therefore has negative curvature along the reaction path.

<u>Reference:</u>
<br>Schlegel, H. B. (2011). Geometry optimization, 1(October), 790–809.
<br>Ot, W. J. (1990). Computational quantum chemistry. Journal of Molecular Structure: THEOCHEM (Vol. 207). http://doi.org/10.1016/0166-1280(90)85035-L

==Exercise 1: Reaction of Butadiene with Ethylene==

===Reaction Scheme===
Butadiene reacts with Ethylene in a concerted, suprafacial [4+2] cycloaddition according to the mechanism shown below.
[[File:Spk15 Reaction Scheme mechanism2.PNG|centre|frame|Mechanism of the reaction of butadiene with ethylene]]

===Trans-butadiene===
For this [4=2] cycloaddition, butadiene has to be in a cis conformation. However, butadiene usually exists as a more stable trans-isomer. (98% of the time butadiene is in the trans conformation). The reaction energy for the conversion from trans to cis-butadiene is +4.16 kj/mol<sup>-1</sup>.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Trans-butadiene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 12; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRANSBUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! Ethylene !! TS !! Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26; mo 12; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE2 MIN PM6.LOG</uploadedFileContents>
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</jmol> || <jmol>
<jmolApplet>
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<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE MIN PM6.LOG</uploadedFileContents>
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</jmol> || <jmol>
<jmolApplet>
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<script>frame 38; mo 16; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TS TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 48; mo 16; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>PRODUCT2 MIN PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-

===MO Analysis of the Reaction===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! MO diagram for the formation of the Butadiene/Ethylene transition state !! Ethylene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE2 MIN PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Butadiene||rowspan="2"|[[File:SPK15 EX1MO diagram2.png|thumb|centre|700px]] || <jmol>
<jmolApplet>
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</jmol> LUMO of Ethylene
|-
| <jmol>
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<uploadedFileContents>BUTADIENE2 MIN PM6.LOG</uploadedFileContents>
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</jmol> HOMO of Butadiene|| <jmol>
<jmolApplet>
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</jmol> HOMO of Ethylene
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In this normal electron demand [4+2] Diels-Alder reaction, the diene (butadiene) is more electron rich than the dienophile (ethylene) since it has more pi electrons due to one more double bond. Hence, butadiene has orbitals that are higher in energy than the orbitals of ethylene. The major interaction is between the antisymmetric LUMO of ethylene and HOMO of butadiene since they are closest in energy. The bonding interaction between these two frontier molecular orbitals produces MO1. The transition state HOMO, MO2 is the bonding interaction between the symmetric LUMO of butadiene and HOMO of ethylene. MO3 is the antibonding pair of MO2, formed from the antibonding interaction between the LUMO of butadiene and HOMO of ethylene. It is only slightly higher in energy than the LUMO of butadiene, indicating it is only destabilised by a small amount. Finally, MO4 is formed by the bonding interaction between the asymmetric highest energy frontier orbital of butadiene and the asymmetric LUMO of ethylene. Due to the close energy of all the frontier molecular orbitals, there is some orbital mixing between the orbital formed by the HOMO of butadiene and LUMO of ethylene and this high energy butadiene orbital.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|+ MOs 1-4 of the transition state
! [[File:Spk15 ex1 MO1.PNG]] !! [[File:Spk15 ex1 MO2.PNG]] !! [[File:Spk15 ex1 MO3.PNG]] !!
[[File:Spk15 exercise1 Mo4.PNG]]
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
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<uploadedFileContents>TS TSPM6.LOG</uploadedFileContents>
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</jmol> || <jmol>
<jmolApplet>
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</jmol> || <jmol>
<jmolApplet>
<color>white</color>
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<script>frame 38; mo 19; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TS TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

===Woodward-Hoffmann Rules and Orbital Symmetry===
A reaction is 'allowed' thermally when the total number of [4q+2]<sub>s</sub> + [4r]<sub>a</sub> components is odd. In this reaction, the orbitals interact with orbitals of the same symmetry (symmetric or asymmetric) so all the components are suprafacial since the new bonds form on the same face at both ends of the component.
[[File:Woodward Hoffmann.png|frame|centre|In this reaction, there is 1 [4q+2]<sub>s</sub> component and 0 [4r]<sub>a</sub> components so the reaction is allowed]]

<div style="text-align: center;"><u>Orbital overlap integral</u></div>
<div style="text-align: center;">Symmetric-Antisymmetric: Zero</div>
<div style="text-align: center;">Symmetric-Symmetric: Non-zero</div>
<div style="text-align: center;">Antisymmetric-Antisymmetric: Non-Zero</div>

===Bond length analysis of the reaction===

[[File:Spk15 bondlengths2.PNG|frame|centre|Bond lengths for reactants, transition state and product]]
[[File:Spk15 IRCplot.png|frame|centre|Changes in bond length throughout the reaction]]

<br>As the reaction proceeds, the carbon centres change from sp<sup>3</sup> to sp<sup>2</sup> hybridised or vice versa. The typical bond lengths based on the hybridisation of the carbon centre is shown below.

[[File:Typical_bond_lengths.PNG|frame|centre|Typical carbon-carbon bond lengths]]
The largest change in bond length is between C1-C2 and C3-C4 where the new sigma bonds are formed. The bond lengths decrease from 3.41A (too far for any bonding interaction so implies different molecules) to 1.54A, which is typical of a sp<sup>3</sup>-sp<sup>3</sup> single bond. At the same time, the C5-C6 bond length decreases from 1.47A to 1.34A (which is the typical bond length of a C=C). The C1-C6 and C4-C5 double bonds increase in length from 1.34A to 1.50A. This is exactly the typical sp<sup>3</sup>-sp<sup>2</sup> bond length and shows the change from a double to single bond. In the TS, the partly formed C-C bonds have a bond length of 2.11A, which is in between the combined VDW radius of the 2 C atoms (1.70A x 2 = 3.40A) and the typical sp<sup>3</sup>-sp<sup>3</sup> single bond length (1.54A).

===Vibration corresponding to the reaction path at the transition state===

[[File:TSvibration.gif|frame|centre|Vibration corresponding to the imaginary frequency of the transition state]]

The formation of the two bonds is synchronous. The movement of the bonds at the transition state show that C2 approaches C1 at the same time as C3 approaches C4, and the two sigma bonds form simultaneously. This implies that the bonds form at the same time, and possibly but not necessarily at the same rate.

==Link to Exercise 2==
https://wiki.ch.ic.ac.uk/wiki/index.php?title=MOD:spk15TSEx2

==Link to Exercise 3==
https://wiki.ch.ic.ac.uk/wiki/index.php?title=MOD:spk15TSEx3

==Conclusion==

This computational lab

File:Spk15 ex1equation.PNG

2018-01-28T18:29:26Z

Spk15:

Rep:MOD:spk15TS

2018-01-28T18:21:58Z

Spk15: /* What are a minimum and transition state? */

==Introduction==

===What is a potential energy surface?===
The potential energy surface (PES) describes how the energy of a system in a particular state changes with the structure of the molecule. A simple representation of the potential energy surface is shown in Figure 1, in which the potential energy of the system is given by the vertical coordinates and two geometric variables are given by the horizontal coordinates. Although most molecules have more than two geometric variables, most of the key features of a PES can be represented in such a landscape.

[[File:Model PES.gif|frame|centre|Figure 1: Model PES ]]

===What are a minimum and transition state?===
A minimum in the potential energy surface represents the equilibrium structure of the reactants, products or intermediates. The lowest energy pathway between the reactant minimum and the product minimum is the reaction path. The highest point on the lowest energy reaction path is the transition state (TS) for the reaction. A TS is a maximum in one direction (the direction connecting reactant and product along the reaction path) but is a minimum in all other directions perpendicular to the reaction path, making it first-order saddle point. The potential energy surface around a transition state is shown more clearly in Figure 2, where the point A is a maximum along the θ direction but a minimum in the R direction.

[[File:Spk15 transitionstatePES.PNG|thumb|centre|frame|Figure 2: Potential energy surface around a transition state]]

===How do energy derivatives vary between minimum and transition states?===
The first and second derivatives of the energy (E) with respect to geometrical parameters (x) can be used to confirm the character of minima and TSs. The matrix of the first derivative is given by the gradient of the PES. Both a minimum and TS are characterised by having a zero gradient on the PES. Since the negative of the gradient is the vector of forces on the atoms in the molecule, the minimum and TSs both have zero forces acting on them and are also termed stationary points. <br>The matrix of second derivatives of the energy is known as the Hessian. The eigenvectors of the Hessian correspond to the normal modes of vibration (plus 5 or 6 modes for translation and rotation). For a structure to be classified as a minimum, the gradient must be zero and all the eigenvalues of the Hessian must be positive. Since the vibrational frequencies are proportional to the square root of the eigenvalues of the mass-weighted Hessian, the vibrational frequencies must therefore all be positive at a minimum. For a TS, the PES is a maximum along the reaction path and a minimum in all other perpendicular direction. Therefore, a TS is characterized by a zero gradient and a Hessian that has one negative eigenvalue which results in one imaginary vibrational frequency in a TS. Since the minimum is a minimum in all direction, the curvature at a minimum is positive. The transition state is the maximum point along the reaction path and therefore has negative curvature.

<u>Reference:</u>
<br>Schlegel, H. B. (2011). Geometry optimization, 1(October), 790–809.

==Exercise 1: Reaction of Butadiene with Ethylene==

===Reaction Scheme===
Butadiene reacts with Ethylene in a concerted, suprafacial [4+2] cycloaddition according to the mechanism shown below.
[[File:Spk15 Reaction Scheme mechanism2.PNG|centre|frame|Mechanism of the reaction of butadiene with ethylene]]

===Trans-butadiene===
For this [4=2] cycloaddition, butadiene has to be in a cis conformation. However, butadiene usually exists as a more stable trans-isomer. (98% of the time butadiene is in the trans conformation). The reaction energy for the conversion from trans to cis-butadiene is +4.16 kj/mol<sup>-1</sup>.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Trans-butadiene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 12; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRANSBUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! Ethylene !! TS !! Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26; mo 12; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE2 MIN PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE MIN PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 16; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TS TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 48; mo 16; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>PRODUCT2 MIN PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-

===MO Analysis of the Reaction===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Butadiene !! MO diagram for the formation of the Butadiene/Ethylene transition state !! Ethylene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE2 MIN PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Butadiene||rowspan="2"|[[File:SPK15 EX1MO diagram2.png|thumb|centre|700px]] || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE MIN PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Ethylene
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 26; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE2 MIN PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Butadiene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE MIN PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Ethylene
|}

In this normal electron demand [4+2] Diels-Alder reaction, the diene (butadiene) is more electron rich than the dienophile (ethylene) since it has more pi electrons due to one more double bond. Hence, butadiene has orbitals that are higher in energy than the orbitals of ethylene. The major interaction is between the antisymmetric LUMO of ethylene and HOMO of butadiene since they are closest in energy. The bonding interaction between these two frontier molecular orbitals produces MO1. The transition state HOMO, MO2 is the bonding interaction between the symmetric LUMO of butadiene and HOMO of ethylene. MO3 is the antibonding pair of MO2, formed from the antibonding interaction between the LUMO of butadiene and HOMO of ethylene. It is only slightly higher in energy than the LUMO of butadiene, indicating it is only destabilised by a small amount. Finally, MO4 is formed by the bonding interaction between the asymmetric highest energy frontier orbital of butadiene and the asymmetric LUMO of ethylene. Due to the close energy of all the frontier molecular orbitals, there is some orbital mixing between the orbital formed by the HOMO of butadiene and LUMO of ethylene and this high energy butadiene orbital.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|+ MOs 1-4 of the transition state
! [[File:Spk15 ex1 MO1.PNG]] !! [[File:Spk15 ex1 MO2.PNG]] !! [[File:Spk15 ex1 MO3.PNG]] !!
[[File:Spk15 exercise1 Mo4.PNG]]
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 16; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TS TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 17; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TS TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 18; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TS TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 38; mo 19; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TS TSPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

===Woodward-Hoffmann Rules and Orbital Symmetry===
A reaction is 'allowed' thermally when the total number of [4q+2]<sub>s</sub> + [4r]<sub>a</sub> components is odd. In this reaction, the orbitals interact with orbitals of the same symmetry (symmetric or asymmetric) so all the components are suprafacial since the new bonds form on the same face at both ends of the component.
[[File:Woodward Hoffmann.png|frame|centre|In this reaction, there is 1 [4q+2]<sub>s</sub> component and 0 [4r]<sub>a</sub> components so the reaction is allowed]]

<div style="text-align: center;"><u>Orbital overlap integral</u></div>
<div style="text-align: center;">Symmetric-Antisymmetric: Zero</div>
<div style="text-align: center;">Symmetric-Symmetric: Non-zero</div>
<div style="text-align: center;">Antisymmetric-Antisymmetric: Non-Zero</div>

===Bond length analysis of the reaction===

[[File:Spk15 bondlengths2.PNG|frame|centre|Bond lengths for reactants, transition state and product]]
[[File:Spk15 IRCplot.png|frame|centre|Changes in bond length throughout the reaction]]

<br>As the reaction proceeds, the carbon centres change from sp<sup>3</sup> to sp<sup>2</sup> hybridised or vice versa. The typical bond lengths based on the hybridisation of the carbon centre is shown below.

[[File:Typical_bond_lengths.PNG|frame|centre|Typical carbon-carbon bond lengths]]
The largest change in bond length is between C1-C2 and C3-C4 where the new sigma bonds are formed. The bond lengths decrease from 3.41A (too far for any bonding interaction so implies different molecules) to 1.54A, which is typical of a sp<sup>3</sup>-sp<sup>3</sup> single bond. At the same time, the C5-C6 bond length decreases from 1.47A to 1.34A (which is the typical bond length of a C=C). The C1-C6 and C4-C5 double bonds increase in length from 1.34A to 1.50A. This is exactly the typical sp<sup>3</sup>-sp<sup>2</sup> bond length and shows the change from a double to single bond. In the TS, the partly formed C-C bonds have a bond length of 2.11A, which is in between the combined VDW radius of the 2 C atoms (1.70A x 2 = 3.40A) and the typical sp<sup>3</sup>-sp<sup>3</sup> single bond length (1.54A).

===Vibration corresponding to the reaction path at the transition state===

[[File:TSvibration.gif|frame|centre|Vibration corresponding to the imaginary frequency of the transition state]]

The formation of the two bonds is synchronous. The movement of the bonds at the transition state show that C2 approaches C1 at the same time as C3 approaches C4, and the two sigma bonds form simultaneously. This implies that the bonds form at the same time, and possibly but not necessarily at the same rate.

==Link to Exercise 2==
https://wiki.ch.ic.ac.uk/wiki/index.php?title=MOD:spk15TSEx2

==Link to Exercise 3==
https://wiki.ch.ic.ac.uk/wiki/index.php?title=MOD:spk15TSEx3

==Conclusion==

This computational lab

File:Spk15 transitionstatePES.PNG

2018-01-28T18:20:57Z

Spk15:

File:Spk15 normal.PNG

2018-01-28T17:43:43Z

Spk15: Spk15 uploaded a new version of File:Spk15 normal.PNG

Rep:MOD:spk15TSEx2

2018-01-28T17:39:21Z

Spk15: /* MO Analysis of Reaction */

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

===Reaction Scheme===
Cyclohexadiene reacts with Dioxole in a concerted, suprafacial [4+2] cycloaddition according to the mechanism shown below to form two products- the exo and endo products.
[[File:Spk15 ex2Reaction Scheme3.png|thumb|frame|centre|600px|Mechanism of reaction between cyclohexadiene and 1,3-dioxole]]

===Jmol Files===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Reactants !! Transition States !! Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXADIENE2_631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Cyclohexadiene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS FREQ 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Exo TS|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO PDT FREQ 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Exo product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIOXOLE2 631GD.LOG </uploadedFileContents>
</jmolApplet>
</jmol><br>Dioxole || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDOTS FREQ 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Endo TS|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO PDT FREQ 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol><br>Endo product
|-
|}

===Single Point Energy Calculation===
In order to determine if the reaction between cyclohexadiene and 1,3-dioxole proceeded via normal or inverse electron demand, the relative levels of the HOMO and LUMO of the reactants were compared by performing a single point energy calculation. This allowed the reactants to be studied on the same potential energy surface and the energies of their MOs to be compared more accurately. In this reaction, the HOMO of 1,3-dioxole, the dienophile, was found to be higher than the HOMO of cyclohexadiene, the diene, as shown below. This indicates the reaction proceeds via inverse electron demand.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Cyclohexadiene !! Relative Energies of the HOMO and LUMO of the Reactants !! 1,3-Dioxole
|-
|<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>REACTANTS ENDO SP.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Cyclohexadiene||rowspan="2"|[[File:Individual Reactant MOs.PNG]] || <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>REACTANTS ENDO SP.LOG</uploadedFileContents>
</jmolApplet>
</jmol> 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>REACTANTS ENDO SP.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Cyclohexadiene|| <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>REACTANTS ENDO SP.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of 1,3-Dioxole
|}

===MO Analysis of Reaction===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|+ Occupied and Unoccupied Orbitals of the TS
! !! Occupied Orbital !! HOMO !! LUMO !! Unoccupied Orbital
|-
| colspan="1"|Exo || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS FREQ 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS FREQ 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS FREQ 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS FREQ 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| colspan="1"|Endo || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS FREQ 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS FREQ 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS FREQ 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS FREQ 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! Cyclohexadiene !! MO diagram for the formation of the Cyclohexadienediene/1,3-Dioxole transition state !! 1,3-Dioxole
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXADIENE2 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of Cyclohexadiene||rowspan="2"|[[File:Spk15 ex2MOdiagram.png|thumb|centre|700px]] || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIOXOLE2 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol> LUMO of 1,3-Dioxole
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXADIENE2 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of Cyclohexadiene|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIOXOLE2 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol> HOMO of 1,3-Dioxole
|}

In this inverse electron demand [4+2] cycloaddition reaction, the 1,3-dioxole acts as a electron rich dienophile since the oxygen atoms can donate their lone pair of electrons into the pi system of the double bond. Hence, the HOMO of the 1,3-dioxole is raised higher than the HOMO of the dienophile and is high enough in energy to interact with the LUMO of the diene (cylohexadiene). MO1 and MO4 are a bonding/antibonding pair formed from the overlap of the HOMO of cyclohexadiene and the LUMO of the 1,3-dioxole. MO2 and MO3 are another bonding/antibonding pair formed from the overlap of the HOMO of the 1,3-dioxole and the LUMO of cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|+ Comparing a normal and inverse electron demand [4+2] cycloaddition
! Normal
! Inverse
|-
| [[File:Spk15 normal.PNG|thumb|500px]]
| [[File:Spk15 inverse.PNG|thumb|500px]]
|}

===Reaction Dynamics===
[[File:Spk15 absoluteenergies.PNG|centre|frame|Absolute Energies of reactants, transition states and products]]
<br> <div style="text-align: center;">Reaction Energy = Energy of Products - Energy of Reactants</div>
<br> <div style="text-align: center;">Reaction Barrier = Energy of Transition State - Energy of Reactants</div>

[[File:Spk15 ex2reactionprofile3.png|thumb|frame|centre|600px|Reaction profile diagram]]
<br>According to the reaction profile shown above, the endo product is both kinetically and thermodynamically favoured. The endo activation energy is lower than the exo activation energy which means that the reactants will form the endo transition state faster than the exo transition state. The endo transition state is lower in energy than the exo transition state since there are secondary orbital interactions between the butadiene pi orbitals and the p orbitals of the oxygen atoms which is discussed more below. This lowers the energy of the endo transition state. The endo Diels-Alder product is also lower in energy than the exo product which indicates that the endo product is more stable and hence thermodynamically favoured. The endo product is lower in energy as there is greater steric clash in the exo product between the CH<sub>2</sub> hydrogens and the oxygen atoms as shown below. On the other hand, in the endo product with the dioxole in an axial position, there is much less steric clash between the CH<sub>2</sub> hydrogens and the other hydrogen atoms since hydrogen has a much smaller VDW radius than oxygen. Furthermore, the endo product is more thermodynamically preferred as the former 1,3-Dioxole component is anti to the carbon bridge group rather than gauche in the exo product. There is reduced steric hindrance in the molecule as the two larger groups are anti to one another. This is shown in the Newman projection below.
[[File:Spk15 endoexostericclash.png|thumb|frame|centre|600px|Steric clash in exo and endo products]][[File:Screen Shot 2018-01-27 at 18.12.33.png|thumb|centre|600px|Newman projection of endo and exo products viewed along the bolded line]]

===Secondary Orbital Interactions===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: 1;"
|-
! HOMO of Exo TS !! HOMO of Endo TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS FREQ 631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo cutoff 0.01; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDOTS TS631GD.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<br>In the endo transition state, there are secondary orbital interactions between the p-orbitals of the butadiene and the non-bonding p-orbitals of the oxygen atoms in dioxole, lowering its energy and making the reaction towards the endo-product faster and more kinetically favourable. This is shown more clearly in the diagram below.
[[File: Spk15secondaryorbitalinteractions.png|thumb|frame|centre|600px|Possibility of secondary orbital interactions]]

File:Spk15 inverse.PNG

2018-01-28T17:34:47Z

Spk15:

File:Spk15 normal.PNG

2018-01-28T17:34:38Z

Spk15: