ChemWiki - User contributions [en]

Rep:Mod:ydf2715ts

2017-12-20T10:39:30Z

Yf2715: /* Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model. <ref>E. G. Lewars, Computational Chemistry, 2010, 9–43</ref>

[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant. <ref>D. L. Pavia, G. M. Lampman, G. S. Kriz and J. R. Vyvyan, Introduction to spectroscopy, Cengage Learning, Australia, 2015.</ref>]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions. <ref>P. J. Atkins, J. D. Paula and J. Keeler, Atkins Physical Chemistry, Oxford Univ. Press, Oxford, 2017.</ref>

 
 

===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
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<color>white</color>
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<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
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<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
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<uploadedFileContents>TTS4.LOG</uploadedFileContents>
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| <jmol>
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<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
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====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Figure 4. Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).<ref>P. Geerlings, P. W. Ayers, A. Toro-Labbé, P. K. Chattaraj and F. D. Proft, Accounts of Chemical Research, 2012, 45, 683–695</ref>
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral
Therefore, with only the MOs with the same symmetry combining together, the reaction between 1,3-butadiene and ethylene is thermally allowed.

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length <ref>E. M. Popov, G. A. Kogan and V. N. Zheltova, Theoretical and Experimental Chemistry, 1972, 6, 11–19.</ref>
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new σ bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional π overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 5. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 6. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 7. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 8. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui<ref>K. Fukui, Frontier Orbitals and Reaction Paths World Scientific Series in 20th Century Chemistry, 1997, 150–170.</ref>, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated π systems in the reaction.<ref>K. N. Houk, Accounts of Chemical Research, 1975, 8, 361–369.</ref> In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration results====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
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<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
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|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 9. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 10. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
====MO diagrams and HOMO-LUMO orbitals====
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 12. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction.<ref>K. Yang, Z. Yang, Q. Dang and X. Bai, European Journal of Organic Chemistry, 2015, 2015, 4344–4347.</ref> 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.<ref>Organic Chemistry, Springer Verlag, 2014.</ref>
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 14. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 

===Conclusion===
In this experiment, a variety of pericyclic reactions were located and their transition structures are characterized. Molecular orbital-based methods were used to numerically solving the Schrödinger equation and locate the transition structures based on the local shape of a potential energy surface. The reaction coordinates, reaction energies and activation barrier heights were also calculated. The roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction was also discussed.
 For the concerted cycloaddtion reaction between 1,3-butadiene and ethylene, the bond formation is synchronous as the two carbons in each pair move towards each other at the same rate. It was also confirmed that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. In exercise 2, the reaction between cyclohexadiene and 1,3-dioxole has an inverse electron demand. From the energy analysis, the endo pathway was proved to be more kinetically and thermodynamically favoured as a result of secondary orbital interactions. In exercise 3, there are three different reaction pathways for xylylene and sulfur dioxide, the endo/exo Diels - Ader reaction and the Cheletropic reaction. From the energy analysis, the endo product was proved to be more kinetically favoured and the cheletropic product was more thermodynamically favoured. A reaction profile was used to help read the reaction more directly.
 
 
===Reference===
<references />
 
 

===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state : [[File:Yf 1 TSIRC.LOG]]

====Exercise 2====
{| class="wikitable"
|+ Table 15. Links to the log files in exercise 2
! rowspan="2" style="center; background: #14866d; color: white;" | Chemicals
! colspan="2" style="center; background: #14866d; color: white;" | Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

====Exercise 3====

{| class="wikitable"
|+ Table 16. Links to the log file of IRC calculations at PM6 level
! colspan="2" style="text-align: center;background: #14866d; color: white;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;background: #14866d; color: white;" | Cheletropic Reaction
|-
| style="text-align: center;background: #14866d; color: white;" | Exo-pathway
| style="text-align: center;background: #14866d; color: white;" | Endo-pathway
|-
| [[File:YfEXOIRC.LOG]]
| [[File:YfENDOIRC.LOG]]
| [[File:YfCHEIRC.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-20T10:38:53Z

Yf2715: /* Bond length Analysis */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model. <ref>E. G. Lewars, Computational Chemistry, 2010, 9–43</ref>

[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant. <ref>D. L. Pavia, G. M. Lampman, G. S. Kriz and J. R. Vyvyan, Introduction to spectroscopy, Cengage Learning, Australia, 2015.</ref>]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions. <ref>P. J. Atkins, J. D. Paula and J. Keeler, Atkins Physical Chemistry, Oxford Univ. Press, Oxford, 2017.</ref>

 
 

===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>TTS4.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Figure 4. Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).<ref>P. Geerlings, P. W. Ayers, A. Toro-Labbé, P. K. Chattaraj and F. D. Proft, Accounts of Chemical Research, 2012, 45, 683–695</ref>
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral
Therefore, with only the MOs with the same symmetry combining together, the reaction between 1,3-butadiene and ethylene is thermally allowed.

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length <ref>E. M. Popov, G. A. Kogan and V. N. Zheltova, Theoretical and Experimental Chemistry, 1972, 6, 11–19.</ref>
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new σ bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional π overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 5. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 6. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 7. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 8. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui<ref>K. Fukui, Frontier Orbitals and Reaction Paths World Scientific Series in 20th Century Chemistry, 1997, 150–170.</ref>, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction.<ref>K. N. Houk, Accounts of Chemical Research, 1975, 8, 361–369.</ref> In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration results====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 9. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 10. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
====MO diagrams and HOMO-LUMO orbitals====
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 12. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction.<ref>K. Yang, Z. Yang, Q. Dang and X. Bai, European Journal of Organic Chemistry, 2015, 2015, 4344–4347.</ref> 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.<ref>Organic Chemistry, Springer Verlag, 2014.</ref>
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 14. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 

===Conclusion===
In this experiment, a variety of pericyclic reactions were located and their transition structures are characterized. Molecular orbital-based methods were used to numerically solving the Schrödinger equation and locate the transition structures based on the local shape of a potential energy surface. The reaction coordinates, reaction energies and activation barrier heights were also calculated. The roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction was also discussed.
 For the concerted cycloaddtion reaction between 1,3-butadiene and ethylene, the bond formation is synchronous as the two carbons in each pair move towards each other at the same rate. It was also confirmed that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. In exercise 2, the reaction between cyclohexadiene and 1,3-dioxole has an inverse electron demand. From the energy analysis, the endo pathway was proved to be more kinetically and thermodynamically favoured as a result of secondary orbital interactions. In exercise 3, there are three different reaction pathways for xylylene and sulfur dioxide, the endo/exo Diels - Ader reaction and the Cheletropic reaction. From the energy analysis, the endo product was proved to be more kinetically favoured and the cheletropic product was more thermodynamically favoured. A reaction profile was used to help read the reaction more directly.
 
 
===Reference===
<references />
 
 

===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state : [[File:Yf 1 TSIRC.LOG]]

====Exercise 2====
{| class="wikitable"
|+ Table 15. Links to the log files in exercise 2
! rowspan="2" style="center; background: #14866d; color: white;" | Chemicals
! colspan="2" style="center; background: #14866d; color: white;" | Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

====Exercise 3====

{| class="wikitable"
|+ Table 16. Links to the log file of IRC calculations at PM6 level
! colspan="2" style="text-align: center;background: #14866d; color: white;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;background: #14866d; color: white;" | Cheletropic Reaction
|-
| style="text-align: center;background: #14866d; color: white;" | Exo-pathway
| style="text-align: center;background: #14866d; color: white;" | Endo-pathway
|-
| [[File:YfEXOIRC.LOG]]
| [[File:YfENDOIRC.LOG]]
| [[File:YfCHEIRC.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-20T10:36:01Z

Yf2715: /* Optimized structures, vibration and MOs */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model. <ref>E. G. Lewars, Computational Chemistry, 2010, 9–43</ref>

[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant. <ref>D. L. Pavia, G. M. Lampman, G. S. Kriz and J. R. Vyvyan, Introduction to spectroscopy, Cengage Learning, Australia, 2015.</ref>]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions. <ref>P. J. Atkins, J. D. Paula and J. Keeler, Atkins Physical Chemistry, Oxford Univ. Press, Oxford, 2017.</ref>

 
 

===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>TTS4.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Figure 4. Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).<ref>P. Geerlings, P. W. Ayers, A. Toro-Labbé, P. K. Chattaraj and F. D. Proft, Accounts of Chemical Research, 2012, 45, 683–695</ref>
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral
Therefore, with only the MOs with the same symmetry combining together, the reaction between 1,3-butadiene and ethylene is thermally allowed.

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length <ref>E. M. Popov, G. A. Kogan and V. N. Zheltova, Theoretical and Experimental Chemistry, 1972, 6, 11–19.</ref>
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 5. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 6. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 7. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 8. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui<ref>K. Fukui, Frontier Orbitals and Reaction Paths World Scientific Series in 20th Century Chemistry, 1997, 150–170.</ref>, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction.<ref>K. N. Houk, Accounts of Chemical Research, 1975, 8, 361–369.</ref> In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration results====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 9. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 10. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
====MO diagrams and HOMO-LUMO orbitals====
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 12. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction.<ref>K. Yang, Z. Yang, Q. Dang and X. Bai, European Journal of Organic Chemistry, 2015, 2015, 4344–4347.</ref> 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.<ref>Organic Chemistry, Springer Verlag, 2014.</ref>
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 14. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 

===Conclusion===
In this experiment, a variety of pericyclic reactions were located and their transition structures are characterized. Molecular orbital-based methods were used to numerically solving the Schrödinger equation and locate the transition structures based on the local shape of a potential energy surface. The reaction coordinates, reaction energies and activation barrier heights were also calculated. The roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction was also discussed.
 For the concerted cycloaddtion reaction between 1,3-butadiene and ethylene, the bond formation is synchronous as the two carbons in each pair move towards each other at the same rate. It was also confirmed that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. In exercise 2, the reaction between cyclohexadiene and 1,3-dioxole has an inverse electron demand. From the energy analysis, the endo pathway was proved to be more kinetically and thermodynamically favoured as a result of secondary orbital interactions. In exercise 3, there are three different reaction pathways for xylylene and sulfur dioxide, the endo/exo Diels - Ader reaction and the Cheletropic reaction. From the energy analysis, the endo product was proved to be more kinetically favoured and the cheletropic product was more thermodynamically favoured. A reaction profile was used to help read the reaction more directly.
 
 
===Reference===
<references />
 
 

===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state : [[File:Yf 1 TSIRC.LOG]]

====Exercise 2====
{| class="wikitable"
|+ Table 15. Links to the log files in exercise 2
! rowspan="2" style="center; background: #14866d; color: white;" | Chemicals
! colspan="2" style="center; background: #14866d; color: white;" | Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

====Exercise 3====

{| class="wikitable"
|+ Table 16. Links to the log file of IRC calculations at PM6 level
! colspan="2" style="text-align: center;background: #14866d; color: white;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;background: #14866d; color: white;" | Cheletropic Reaction
|-
| style="text-align: center;background: #14866d; color: white;" | Exo-pathway
| style="text-align: center;background: #14866d; color: white;" | Endo-pathway
|-
| [[File:YfEXOIRC.LOG]]
| [[File:YfENDOIRC.LOG]]
| [[File:YfCHEIRC.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-20T10:33:30Z

Yf2715: /* Optimized structures */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model. <ref>E. G. Lewars, Computational Chemistry, 2010, 9–43</ref>

[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant. <ref>D. L. Pavia, G. M. Lampman, G. S. Kriz and J. R. Vyvyan, Introduction to spectroscopy, Cengage Learning, Australia, 2015.</ref>]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions. <ref>P. J. Atkins, J. D. Paula and J. Keeler, Atkins Physical Chemistry, Oxford Univ. Press, Oxford, 2017.</ref>

 
 

===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>TTS4.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Figure 4. Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).<ref>P. Geerlings, P. W. Ayers, A. Toro-Labbé, P. K. Chattaraj and F. D. Proft, Accounts of Chemical Research, 2012, 45, 683–695</ref>
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral
Therefore, with only the MOs with the same symmetry combining together, the reaction between 1,3-butadiene and ethylene is thermally allowed.

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length <ref>E. M. Popov, G. A. Kogan and V. N. Zheltova, Theoretical and Experimental Chemistry, 1972, 6, 11–19.</ref>
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 5. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 6. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 7. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 8. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui<ref>K. Fukui, Frontier Orbitals and Reaction Paths World Scientific Series in 20th Century Chemistry, 1997, 150–170.</ref>, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction.<ref>K. N. Houk, Accounts of Chemical Research, 1975, 8, 361–369.</ref> In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 9. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 10. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 12. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction.<ref>K. Yang, Z. Yang, Q. Dang and X. Bai, European Journal of Organic Chemistry, 2015, 2015, 4344–4347.</ref> 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.<ref>Organic Chemistry, Springer Verlag, 2014.</ref>
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 14. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 

===Conclusion===
In this experiment, a variety of pericyclic reactions were located and their transition structures are characterized. Molecular orbital-based methods were used to numerically solving the Schrödinger equation and locate the transition structures based on the local shape of a potential energy surface. The reaction coordinates, reaction energies and activation barrier heights were also calculated. The roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction was also discussed.
 For the concerted cycloaddtion reaction between 1,3-butadiene and ethylene, the bond formation is synchronous as the two carbons in each pair move towards each other at the same rate. It was also confirmed that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. In exercise 2, the reaction between cyclohexadiene and 1,3-dioxole has an inverse electron demand. From the energy analysis, the endo pathway was proved to be more kinetically and thermodynamically favoured as a result of secondary orbital interactions. In exercise 3, there are three different reaction pathways for xylylene and sulfur dioxide, the endo/exo Diels - Ader reaction and the Cheletropic reaction. From the energy analysis, the endo product was proved to be more kinetically favoured and the cheletropic product was more thermodynamically favoured. A reaction profile was used to help read the reaction more directly.
 
 
===Reference===
<references />
 
 

===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state : [[File:Yf 1 TSIRC.LOG]]

====Exercise 2====
{| class="wikitable"
|+ Table 15. Links to the log files in exercise 2
! rowspan="2" style="center; background: #14866d; color: white;" | Chemicals
! colspan="2" style="center; background: #14866d; color: white;" | Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

====Exercise 3====

{| class="wikitable"
|+ Table 16. Links to the log file of IRC calculations at PM6 level
! colspan="2" style="text-align: center;background: #14866d; color: white;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;background: #14866d; color: white;" | Cheletropic Reaction
|-
| style="text-align: center;background: #14866d; color: white;" | Exo-pathway
| style="text-align: center;background: #14866d; color: white;" | Endo-pathway
|-
| [[File:YfEXOIRC.LOG]]
| [[File:YfENDOIRC.LOG]]
| [[File:YfCHEIRC.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-20T10:29:39Z

Yf2715: /* Normal or inverse demand DA reaction ? */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model. <ref>E. G. Lewars, Computational Chemistry, 2010, 9–43</ref>

[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant. <ref>D. L. Pavia, G. M. Lampman, G. S. Kriz and J. R. Vyvyan, Introduction to spectroscopy, Cengage Learning, Australia, 2015.</ref>]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions. <ref>P. J. Atkins, J. D. Paula and J. Keeler, Atkins Physical Chemistry, Oxford Univ. Press, Oxford, 2017.</ref>

 
 

===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>TTS4.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Figure 4. Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).<ref>P. Geerlings, P. W. Ayers, A. Toro-Labbé, P. K. Chattaraj and F. D. Proft, Accounts of Chemical Research, 2012, 45, 683–695</ref>
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral
Therefore, with only the MOs with the same symmetry combining together, the reaction between 1,3-butadiene and ethylene is thermally allowed.

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length <ref>E. M. Popov, G. A. Kogan and V. N. Zheltova, Theoretical and Experimental Chemistry, 1972, 6, 11–19.</ref>
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 5. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 6. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 7. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 8. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui<ref>K. Fukui, Frontier Orbitals and Reaction Paths World Scientific Series in 20th Century Chemistry, 1997, 150–170.</ref>, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction.<ref>K. N. Houk, Accounts of Chemical Research, 1975, 8, 361–369.</ref> In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 9. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 10. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 12. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction.<ref>K. Yang, Z. Yang, Q. Dang and X. Bai, European Journal of Organic Chemistry, 2015, 2015, 4344–4347.</ref> 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 14. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 

===Conclusion===
In this experiment, a variety of pericyclic reactions were located and their transition structures are characterized. Molecular orbital-based methods were used to numerically solving the Schrödinger equation and locate the transition structures based on the local shape of a potential energy surface. The reaction coordinates, reaction energies and activation barrier heights were also calculated. The roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction was also discussed.
 For the concerted cycloaddtion reaction between 1,3-butadiene and ethylene, the bond formation is synchronous as the two carbons in each pair move towards each other at the same rate. It was also confirmed that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. In exercise 2, the reaction between cyclohexadiene and 1,3-dioxole has an inverse electron demand. From the energy analysis, the endo pathway was proved to be more kinetically and thermodynamically favoured as a result of secondary orbital interactions. In exercise 3, there are three different reaction pathways for xylylene and sulfur dioxide, the endo/exo Diels - Ader reaction and the Cheletropic reaction. From the energy analysis, the endo product was proved to be more kinetically favoured and the cheletropic product was more thermodynamically favoured. A reaction profile was used to help read the reaction more directly.
 
 
===Reference===
<references />
 
 

===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state : [[File:Yf 1 TSIRC.LOG]]

====Exercise 2====
{| class="wikitable"
|+ Table 15. Links to the log files in exercise 2
! rowspan="2" style="center; background: #14866d; color: white;" | Chemicals
! colspan="2" style="center; background: #14866d; color: white;" | Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

====Exercise 3====

{| class="wikitable"
|+ Table 16. Links to the log file of IRC calculations at PM6 level
! colspan="2" style="text-align: center;background: #14866d; color: white;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;background: #14866d; color: white;" | Cheletropic Reaction
|-
| style="text-align: center;background: #14866d; color: white;" | Exo-pathway
| style="text-align: center;background: #14866d; color: white;" | Endo-pathway
|-
| [[File:YfEXOIRC.LOG]]
| [[File:YfENDOIRC.LOG]]
| [[File:YfCHEIRC.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-20T10:25:52Z

Yf2715: /* Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model. <ref>E. G. Lewars, Computational Chemistry, 2010, 9–43</ref>

[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant. <ref>D. L. Pavia, G. M. Lampman, G. S. Kriz and J. R. Vyvyan, Introduction to spectroscopy, Cengage Learning, Australia, 2015.</ref>]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions. <ref>P. J. Atkins, J. D. Paula and J. Keeler, Atkins Physical Chemistry, Oxford Univ. Press, Oxford, 2017.</ref>

 
 

===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>TTS4.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Figure 4. Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).<ref>P. Geerlings, P. W. Ayers, A. Toro-Labbé, P. K. Chattaraj and F. D. Proft, Accounts of Chemical Research, 2012, 45, 683–695</ref>
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral
Therefore, with only the MOs with the same symmetry combining together, the reaction between 1,3-butadiene and ethylene is thermally allowed.

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length <ref>E. M. Popov, G. A. Kogan and V. N. Zheltova, Theoretical and Experimental Chemistry, 1972, 6, 11–19.</ref>
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 5. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 6. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 7. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 8. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui<ref>K. Fukui, Frontier Orbitals and Reaction Paths World Scientific Series in 20th Century Chemistry, 1997, 150–170.</ref>, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction.<ref>K. N. Houk, Accounts of Chemical Research, 1975, 8, 361–369.</ref> In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 9. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 10. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 12. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
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| <jmol>
<jmolApplet>
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<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
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|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 14. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 

===Conclusion===
In this experiment, a variety of pericyclic reactions were located and their transition structures are characterized. Molecular orbital-based methods were used to numerically solving the Schrödinger equation and locate the transition structures based on the local shape of a potential energy surface. The reaction coordinates, reaction energies and activation barrier heights were also calculated. The roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction was also discussed.
 For the concerted cycloaddtion reaction between 1,3-butadiene and ethylene, the bond formation is synchronous as the two carbons in each pair move towards each other at the same rate. It was also confirmed that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. In exercise 2, the reaction between cyclohexadiene and 1,3-dioxole has an inverse electron demand. From the energy analysis, the endo pathway was proved to be more kinetically and thermodynamically favoured as a result of secondary orbital interactions. In exercise 3, there are three different reaction pathways for xylylene and sulfur dioxide, the endo/exo Diels - Ader reaction and the Cheletropic reaction. From the energy analysis, the endo product was proved to be more kinetically favoured and the cheletropic product was more thermodynamically favoured. A reaction profile was used to help read the reaction more directly.
 
 
===Reference===
<references />
 
 

===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state : [[File:Yf 1 TSIRC.LOG]]

====Exercise 2====
{| class="wikitable"
|+ Table 15. Links to the log files in exercise 2
! rowspan="2" style="center; background: #14866d; color: white;" | Chemicals
! colspan="2" style="center; background: #14866d; color: white;" | Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

====Exercise 3====

{| class="wikitable"
|+ Table 16. Links to the log file of IRC calculations at PM6 level
! colspan="2" style="text-align: center;background: #14866d; color: white;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;background: #14866d; color: white;" | Cheletropic Reaction
|-
| style="text-align: center;background: #14866d; color: white;" | Exo-pathway
| style="text-align: center;background: #14866d; color: white;" | Endo-pathway
|-
| [[File:YfEXOIRC.LOG]]
| [[File:YfENDOIRC.LOG]]
| [[File:YfCHEIRC.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-20T10:24:13Z

Yf2715: /* Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model. <ref>E. G. Lewars, Computational Chemistry, 2010, 9–43</ref>

[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant. <ref>D. L. Pavia, G. M. Lampman, G. S. Kriz and J. R. Vyvyan, Introduction to spectroscopy, Cengage Learning, Australia, 2015.</ref>]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions. <ref>P. J. Atkins, J. D. Paula and J. Keeler, Atkins Physical Chemistry, Oxford Univ. Press, Oxford, 2017.</ref>

 
 

===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>TTS4.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Figure 4. Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).<ref>P. Geerlings, P. W. Ayers, A. Toro-Labbé, P. K. Chattaraj and F. D. Proft, Accounts of Chemical Research, 2012, 45, 683–695</ref>
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral
Therefore, with only the MOs with the same symmetry combining together, the reaction between 1,3-butadiene and ethylene is thermally allowed.

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length <ref>E. M. Popov, G. A. Kogan and V. N. Zheltova, Theoretical and Experimental Chemistry, 1972, 6, 11–19.</ref>
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 5. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 6. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 7. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 8. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui<ref>K. Fukui, Frontier Orbitals and Reaction Paths World Scientific Series in 20th Century Chemistry, 1997, 150–170.</ref>, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 9. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 10. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 12. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 14. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 

===Conclusion===
In this experiment, a variety of pericyclic reactions were located and their transition structures are characterized. Molecular orbital-based methods were used to numerically solving the Schrödinger equation and locate the transition structures based on the local shape of a potential energy surface. The reaction coordinates, reaction energies and activation barrier heights were also calculated. The roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction was also discussed.
 For the concerted cycloaddtion reaction between 1,3-butadiene and ethylene, the bond formation is synchronous as the two carbons in each pair move towards each other at the same rate. It was also confirmed that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. In exercise 2, the reaction between cyclohexadiene and 1,3-dioxole has an inverse electron demand. From the energy analysis, the endo pathway was proved to be more kinetically and thermodynamically favoured as a result of secondary orbital interactions. In exercise 3, there are three different reaction pathways for xylylene and sulfur dioxide, the endo/exo Diels - Ader reaction and the Cheletropic reaction. From the energy analysis, the endo product was proved to be more kinetically favoured and the cheletropic product was more thermodynamically favoured. A reaction profile was used to help read the reaction more directly.
 
 
===Reference===
<references />
 
 

===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state : [[File:Yf 1 TSIRC.LOG]]

====Exercise 2====
{| class="wikitable"
|+ Table 15. Links to the log files in exercise 2
! rowspan="2" style="center; background: #14866d; color: white;" | Chemicals
! colspan="2" style="center; background: #14866d; color: white;" | Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

====Exercise 3====

{| class="wikitable"
|+ Table 16. Links to the log file of IRC calculations at PM6 level
! colspan="2" style="text-align: center;background: #14866d; color: white;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;background: #14866d; color: white;" | Cheletropic Reaction
|-
| style="text-align: center;background: #14866d; color: white;" | Exo-pathway
| style="text-align: center;background: #14866d; color: white;" | Endo-pathway
|-
| [[File:YfEXOIRC.LOG]]
| [[File:YfENDOIRC.LOG]]
| [[File:YfCHEIRC.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-20T10:20:23Z

Yf2715: /* Bond length Analysis */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model. <ref>E. G. Lewars, Computational Chemistry, 2010, 9–43</ref>

[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant. <ref>D. L. Pavia, G. M. Lampman, G. S. Kriz and J. R. Vyvyan, Introduction to spectroscopy, Cengage Learning, Australia, 2015.</ref>]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions. <ref>P. J. Atkins, J. D. Paula and J. Keeler, Atkins Physical Chemistry, Oxford Univ. Press, Oxford, 2017.</ref>

 
 

===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
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<script>frame 6</script>
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|<jmol>
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====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Figure 4. Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).<ref>P. Geerlings, P. W. Ayers, A. Toro-Labbé, P. K. Chattaraj and F. D. Proft, Accounts of Chemical Research, 2012, 45, 683–695</ref>
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral
Therefore, with only the MOs with the same symmetry combining together, the reaction between 1,3-butadiene and ethylene is thermally allowed.

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length <ref>E. M. Popov, G. A. Kogan and V. N. Zheltova, Theoretical and Experimental Chemistry, 1972, 6, 11–19.</ref>
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 5. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 6. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 7. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 8. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
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|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 9. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 10. The vibration of exo TS]]
|-
|<jmol>
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<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
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|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 12. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
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| <jmol>
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<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
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| <jmol>
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<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
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|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
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| style="text-align:center;"| Products
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As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 14. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 

===Conclusion===
In this experiment, a variety of pericyclic reactions were located and their transition structures are characterized. Molecular orbital-based methods were used to numerically solving the Schrödinger equation and locate the transition structures based on the local shape of a potential energy surface. The reaction coordinates, reaction energies and activation barrier heights were also calculated. The roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction was also discussed.
 For the concerted cycloaddtion reaction between 1,3-butadiene and ethylene, the bond formation is synchronous as the two carbons in each pair move towards each other at the same rate. It was also confirmed that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. In exercise 2, the reaction between cyclohexadiene and 1,3-dioxole has an inverse electron demand. From the energy analysis, the endo pathway was proved to be more kinetically and thermodynamically favoured as a result of secondary orbital interactions. In exercise 3, there are three different reaction pathways for xylylene and sulfur dioxide, the endo/exo Diels - Ader reaction and the Cheletropic reaction. From the energy analysis, the endo product was proved to be more kinetically favoured and the cheletropic product was more thermodynamically favoured. A reaction profile was used to help read the reaction more directly.
 
 
===Reference===
<references />
 
 

===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state : [[File:Yf 1 TSIRC.LOG]]

====Exercise 2====
{| class="wikitable"
|+ Table 15. Links to the log files in exercise 2
! rowspan="2" style="center; background: #14866d; color: white;" | Chemicals
! colspan="2" style="center; background: #14866d; color: white;" | Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

====Exercise 3====

{| class="wikitable"
|+ Table 16. Links to the log file of IRC calculations at PM6 level
! colspan="2" style="text-align: center;background: #14866d; color: white;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;background: #14866d; color: white;" | Cheletropic Reaction
|-
| style="text-align: center;background: #14866d; color: white;" | Exo-pathway
| style="text-align: center;background: #14866d; color: white;" | Endo-pathway
|-
| [[File:YfEXOIRC.LOG]]
| [[File:YfENDOIRC.LOG]]
| [[File:YfCHEIRC.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-20T10:18:18Z

Yf2715: /* Introduction */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model. <ref>E. G. Lewars, Computational Chemistry, 2010, 9–43</ref>

[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant. <ref>D. L. Pavia, G. M. Lampman, G. S. Kriz and J. R. Vyvyan, Introduction to spectroscopy, Cengage Learning, Australia, 2015.</ref>]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions. <ref>P. J. Atkins, J. D. Paula and J. Keeler, Atkins Physical Chemistry, Oxford Univ. Press, Oxford, 2017.</ref>

 
 

===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
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<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
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<uploadedFileContents>TTS4.LOG</uploadedFileContents>
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<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
</jmolApplet>
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====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Figure 4. Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).<ref>P. Geerlings, P. W. Ayers, A. Toro-Labbé, P. K. Chattaraj and F. D. Proft, Accounts of Chemical Research, 2012, 45, 683–695</ref>
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral
Therefore, with only the MOs with the same symmetry combining together, the reaction between 1,3-butadiene and ethylene is thermally allowed.

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length <ref>J. F. Chiang and S. H. Bauer, Journal of the American Chemical Society, 1969, 91, 1898–1901.</ref>
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 5. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 6. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 7. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 8. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
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<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
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|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 9. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 10. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 12. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 14. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 

===Conclusion===
In this experiment, a variety of pericyclic reactions were located and their transition structures are characterized. Molecular orbital-based methods were used to numerically solving the Schrödinger equation and locate the transition structures based on the local shape of a potential energy surface. The reaction coordinates, reaction energies and activation barrier heights were also calculated. The roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction was also discussed.
 For the concerted cycloaddtion reaction between 1,3-butadiene and ethylene, the bond formation is synchronous as the two carbons in each pair move towards each other at the same rate. It was also confirmed that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. In exercise 2, the reaction between cyclohexadiene and 1,3-dioxole has an inverse electron demand. From the energy analysis, the endo pathway was proved to be more kinetically and thermodynamically favoured as a result of secondary orbital interactions. In exercise 3, there are three different reaction pathways for xylylene and sulfur dioxide, the endo/exo Diels - Ader reaction and the Cheletropic reaction. From the energy analysis, the endo product was proved to be more kinetically favoured and the cheletropic product was more thermodynamically favoured. A reaction profile was used to help read the reaction more directly.
 
 
===Reference===
<references />
 
 

===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state : [[File:Yf 1 TSIRC.LOG]]

====Exercise 2====
{| class="wikitable"
|+ Table 15. Links to the log files in exercise 2
! rowspan="2" style="center; background: #14866d; color: white;" | Chemicals
! colspan="2" style="center; background: #14866d; color: white;" | Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

====Exercise 3====

{| class="wikitable"
|+ Table 16. Links to the log file of IRC calculations at PM6 level
! colspan="2" style="text-align: center;background: #14866d; color: white;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;background: #14866d; color: white;" | Cheletropic Reaction
|-
| style="text-align: center;background: #14866d; color: white;" | Exo-pathway
| style="text-align: center;background: #14866d; color: white;" | Endo-pathway
|-
| [[File:YfEXOIRC.LOG]]
| [[File:YfENDOIRC.LOG]]
| [[File:YfCHEIRC.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-20T10:16:00Z

Yf2715: /* Bond length Analysis */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model. <ref>E. G. Lewars, Computational Chemistry, 2010, 9–43</ref>

[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant.]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions. <ref>P. J. Atkins, J. D. Paula and J. Keeler, Atkins Physical Chemistry, Oxford Univ. Press, Oxford, 2017.</ref>

 
 

===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
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====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Figure 4. Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).<ref>P. Geerlings, P. W. Ayers, A. Toro-Labbé, P. K. Chattaraj and F. D. Proft, Accounts of Chemical Research, 2012, 45, 683–695</ref>
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral
Therefore, with only the MOs with the same symmetry combining together, the reaction between 1,3-butadiene and ethylene is thermally allowed.

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length <ref>J. F. Chiang and S. H. Bauer, Journal of the American Chemical Society, 1969, 91, 1898–1901.</ref>
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 5. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 6. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 7. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 8. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
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|<jmol>
<jmolApplet>
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|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 9. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 10. The vibration of exo TS]]
|-
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There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 12. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
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<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
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</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
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<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
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|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
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</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
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<size>240</size>
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<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
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As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 14. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 

===Conclusion===
In this experiment, a variety of pericyclic reactions were located and their transition structures are characterized. Molecular orbital-based methods were used to numerically solving the Schrödinger equation and locate the transition structures based on the local shape of a potential energy surface. The reaction coordinates, reaction energies and activation barrier heights were also calculated. The roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction was also discussed.
 For the concerted cycloaddtion reaction between 1,3-butadiene and ethylene, the bond formation is synchronous as the two carbons in each pair move towards each other at the same rate. It was also confirmed that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. In exercise 2, the reaction between cyclohexadiene and 1,3-dioxole has an inverse electron demand. From the energy analysis, the endo pathway was proved to be more kinetically and thermodynamically favoured as a result of secondary orbital interactions. In exercise 3, there are three different reaction pathways for xylylene and sulfur dioxide, the endo/exo Diels - Ader reaction and the Cheletropic reaction. From the energy analysis, the endo product was proved to be more kinetically favoured and the cheletropic product was more thermodynamically favoured. A reaction profile was used to help read the reaction more directly.
 
 
===Reference===
<references />
 
 

===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state : [[File:Yf 1 TSIRC.LOG]]

====Exercise 2====
{| class="wikitable"
|+ Table 15. Links to the log files in exercise 2
! rowspan="2" style="center; background: #14866d; color: white;" | Chemicals
! colspan="2" style="center; background: #14866d; color: white;" | Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

====Exercise 3====

{| class="wikitable"
|+ Table 16. Links to the log file of IRC calculations at PM6 level
! colspan="2" style="text-align: center;background: #14866d; color: white;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;background: #14866d; color: white;" | Cheletropic Reaction
|-
| style="text-align: center;background: #14866d; color: white;" | Exo-pathway
| style="text-align: center;background: #14866d; color: white;" | Endo-pathway
|-
| [[File:YfEXOIRC.LOG]]
| [[File:YfENDOIRC.LOG]]
| [[File:YfCHEIRC.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-20T10:12:51Z

Yf2715: /* MO diagram and HOMO-LUMO orbitals */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model. <ref>E. G. Lewars, Computational Chemistry, 2010, 9–43</ref>

[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant.]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions. <ref>P. J. Atkins, J. D. Paula and J. Keeler, Atkins Physical Chemistry, Oxford Univ. Press, Oxford, 2017.</ref>

 
 

===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
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<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
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<uploadedFileContents>TTS4.LOG</uploadedFileContents>
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<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Figure 4. Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).<ref>P. Geerlings, P. W. Ayers, A. Toro-Labbé, P. K. Chattaraj and F. D. Proft, Accounts of Chemical Research, 2012, 45, 683–695</ref>
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral
Therefore, with only the MOs with the same symmetry combining together, the reaction between 1,3-butadiene and ethylene is thermally allowed.

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 5. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 6. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 7. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 8. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 9. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 10. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 12. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 14. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 

===Conclusion===
In this experiment, a variety of pericyclic reactions were located and their transition structures are characterized. Molecular orbital-based methods were used to numerically solving the Schrödinger equation and locate the transition structures based on the local shape of a potential energy surface. The reaction coordinates, reaction energies and activation barrier heights were also calculated. The roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction was also discussed.
 For the concerted cycloaddtion reaction between 1,3-butadiene and ethylene, the bond formation is synchronous as the two carbons in each pair move towards each other at the same rate. It was also confirmed that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. In exercise 2, the reaction between cyclohexadiene and 1,3-dioxole has an inverse electron demand. From the energy analysis, the endo pathway was proved to be more kinetically and thermodynamically favoured as a result of secondary orbital interactions. In exercise 3, there are three different reaction pathways for xylylene and sulfur dioxide, the endo/exo Diels - Ader reaction and the Cheletropic reaction. From the energy analysis, the endo product was proved to be more kinetically favoured and the cheletropic product was more thermodynamically favoured. A reaction profile was used to help read the reaction more directly.
 
 
===Reference===
<references />
 
 

===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state : [[File:Yf 1 TSIRC.LOG]]

====Exercise 2====
{| class="wikitable"
|+ Table 15. Links to the log files in exercise 2
! rowspan="2" style="center; background: #14866d; color: white;" | Chemicals
! colspan="2" style="center; background: #14866d; color: white;" | Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

====Exercise 3====

{| class="wikitable"
|+ Table 16. Links to the log file of IRC calculations at PM6 level
! colspan="2" style="text-align: center;background: #14866d; color: white;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;background: #14866d; color: white;" | Cheletropic Reaction
|-
| style="text-align: center;background: #14866d; color: white;" | Exo-pathway
| style="text-align: center;background: #14866d; color: white;" | Endo-pathway
|-
| [[File:YfEXOIRC.LOG]]
| [[File:YfENDOIRC.LOG]]
| [[File:YfCHEIRC.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-20T10:10:11Z

Yf2715: /* Reference */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model. <ref>E. G. Lewars, Computational Chemistry, 2010, 9–43</ref>

[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant.]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions. <ref>P. J. Atkins, J. D. Paula and J. Keeler, Atkins Physical Chemistry, Oxford Univ. Press, Oxford, 2017.</ref>

 
 

===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
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====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Figure 4. Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral
Therefore, with only the MOs with the same symmetry combining together, the reaction between 1,3-butadiene and ethylene is thermally allowed.

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 5. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 6. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 7. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 8. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
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|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 9. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 10. The vibration of exo TS]]
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There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 12. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 14. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 

===Conclusion===
In this experiment, a variety of pericyclic reactions were located and their transition structures are characterized. Molecular orbital-based methods were used to numerically solving the Schrödinger equation and locate the transition structures based on the local shape of a potential energy surface. The reaction coordinates, reaction energies and activation barrier heights were also calculated. The roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction was also discussed.
 For the concerted cycloaddtion reaction between 1,3-butadiene and ethylene, the bond formation is synchronous as the two carbons in each pair move towards each other at the same rate. It was also confirmed that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. In exercise 2, the reaction between cyclohexadiene and 1,3-dioxole has an inverse electron demand. From the energy analysis, the endo pathway was proved to be more kinetically and thermodynamically favoured as a result of secondary orbital interactions. In exercise 3, there are three different reaction pathways for xylylene and sulfur dioxide, the endo/exo Diels - Ader reaction and the Cheletropic reaction. From the energy analysis, the endo product was proved to be more kinetically favoured and the cheletropic product was more thermodynamically favoured. A reaction profile was used to help read the reaction more directly.
 
 
===Reference===
<references />
 
 

===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state : [[File:Yf 1 TSIRC.LOG]]

====Exercise 2====
{| class="wikitable"
|+ Table 15. Links to the log files in exercise 2
! rowspan="2" style="center; background: #14866d; color: white;" | Chemicals
! colspan="2" style="center; background: #14866d; color: white;" | Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

====Exercise 3====

{| class="wikitable"
|+ Table 16. Links to the log file of IRC calculations at PM6 level
! colspan="2" style="text-align: center;background: #14866d; color: white;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;background: #14866d; color: white;" | Cheletropic Reaction
|-
| style="text-align: center;background: #14866d; color: white;" | Exo-pathway
| style="text-align: center;background: #14866d; color: white;" | Endo-pathway
|-
| [[File:YfEXOIRC.LOG]]
| [[File:YfENDOIRC.LOG]]
| [[File:YfCHEIRC.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-20T10:09:37Z

Yf2715: /* Introduction */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model. <ref>E. G. Lewars, Computational Chemistry, 2010, 9–43</ref>

[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant.]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions. <ref>P. J. Atkins, J. D. Paula and J. Keeler, Atkins Physical Chemistry, Oxford Univ. Press, Oxford, 2017.</ref>

 
 

===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>TTS4.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Figure 4. Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral
Therefore, with only the MOs with the same symmetry combining together, the reaction between 1,3-butadiene and ethylene is thermally allowed.

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 5. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 6. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 7. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 8. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 9. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 10. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 12. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 14. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 

===Conclusion===
In this experiment, a variety of pericyclic reactions were located and their transition structures are characterized. Molecular orbital-based methods were used to numerically solving the Schrödinger equation and locate the transition structures based on the local shape of a potential energy surface. The reaction coordinates, reaction energies and activation barrier heights were also calculated. The roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction was also discussed.
 For the concerted cycloaddtion reaction between 1,3-butadiene and ethylene, the bond formation is synchronous as the two carbons in each pair move towards each other at the same rate. It was also confirmed that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. In exercise 2, the reaction between cyclohexadiene and 1,3-dioxole has an inverse electron demand. From the energy analysis, the endo pathway was proved to be more kinetically and thermodynamically favoured as a result of secondary orbital interactions. In exercise 3, there are three different reaction pathways for xylylene and sulfur dioxide, the endo/exo Diels - Ader reaction and the Cheletropic reaction. From the energy analysis, the endo product was proved to be more kinetically favoured and the cheletropic product was more thermodynamically favoured. A reaction profile was used to help read the reaction more directly.
 
 
===Reference===
<references />

===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state : [[File:Yf 1 TSIRC.LOG]]

====Exercise 2====
{| class="wikitable"
|+ Table 15. Links to the log files in exercise 2
! rowspan="2" style="center; background: #14866d; color: white;" | Chemicals
! colspan="2" style="center; background: #14866d; color: white;" | Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

====Exercise 3====

{| class="wikitable"
|+ Table 16. Links to the log file of IRC calculations at PM6 level
! colspan="2" style="text-align: center;background: #14866d; color: white;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;background: #14866d; color: white;" | Cheletropic Reaction
|-
| style="text-align: center;background: #14866d; color: white;" | Exo-pathway
| style="text-align: center;background: #14866d; color: white;" | Endo-pathway
|-
| [[File:YfEXOIRC.LOG]]
| [[File:YfENDOIRC.LOG]]
| [[File:YfCHEIRC.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-20T10:09:09Z

Yf2715: /* Introduction */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model. <ref>E. G. Lewars, Computational Chemistry, 2010, 9–43</ref>

[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant.]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions. (b)<ref>P. J. Atkins, J. D. Paula and J. Keeler, Atkins Physical Chemistry, Oxford Univ. Press, Oxford, 2017.</ref>

 
 

===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>TTS4.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Figure 4. Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral
Therefore, with only the MOs with the same symmetry combining together, the reaction between 1,3-butadiene and ethylene is thermally allowed.

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 5. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 6. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 7. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 8. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 9. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 10. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 12. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 14. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 

===Conclusion===
In this experiment, a variety of pericyclic reactions were located and their transition structures are characterized. Molecular orbital-based methods were used to numerically solving the Schrödinger equation and locate the transition structures based on the local shape of a potential energy surface. The reaction coordinates, reaction energies and activation barrier heights were also calculated. The roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction was also discussed.
 For the concerted cycloaddtion reaction between 1,3-butadiene and ethylene, the bond formation is synchronous as the two carbons in each pair move towards each other at the same rate. It was also confirmed that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. In exercise 2, the reaction between cyclohexadiene and 1,3-dioxole has an inverse electron demand. From the energy analysis, the endo pathway was proved to be more kinetically and thermodynamically favoured as a result of secondary orbital interactions. In exercise 3, there are three different reaction pathways for xylylene and sulfur dioxide, the endo/exo Diels - Ader reaction and the Cheletropic reaction. From the energy analysis, the endo product was proved to be more kinetically favoured and the cheletropic product was more thermodynamically favoured. A reaction profile was used to help read the reaction more directly.
 
 
===Reference===
<references />

===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state : [[File:Yf 1 TSIRC.LOG]]

====Exercise 2====
{| class="wikitable"
|+ Table 15. Links to the log files in exercise 2
! rowspan="2" style="center; background: #14866d; color: white;" | Chemicals
! colspan="2" style="center; background: #14866d; color: white;" | Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

====Exercise 3====

{| class="wikitable"
|+ Table 16. Links to the log file of IRC calculations at PM6 level
! colspan="2" style="text-align: center;background: #14866d; color: white;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;background: #14866d; color: white;" | Cheletropic Reaction
|-
| style="text-align: center;background: #14866d; color: white;" | Exo-pathway
| style="text-align: center;background: #14866d; color: white;" | Endo-pathway
|-
| [[File:YfEXOIRC.LOG]]
| [[File:YfENDOIRC.LOG]]
| [[File:YfCHEIRC.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-20T10:08:42Z

Yf2715: /* Introduction */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model. (a)<ref>E. G. Lewars, Computational Chemistry, 2010, 9–43</ref>

[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant.]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions. (b)<ref>P. J. Atkins, J. D. Paula and J. Keeler, Atkins Physical Chemistry, Oxford Univ. Press, Oxford, 2017.</ref>

 
 

===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>TTS4.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Figure 4. Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral
Therefore, with only the MOs with the same symmetry combining together, the reaction between 1,3-butadiene and ethylene is thermally allowed.

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 5. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 6. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 7. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 8. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 9. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 10. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 12. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 14. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 

===Conclusion===
In this experiment, a variety of pericyclic reactions were located and their transition structures are characterized. Molecular orbital-based methods were used to numerically solving the Schrödinger equation and locate the transition structures based on the local shape of a potential energy surface. The reaction coordinates, reaction energies and activation barrier heights were also calculated. The roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction was also discussed.
 For the concerted cycloaddtion reaction between 1,3-butadiene and ethylene, the bond formation is synchronous as the two carbons in each pair move towards each other at the same rate. It was also confirmed that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. In exercise 2, the reaction between cyclohexadiene and 1,3-dioxole has an inverse electron demand. From the energy analysis, the endo pathway was proved to be more kinetically and thermodynamically favoured as a result of secondary orbital interactions. In exercise 3, there are three different reaction pathways for xylylene and sulfur dioxide, the endo/exo Diels - Ader reaction and the Cheletropic reaction. From the energy analysis, the endo product was proved to be more kinetically favoured and the cheletropic product was more thermodynamically favoured. A reaction profile was used to help read the reaction more directly.
 
 
===Reference===
<references />

===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state : [[File:Yf 1 TSIRC.LOG]]

====Exercise 2====
{| class="wikitable"
|+ Table 15. Links to the log files in exercise 2
! rowspan="2" style="center; background: #14866d; color: white;" | Chemicals
! colspan="2" style="center; background: #14866d; color: white;" | Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

====Exercise 3====

{| class="wikitable"
|+ Table 16. Links to the log file of IRC calculations at PM6 level
! colspan="2" style="text-align: center;background: #14866d; color: white;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;background: #14866d; color: white;" | Cheletropic Reaction
|-
| style="text-align: center;background: #14866d; color: white;" | Exo-pathway
| style="text-align: center;background: #14866d; color: white;" | Endo-pathway
|-
| [[File:YfEXOIRC.LOG]]
| [[File:YfENDOIRC.LOG]]
| [[File:YfCHEIRC.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-20T10:02:19Z

Yf2715: /* Conclusion */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model.
[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant.]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions.

 
 
===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>TTS4.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Figure 4. Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral
Therefore, with only the MOs with the same symmetry combining together, the reaction between 1,3-butadiene and ethylene is thermally allowed.

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 5. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 6. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 7. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 8. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 9. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 10. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 12. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 14. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 

===Conclusion===
In this experiment, a variety of pericyclic reactions were located and their transition structures are characterized. Molecular orbital-based methods were used to numerically solving the Schrödinger equation and locate the transition structures based on the local shape of a potential energy surface. The reaction coordinates, reaction energies and activation barrier heights were also calculated. The roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction was also discussed.
 For the concerted cycloaddtion reaction between 1,3-butadiene and ethylene, the bond formation is synchronous as the two carbons in each pair move towards each other at the same rate. It was also confirmed that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. In exercise 2, the reaction between cyclohexadiene and 1,3-dioxole has an inverse electron demand. From the energy analysis, the endo pathway was proved to be more kinetically and thermodynamically favoured as a result of secondary orbital interactions. In exercise 3, there are three different reaction pathways for xylylene and sulfur dioxide, the endo/exo Diels - Ader reaction and the Cheletropic reaction. From the energy analysis, the endo product was proved to be more kinetically favoured and the cheletropic product was more thermodynamically favoured. A reaction profile was used to help read the reaction more directly.
 
 
===Reference===
<references />

===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state : [[File:Yf 1 TSIRC.LOG]]

====Exercise 2====
{| class="wikitable"
|+ Table 15. Links to the log files in exercise 2
! rowspan="2" style="center; background: #14866d; color: white;" | Chemicals
! colspan="2" style="center; background: #14866d; color: white;" | Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

====Exercise 3====

{| class="wikitable"
|+ Table 16. Links to the log file of IRC calculations at PM6 level
! colspan="2" style="text-align: center;background: #14866d; color: white;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;background: #14866d; color: white;" | Cheletropic Reaction
|-
| style="text-align: center;background: #14866d; color: white;" | Exo-pathway
| style="text-align: center;background: #14866d; color: white;" | Endo-pathway
|-
| [[File:YfEXOIRC.LOG]]
| [[File:YfENDOIRC.LOG]]
| [[File:YfCHEIRC.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-19T22:40:35Z

Yf2715: /* Energy analysis */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model.
[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant.]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions.

 
 
===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>TTS4.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Figure 4. Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral
Therefore, with only the MOs with the same symmetry combining together, the reaction between 1,3-butadiene and ethylene is thermally allowed.

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 5. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 6. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 7. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 8. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 9. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 10. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 12. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 14. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 

===Conclusion===
In this experiment, a variety of pericyclic reactions were located and their transition structures are characterized. Molecular orbital-based methods were used to numerically solving the Schrödinger equation and locate the transition structures based on the local shape of a potential energy surface. The reaction coordinates, reaction energies and activation barrier heights were also calculated. The roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction was also discussed. For the concerted cycloaddtion reaction between 1,3-butadiene and ethylene, the bond formation is synchronous as the two carbons in each pair move towards each other at the same rate. It was also confirmed that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. In exercise 2, the reaction between cyclohexadiene and 1,3-dioxole has an inverse electron demand. From the energy analysis, the endo pathway was proved to be more kinetically and thermodynamically favoured as a result of secondary orbital interactions. In exercise 3, there are three different reaction pathways for xylylene and sulfur dioxide, the endo/exo Diels - Ader reaction and the Cheletropic reaction. From the energy analysis, the endo product was proved to be more kinetically favoured and the cheletropic product was more thermodynamically favoured. A reaction profile was used to help read the reaction more directly.
 
 
===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state : [[File:Yf 1 TSIRC.LOG]]

====Exercise 2====
{| class="wikitable"
|+ Table 15. Links to the log files in exercise 2
! rowspan="2" style="center; background: #14866d; color: white;" | Chemicals
! colspan="2" style="center; background: #14866d; color: white;" | Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

====Exercise 3====

{| class="wikitable"
|+ Table 16. Links to the log file of IRC calculations at PM6 level
! colspan="2" style="text-align: center;background: #14866d; color: white;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;background: #14866d; color: white;" | Cheletropic Reaction
|-
| style="text-align: center;background: #14866d; color: white;" | Exo-pathway
| style="text-align: center;background: #14866d; color: white;" | Endo-pathway
|-
| [[File:YfEXOIRC.LOG]]
| [[File:YfENDOIRC.LOG]]
| [[File:YfCHEIRC.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-19T22:40:16Z

Yf2715: /* Exercise 3: Diels-Alder vs Cheletropic */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model.
[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant.]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions.

 
 
===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>TTS4.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Figure 4. Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral
Therefore, with only the MOs with the same symmetry combining together, the reaction between 1,3-butadiene and ethylene is thermally allowed.

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 5. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 6. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 7. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 8. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 9. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 10. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 12. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 

===Conclusion===
In this experiment, a variety of pericyclic reactions were located and their transition structures are characterized. Molecular orbital-based methods were used to numerically solving the Schrödinger equation and locate the transition structures based on the local shape of a potential energy surface. The reaction coordinates, reaction energies and activation barrier heights were also calculated. The roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction was also discussed. For the concerted cycloaddtion reaction between 1,3-butadiene and ethylene, the bond formation is synchronous as the two carbons in each pair move towards each other at the same rate. It was also confirmed that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. In exercise 2, the reaction between cyclohexadiene and 1,3-dioxole has an inverse electron demand. From the energy analysis, the endo pathway was proved to be more kinetically and thermodynamically favoured as a result of secondary orbital interactions. In exercise 3, there are three different reaction pathways for xylylene and sulfur dioxide, the endo/exo Diels - Ader reaction and the Cheletropic reaction. From the energy analysis, the endo product was proved to be more kinetically favoured and the cheletropic product was more thermodynamically favoured. A reaction profile was used to help read the reaction more directly.
 
 
===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state : [[File:Yf 1 TSIRC.LOG]]

====Exercise 2====
{| class="wikitable"
|+ Table 15. Links to the log files in exercise 2
! rowspan="2" style="center; background: #14866d; color: white;" | Chemicals
! colspan="2" style="center; background: #14866d; color: white;" | Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

====Exercise 3====

{| class="wikitable"
|+ Table 16. Links to the log file of IRC calculations at PM6 level
! colspan="2" style="text-align: center;background: #14866d; color: white;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;background: #14866d; color: white;" | Cheletropic Reaction
|-
| style="text-align: center;background: #14866d; color: white;" | Exo-pathway
| style="text-align: center;background: #14866d; color: white;" | Endo-pathway
|-
| [[File:YfEXOIRC.LOG]]
| [[File:YfENDOIRC.LOG]]
| [[File:YfCHEIRC.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-19T22:40:00Z

Yf2715: /* Optimized structures, vibration and MOs */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model.
[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant.]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions.

 
 
===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>TTS4.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Figure 4. Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral
Therefore, with only the MOs with the same symmetry combining together, the reaction between 1,3-butadiene and ethylene is thermally allowed.

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 5. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 6. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 7. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 8. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 9. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 10. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 12. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 12. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 
===Conclusion===
In this experiment, a variety of pericyclic reactions were located and their transition structures are characterized. Molecular orbital-based methods were used to numerically solving the Schrödinger equation and locate the transition structures based on the local shape of a potential energy surface. The reaction coordinates, reaction energies and activation barrier heights were also calculated. The roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction was also discussed. For the concerted cycloaddtion reaction between 1,3-butadiene and ethylene, the bond formation is synchronous as the two carbons in each pair move towards each other at the same rate. It was also confirmed that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. In exercise 2, the reaction between cyclohexadiene and 1,3-dioxole has an inverse electron demand. From the energy analysis, the endo pathway was proved to be more kinetically and thermodynamically favoured as a result of secondary orbital interactions. In exercise 3, there are three different reaction pathways for xylylene and sulfur dioxide, the endo/exo Diels - Ader reaction and the Cheletropic reaction. From the energy analysis, the endo product was proved to be more kinetically favoured and the cheletropic product was more thermodynamically favoured. A reaction profile was used to help read the reaction more directly.
 
 
===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state : [[File:Yf 1 TSIRC.LOG]]

====Exercise 2====
{| class="wikitable"
|+ Table 15. Links to the log files in exercise 2
! rowspan="2" style="center; background: #14866d; color: white;" | Chemicals
! colspan="2" style="center; background: #14866d; color: white;" | Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

====Exercise 3====

{| class="wikitable"
|+ Table 16. Links to the log file of IRC calculations at PM6 level
! colspan="2" style="text-align: center;background: #14866d; color: white;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;background: #14866d; color: white;" | Cheletropic Reaction
|-
| style="text-align: center;background: #14866d; color: white;" | Exo-pathway
| style="text-align: center;background: #14866d; color: white;" | Endo-pathway
|-
| [[File:YfEXOIRC.LOG]]
| [[File:YfENDOIRC.LOG]]
| [[File:YfCHEIRC.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-19T22:39:44Z

Yf2715: /* Optimized structures, vibration and MOs */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model.
[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant.]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions.

 
 
===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>TTS4.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Figure 4. Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral
Therefore, with only the MOs with the same symmetry combining together, the reaction between 1,3-butadiene and ethylene is thermally allowed.

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 5. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 6. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 7. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 8. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 9. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 10. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 10. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 12. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 
===Conclusion===
In this experiment, a variety of pericyclic reactions were located and their transition structures are characterized. Molecular orbital-based methods were used to numerically solving the Schrödinger equation and locate the transition structures based on the local shape of a potential energy surface. The reaction coordinates, reaction energies and activation barrier heights were also calculated. The roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction was also discussed. For the concerted cycloaddtion reaction between 1,3-butadiene and ethylene, the bond formation is synchronous as the two carbons in each pair move towards each other at the same rate. It was also confirmed that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. In exercise 2, the reaction between cyclohexadiene and 1,3-dioxole has an inverse electron demand. From the energy analysis, the endo pathway was proved to be more kinetically and thermodynamically favoured as a result of secondary orbital interactions. In exercise 3, there are three different reaction pathways for xylylene and sulfur dioxide, the endo/exo Diels - Ader reaction and the Cheletropic reaction. From the energy analysis, the endo product was proved to be more kinetically favoured and the cheletropic product was more thermodynamically favoured. A reaction profile was used to help read the reaction more directly.
 
 
===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state : [[File:Yf 1 TSIRC.LOG]]

====Exercise 2====
{| class="wikitable"
|+ Table 15. Links to the log files in exercise 2
! rowspan="2" style="center; background: #14866d; color: white;" | Chemicals
! colspan="2" style="center; background: #14866d; color: white;" | Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

====Exercise 3====

{| class="wikitable"
|+ Table 16. Links to the log file of IRC calculations at PM6 level
! colspan="2" style="text-align: center;background: #14866d; color: white;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;background: #14866d; color: white;" | Cheletropic Reaction
|-
| style="text-align: center;background: #14866d; color: white;" | Exo-pathway
| style="text-align: center;background: #14866d; color: white;" | Endo-pathway
|-
| [[File:YfEXOIRC.LOG]]
| [[File:YfENDOIRC.LOG]]
| [[File:YfCHEIRC.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-19T22:39:27Z

Yf2715: /* Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model.
[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant.]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions.

 
 
===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>TTS4.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Figure 4. Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral
Therefore, with only the MOs with the same symmetry combining together, the reaction between 1,3-butadiene and ethylene is thermally allowed.

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 5. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 6. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 7. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 8. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 8. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 9. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 10. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 12. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 
===Conclusion===
In this experiment, a variety of pericyclic reactions were located and their transition structures are characterized. Molecular orbital-based methods were used to numerically solving the Schrödinger equation and locate the transition structures based on the local shape of a potential energy surface. The reaction coordinates, reaction energies and activation barrier heights were also calculated. The roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction was also discussed. For the concerted cycloaddtion reaction between 1,3-butadiene and ethylene, the bond formation is synchronous as the two carbons in each pair move towards each other at the same rate. It was also confirmed that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. In exercise 2, the reaction between cyclohexadiene and 1,3-dioxole has an inverse electron demand. From the energy analysis, the endo pathway was proved to be more kinetically and thermodynamically favoured as a result of secondary orbital interactions. In exercise 3, there are three different reaction pathways for xylylene and sulfur dioxide, the endo/exo Diels - Ader reaction and the Cheletropic reaction. From the energy analysis, the endo product was proved to be more kinetically favoured and the cheletropic product was more thermodynamically favoured. A reaction profile was used to help read the reaction more directly.
 
 
===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state : [[File:Yf 1 TSIRC.LOG]]

====Exercise 2====
{| class="wikitable"
|+ Table 15. Links to the log files in exercise 2
! rowspan="2" style="center; background: #14866d; color: white;" | Chemicals
! colspan="2" style="center; background: #14866d; color: white;" | Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

====Exercise 3====

{| class="wikitable"
|+ Table 16. Links to the log file of IRC calculations at PM6 level
! colspan="2" style="text-align: center;background: #14866d; color: white;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;background: #14866d; color: white;" | Cheletropic Reaction
|-
| style="text-align: center;background: #14866d; color: white;" | Exo-pathway
| style="text-align: center;background: #14866d; color: white;" | Endo-pathway
|-
| [[File:YfEXOIRC.LOG]]
| [[File:YfENDOIRC.LOG]]
| [[File:YfCHEIRC.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-19T22:39:16Z

Yf2715: /* Vibration analysis */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model.
[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant.]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions.

 
 
===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>TTS4.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Figure 4. Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral
Therefore, with only the MOs with the same symmetry combining together, the reaction between 1,3-butadiene and ethylene is thermally allowed.

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 5. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 6. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 7. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 7. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 8. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 9. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 10. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 12. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 
===Conclusion===
In this experiment, a variety of pericyclic reactions were located and their transition structures are characterized. Molecular orbital-based methods were used to numerically solving the Schrödinger equation and locate the transition structures based on the local shape of a potential energy surface. The reaction coordinates, reaction energies and activation barrier heights were also calculated. The roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction was also discussed. For the concerted cycloaddtion reaction between 1,3-butadiene and ethylene, the bond formation is synchronous as the two carbons in each pair move towards each other at the same rate. It was also confirmed that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. In exercise 2, the reaction between cyclohexadiene and 1,3-dioxole has an inverse electron demand. From the energy analysis, the endo pathway was proved to be more kinetically and thermodynamically favoured as a result of secondary orbital interactions. In exercise 3, there are three different reaction pathways for xylylene and sulfur dioxide, the endo/exo Diels - Ader reaction and the Cheletropic reaction. From the energy analysis, the endo product was proved to be more kinetically favoured and the cheletropic product was more thermodynamically favoured. A reaction profile was used to help read the reaction more directly.
 
 
===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state : [[File:Yf 1 TSIRC.LOG]]

====Exercise 2====
{| class="wikitable"
|+ Table 15. Links to the log files in exercise 2
! rowspan="2" style="center; background: #14866d; color: white;" | Chemicals
! colspan="2" style="center; background: #14866d; color: white;" | Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

====Exercise 3====

{| class="wikitable"
|+ Table 16. Links to the log file of IRC calculations at PM6 level
! colspan="2" style="text-align: center;background: #14866d; color: white;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;background: #14866d; color: white;" | Cheletropic Reaction
|-
| style="text-align: center;background: #14866d; color: white;" | Exo-pathway
| style="text-align: center;background: #14866d; color: white;" | Endo-pathway
|-
| [[File:YfEXOIRC.LOG]]
| [[File:YfENDOIRC.LOG]]
| [[File:YfCHEIRC.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-19T22:38:58Z

Yf2715: /* MO diagram and HOMO-LUMO orbitals */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model.
[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant.]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions.

 
 
===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>TTS4.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Figure 4. Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral
Therefore, with only the MOs with the same symmetry combining together, the reaction between 1,3-butadiene and ethylene is thermally allowed.

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 4. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 5. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 6. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 7. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 8. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 9. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 10. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 12. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 
===Conclusion===
In this experiment, a variety of pericyclic reactions were located and their transition structures are characterized. Molecular orbital-based methods were used to numerically solving the Schrödinger equation and locate the transition structures based on the local shape of a potential energy surface. The reaction coordinates, reaction energies and activation barrier heights were also calculated. The roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction was also discussed. For the concerted cycloaddtion reaction between 1,3-butadiene and ethylene, the bond formation is synchronous as the two carbons in each pair move towards each other at the same rate. It was also confirmed that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. In exercise 2, the reaction between cyclohexadiene and 1,3-dioxole has an inverse electron demand. From the energy analysis, the endo pathway was proved to be more kinetically and thermodynamically favoured as a result of secondary orbital interactions. In exercise 3, there are three different reaction pathways for xylylene and sulfur dioxide, the endo/exo Diels - Ader reaction and the Cheletropic reaction. From the energy analysis, the endo product was proved to be more kinetically favoured and the cheletropic product was more thermodynamically favoured. A reaction profile was used to help read the reaction more directly.
 
 
===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state : [[File:Yf 1 TSIRC.LOG]]

====Exercise 2====
{| class="wikitable"
|+ Table 15. Links to the log files in exercise 2
! rowspan="2" style="center; background: #14866d; color: white;" | Chemicals
! colspan="2" style="center; background: #14866d; color: white;" | Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

====Exercise 3====

{| class="wikitable"
|+ Table 16. Links to the log file of IRC calculations at PM6 level
! colspan="2" style="text-align: center;background: #14866d; color: white;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;background: #14866d; color: white;" | Cheletropic Reaction
|-
| style="text-align: center;background: #14866d; color: white;" | Exo-pathway
| style="text-align: center;background: #14866d; color: white;" | Endo-pathway
|-
| [[File:YfEXOIRC.LOG]]
| [[File:YfENDOIRC.LOG]]
| [[File:YfCHEIRC.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-19T22:38:16Z

Yf2715: /* transition states and reactivity */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model.
[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant.]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions.

 
 
===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>TTS4.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral
Therefore, with only the MOs with the same symmetry combining together, the reaction between 1,3-butadiene and ethylene is thermally allowed.
====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 4. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 5. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 6. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 7. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 8. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 9. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 10. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 12. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 
===Conclusion===
In this experiment, a variety of pericyclic reactions were located and their transition structures are characterized. Molecular orbital-based methods were used to numerically solving the Schrödinger equation and locate the transition structures based on the local shape of a potential energy surface. The reaction coordinates, reaction energies and activation barrier heights were also calculated. The roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction was also discussed. For the concerted cycloaddtion reaction between 1,3-butadiene and ethylene, the bond formation is synchronous as the two carbons in each pair move towards each other at the same rate. It was also confirmed that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. In exercise 2, the reaction between cyclohexadiene and 1,3-dioxole has an inverse electron demand. From the energy analysis, the endo pathway was proved to be more kinetically and thermodynamically favoured as a result of secondary orbital interactions. In exercise 3, there are three different reaction pathways for xylylene and sulfur dioxide, the endo/exo Diels - Ader reaction and the Cheletropic reaction. From the energy analysis, the endo product was proved to be more kinetically favoured and the cheletropic product was more thermodynamically favoured. A reaction profile was used to help read the reaction more directly.
 
 
===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state : [[File:Yf 1 TSIRC.LOG]]

====Exercise 2====
{| class="wikitable"
|+ Table 15. Links to the log files in exercise 2
! rowspan="2" style="center; background: #14866d; color: white;" | Chemicals
! colspan="2" style="center; background: #14866d; color: white;" | Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

====Exercise 3====

{| class="wikitable"
|+ Table 16. Links to the log file of IRC calculations at PM6 level
! colspan="2" style="text-align: center;background: #14866d; color: white;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;background: #14866d; color: white;" | Cheletropic Reaction
|-
| style="text-align: center;background: #14866d; color: white;" | Exo-pathway
| style="text-align: center;background: #14866d; color: white;" | Endo-pathway
|-
| [[File:YfEXOIRC.LOG]]
| [[File:YfENDOIRC.LOG]]
| [[File:YfCHEIRC.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-19T22:16:41Z

Yf2715: /* Exercise 3 */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model.
[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant.]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions.

 
 
===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>TTS4.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 4. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 5. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 6. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 7. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 8. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 9. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 10. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 12. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 
===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state : [[File:Yf 1 TSIRC.LOG]]

====Exercise 2====
{| class="wikitable"
|+ Table 15. Links to the log files in exercise 2
! rowspan="2" style="center; background: #14866d; color: white;" | Chemicals
! colspan="2" style="center; background: #14866d; color: white;" | Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

====Exercise 3====

{| class="wikitable"
|+ Table 16. Links to the log file of IRC calculations at PM6 level
! colspan="2" style="text-align: center;background: #14866d; color: white;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;background: #14866d; color: white;" | Cheletropic Reaction
|-
| style="text-align: center;background: #14866d; color: white;" | Exo-pathway
| style="text-align: center;background: #14866d; color: white;" | Endo-pathway
|-
| [[File:YfEXOIRC.LOG]]
| [[File:YfENDOIRC.LOG]]
| [[File:YfCHEIRC.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-19T22:16:25Z

Yf2715: /* Exercise 1 */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model.
[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant.]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions.

 
 
===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>TTS4.LOG</uploadedFileContents>
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| <jmol>
<jmolApplet>
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<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
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====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 4. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 5. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 6. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 7. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
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|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 8. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 9. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
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|<jmol>
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<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
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<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
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There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 10. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 12. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
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| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 
===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state : [[File:Yf 1 TSIRC.LOG]]

====Exercise 2====
{| class="wikitable"
|+ Table 15. Links to the log files in exercise 2
! rowspan="2" style="center; background: #14866d; color: white;" | Chemicals
! colspan="2" style="center; background: #14866d; color: white;" | Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

====Exercise 3====

{| class="wikitable"
|+ Table 15. Links to the log file of IRC calculations at PM6 level
! colspan="2" style="text-align: center;background: #14866d; color: white;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;background: #14866d; color: white;" | Cheletropic Reaction
|-
| style="text-align: center;background: #14866d; color: white;" | Exo-pathway
| style="text-align: center;background: #14866d; color: white;" | Endo-pathway
|-
| [[File:YfEXOIRC.LOG]]
| [[File:YfENDOIRC.LOG]]
| [[File:YfCHEIRC.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-19T22:14:10Z

Yf2715: /* Exercise 3 */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model.
[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant.]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions.

 
 
===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>TTS4.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
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====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 4. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 5. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 6. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 7. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 8. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 9. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 10. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 12. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 
===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state.[[File:Yf 1 TSIRC.LOG]]
====Exercise 2====
{| class="wikitable"
|+ Table 15. Links to the log files in exercise 2
! rowspan="2" style="center; background: #14866d; color: white;" | Chemicals
! colspan="2" style="center; background: #14866d; color: white;" | Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

====Exercise 3====

{| class="wikitable"
|+ Table 15. Links to the log file of IRC calculations at PM6 level
! colspan="2" style="text-align: center;background: #14866d; color: white;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;background: #14866d; color: white;" | Cheletropic Reaction
|-
| style="text-align: center;background: #14866d; color: white;" | Exo-pathway
| style="text-align: center;background: #14866d; color: white;" | Endo-pathway
|-
| [[File:YfEXOIRC.LOG]]
| [[File:YfENDOIRC.LOG]]
| [[File:YfCHEIRC.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-19T22:13:41Z

Yf2715: /* Links to the log files */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model.
[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant.]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions.

 
 
===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
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====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 4. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 5. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 6. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 7. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
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|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 8. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 9. The vibration of exo TS]]
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There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 10. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 12. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
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| <jmol>
<jmolApplet>
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<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
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| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
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|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
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| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
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| <jmol>
<jmolApplet>
<color>white</color>
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<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
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As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 
===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state.[[File:Yf 1 TSIRC.LOG]]
====Exercise 2====
{| class="wikitable"
|+ Table 15. Links to the log files in exercise 2
! rowspan="2" style="center; background: #14866d; color: white;" | Chemicals
! colspan="2" style="center; background: #14866d; color: white;" | Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

====Exercise 3====

{| class="wikitable"
|+ Table 15. Links to the log file of IRC calculations at PM6 level
! colspan="2" style="text-align: center;background: #14866d; color: white;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;background: #14866d; color: white;" | Cheletropic Reaction
|-
| style="text-align: center;" | Exo-pathway
| style="text-align: center;" | Endo-pathway
|-
| [[File:YfEXOIRC.LOG]]
| [[File:YfENDOIRC.LOG]]
| [[File:YfCHEIRC.LOG]]
|}

File:YfCHEIRC.LOG

2017-12-19T22:13:29Z

Yf2715:

File:YfENDOIRC.LOG

2017-12-19T22:13:04Z

Yf2715:

File:YfEXOIRC.LOG

2017-12-19T22:12:18Z

Yf2715:

Rep:Mod:ydf2715ts

2017-12-19T22:08:57Z

Yf2715: /* Exercise 2 */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model.
[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant.]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions.

 
 
===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>TTS4.LOG</uploadedFileContents>
</jmolApplet>
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| <jmol>
<jmolApplet>
<color>white</color>
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<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 4. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 5. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 6. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 7. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 8. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 9. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 10. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 12. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 
===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state.[[File:Yf 1 TSIRC.LOG]]
====Exercise 2====
{| class="wikitable"
! rowspan="2" style="center; background: #14866d; color: white;" | Chemicals
! colspan="2" style="center; background: #14866d; color: white;" | Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-19T22:08:39Z

Yf2715: /* Exercise 2 */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model.
[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant.]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions.

 
 
===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>TTS4.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 4. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 5. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 6. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 7. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 8. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 9. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 10. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 12. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
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<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
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<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
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As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 
===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state.[[File:Yf 1 TSIRC.LOG]]
====Exercise 2====
{| class="wikitable"
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-19T22:07:21Z

Yf2715: /* Exercise 2 */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model.
[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant.]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions.

 
 
===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
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|<jmol>
<jmolApplet>
<color>white</color>
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<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
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<uploadedFileContents>TTS4.LOG</uploadedFileContents>
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====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 4. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 5. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 6. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 7. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
</jmolApplet>
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|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 8. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 9. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 10. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 12. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 
===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state.[[File:Yf 1 TSIRC.LOG]]
====Exercise 2====
{| class="wikitable"
! rowspan="2"style="text-align: center; background: #14866d; color: white;"|Chemicals
! colspan="2"style="text-align: center; background: #14866d; color: white;"|Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-19T22:06:59Z

Yf2715: /* Exercise 2 */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model.
[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant.]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions.

 
 
===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>TTS4.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 4. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 5. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 6. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 7. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 8. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 9. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 10. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 12. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 
===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state.[[File:Yf 1 TSIRC.LOG]]
====Exercise 2====
{| class="wikitable"
! rwospan="2"style="text-align: center; background: #14866d; color: white;"|Chemicals
! colspan="2"style="text-align: center; background: #14866d; color: white;"|Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-19T22:06:34Z

Yf2715: /* Exercise 2 */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model.
[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant.]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions.

 
 
===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>TTS4.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 4. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 5. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 6. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 7. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 8. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 9. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 10. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 12. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 
===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state.[[File:Yf 1 TSIRC.LOG]]
====Exercise 2====
{| class="wikitable"
! colspan="2"style="text-align: center; background: #14866d; color: white;"|Chemicals
! style="text-align: center; background: #14866d; color: white;"|Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-19T22:06:15Z

Yf2715: /* Exercise 2 */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model.
[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant.]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions.

 
 
===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>TTS4.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 4. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 5. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 6. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 7. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 8. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 9. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 10. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 12. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 
===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state.[[File:Yf 1 TSIRC.LOG]]
====Exercise 2====
{| class="wikitable"
! rowspan="2"style="text-align: center; background: #14866d; color: white;"|Chemicals
! style="text-align: center; background: #14866d; color: white;"|Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|-
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

Rep:Mod:ydf2715ts

2017-12-19T22:05:35Z

Yf2715: /* transition states and reactivity */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model.
[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant.]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions.

 
 
===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>TTS4.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 4. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 5. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 6. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 7. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 8. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 9. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 10. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 12. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
 
 
===Links to the log files===
====Exercise 1====
The IRC calculation for the transition state.[[File:Yf 1 TSIRC.LOG]]
====Exercise 2====
{| class="wikitable"
! rowspan="2"style="text-align: center; background: #14866d; color: white;"|Chemicals
! style="text-align: center; background: #14866d; color: white;"|Methods
|-
|style="text-align: center; background: #14866d; color: white;"|PM 6
|style="text-align: center; background: #14866d; color: white;"|B3YLP
|Cyclohexadiene
|[[File:YFCYCLO.LOG]]
|[[File:YF631CYC.LOG]]
|-
|1,3-dioxole
|[[File:YFDIO1.LOG]]
|[[File:YF631DIO.LOG]]
|-
|TS of EXO
|[[File:YfEXOTS3.LOG]]
|[[File:YF631TSEXO.LOG]]
|-
|TS of Endo
|[[File:YfENDOTS3.LOG]]
|[[File:YF631TSENDO.LOG]]
|-
|Exo product
|[[File:YfEXO3.LOG]]
|[[File:YF631EXO.LOG]]
|-
|Endo product
|[[File:YfENDO3.LOG]]
|[[File:YF631ENDO.LOG]]
|}

File:YF631TSENDO.LOG

2017-12-19T22:04:25Z

Yf2715:

File:YF631DIO.LOG

2017-12-19T22:04:05Z

Yf2715:

File:YF631CYC.LOG

2017-12-19T22:03:47Z

Yf2715:

File:YF631ENDO.LOG

2017-12-19T22:03:28Z

Yf2715:

File:YF631EXO.LOG

2017-12-19T22:03:04Z

Yf2715:

File:YF631TSEXO.LOG

2017-12-19T22:02:44Z

Yf2715:

File:Yf 1 TSIRC.LOG

2017-12-19T21:55:56Z

Yf2715:

Rep:Mod:ydf2715ts

2017-12-19T21:47:07Z

Yf2715: /* Energy analysis */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model.
[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant.]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions.

 
 
===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>TTS4.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 4. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 5. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 6. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 7. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 8. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 9. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 10. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 12. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
 As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
 As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]

Rep:Mod:ydf2715ts

2017-12-19T21:46:29Z

Yf2715: /* Energy analysis */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model.
[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant.]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions.

 
 
===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
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====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 4. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 5. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 6. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 7. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
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|<jmol>
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<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
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|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 8. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 9. The vibration of exo TS]]
|-
|<jmol>
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There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 10. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 12. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
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| style="text-align:center;"| Transition State
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| style="text-align:center;"| Products
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As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.
As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]

Rep:Mod:ydf2715ts

2017-12-19T21:45:11Z

Yf2715: /* Exercise 1: Reaction of butadiene with ethylene */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model.
[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant.]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions.

 
 
===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
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====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 4. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 5. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 6. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 7. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
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|<jmol>
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|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 8. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 9. The vibration of exo TS]]
|-
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There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 10. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 12. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
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| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
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| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
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|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
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| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
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| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
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As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]

Rep:Mod:ydf2715ts

2017-12-19T21:44:54Z

Yf2715: /* Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model.
[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant.]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions.

===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YDFBBB.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>yfETHENE.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>240</size>
<uploadedFileContents>TTS4.LOG</uploadedFileContents>
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| <jmol>
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<uploadedFileContents>yfHEXENE.LOG</uploadedFileContents>
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</jmol>
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====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 4. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 5. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 6. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

 
 
===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 7. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Cyclohexadiene</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFCYCLO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of endo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 8. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 9. The vibration of exo TS]]
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>1,3-dioxole</title>
<size>240</size>
<uploadedFileContents>YFDIO1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Endo product</title>
<size>240</size>
<uploadedFileContents>YfENDO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<title>Exo product</title>
<size>240</size>
<uploadedFileContents>YfEXO3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 10. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 

===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 12. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]

Rep:Mod:ydf2715ts

2017-12-19T21:44:36Z

Yf2715: /* Exercise 3: Diels-Alder vs Cheletropic */

==transition states and reactivity==

===Introduction===
A potential energy suface is often used as a tool to support the analysis of chemical reaction dynamics and molelcular geometry. The stationay points, the points with a zero gradient, are mostly meaningful. The reactants and products correspond to the minima while the saddle points represent the transition states, which is the highest energy point on the reaction coordinate (the minimum energy path between the reactants and the products). When evaluating the necessary points on a potential energy surface, the first and second derivatives of the energy with respect to poision are usually used, which correspond to the gradient and the curvature respectively. The total gradient of a potential energy surface will be zero.
For linear molecules, there are 3N - 5 vibrition modes while for non-linear molecules, there are 3N - 6 vibration modes. On the other word, there are 3N - 6 degrees of freedom and each one corresponds to a normal mode, which can be visualised using a classical harmonic oscillator model.
[[File:Yfintro1.PNG|center|thumb|999px|Figure 1. The Hooke's law.]]
Located in the minima of the potential energy surface, the reactants and products are stable and tend to stay where they are and vibrate constantly unless sufficient energy is given to help overcome the activation barrier. The transition state, on the other hand, is semi-stable and is ready to vibrate downhill towards the energy minima, i.e. the reactants and the products. The vibration modes of transition states give a negative force constant and the modes of reactants and products give a positive force constant, which makes it easy to distinguish the formars and the latters using the curvature, the second deravative of the energy with respect to bond distances.(∂2V(ri)/∂ri2).
[[File:Yfintro2.png|center|thumb|999px|Figure 2. Frequency is proportional to the square root of the force constant.]]
A positive value indicates a minimum, i.e. the reactants or the products, while a negative value indicates a maximum, a transition state.
The frequency calculation is also used as a tool to confirm the position of a structure on the potential energy surface.
Since the square root of the force constant is used to calculate the frequency, the second derivative of gradient can also distinguish reactants/products and transition states. The chemical pathways can be divided into two kinds, the thermodynamically controlled and the kinetically controlled ones. Under thermodynamic conditions, more stable products are afforded as the dominate product and the reaction is reversible, which makes the energy level of the transition states not important. On the other hand, under kinetic conditions, the reaction is irreversible and the energy of transition states is determinant. The lower the activation energy, the faster the kinetic product can form. Therefore, a transition state of lower energy is required to make the most rapidly afforded products predominate in kinetically controlled reactions.

===Exercise 1: Reaction of butadiene with ethylene===
Below presents the reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.
[[File:Yf1mech.PNG|center|thumb|999px|Figure 3. reaction scheme for the cycloaddition reaction between 1,3-butadiene and ethylene.]]
The reactants are optimised at the PM6 level. In this diels alder reaction, the cis geometry of butadiene gives rise to the correct orbital overlap to have the reaction take place. As the structure of the product is wholy predictable, method 3 in the tutorial was used to construct the structure of the transition state in this reaction after the optimizition of the product at PM6 level. The distance of 2.2Å was an intermidiate value between a normal single C-C bond (1.54Å) and the Van der Waals distance between two carbon atoms (3.4Å) and was used in C-C bond formation for the separation between the terminal carbons in both alkenes. After confirming the guess TS structure was correct, the guess structure was reoptimised with a more accurate method, B3LYP/6-31G(d), and then used to run a IRC.
====Optimized structures====
Below presents the optimized structures of the reactants, product and the transition state.

{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 1. Optimized structures by PM6 calculation
|-
| style=" text-align:center" | 1,3-butadiene
| style=" text-align:center" | Ethylene
| style=" text-align:center" | Transition State
| style=" text-align:center" | Cyclohexene
|-
|<jmol>
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<script>frame 6</script>
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| <jmol>
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====confirmation of TS====
The vibrition modes of the TS and the IRC spectra are shown in the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ydf2715ts#Vibration_analysis | vibration analysis] part.
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state, and the animation corresponds to the right reaction coordination, which indicates that the guess TS has the right structure. The IRC gave more direct proof of a correct TS structure by showing the correct reaction coordinate with minimum energy pathway. As shown in Figure 5, the energy of reactants go up to reach the level of transition state, crossing the activation barrier to for the products. The RMS gradient Norm along IRC shows that the gradients of reactants, products and the TS are all equal to zero.

====MO diagram and HOMO-LUMO orbitals====
Below presents the MO diagram and HOMO and LUMO of reactants and transition state.
{| class="wikitable"
|+ Table 2. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemical Structure
! style="background: #14866d; color: white;" | HOMO
! style="background: #14866d; color: white;" | LUMO
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|[[File:yfBUTADIENE_HHOMO.PNG|thumb|center|210px|MO1, Antisymmetric]]
|[[File:yfBUTADIENE_LLOMO.PNG|thumb|center|210px|MO2, Symmetric]]
|rowspan="3"|[[File:YdfMO.PNG|thumb|upforward|700px|Idealized MO diagram for [4+2] cycloaddition reaction.]]
|-
|<nowiki>Ethylene</nowiki>
|[[File:yfETHYLENE_HOMO.PNG|thumb|center|210px|MO3, Symmetric]]
|[[File:yfETHYLENE_LUMO.PNG|thumb|center|210px|MO4, Antisymmetric]]
|-
|<nowiki>Transition State</nowiki>
|[[File:ydfhomo.PNG|thumb|center|210px|MO6, HOMO, Symmetric]] [[File:ydfhomo+1.PNG|thumb|center|210px|MO5, HOMO-1, Antisymmetric]]
|[[File:ydflumo.PNG|thumb|center|210px|MO7, LUMO, Symmetric]] [[File:ydflumo+1.PNG|thumb|center|210px|MO8, LUMO+1, Antisymmetric]]
|}
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented above.
The HOMO-LUMO gap of butadiene is smaller than that of ethylene as a result of its electron sufficient property. In the stage of TS, the electrons are rearranged to spins and geometries that can better delocalise the whole molecule.

As stated in Woodward Hoffmann rule, the total number of (4q+2)s + (4r)amust be odd in order to allow bimolecular cycloaddition reaction to take place. 'q' and 'r' represent integers starting from zero. The suffix 's' represents supprafacial (new bonds on the same face) and 'a' represents antarafacial (opposite faces are involved).
Below presents the [π4s + π2s] cycloaddtion in this investigated reaction.
(4q+2)s + (4r)a
=1 + 0
=1 => odd result, thermally allowed when q = r = 0

From the table above, it can be clearly concluded that only the MOs with the same symmetry are allowed to combine with each other to give a TS MO with the same symmetry. The symmetric HOMO of ethylene (MO3) interacts with symmetric LUMO of butadiene (MO 1) to afford symmetric HOMO (MO 6) and LUMO (MO 7) of TS. The antisymmetric LUMO of ethylene (MO 4) interacts with antisymmetric HOMO of butadiene (MO 1) to afford antisymmetric HOMO-1 (MO 5) and LUMO+1 (MO8) of TS. It is easy to understand as the symmetries have be matching since the combination of antisymmetric and symmetric orbitals gives rise to a zero overlap integral.
symmetric - symmetric interaction ==> non zero orbital overlap integral
antisymmetric - antisymmetric interaction ==> non zero orbital overlap integral
symmetric - antisymmetric interaction ==> zero orbital overlap integral

====Bond length Analysis====
{| class="wikitable"
|+ Table 3. The C-C bond lengths in the reaction coordinate
! style="background: #14866d; color: white;" | 1,3-butadiene
! style="background: #14866d; color: white;" | ethylene
! style="background: #14866d; color: white;" | Transition state
! style="background: #14866d; color: white;" | Product cyclohexeneh
|-
| [[File:Yfbutatata.PNG|thumb|center|300px]]
| [[File:Yfethyyy.PNG|thumb|center|295px]]
| [[File:YfTSSS.PNG|thumb|center|325px]]
| [[File:Yf1proo.PNG|thumb|center|320px]]
|-
|Double bond C1- C2 = 1.34Å
Single bond C2 - C3 = 1,47Å 
Double bond C3 - C4 = 1.34Å
|Double bond C5 - C6 = 1.33Å
|Double bond breaking C1 - C2 = 1.38Å >1.34Å
Double bond breaking C3 - C4 = 1.38Å > 1.34Å 
Double bond breaking C5 - C6 = 1.38Å >1.33Å 
Double bond forming C2 - C3 = 1.41Å < 1.47Å 
Single bond forming C3 - C4 = 2.11Å 
Single bond forming C1 - C6 = 2.11Å
|C1 - C2 = 1.50Å, C-C sp3 - sp2 
C3 - C4 = 1.50Å, C-C sp2 - sp3 
C5 - C6 = 1.54Å, C-C sp3 - sp3 
C2 - C3 = 1.34Å, C=C sp2 - sp2 
C3 - C4 = 1.54Å, C-C sp3 - sp3 
C1 - C6 = 1.54Å, C-C sp3 - sp3
|}
The C-C bond lengths of the reactants, product and the TS are presented in the table above.
The typical C-C bond lengths and the Van der Waals radius of the C atom are presented below.
{| class="wikitable"
|+
! colspan="6" style="background: #14866d; color: white;" | Table 4. typical C-C bond length
|-
|C-C bond type
|sp3 - sp3
|sp3 - sp2
|sp2 - sp2
|vdW radius of C
|vdW distance of 2 C
|-
|Bond length
|center|1.54Å
| 1.50Å
| 1.47Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
In the TS, there are three types of bonds, the partly breaking double bond, the partly forming single bond and the partly forming double bond. As the reaction progresses, the bond lengthes of the double bonds in butadiene (C1 - C2 and C3 - C4) increase from 1.34Å to 1.38Å in the TS and then to 1.50Å in the product. This is due to the change in the carbon hybridisation from sp2 to sp3 and the formation of the new sigma bonds. The bond lengths of the two partly formed single bonds (C3 - C4 and C1 - C6) in the TS is 2.11Å, which is between the value of typical sp3 C-C bond length and the Van der Waals distance of 2 C atoms.
The double bond in ethylene (C5 - C6) is weakened from 1.34Å to 1.38Å in the TS and then to 1.54Å in the product. The newly formed double bond (C2 - C3) grows from 1.47Å in butadiene to 1.41Å in the TS and then to 1.34Å in the product. The decrease of bond length reveals the additional pi overlap between the two carbons, which largely strengthens the bond.

====Vibration analysis====
Below presents the vibration that corresponds to the reaction path at the transition state.
{| class="wikitable"
|+
! colspan="4" style="center; background: #14866d; color: white;"| Table 5. The vibration and IRC of TS.
|-
| [[File:Yfproof.PNG|thumb|center|1000px|Figure 4. the vibration of the guess TS structure]]
| [[File:Yf1irc.PNG|thumb|center|1100px|Figure 5. the total energy alone intrinsic reaction coordinate]]
|-
| [[File:YfTSanimation.gif|thumb|center|666px|The animation of the vibration]]
| [[File:Yf1ircc.PNG|thumb|center|1100px|Figure 6. RMS gradient norm along IRC]]
|}
There is only one negative value of the vibration, which represents the saddle point, i.e. the transition state and the vibration frequency to reaction path is -948.37cm-1. From the animation, it is clear that the formation of the two C-C bonds is synchronous, since the two carbons in each pair move towards each other at the same rate.

===Exercise 2: Cycloaddtion of cyclohexadiene and 1,3-dioxole===
The Diels - Alder reaction is an organic [4+2] cycloaddition reaction between a conjugated diene and a substituted alkene, usually termed the dienophile, to produce a substituted cyclohexene system. In Exercise 2, the pericyclic reaction between cyclohexadiene and 1,3-dioxole was investigated. Below presents the reaction scheme.
[[File:Yfmechanism2.PNG|thumb|center|888px|Figure 7. the reaction scheme between cyclohexadiene and 1,3-dioxole.]]

Resulting from the significant stereoselectivity and regioselectivity of the 6-membered ring genenrated, this reaction is of great synthetic utility and has been a research topic fasinating for many years. The frontier molecular orbital model of cycloaddition reactions was raised by Kenichi Fukui, and is an approximation that remarkably succeeds in rationalizing the chemical properties in Diels - Alder reactions. It is assumed that it is the interactions of the HOMO of one molecule with the LUMO of the second molecule that determines the chemistry of the conjugated pi systems in the reaction. In the reaction between cyclohexadiene and 1,3-dioxole, the ring structures in both reactants give rise to two products, the exo and the endo products. The stereoselectivity was also studied in this exercise.

====Optimized structures, vibration and MOs====

As the structures of the products are predictable, method 3 in the tutorial was used to construct the structure of the TSs in this reaction after the optimizition of the products. As shown After confirming the guess TS structure was correct, both endo and exo TSs were optimised at PM6 level first and then reoptimised with B3LYP/6-31G(d). Frequency calculation and the IRC were also carried out in the experiment.
Below presents the structures for reactants, TSs and products after optimization.
{| class="wikitable"
|+
! colspan="6" style="center; background: #14866d; color: white;"| Table 6. Structures of reactans, TSs and products in the DA reaction.
|-
| style="text-align:center" | Reactants
| style="text-align:center" | Endo Pathway
| style="text-align:center" | Exo Pathway
| style="text-align:center" | The vibration of endo TS
| style="text-align:center" | The vibration of exo TS
|-
|<jmol>
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<title>Cyclohexadiene</title>
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|<jmol>
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<script>frame 6</script>
<uploadedFileContents>YfENDOTS3.LOG</uploadedFileContents>
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|<jmol>
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<color>white</color>
<title>TS of exo pathway</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YfEXOTS3.LOG</uploadedFileContents>
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|rowspan="2"|[[File:Yfvibendo.PNG|thumb|center|700px|Figure 8. The vibration of endo TS]]
|rowspan="2"|[[File:Yfvibexo.PNG|thumb|center|700px|Figure 9. The vibration of exo TS]]
|-
|<jmol>
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<title>1,3-dioxole</title>
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There is only one negative value in each vibration, which corresponds to the saddle point, i.e. the transition state, and indicates that the guess TS has the right structure.
The capital letters A and S correspond to 'antisymmetric' and 'symmetric' respectively. The combination of the MOs from the reactants and the formation of the MOs from the TS are clearly presented below. The occupied and unoccupied orbitals associated with the DA reaction for both TSs were located by symmetry. The HOMO/LUMO orbitals of the chemicals involved in this reaction and the two MO diagrams for both endo and exo pathways are all presented in the table below.

{| class="wikitable"
|+ Table 7. the HOMO and LUMO of both reactants and the transition state with the MO diagram
! style="text-align:center;background: #14866d; color: white;" | Chemicals and pathways
! style="background: #14866d; color: white;" | HOMO (HOMO - 1)
! style="background: #14866d; color: white;" | LUMO (LUMO + 1)
! style="background: #14866d; color: white;" | MO interactions
|-
|<nowiki>Cyclohexadiene</nowiki>
|[[File:Yfcyclu.PNG|thumb|center|210px|MO9, HOMO, Anitisymmetric, -0.326a.u.]]
|[[File:Yfcycho.PNG|thumb|center|210px|MO10, LUMO, Symmetric, 0.021a.u.]]
|rowspan="4"|[[File:YfendoMOD.PNG|thumb|center|700px|Figure 10. The idealized MO diagram for the formation of endo transition state.]][[File:YfexoMOD.PNG|thumb|center|700px|Figure 11. The idealized MO diagram for the formation of endo transition state.]]
|-
|<nowiki>1,3-dioxole</nowiki>
|[[File:Yfdioho.PNG|thumb|center|210px|MO11, HOMO, Symmetric, -0.192a.u.]]
|[[File:Yfdiolu.PNG|thumb|center|210px|MO12, LUMO, Antisymmetric, 0.041a.u.]]
|-
|<nowiki>Endo TS</nowiki>
|[[File:Yfentsho.PNG|thumb|center|210px|MO13, HOMO, Symmetric]][[File:Yfentshoo.PNG|thumb|center|210px|MO14, HOMO - 1, Antisymmetric]]
|[[File:Yfentslu.PNG|thumb|center|210px|MO15, LUMO, Symmetric]] [[File:Yfentsluu.PNG|thumb|center|210px|MO16, LUMO + 1, Antisymmetric]]
|-
|<nowiki>Exo TS</nowiki>
|[[File:Yfexotsho.PNG|thumb|center|210px|MO17, HOMO, Symmetric]][[File:Yfexotshoo.PNG|thumb|center|210px|MO18, HOMO - 1, Antisymmetric]]
|[[File:Yfexotsluu.PNG|thumb|center|210px|MO19, LUMO, Symmetric]] [[File:Yfexotslu.PNG|thumb|center|210px|MO20, LUMO + 1, Antisymmetric]]
|}

====Normal or inverse demand DA reaction ?====
As mentioned in the first paragraph, Diels - Alder reaction is a concerted [4+2] cycloaddition reaction between a conjugated diene and a substituted dienophile. The DA reaction can be divided into two types depanding on the relative energy level of the frontier MOs during the formation of the new single bonds. In normal DA reactions, TSs have highly stabilizing interactions between the HOMO of diene and the LUMO of dipolarophile, which results from the small energy gap between the HOMO-LUMO. Resulting from the absence of a largely stabilizing interaction, the electron - sufficient alkenes are unreactive with simple dienes. On the other hand, Diels - Alder reactions with 'inverse electron demand' arise under the circumstance that the interaction between LUMO of diene and HOMO of dienophile is greater, i.e. the energy gap is small than that between HOMO of diene and LUMO of dieophile. Since electron sufficiency can higher the HOMO of dienophile and electron defficiency can lower the LUMO of diene, electron rich dienophiles and electron defficient dienes would have smaller HOMO-LUMO gap and accelerate the reaction rate of an inverse electron demand DA reaction. 
For the DA reaction between cyclohexadiene and 1,3-dioxole, the energy gap between the LUMO of dienophile (MO12, 0.041a.u.) and the HOMO of diene (MO0, -0.326a.u.) is 0.367au. The LUMO of diene (MO10, 0.021a.u.) and the HOMO of dienophile (MO11, -0.192a.u.) have a smaller energy gap (0.213a.u.), which enhance the inverse electron demand DA reaction to form MO 13 and MO 15 (as presented in table 7). This is easy to understand, as the 1,3-dioxole benefits from the the electro - releasing oxygen atoms and is highly electron rich.

====Energy analysis====

{| class="wikitable"
|+ Table 8. Energies of reactants, TSs and products using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Compounds
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / Hatress
! style="text-align:center;background: #14866d; color: white;" | Energy calculated at PM6 level / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) /Hatree
! style="text-align:center;background: #14866d; color: white;" | Energy calculated using B3LYP/6-31G(d) x 105/ kJmol-1
|-
|style="text-align:center"|Cyclohexadiene
|style="text-align:center"| 0.1171
|style="text-align:center"| 307.39
|style="text-align:center"| -233.430962
|style="text-align:center"| -6.12756276
|-
|style="text-align:center"|1,3-dioxole
|style="text-align:center"| -0.0513
|style="text-align:center"| -134.66
|style="text-align:center"| -267.116106
|style="text-align:center"| -7.01179778
|-
|style="text-align:center"|sum of reactants
|style="text-align:center"| 0.0658
|style="text-align:center"| 172.73
|style="text-align:center"| -500.547068
|style="text-align:center"| -13.1394904
|-
|style="text-align:center"|Endo TS
|style="text-align:center"| 0.1380
|style="text-align:center"| 362.25
|style="text-align:center"| -500.427867
|style="text-align:center"| -13.1362315
|-

|style="text-align:center"|Exo TS
|style="text-align:center"| 0.1391
|style="text-align:center"| 365.14
|style="text-align:center"| -500.506565
|style="text-align:center"| -13.1382973
|-

|style="text-align:center"|Endo product
|style="text-align:center"| 0.0377
|style="text-align:center"| 98.96
|style="text-align:center"| -500.602493
|style="text-align:center"| -13.1410815
|-
|style="text-align:center"|Exo product
|style="text-align:center"| 0.0379
|style="text-align:center"| 99.49
|style="text-align:center"| -500.601679
|style="text-align:center"| -13.1407941
|-
|}

The kinetically favoured product is determined by the activation energy. The smaller the activation energy, the faster the product can be formed. For the thermodynamically favoured product, the reaction energy is a factor more important. Under thermodynamic conditions, the reaction is reversible and is an equilibrium. The more exothermic or less endothermic pathway will give more smaller (more negative) reaction energy and more stable product.

{| class="wikitable"
|+ Table 9. Activation energies and Reaction energies for exo/endo pathways using Semi empirical methods and DFT methods
! style="text-align:center;background: #14866d; color: white;" | Pathways with methods
! style="text-align:center;background: #14866d; color: white;" | Activation barrier (Ea) / kJmol-1
! style="text-align:center;background: #14866d; color: white;" | Reaction energy / kJmol-1
|-
|style="text-align:center"|Endo (PM 6)
|style="text-align:center"| +189.52
|style="text-align:center"| -73.77
|-
|style="text-align:center"|Endo(B3LYP)
|style="text-align:center"| +158.76
|style="text-align:center"| -67.41
|-
|style="text-align:center"|Exo (PM 6)
|style="text-align:center"| +192.41
|style="text-align:center"| -73.24
|-
|style="text-align:center"|Exo(B3LYP)
|style="text-align:center"| +167.29
|style="text-align:center"| -63.84
|}
Activation energy : +189.52 < +192.41 (PM6)
+158.76 < +167.29 (B3LYP) ==> Endo product more kinetically favoured.
Reaction energy : -73.77 < -73.24 (PM6)
-67.41 < -63.84 (B3LYP) ==> Endo product more thermodynamically favoured.

Consequently, the endo product is both kinetically and thermodynamically favoured in this reaction. This is easy to understand, as the exo product is kinetically more hindered and thermodynamically less stable. This conclusion can be further confirmed by considering the secondary orbital interactions. Below presents the HOMOs of both endo and exo TSs. The isovalue was set to 0.01 in Gaussiview.

{| class="wikitable"
|+ Table 10. the HOMOs of both endo and exo TSs
! style="text-align:center;background: #14866d; color: white;" | Endo TS HOMO (MO 13)
! style="text-align:center;background: #14866d; color: white;" | Exo TS HOMO (MO 17)
! style="text-align:center;background: #14866d; color: white;" | Discussion
|-
|[[File:YfSECendoHOMO.PNG|thumb|center]]
|[[File:YfSECexoHOMO.PNG|thumb|center]]
| The secondary orbital interaction is the determinant factor of the dominate product in this reaction. As proved above, the endo pathway is kinetically more favoured, which means the corresponding activation energy is lower and the energy of endo TS is also lower than that of the exo TS. In the endo TS, the non - bonding p orbital on the oxygen atoms of 1,3 - dioxole interacts with the LUMO of cyclohexadiene, nOp → LUMO of cyclohexadiene, which strongly stablise the endo TS and lower the activation energy.
This seconday orbital interaction works on both the transition state and the final products. The endo product benefits from this interaction and is stabilised with a lower energy. Therefore the overall reaction energy of the endo pathway is more exothermic.
 There are rigid ring structures in both reactants, which gives rise to some steric slashing during the reaction course. In the endo pathway, the steric hinderance makes the reactant FMOs reorient and overlap better. This is a minor factor compared with the secondary orbital intercations. In the exo pathway, the reactants are also slightly hindered with the presence of a small steric slashing. Although this is not obvious in the MO figures.
|}

 
 
===Exercise 3: Diels-Alder vs Cheletropic===
Below presents the reaction scheme for the cycloaddition reaction between o-xylylene and SO2.
[[File:Yf3mechanism.PNG|center|thumb|666px|Figure 12. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]
Similar to exercise 2, there are two pathways for this Diels - Alder reaction, the endo pathway and the exo pathway. The two reactants, the o-yxlylene and SO2 are sptimised at the PM6 level. During the experimental, the endo DA TS and the corresponding adduct were drawn. Method 3 was used to construct a guess exo TS structure. The newly formed bonds in the reaction were broken and the C-O separation was set at 2.0Å and the C-S separation was set at 2.4Å. After having the relative atoms frozen in space, optimization was carried out at the PM6 level to afford the guess exo TS structure. The guess TS structure reoptimised before the IRC and frequency calculations were carried out. After confirming the guess TS structure was correct, the reaction coordination with an IRC calculation for each reaction pathway were visalised. The reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the three reaction pathways were drawn in the analysis part.
====Optimized structures====
The TSs for the endo- and exo- Diels - Alder reaction and the Cheletropic reactions were all optimized at the PM6 level. Below presents all the optimized structures for reactants, TSs and products.
{| class="wikitable"
|+ Table 11. Structure for reactants, transition states (TS) and products for all 3 reaction pathways
! rowspan="2" style="center; background: #14866d; color: white;" | Optimized reactants
! rowspan="2" style="center; background: #14866d; color: white;" | Species
! colspan="2" style="center; background: #14866d; color: white;" | Diels-Alder Reaction
! rowspan="2" style="center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align:center; background: #14866d; color: white;" | Endo pathway
| style="text-align:center; background: #14866d; color: white;" | Exo pathway
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Sulfur dioxide</title>
<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YFSO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>YF3ENDOTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>YF3EXOTS2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>YF3CHETS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<title>Xylylene</title>
<size>240</size>
<uploadedFileContents>YFXYL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| style="text-align:center;"| Products
|<jmol>
<jmolApplet>
<color>white</color>

<size>240</size>
<script>frame 6</script>
<uploadedFileContents>YF3DAENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>YF3DAEXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>YF3CHE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
As shown in reaction scheme, one of the major driving force of the reaction between xylylene and SO2 is the recovery of the bezene ring and the aromatic chararter. Xylylene is often produced through the pyrolysis reaction of xylene and the significant thermal energy destroys the bezene structure. According to Huckel's rule, a molecule has to have the requirements below satisfied, to be considered as aromatic.
1. the molecule must have 4n + 2 electrons in p orbitals
2. the molecule must be planar
3. the molecule must be cyclic
4. the molecule must have a continuous ring of p orbitals
In spite of the planar structure with conjugated double bonds, xylylene is considered as a non - aromatic molecule. Although it has 6 π electrons in total, only 4 of them are in the ring, and with the presence of a diradical, the molecule is remarkably unstable. The non - aromatic character gives rise to a relatively high energy π system, which is readily reactive.

====IRC analysis====
Below presents the IRC calculation and the reaction trajectories for the three reactions. The energy changes along the reaction coordinate and the way reactants approaching each other to form the products are all clearly shown below.
{| class="wikitable"
|+ Table 12. Visualisation of the reaction coordinatea with an IRC calculation for each path
! style="text-align:center; background: #14866d; color: white;" | Reaction pathways
! style="text-align:center; background: #14866d; color: white;" | IRC calculation
! style="text-align:center; background: #14866d; color: white;" | IRC animation
|-
| style="text-align: center;" | DA - Endo
| [[File:YFENDOANIMA.gif|640px]]
| [[File:YF3ENDOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | DA - Exo
| [[File:Yf7537.gif|640px]]
| [[File:YF3EXOIRC.PNG|thumb|center|400px]]
|-
| style="text-align: center;" | Cheletropic
| [[File:YFCHEANIMA.gif|640px]]
| [[File:YF3CHEIRC.PNG|thumb|center|500px]]
|}

As mentioned above, xylylene is highly unstable. The IRC calculation provides proofs for this. From graphs of total energy against IRC, the large reaction energy indicates that the three reactions are all highly exotermic and the small activation energy indicates the high reactivity of xylylene. The three products benefit from the aromaticity (as there are 6 π electrons in the cyclic π system in the ring, 4n+2, n=1) and are all stablized by the the strong resonance in the benzene ring. During the course of the reaction, the changes of the bond lengths in the 6 - membered ring are presented below.

{| class="wikitable"
|+
! colspan="5" style="background: #14866d; color: white;" | Table 13. Changes of bond lengths in the reaction
|-
|rowspan="2" |C-C bond type
|colspan="2" style="text-align: center;"| Xylylene
|rowspan="2" | Exo/Endo C-C bond
|rowspan="2" | Cheletropic C-C bond
|-
|C=C bond
|C-C bond
|-
|style="text-align: center;"|Bond length
|style="text-align: center;"|1.35Å
|style="text-align: center;"|1.46Å, 1.47Å, 1.49Å
|style="text-align: center;"|1.47Å
|style="text-align: center;"|1.47Å
|}
As mentioned in Exercise 1, the C-C bond of sp2 - sp2 hybridisation is 1.47Å, which lies between C-C single bond (1.54Å) and C=C double bond (1.34Å). From table 12, it is clear that the bond lengths of the C-C bonds in the products are all 1.47Å. The strong delocalisation of the π electrons in the benzene ring strengthens the C-C bonds in the products.

====Energy analysis====
Below presents the activation energies and reaction energies for the three pathways.
{| class="wikitable"
|+ Table 14. Energies of reactants, TS, and products of endo/exo Diels-Alder and cheletropic reaction
! rowspan="3" style="text-align: center; background: #14866d; color: white;" | Measurement
! colspan="3" style="text-align: center; background: #14866d; color: white;" | Energies / kJmol-1
|-
| colspan="2" style="text-align: center; background: #14866d; color: white;" | DA
| rowspan="2" style="text-align: center; background: #14866d; color: white;" | Cheletropic reaction
|-
| style="text-align: center; background: #14866d; color: white;" | Exo
| style="text-align: center; background: #14866d; color: white;" | Endo
|-
| style="text-align: center"| xylylene
| colspan="3" style="text-align: center;" | + 467.89
|-
|style="text-align: center"| Sulfur dioxide
| colspan="3" style="text-align: center;" | - 312.01
|-
|style="text-align: center"| Sum of reactant energy
| colspan="3" style="text-align: center;" | + 155.88
|-
|style="text-align: center"| Transition states
| style="text-align: center;" | + 241.76
| style="text-align: center;" | + 238.02
| style="text-align: center;" | + 259.98
|-
|style="text-align: center"| Product
| style="text-align: center;" | + 56.37
| style="text-align: center;" | + 57.02
| style="text-align: center;" | + 0.0105
|-
|style="text-align: center"| Activation barrier (Ea) /kJmol-1
| style="text-align: center;" | + 85.88
| style="text-align: center;" | + 82.14
| style="text-align: center;" | + 104.10
|-
| style="text-align: center"| Reaction energy /kJmol-1
| style="text-align: center;" | - 99.51
| style="text-align: center;" | - 98.86
| style="text-align: center;" | - 155.87
|}
As the endo DA reaction has the lowest activation energy, the endo DA reaction is the kinetically favoured reaction. And exo DA the second, Cheletropic reaction the third thermodynamically favoured.
As the reaction energy of Cheletropic reaction is most exothermic, the Cheletropic reaction is the thermodynamically favoured reaction. And exo DA the second, endo DA reaction the third thermodynamically favoured.

Below presents the reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels - Alder reactions and the cheletropic reaction.
[[File:Yf3reactionprofile.png|center|thumb|666px|Figure 13. reaction scheme for the cycloaddition reaction between o-xylylene and SO2]]