ChemWiki - User contributions [en]

Rep:Mod:KZ1015TS

Rep:Mod:KZ1015TS

File:ZkwEXO TS PM6-3.LOG

2017-12-15T16:15:02Z

Kz1015:

File:ZkwCYCLO PM6.LOG

2017-12-15T16:13:21Z

Kz1015:

Rep:Mod:KZ1015TS

2017-12-15T16:11:19Z

Kz1015: /* Exercise 1 */

=''' Transition states and reactivity '''=
== Introduction ==

In this experiment, we used three pericyclic reactions to understand the transition states. Transition states could be identified through the potential energy surface, which shows that the energy of a molecule acts as a function
of molecule's geometry. Generally, the number of geometric degrees of freedom of the non-linear molecule is equal to the dimensionality of its PES. This obey the equatoin (3N-6), where N= number of atoms.

In the PES, reactants and products locate at minimum points while the saddle(maximum) points represents the transition state. At saddle points, the gradient equals to zero and all forces vanish. Since the value of first derivatives of both minimum and maximum points are equal to zero, the second derivatives is needed to differentiate these two points. When the second derivatives is positive, it suggests the minimum point and once the geometry is changed, the energy will increase. In contrast, negative second derivatives leads to the transition state and the energy will decrease in the pathway to the product.

For non-linear molecules, their vibration modes also associate with the equation 3N-6 and each mode has its own force constant. After doing the optimisaition calculations, there should be only one imaginary frequency. It proves that we have the transition state structure because the imaginary frequency aries from the negative curvature of the 3N-6 dimensions of the PES at transition state.

=== Method ===
In the following three exercises, all the transition states were obtained through optimisation of products. First, drawing the product structure in the GaussView and let the structure being optimised to minimum at semi-empirical PM6 level. Then, breaking the bonds that were formed during the reaction and adjust and 'freeze' those bonds to a certain length. For instance, setting C-C=2.2 Å, C-O=2.0 Å and C-S=2.4 Å. At the same time, fixing the coordinates of the atoms that related to the breaking bonds. After these, the structure was optimised again at PM6 level followed by a futher optimisation, which was run to obtain the TS. Once we got the TS, there should be only one imaginary frequency and a perfect IRC figure was obtained to make sure that the TS was correct (gradient = 0 at TS).

== Exercise 1 ==
For exercise 1, butadiene and ethlyene were used to do diels-alder reaction.

=== Optimization ===
{| class="wikitable"
! center; style="background: #EDEDED; color: black;" | Butadiene
! center; style="background: #EDEDED; color: black;" | Ethlyene
! center; style="background: #EDEDED; color: black;" | Transition State
! center; style="background: #EDEDED; color: black;" | Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; vibration 2;rotate x -20; </script>
<uploadedFileContents>ZKW_BUTADIENE_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; vibration 2;rotate x -20; </script>
<uploadedFileContents>ZKW_Ethlyene1_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1 Transition.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_PRODUCT_IRC.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|+ Table 1. optimisation at PM6 level
|}

=== IRC and frequency calculation analysis ===
The figure below suggests that the correct TS is got because only one imaginary frequency was obtained and when the value of IRC in RMS gradient along IRC equals to zero, the gradient=0 as well. In addition, we found that the formation of the two bonds in DA reaction is a synchronous procedure.
{| class="wikitable" border="1"
|-
| [[File:EX1 PRODUCT3 IRC.PNG|350px|thumb|center |]] || [[File:EX1 PRODUCT3 VIBRATION.PNG|350px|thumb|center |]]
|-
|}

=== Molecular orbital analysis ===
The following table shows the HOMO/LUMO of reactants and transition state.
{| class="wikitable" border="1"
|+ Table 2. HOMO/LUMO and MO diagrams
! !! Butadiene !!Ethylene!!Transition state!!Transition state
|+
| HOMO || [[File:EX1 BUTDIENE HOMO11.png|thumb|150px|centre|HOMO of Butadiene, MO11]]|| [[File:EX1 ALKENE HOMO6.png|thumb|150px|centre|HOMO of Ethylene, MO6]]|| [[File:EX1 TS HOMO17.png|thumb|150px|centre|HOMO of the TS, MO17]]||[[File:EX1 TS HOMO 1 16.png|thumb|150px|centre|HOMO-1 of the TS, MO16]]
|-
| LUMO || [[File:EX1 BUTDIENE LUMO12.png|thumb|150px|centre|LUMO of Butadiene, MO12]] || [[File:EX1 ALKENE LUMO7.png|thumb|150px|centre|LUMO of Ethylene, MO7]]|| [[File:EX1 TS LUMO18.png|thumb|150px|centre|LUMO of the TS, MO18]]||[[File:EX1 TS LUMO+1 19.png|thumb|150px|centre|LUMO+1 of the TS, MO19]]
|}

Only the orbitals that have the same symmetry can combine with each other to give the transition state MO because if the orbitals are miss matching, the overlap will be zero.
Figure below was the idealized MO diagram for the reaction between butadiene and ethylene.
The HOMO - LUMO interaction are summarised below: (S and AS are symmetric and asymmetric respectively)
Ethylene LUMO (MO7, AS) - Butadiene HOMO (MO11, AS) ---> TS LUMO+1 (MO19, AS)
Ethylene LUMO (MO7, AS) - Butadiene HOMO (MO11, AS) ---> TS HOMO-1 (MO16, AS)
Ethylene HOMO (MO6, S) - Butadiene LUMO (MO12, S) ---> TS LUMO (MO18, S)
Ethylene HOMO (MO6, S) - Butadiene LUMO (MO12, S) ---> TS HOMO (MO17, S)

The effect arise from the symmetry of the orbital on the orbital overlap integral:
symmetric-antisymmetric interaction ---> Zero
symmetric-symmetric interaction ---> Non-zero
antisymmetric-antisymmetric interaction ---> Non-zero

{|
|
|[[File:EX1_MO_FIG.PNG|thumb|600px|left|MO diagram]]
|}
In this experiment, butadiene and ethylene were doing [4+2] cycloaddition, which is a pericyclic chemical reaction. For pericyclic reactions, we have to obey the Woodward-Hoffmann Rules. The rules state that in order to make the reaction to be thermal allowed, the sum of (4q+2)s and (4r)a must be odd, where 's' represents suprafacial, 'a' stands for antarafacial and q,r are integers from 0. If the sum of (4q+2)s and (4r)a is an even number, then the reaction will be forbidden. According to the MO, we know that the cycloaddition between butadiene and ethylene was thermal allowed because :
(4q + 2)s + (4r)a
= 1 + 0
= 1 ----> odd number, q=0,r=0.

=== Bond lengths analysis ===
The typical C-C bond lengths are shown below:
sp<sup>3</sup> C- sp<sup>3</sup> C 1.54Å
sp<sup>2</sup> C- sp<sup>2</sup> C 1.47Å
sp<sup>3</sup> C- sp<sup>2</sup> C 1.50Å

{| class="wikitable" border="1"
|+ Table 3. C-C Bond lengths changes during the reaction
! molecules !! Bond lenghts !!molecules!!Bond lengths
|+
| [[File:C1-C4-2.PNG|thumb|150px|centre]]||
*reactant ethylene
*C1=C4 1.33Å
|| [[File:BUT C-C2.PNG|thumb|150px|centre]]||
*reactant butadiene
*C12=C14 1.33Å
*C12-C10 1.47Å
*C10-C7 1.33Å
|-
|| [[File:PRODUCT C-C-2.PNG|thumb|150px|centre]]||
*Product
*C7-C1 1.54Å sp3-sp3
*C1-C4 1.53Å sp3-sp3
*C4-C14 1.54Å sp3-sp3
*C14-C12 1.50Å sp3-sp2
*C12=C10 1.34Å sp2-sp2
*C10-C7 1.50Å sp2-sp3
|| [[File:TS C-C-2.PNG|thumb|150px|centre]]||
*Transition state
*C1=C4 1.38Å bond rupture
*C12=C10 1.41Å bond formation
*C10=C7 1.38Å bond rupture
*C7-C1 2.11Å bond formation
*C12=C14 1.38Å bond rupture
*C14-C4 2.11Å bond formation
|}

The Van der Waals radius of the C atom is 1.7Å, so the expected VDW C-C bond length shoule be 3.4Å. After comparing, we can see that the length of the partly formed C-C bonds (C14-C4 and C7-C1) in TS are smaller than the expected one while larger than the typical sp<sup>3</sup> C- sp<sup>3</sup> C bond length. It shows that the bond is forming. In addition, in TS, a partial double bond is formed between C12 and C10, as a result, the length of C12-C10 is smaller than the standard sp<sup>2</sup> C- sp<sup>2</sup> C bonds.

== Exercise 2 ==
In exercise 2, we looked at the reaction between cyclohexadiene and 1,3-dioxole.
=== Optimisation at B3LYP/6-31G(d) level ===
{| class="wikitable"
!
! center; style="background: #EDEDED; color: black;" | Structure
! center; style="background: #EDEDED; color: black;" | Frequency

|-
|Cyclohexadiene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18 </script>
<uploadedFileContents>Zkw CYCLO 631G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zkw CYCLO FRE.PNG|thumb|300px|center]]
|-

| 1,3-Dioxole
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>Zkw DIO 631G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:DIO FRE.PNG|thumb|300px|center]]
|-

|-
|Exo TS
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18 </script>
<uploadedFileContents>Zkw EXO TS 631G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:EXO TS FRE.PNG|thumb|300px|center]]
|-
|Exo Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18 </script>
<uploadedFileContents>ZKW EXO PRODUCT 631G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:EXO PRODUCT FRE.PNG|thumb|300px|center]]
|-
|Endo TS
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18 </script>
<uploadedFileContents>ZKW ENDO TS 631G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ENDO TS FRE.PNG|thumb|300px|center]]
|-
|Endo Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18 </script>
<uploadedFileContents>ZKWENDO PRODUCT 631G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ENDO PRODUCT FRE.PNG|thumb|300px|center]]
|}

=== HOMO/LUMO of Transition State ===
{| class="wikitable" border="1"
|+ Table 4. HOMO/LUMO of TS
! !! TS HOMO MO41 !!TS LUMO MO42!!TS HOMO-1 MO40!! TS LUMO+1 MO43
|+
| ENDO|| [[File:ENDO HOMO 41.png|thumb|150px|centre]]||[[File:ENDO LUMO 42.png|thumb|150px|centre]] || [[File:ENDO HOMO-1 40.png|thumb|150px|centre]]||[[File:ENDO LUMO+1 43.png|thumb|150px|centre]]
|-
| EXO|| [[File:ZKWEXO HOMO 41.png|thumb|150px|centre]]||[[File:EXO LUMO 42.png|thumb|150px|centre]] || [[File:EXO HOMO-1 40.png|thumb|150px|centre]]||[[File:EXO LUMO+1 43.png|thumb|150px|centre]]
|}

=== Molecular Orbital Analysis ===
{| class="wikitable" border="1"
|-
| [[File:EX2 ENDO MO.png|400px|thumb|center|Fig.1 MO diagram of ENDO TS ]] || [[File:屏幕快照 2017-12-13 23.29.47.png|400px|thumb|center|Fig.2 MO diagram of EXO TS]]
|}

There are two types of Diels–Alder reaction, one is the standard DA reaction, the other is inverse electron demand DA reaction. Generally, for most of the DA reactions, MOs of the electron rich diene would have higher energy levels than the MOs of electron poor dienophile. Then, according to the frontier molecular orbital theory, there are interactions between the HOMO of diene and LUMO of dienophile because their energy levels are close to each other. In contrast, for inverse electron demand DA reactions, the energy of diene's LUMO is more similar to the dienophile's HOMO. As a result, in the inverse situation, LUMO<sub>diene</sub> and HOMO<sub>dienophile</sub> are the frontier molecular orbitals.

In both MO diagrams (Fig.1 and Fig.2), the energy levels of HOMO/LUMO of the diene (cyclohexadiene) are lower than the ones of dienophile (1,3-dioxole). Also, the FMO are LUMO<sub>cyclohexadiene</sub>(MO 23) and HOMO<sub>1,3-dioxole</sub> (MO 19). The small energy gap between them lead to the strong interactio and favourable the bond formation. These indicate that cyclohexadiene and 1,3-dioxole will do an inverse electron demand DA reaction.

=== Thermochemistry - Reaction Energies and Barriers ===
The following energies' units are converted from Hartree. (1 Kjmol<sup>-1</sup> = 3.8088 X10<sup>-4</sup> Hartree)
{| class="wikitable" border="1"
|+ Table 5. Energies of reactants, products, TS
!Molecules!!Energies under B3LYP/631G(d) mode / Kjmol<sup>-1</sup>
|+
|Cyclohexadiene||-6.12582 x 10<sup>5</sup>
|-
|1,3-Dioxole||-7.01158 x 10<sup>5</sup>
|-
|ENDO TS|| -1.313614 x 10<sup>6</sup>
|-
|ENDO product||-1.313815 x 10<sup>6</sup>
|-
|EXO TS||-1.3136 x 10<sup>6</sup>
|-
|EXO product||-1.3138 x 10<sup>6</sup>
|}

In order to get the reaction energy and activation energy, we need to use the following equations:
Reaction energy = Product's energy - Reactants' energies
Activation energy = TS's energy - Reactants' energies

{| class="wikitable" border="1"
|+ Table 6. E<sub>activation</sub> and E<sub>reaction</sub> of Endo/Exo product
!!!Activation Energy / Kjmol<sup>-1</sup>!!Reaction Energy / Kjmol<sup>-1
|+
|Exo Product||+140.0||-60.0
|-
|Endo Product||+126.0||-75.0
|}

After comparing the data in table.6 we can see that the Exo product has more positive E<sub>activation</sub> than the Endo one, with +14Kjmol<sup>-1</sup>. At the same time, the E<sub>reaction</sub> of Endo product has more negative value (-15Kjmol) than the Exo one.
The lower the activation energy, the faster the reactants can reach the TS and fewer energy is needed. Therefore, smaller E<sub>activation</sub> means the product is kinetically favourable and in this exercise, endo product is the kinetically favourable one.
The reaction energy represents the stability of the product. More negative the reaction energy is, more heat is released to the environment to form the stable product. As a result, the endo product is thermodynamically favoured as well.

=== Secondary Orbital Interaction ===
Both secondary orbital interaction and primary orbital interaction can be seen in the endo TS while in exo TS, only primary orbital interaction presents. The secondary orbital interaction indicates that the lone paired electrons in p orbitals on oxygen will overlap with the LUMO<sub>diene</sub>. As a result, the endo approaching is more preferred. Also, because of the SOI, the activation energy is decreased and then, the TS is stabilised. When the dienophile doing exo approach, sterics effect arose, which lead to a larger reaction barrier energy.

== Exercise 3 ==
Exercise 3 is the DA cycloaddition of Xylylene and SO<sub>2</sub>.

=== Optimisation at PM6 level ===
{| class="wikitable"
! center; style="background: #EDEDED; color: black;" | Xylylene
! style="background: #EDEDED; color: black;" | EXO TS
! style="background: #EDEDED; color: black;" | ENDO TS
! style="background: #EDEDED; color: black;" | Cheletropic TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 34; vibration 2;rotate x -20; </script>
<uploadedFileContents>XYL PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; vibration 2;rotate x -20; </script>
<uploadedFileContents>EXO PM6-3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; vibration 2;rotate x -20; </script>
<uploadedFileContents>ZkwENDO PM6-3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 58; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ex3CHE PM6-3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! center; style="background: #EDEDED; color: black;" | SO<sub>2</sub>
! style="background: #EDEDED; color: black;" | Exo Product
! style="background: #EDEDED; color: black;" | Endo Product
! style="background: #EDEDED; color: black;" | Cheletropic Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; vibration 2;rotate x -20; </script>
<uploadedFileContents>ZKWSO2PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; vibration 2;rotate x -20; </script>
<uploadedFileContents>EXO PM6-1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 28; vibration 2;rotate x -20; </script>
<uploadedFileContents>ZkwENDO PM6-1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; vibration 2;rotate x -20; </script>
<uploadedFileContents>ZkwCHE PM6-1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|+ Table 7. Optimisation of reactants, transition states, products at PM6 Level
|}

=== IRC calculation ===
{| class="wikitable"
! style="background: #EDEDED; color: black;" |Reaction
! style="background: #EDEDED; color: black;" | gif
! style="background: #EDEDED; color: black;" | IRC
|-
| EXO DA reaction
| [[File:EXO22 IRC GIF.gif ]]
| [[File:ZKWEXO IRC.PNG|ZKWEXO IRC.PNG]]
|-
| ENDO DA reaction
| [[File:Zkwex3ENDO IRC GIF.gif]]
| [[File:EX3 ENDO IRC.PNG|none ]]
|-
| Cheletropic
| [[File:Zkwex3CHE IRC GIF.gif]]
| [[File:ZkwCHE IRC.PNG|none ‎ ]]
|-
|}
Since the xylylene has two cis-diene in its structure and both of them can do the cycloaddition reactions with dienophiles, we said that it is highly reactive. The gif above showed the trajectories of the three reactions. As it showed in the graph, when the six-membered ring is forming, aromatic ring arose because the lone pairs on oxygen and sulfur is participating and further stable the structure.
=== Activation and reaction energies ===
The following energies' units are converted from Hartree. (1 Kjmol-1 = 3.8088 X10-4 Hartree)
{| class="wikitable"
! style="background: #EDEDED; color: black;" | Molecule
! style="background: #EDEDED; color: black;" | Exo approach
! style="background: #EDEDED; color: black;" | Endo approach
! style="background: #EDEDED; color: black;" | Cheletropic
|-
| xylylene
| +469.287
| +469.287
| +469.287
|-
| SO2
| -313.143
| -313.143
| -313.143
|-
|Transition State
| +241.748
| +237.770
| +260.085
|-
| Product
| +56.214
| +56.973
| +0.0131
|-
| Activation Energy/kjmol<sup>-1</sup>
| +85.604
| +81.626
| +103.941
|-
| Reaction Energy/kjmol<sup>-1</sup>
| -99.930
| -99.171
| -156.131
|+ Table 9.Activation and reaction energies at PM6 Level/kjmol<sup>-1</sup>
|-
|}
According to Table.8 we can see that the cheletropic reaction has the most negative value of reaction energy, which means it is the most exothermic reaction among these three reactions followed by DA exo pathway and endo pathway. In addition, the DA endo pathway has the lowest activation followed by exo pathway and cheletropic reaction. Therefore, in comparison, the cheletropic product is thermodynamic favoured and the endo product is kinetically favoured. The endo product is slightly less stable than the exo one because there is more steric replusion.

=== Reaction profile ===
{| class="wikitable" border="1"
|-
| [[File:ZkwEnergy profile.PNG|thumb|450px|left|Energy Profile of three reactions.]]
|}

== Conclusion ==
The transition states of different DA/Cheletropic reactions were investigated through the experiment by using GaussView. In each exercise, the experimental product was optimised to minimum at semi-empirical PM6 level, changed the breaking-bond distance, optimised to minimum again and then, optimised to the TS. All the TS structures were checked with their frequency calculation and IRC. Since each TS structure that we got has only one imaginary frequency, we said that those structures were obtained correctly. The IRC presented the pathway of reactants in DA reactions and indicated that the formation of the two bonds are synchronous. Also, through exercise 2 we could know that when there is an inverse demand DA reaction, the frontier molecular orbitals of this kind of reaction will be the HOMO of dienophile and the LUMO of diene. Furthermore, the products could be classified into two types: thermodynamically favored one (when the reaction has larger reaction energy) and kinetically favored one (when the reaction has samller activation barrier).

== Log Files ==

=== Exercise 1 ===
#IRC:[[File:EX1 PRODUCT IRC.LOG]]

=== Exercise 2 ===

Rep:Mod:KZ1015TS

2017-12-15T16:10:16Z

Kz1015:

=''' Transition states and reactivity '''=
== Introduction ==

In this experiment, we used three pericyclic reactions to understand the transition states. Transition states could be identified through the potential energy surface, which shows that the energy of a molecule acts as a function
of molecule's geometry. Generally, the number of geometric degrees of freedom of the non-linear molecule is equal to the dimensionality of its PES. This obey the equatoin (3N-6), where N= number of atoms.

In the PES, reactants and products locate at minimum points while the saddle(maximum) points represents the transition state. At saddle points, the gradient equals to zero and all forces vanish. Since the value of first derivatives of both minimum and maximum points are equal to zero, the second derivatives is needed to differentiate these two points. When the second derivatives is positive, it suggests the minimum point and once the geometry is changed, the energy will increase. In contrast, negative second derivatives leads to the transition state and the energy will decrease in the pathway to the product.

For non-linear molecules, their vibration modes also associate with the equation 3N-6 and each mode has its own force constant. After doing the optimisaition calculations, there should be only one imaginary frequency. It proves that we have the transition state structure because the imaginary frequency aries from the negative curvature of the 3N-6 dimensions of the PES at transition state.

=== Method ===
In the following three exercises, all the transition states were obtained through optimisation of products. First, drawing the product structure in the GaussView and let the structure being optimised to minimum at semi-empirical PM6 level. Then, breaking the bonds that were formed during the reaction and adjust and 'freeze' those bonds to a certain length. For instance, setting C-C=2.2 Å, C-O=2.0 Å and C-S=2.4 Å. At the same time, fixing the coordinates of the atoms that related to the breaking bonds. After these, the structure was optimised again at PM6 level followed by a futher optimisation, which was run to obtain the TS. Once we got the TS, there should be only one imaginary frequency and a perfect IRC figure was obtained to make sure that the TS was correct (gradient = 0 at TS).

== Exercise 1 ==
For exercise 1, butadiene and ethlyene were used to do diels-alder reaction.

=== Optimization ===
{| class="wikitable"
! center; style="background: #EDEDED; color: black;" | Butadiene
! center; style="background: #EDEDED; color: black;" | Ethlyene
! center; style="background: #EDEDED; color: black;" | Transition State
! center; style="background: #EDEDED; color: black;" | Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; vibration 2;rotate x -20; </script>
<uploadedFileContents>ZKW_BUTADIENE_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; vibration 2;rotate x -20; </script>
<uploadedFileContents>ZKW_Ethlyene1_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1 Transition.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_PRODUCT_IRC.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|+ Table 1. optimisation at PM6 level
|}

=== IRC and frequency calculation analysis ===
The figure below suggests that the correct TS is got because only one imaginary frequency was obtained and when the value of IRC in RMS gradient along IRC equals to zero, the gradient=0 as well. In addition, we found that the formation of the two bonds in DA reaction is a synchronous procedure.
{| class="wikitable" border="1"
|-
| [[File:EX1 PRODUCT3 IRC.PNG|350px|thumb|center |]] || [[File:EX1 PRODUCT3 VIBRATION.PNG|350px|thumb|center |]]
|-
|}

=== Molecular orbital analysis ===
The following table shows the HOMO/LUMO of reactants and transition state.
{| class="wikitable" border="1"
|+ Table 2. HOMO/LUMO and MO diagrams
! !! Butadiene !!Ethylene!!Transition state!!Transition state
|+
| HOMO || [[File:EX1 BUTDIENE HOMO11.png|thumb|150px|centre|HOMO of Butadiene, MO11]]|| [[File:EX1 ALKENE HOMO6.png|thumb|150px|centre|HOMO of Ethylene, MO6]]|| [[File:EX1 TS HOMO17.png|thumb|150px|centre|HOMO of the TS, MO17]]||[[File:EX1 TS HOMO 1 16.png|thumb|150px|centre|HOMO-1 of the TS, MO16]]
|-
| LUMO || [[File:EX1 BUTDIENE LUMO12.png|thumb|150px|centre|LUMO of Butadiene, MO12]] || [[File:EX1 ALKENE LUMO7.png|thumb|150px|centre|LUMO of Ethylene, MO7]]|| [[File:EX1 TS LUMO18.png|thumb|150px|centre|LUMO of the TS, MO18]]||[[File:EX1 TS LUMO+1 19.png|thumb|150px|centre|LUMO+1 of the TS, MO19]]
|}

Only the orbitals that have the same symmetry can combine with each other to give the transition state MO because if the orbitals are miss matching, the overlap will be zero.
Figure below was the idealized MO diagram for the reaction between butadiene and ethylene.
The HOMO - LUMO interaction are summarised below: (S and AS are symmetric and asymmetric respectively)
Ethylene LUMO (MO7, AS) - Butadiene HOMO (MO11, AS) ---> TS LUMO+1 (MO19, AS)
Ethylene LUMO (MO7, AS) - Butadiene HOMO (MO11, AS) ---> TS HOMO-1 (MO16, AS)
Ethylene HOMO (MO6, S) - Butadiene LUMO (MO12, S) ---> TS LUMO (MO18, S)
Ethylene HOMO (MO6, S) - Butadiene LUMO (MO12, S) ---> TS HOMO (MO17, S)

The effect arise from the symmetry of the orbital on the orbital overlap integral:
symmetric-antisymmetric interaction ---> Zero
symmetric-symmetric interaction ---> Non-zero
antisymmetric-antisymmetric interaction ---> Non-zero

{|
|
|[[File:EX1_MO_FIG.PNG|thumb|600px|left|MO diagram]]
|}
In this experiment, butadiene and ethylene were doing [4+2] cycloaddition, which is a pericyclic chemical reaction. For pericyclic reactions, we have to obey the Woodward-Hoffmann Rules. The rules state that in order to make the reaction to be thermal allowed, the sum of (4q+2)s and (4r)a must be odd, where 's' represents suprafacial, 'a' stands for antarafacial and q,r are integers from 0. If the sum of (4q+2)s and (4r)a is an even number, then the reaction will be forbidden. According to the MO, we know that the cycloaddition between butadiene and ethylene was thermal allowed because :
(4q + 2)s + (4r)a
= 1 + 0
= 1 ----> odd number, q=0,r=0.

=== Bond lengths analysis ===
The typical C-C bond lengths are shown below:
sp<sup>3</sup> C- sp<sup>3</sup> C 1.54Å
sp<sup>2</sup> C- sp<sup>2</sup> C 1.47Å
sp<sup>3</sup> C- sp<sup>2</sup> C 1.50Å

{| class="wikitable" border="1"
|+ Table 3. C-C Bond lengths changes during the reaction
! molecules !! Bond lenghts !!molecules!!Bond lengths
|+
| [[File:C1-C4-2.PNG|thumb|150px|centre]]||
*reactant ethylene
*C1=C4 1.33Å
|| [[File:BUT C-C2.PNG|thumb|150px|centre]]||
*reactant butadiene
*C12=C14 1.33Å
*C12-C10 1.47Å
*C10-C7 1.33Å
|-
|| [[File:PRODUCT C-C-2.PNG|thumb|150px|centre]]||
*Product
*C7-C1 1.54Å sp3-sp3
*C1-C4 1.53Å sp3-sp3
*C4-C14 1.54Å sp3-sp3
*C14-C12 1.50Å sp3-sp2
*C12=C10 1.34Å sp2-sp2
*C10-C7 1.50Å sp2-sp3
|| [[File:TS C-C-2.PNG|thumb|150px|centre]]||
*Transition state
*C1=C4 1.38Å bond rupture
*C12=C10 1.41Å bond formation
*C10=C7 1.38Å bond rupture
*C7-C1 2.11Å bond formation
*C12=C14 1.38Å bond rupture
*C14-C4 2.11Å bond formation
|}

The Van der Waals radius of the C atom is 1.7Å, so the expected VDW C-C bond length shoule be 3.4Å. After comparing, we can see that the length of the partly formed C-C bonds (C14-C4 and C7-C1) in TS are smaller than the expected one while larger than the typical sp<sup>3</sup> C- sp<sup>3</sup> C bond length. It shows that the bond is forming. In addition, in TS, a partial double bond is formed between C12 and C10, as a result, the length of C12-C10 is smaller than the standard sp<sup>2</sup> C- sp<sup>2</sup> C bonds.

== Exercise 2 ==
In exercise 2, we looked at the reaction between cyclohexadiene and 1,3-dioxole.
=== Optimisation at B3LYP/6-31G(d) level ===
{| class="wikitable"
!
! center; style="background: #EDEDED; color: black;" | Structure
! center; style="background: #EDEDED; color: black;" | Frequency

|-
|Cyclohexadiene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18 </script>
<uploadedFileContents>Zkw CYCLO 631G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zkw CYCLO FRE.PNG|thumb|300px|center]]
|-

| 1,3-Dioxole
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>Zkw DIO 631G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:DIO FRE.PNG|thumb|300px|center]]
|-

|-
|Exo TS
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18 </script>
<uploadedFileContents>Zkw EXO TS 631G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:EXO TS FRE.PNG|thumb|300px|center]]
|-
|Exo Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18 </script>
<uploadedFileContents>ZKW EXO PRODUCT 631G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:EXO PRODUCT FRE.PNG|thumb|300px|center]]
|-
|Endo TS
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18 </script>
<uploadedFileContents>ZKW ENDO TS 631G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ENDO TS FRE.PNG|thumb|300px|center]]
|-
|Endo Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18 </script>
<uploadedFileContents>ZKWENDO PRODUCT 631G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ENDO PRODUCT FRE.PNG|thumb|300px|center]]
|}

=== HOMO/LUMO of Transition State ===
{| class="wikitable" border="1"
|+ Table 4. HOMO/LUMO of TS
! !! TS HOMO MO41 !!TS LUMO MO42!!TS HOMO-1 MO40!! TS LUMO+1 MO43
|+
| ENDO|| [[File:ENDO HOMO 41.png|thumb|150px|centre]]||[[File:ENDO LUMO 42.png|thumb|150px|centre]] || [[File:ENDO HOMO-1 40.png|thumb|150px|centre]]||[[File:ENDO LUMO+1 43.png|thumb|150px|centre]]
|-
| EXO|| [[File:ZKWEXO HOMO 41.png|thumb|150px|centre]]||[[File:EXO LUMO 42.png|thumb|150px|centre]] || [[File:EXO HOMO-1 40.png|thumb|150px|centre]]||[[File:EXO LUMO+1 43.png|thumb|150px|centre]]
|}

=== Molecular Orbital Analysis ===
{| class="wikitable" border="1"
|-
| [[File:EX2 ENDO MO.png|400px|thumb|center|Fig.1 MO diagram of ENDO TS ]] || [[File:屏幕快照 2017-12-13 23.29.47.png|400px|thumb|center|Fig.2 MO diagram of EXO TS]]
|}

There are two types of Diels–Alder reaction, one is the standard DA reaction, the other is inverse electron demand DA reaction. Generally, for most of the DA reactions, MOs of the electron rich diene would have higher energy levels than the MOs of electron poor dienophile. Then, according to the frontier molecular orbital theory, there are interactions between the HOMO of diene and LUMO of dienophile because their energy levels are close to each other. In contrast, for inverse electron demand DA reactions, the energy of diene's LUMO is more similar to the dienophile's HOMO. As a result, in the inverse situation, LUMO<sub>diene</sub> and HOMO<sub>dienophile</sub> are the frontier molecular orbitals.

In both MO diagrams (Fig.1 and Fig.2), the energy levels of HOMO/LUMO of the diene (cyclohexadiene) are lower than the ones of dienophile (1,3-dioxole). Also, the FMO are LUMO<sub>cyclohexadiene</sub>(MO 23) and HOMO<sub>1,3-dioxole</sub> (MO 19). The small energy gap between them lead to the strong interactio and favourable the bond formation. These indicate that cyclohexadiene and 1,3-dioxole will do an inverse electron demand DA reaction.

=== Thermochemistry - Reaction Energies and Barriers ===
The following energies' units are converted from Hartree. (1 Kjmol<sup>-1</sup> = 3.8088 X10<sup>-4</sup> Hartree)
{| class="wikitable" border="1"
|+ Table 5. Energies of reactants, products, TS
!Molecules!!Energies under B3LYP/631G(d) mode / Kjmol<sup>-1</sup>
|+
|Cyclohexadiene||-6.12582 x 10<sup>5</sup>
|-
|1,3-Dioxole||-7.01158 x 10<sup>5</sup>
|-
|ENDO TS|| -1.313614 x 10<sup>6</sup>
|-
|ENDO product||-1.313815 x 10<sup>6</sup>
|-
|EXO TS||-1.3136 x 10<sup>6</sup>
|-
|EXO product||-1.3138 x 10<sup>6</sup>
|}

In order to get the reaction energy and activation energy, we need to use the following equations:
Reaction energy = Product's energy - Reactants' energies
Activation energy = TS's energy - Reactants' energies

{| class="wikitable" border="1"
|+ Table 6. E<sub>activation</sub> and E<sub>reaction</sub> of Endo/Exo product
!!!Activation Energy / Kjmol<sup>-1</sup>!!Reaction Energy / Kjmol<sup>-1
|+
|Exo Product||+140.0||-60.0
|-
|Endo Product||+126.0||-75.0
|}

After comparing the data in table.6 we can see that the Exo product has more positive E<sub>activation</sub> than the Endo one, with +14Kjmol<sup>-1</sup>. At the same time, the E<sub>reaction</sub> of Endo product has more negative value (-15Kjmol) than the Exo one.
The lower the activation energy, the faster the reactants can reach the TS and fewer energy is needed. Therefore, smaller E<sub>activation</sub> means the product is kinetically favourable and in this exercise, endo product is the kinetically favourable one.
The reaction energy represents the stability of the product. More negative the reaction energy is, more heat is released to the environment to form the stable product. As a result, the endo product is thermodynamically favoured as well.

=== Secondary Orbital Interaction ===
Both secondary orbital interaction and primary orbital interaction can be seen in the endo TS while in exo TS, only primary orbital interaction presents. The secondary orbital interaction indicates that the lone paired electrons in p orbitals on oxygen will overlap with the LUMO<sub>diene</sub>. As a result, the endo approaching is more preferred. Also, because of the SOI, the activation energy is decreased and then, the TS is stabilised. When the dienophile doing exo approach, sterics effect arose, which lead to a larger reaction barrier energy.

== Exercise 3 ==
Exercise 3 is the DA cycloaddition of Xylylene and SO<sub>2</sub>.

=== Optimisation at PM6 level ===
{| class="wikitable"
! center; style="background: #EDEDED; color: black;" | Xylylene
! style="background: #EDEDED; color: black;" | EXO TS
! style="background: #EDEDED; color: black;" | ENDO TS
! style="background: #EDEDED; color: black;" | Cheletropic TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 34; vibration 2;rotate x -20; </script>
<uploadedFileContents>XYL PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; vibration 2;rotate x -20; </script>
<uploadedFileContents>EXO PM6-3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; vibration 2;rotate x -20; </script>
<uploadedFileContents>ZkwENDO PM6-3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 58; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ex3CHE PM6-3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! center; style="background: #EDEDED; color: black;" | SO<sub>2</sub>
! style="background: #EDEDED; color: black;" | Exo Product
! style="background: #EDEDED; color: black;" | Endo Product
! style="background: #EDEDED; color: black;" | Cheletropic Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; vibration 2;rotate x -20; </script>
<uploadedFileContents>ZKWSO2PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; vibration 2;rotate x -20; </script>
<uploadedFileContents>EXO PM6-1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 28; vibration 2;rotate x -20; </script>
<uploadedFileContents>ZkwENDO PM6-1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; vibration 2;rotate x -20; </script>
<uploadedFileContents>ZkwCHE PM6-1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|+ Table 7. Optimisation of reactants, transition states, products at PM6 Level
|}

=== IRC calculation ===
{| class="wikitable"
! style="background: #EDEDED; color: black;" |Reaction
! style="background: #EDEDED; color: black;" | gif
! style="background: #EDEDED; color: black;" | IRC
|-
| EXO DA reaction
| [[File:EXO22 IRC GIF.gif ]]
| [[File:ZKWEXO IRC.PNG|ZKWEXO IRC.PNG]]
|-
| ENDO DA reaction
| [[File:Zkwex3ENDO IRC GIF.gif]]
| [[File:EX3 ENDO IRC.PNG|none ]]
|-
| Cheletropic
| [[File:Zkwex3CHE IRC GIF.gif]]
| [[File:ZkwCHE IRC.PNG|none ‎ ]]
|-
|}
Since the xylylene has two cis-diene in its structure and both of them can do the cycloaddition reactions with dienophiles, we said that it is highly reactive. The gif above showed the trajectories of the three reactions. As it showed in the graph, when the six-membered ring is forming, aromatic ring arose because the lone pairs on oxygen and sulfur is participating and further stable the structure.
=== Activation and reaction energies ===
The following energies' units are converted from Hartree. (1 Kjmol-1 = 3.8088 X10-4 Hartree)
{| class="wikitable"
! style="background: #EDEDED; color: black;" | Molecule
! style="background: #EDEDED; color: black;" | Exo approach
! style="background: #EDEDED; color: black;" | Endo approach
! style="background: #EDEDED; color: black;" | Cheletropic
|-
| xylylene
| +469.287
| +469.287
| +469.287
|-
| SO2
| -313.143
| -313.143
| -313.143
|-
|Transition State
| +241.748
| +237.770
| +260.085
|-
| Product
| +56.214
| +56.973
| +0.0131
|-
| Activation Energy/kjmol<sup>-1</sup>
| +85.604
| +81.626
| +103.941
|-
| Reaction Energy/kjmol<sup>-1</sup>
| -99.930
| -99.171
| -156.131
|+ Table 9.Activation and reaction energies at PM6 Level/kjmol<sup>-1</sup>
|-
|}
According to Table.8 we can see that the cheletropic reaction has the most negative value of reaction energy, which means it is the most exothermic reaction among these three reactions followed by DA exo pathway and endo pathway. In addition, the DA endo pathway has the lowest activation followed by exo pathway and cheletropic reaction. Therefore, in comparison, the cheletropic product is thermodynamic favoured and the endo product is kinetically favoured. The endo product is slightly less stable than the exo one because there is more steric replusion.

=== Reaction profile ===
{| class="wikitable" border="1"
|-
| [[File:ZkwEnergy profile.PNG|thumb|450px|left|Energy Profile of three reactions.]]
|}

== Conclusion ==
The transition states of different DA/Cheletropic reactions were investigated through the experiment by using GaussView. In each exercise, the experimental product was optimised to minimum at semi-empirical PM6 level, changed the breaking-bond distance, optimised to minimum again and then, optimised to the TS. All the TS structures were checked with their frequency calculation and IRC. Since each TS structure that we got has only one imaginary frequency, we said that those structures were obtained correctly. The IRC presented the pathway of reactants in DA reactions and indicated that the formation of the two bonds are synchronous. Also, through exercise 2 we could know that when there is an inverse demand DA reaction, the frontier molecular orbitals of this kind of reaction will be the HOMO of dienophile and the LUMO of diene. Furthermore, the products could be classified into two types: thermodynamically favored one (when the reaction has larger reaction energy) and kinetically favored one (when the reaction has samller activation barrier).

== Log Files ==

=== Exercise 1 ===
#IRC:[[File:EX1 PRODUCT IRC.LOG]]

Kz1015:

Rep:Mod:KZ1015TS

2017-12-15T13:40:33Z

Kz1015: /* IRC calculation */

=''' Transition states and reactivity '''=
== Introduction ==

In this experiment, we used three pericyclic reactions to understand the transition states. Transition states could be identified through the potential energy surface, which shows that the energy of a molecule acts as a function
of molecule's geometry. Generally, the number of geometric degrees of freedom of the non-linear molecule is equal to the dimensionality of its PES. This obey the equatoin (3N-6), where N= number of atoms.

In the PES, reactants and products locate at minimum points while the saddle(maximum) points represents the transition state. At saddle points, the gradient equals to zero and all forces vanish. Since the value of first derivatives of both minimum and maximum points are equal to zero, the second derivatives is needed to differentiate these two points. When the second derivatives is positive, it suggests the minimum point and once the geometry is changed, the energy will increase. In contrast, negative second derivatives leads to the transition state and the energy will decrease in the pathway to the product.

For non-linear molecules, their vibration modes also associate with the equation 3N-6 and each mode has its own force constant. After doing the optimisaition calculations, there should be only one imaginary frequency. It proves that we have the transition state structure because the imaginary frequency aries from the negative curvature of the 3N-6 dimensions of the PES at transition state.

=== Method ===
In the following three exercises, all the transition states were obtained through optimisation of products. First, drawing the product structure in the GaussView and let the structure being optimised to minimum at semi-empirical PM6 level. Then, breaking the bonds that were formed during the reaction and adjust and 'freeze' those bonds to a certain length. For instance, setting C-C=2.2 Å, C-O=2.0 Å and C-S=2.4 Å. At the same time, fixing the coordinates of the atoms that related to the breaking bonds. After these, the structure was optimised again at PM6 level followed by a futher optimisation, which was run to obtain the TS. Once we got the TS, there should be only one imaginary frequency and a perfect IRC figure was obtained to make sure that the TS was correct (gradient = 0 at TS).

== Exercise 1 ==
For exercise 1, butadiene and ethlyene were used to do diels-alder reaction.

=== Optimization ===
{| class="wikitable"
! center; style="background: #EDEDED; color: black;" | Butadiene
! center; style="background: #EDEDED; color: black;" | Ethlyene
! center; style="background: #EDEDED; color: black;" | Transition State
! center; style="background: #EDEDED; color: black;" | Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; vibration 2;rotate x -20; </script>
<uploadedFileContents>ZKW_BUTADIENE_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; vibration 2;rotate x -20; </script>
<uploadedFileContents>ZKW_Ethlyene1_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1 Transition.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_PRODUCT_IRC.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|+ Table 1. optimisation at PM6 level
|}

=== IRC and frequency calculation analysis ===
The figure below suggests that the correct TS is got because only one imaginary frequency was obtained and when the value of IRC in RMS gradient along IRC equals to zero, the gradient=0 as well. In addition, we found that the bond rupture and bond formation happened at the same time, which means it is a synchronous procedure.
{| class="wikitable" border="1"
|-
| [[File:EX1 PRODUCT3 IRC.PNG|350px|thumb|center |]] || [[File:EX1 PRODUCT3 VIBRATION.PNG|350px|thumb|center |]]
|-
|}

=== Molecular orbital analysis ===
The following table shows the HOMO/LUMO of reactants and transition state.
{| class="wikitable" border="1"
|+ Table 2. HOMO/LUMO and MO diagrams
! !! Butadiene !!Ethylene!!Transition state!!Transition state
|+
| HOMO || [[File:EX1 BUTDIENE HOMO11.png|thumb|150px|centre|HOMO of Butadiene, MO11]]|| [[File:EX1 ALKENE HOMO6.png|thumb|150px|centre|HOMO of Ethylene, MO6]]|| [[File:EX1 TS HOMO17.png|thumb|150px|centre|HOMO of the TS, MO17]]||[[File:EX1 TS HOMO 1 16.png|thumb|150px|centre|HOMO-1 of the TS, MO16]]
|-
| LUMO || [[File:EX1 BUTDIENE LUMO12.png|thumb|150px|centre|LUMO of Butadiene, MO12]] || [[File:EX1 ALKENE LUMO7.png|thumb|150px|centre|LUMO of Ethylene, MO7]]|| [[File:EX1 TS LUMO18.png|thumb|150px|centre|LUMO of the TS, MO18]]||[[File:EX1 TS LUMO+1 19.png|thumb|150px|centre|LUMO+1 of the TS, MO19]]
|}

Only the orbitals that have the same symmetry can combine with each other to give the transition state MO because if the orbitals are miss matching, the overlap will be zero.
Figure below was the idealized MO diagram for the reaction between butadiene and ethylene.
The HOMO - LUMO interaction are summarised below: (S and AS are symmetric and asymmetric respectively)
Ethylene LUMO (MO7, AS) - Butadiene HOMO (MO11, AS) ---> TS LUMO+1 (MO19, AS)
Ethylene LUMO (MO7, AS) - Butadiene HOMO (MO11, AS) ---> TS HOMO-1 (MO16, AS)
Ethylene HOMO (MO6, S) - Butadiene LUMO (MO12, S) ---> TS LUMO (MO18, S)
Ethylene HOMO (MO6, S) - Butadiene LUMO (MO12, S) ---> TS HOMO (MO17, S)

The effect arise from the symmetry of the orbital on the orbital overlap integral:
symmetric-antisymmetric interaction ---> Zero
symmetric-symmetric interaction ---> Non-zero
antisymmetric-antisymmetric interaction ---> Non-zero

{|
|
|[[File:EX1_MO_FIG.PNG|thumb|600px|left|MO diagram]]
|}
In this experiment, butadiene and ethylene were doing [4+2] cycloaddition, which is a pericyclic chemical reaction. For pericyclic reactions, we have to obey the Woodward-Hoffmann Rules. The rules state that in order to make the reaction to be thermal allowed, the sum of (4q+2)s and (4r)a must be odd, where 's' represents suprafacial, 'a' stands for antarafacial and q,r are integers from 0. If the sum of (4q+2)s and (4r)a is an even number, then the reaction will be forbidden. According to the MO, we know that the cycloaddition between butadiene and ethylene was thermal allowed because :
(4q + 2)s + (4r)a
= 1 + 0
= 1 ----> odd number, q=0,r=0.

=== Bond lengths analysis ===
The typical C-C bond lengths are shown below:
sp<sup>3</sup> C- sp<sup>3</sup> C 1.54Å
sp<sup>2</sup> C- sp<sup>2</sup> C 1.47Å
sp<sup>3</sup> C- sp<sup>2</sup> C 1.50Å

{| class="wikitable" border="1"
|+ Table 3. C-C Bond lengths changes during the reaction
! molecules !! Bond lenghts !!molecules!!Bond lengths
|+
| [[File:C1-C4-2.PNG|thumb|150px|centre]]||
*reactant ethylene
*C1=C4 1.33Å
|| [[File:BUT C-C2.PNG|thumb|150px|centre]]||
*reactant butadiene
*C12=C14 1.33Å
*C12-C10 1.47Å
*C10-C7 1.33Å
|-
|| [[File:PRODUCT C-C-2.PNG|thumb|150px|centre]]||
*Product
*C7-C1 1.54Å sp3-sp3
*C1-C4 1.53Å sp3-sp3
*C4-C14 1.54Å sp3-sp3
*C14-C12 1.50Å sp3-sp2
*C12=C10 1.34Å sp2-sp2
*C10-C7 1.50Å sp2-sp3
|| [[File:TS C-C-2.PNG|thumb|150px|centre]]||
*Transition state
*C1=C4 1.38Å bond rupture
*C12=C10 1.41Å bond formation
*C10=C7 1.38Å bond rupture
*C7-C1 2.11Å bond formation
*C12=C14 1.38Å bond rupture
*C14-C4 2.11Å bond formation
|}

The Van der Waals radius of the C atom is 1.7Å, so the expected VDW C-C bond length shoule be 3.4Å. After comparing, we can see that the length of the partly formed C-C bonds (C14-C4 and C7-C1) in TS are smaller than the expected one while larger than the typical sp<sup>3</sup> C- sp<sup>3</sup> C bond length. It shows that the bond is forming. In addition, in TS, a partial double bond is formed between C12 and C10, as a result, the length of C12-C10 is smaller than the standard sp<sup>2</sup> C- sp<sup>2</sup> C bonds.

== Exercise 2 ==
In exercise 2, we looked at the reaction between cyclohexadiene and 1,3-dioxole.
=== Optimisation at B3LYP/6-31G(d) level ===
{| class="wikitable"
!
! center; style="background: #EDEDED; color: black;" | Structure
! center; style="background: #EDEDED; color: black;" | Frequency

|-
|Cyclohexadiene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18 </script>
<uploadedFileContents>Zkw CYCLO 631G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zkw CYCLO FRE.PNG|thumb|300px|center]]
|-

| 1,3-Dioxole
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>Zkw DIO 631G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:DIO FRE.PNG|thumb|300px|center]]
|-

|-
|Exo TS
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18 </script>
<uploadedFileContents>Zkw EXO TS 631G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:EXO TS FRE.PNG|thumb|300px|center]]
|-
|Exo Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18 </script>
<uploadedFileContents>ZKW EXO PRODUCT 631G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:EXO PRODUCT FRE.PNG|thumb|300px|center]]
|-
|Endo TS
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18 </script>
<uploadedFileContents>ZKW ENDO TS 631G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ENDO TS FRE.PNG|thumb|300px|center]]
|-
|Endo Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18 </script>
<uploadedFileContents>ZKWENDO PRODUCT 631G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ENDO PRODUCT FRE.PNG|thumb|300px|center]]
|}

=== HOMO/LUMO of Transition State ===
{| class="wikitable" border="1"
|+ Table 4. HOMO/LUMO of TS
! !! TS HOMO MO41 !!TS LUMO MO42!!TS HOMO-1 MO40!! TS LUMO+1 MO43
|+
| ENDO|| [[File:ENDO HOMO 41.png|thumb|150px|centre]]||[[File:ENDO LUMO 42.png|thumb|150px|centre]] || [[File:ENDO HOMO-1 40.png|thumb|150px|centre]]||[[File:ENDO LUMO+1 43.png|thumb|150px|centre]]
|-
| EXO|| [[File:ZKWEXO HOMO 41.png|thumb|150px|centre]]||[[File:EXO LUMO 42.png|thumb|150px|centre]] || [[File:EXO HOMO-1 40.png|thumb|150px|centre]]||[[File:EXO LUMO+1 43.png|thumb|150px|centre]]
|}

=== Molecular Orbital Analysis ===
{| class="wikitable" border="1"
|-
| [[File:EX2 ENDO MO.png|400px|thumb|center|Fig.1 MO diagram of ENDO TS ]] || [[File:屏幕快照 2017-12-13 23.29.47.png|400px|thumb|center|Fig.2 MO diagram of EXO TS]]
|}

There are two types of Diels–Alder reaction, one is the standard DA reaction, the other is inverse electron demand DA reaction. Generally, for most of the DA reactions, MOs of the electron rich diene would have higher energy levels than the MOs of electron poor dienophile. Then, according to the frontier molecular orbital theory, there are interactions between the HOMO of diene and LUMO of dienophile because their energy levels are close to each other. In contrast, for inverse electron demand DA reactions, the energy of diene's LUMO is more similar to the dienophile's HOMO. As a result, in the inverse situation, LUMO<sub>diene</sub> and HOMO<sub>dienophile</sub> are the frontier molecular orbitals.

In both MO diagrams (Fig.1 and Fig.2), the energy levels of HOMO/LUMO of the diene (cyclohexadiene) are lower than the ones of dienophile (1,3-dioxole). Also, the FMO are LUMO<sub>cyclohexadiene</sub>(MO 23) and HOMO<sub>1,3-dioxole</sub> (MO 19). The small energy gap between them lead to the strong interactio and favourable the bond formation. These indicate that cyclohexadiene and 1,3-dioxole will do an inverse electron demand DA reaction.

=== Thermochemistry - Reaction Energies and Barriers ===
The following energies' units are converted from Hartree. (1 Kjmol<sup>-1</sup> = 3.8088 X10<sup>-4</sup> Hartree)
{| class="wikitable" border="1"
|+ Table 5. Energies of reactants, products, TS
!Molecules!!Energies under B3LYP/631G(d) mode / Kjmol<sup>-1</sup>
|+
|Cyclohexadiene||-6.12582 x 10<sup>5</sup>
|-
|1,3-Dioxole||-7.01158 x 10<sup>5</sup>
|-
|ENDO TS|| -1.313614 x 10<sup>6</sup>
|-
|ENDO product||-1.313815 x 10<sup>6</sup>
|-
|EXO TS||-1.3136 x 10<sup>6</sup>
|-
|EXO product||-1.3138 x 10<sup>6</sup>
|}

In order to get the reaction energy and activation energy, we need to use the following equations:
Reaction energy = Product's energy - Reactants' energies
Activation energy = TS's energy - Reactants' energies

{| class="wikitable" border="1"
|+ Table 6. E<sub>activation</sub> and E<sub>reaction</sub> of Endo/Exo product
!!!Activation Energy / Kjmol<sup>-1</sup>!!Reaction Energy / Kjmol<sup>-1
|+
|Exo Product||+140.0||-60.0
|-
|Endo Product||+126.0||-75.0
|}

After comparing the data in table.6 we can see that the Exo product has more positive E<sub>activation</sub> than the Endo one, with +14Kjmol<sup>-1</sup>. At the same time, the E<sub>reaction</sub> of Endo product has more negative value (-15Kjmol) than the Exo one.
The lower the activation energy, the faster the reactants can reach the TS and fewer energy is needed. Therefore, smaller E<sub>activation</sub> means the product is kinetically favourable and in this exercise, endo product is the kinetically favourable one.
The reaction energy represents the stability of the product. More negative the reaction energy is, more heat is released to the environment to form the stable product. As a result, the endo product is thermodynamically favoured as well.

=== Secondary Orbital Interaction ===
Both secondary orbital interaction and primary orbital interaction can be seen in the endo TS while in exo TS, only primary orbital interaction presents. The secondary orbital interaction indicates that the lone paired electrons in p orbitals on oxygen will overlap with the LUMO<sub>diene</sub>. As a result, the endo approaching is more preferred. Also, because of the SOI, the activation energy is decreased and then, the TS is stabilised. When the dienophile doing exo approach, sterics effect arose, which lead to a larger reaction barrier energy.

== Exercise 3 ==
Exercise 3 is the DA cycloaddition of Xylylene and SO<sub>2</sub>.

=== Optimisation at PM6 level ===
{| class="wikitable"
! center; style="background: #EDEDED; color: black;" | Xylylene
! style="background: #EDEDED; color: black;" | EXO TS
! style="background: #EDEDED; color: black;" | ENDO TS
! style="background: #EDEDED; color: black;" | Cheletropic TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 34; vibration 2;rotate x -20; </script>
<uploadedFileContents>XYL PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; vibration 2;rotate x -20; </script>
<uploadedFileContents>EXO PM6-3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; vibration 2;rotate x -20; </script>
<uploadedFileContents>ZkwENDO PM6-3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 58; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ex3CHE PM6-3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! center; style="background: #EDEDED; color: black;" | SO<sub>2</sub>
! style="background: #EDEDED; color: black;" | Exo Product
! style="background: #EDEDED; color: black;" | Endo Product
! style="background: #EDEDED; color: black;" | Cheletropic Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; vibration 2;rotate x -20; </script>
<uploadedFileContents>ZKWSO2PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; vibration 2;rotate x -20; </script>
<uploadedFileContents>EXO PM6-1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 28; vibration 2;rotate x -20; </script>
<uploadedFileContents>ZkwENDO PM6-1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; vibration 2;rotate x -20; </script>
<uploadedFileContents>ZkwCHE PM6-1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|+ Table 7. Optimisation of reactants, transition states, products at PM6 Level
|}

=== IRC calculation ===
{| class="wikitable"
! style="background: #EDEDED; color: black;" |Reaction
! style="background: #EDEDED; color: black;" | gif
! style="background: #EDEDED; color: black;" | IRC
|-
| EXO DA reaction
| [[File:Zkwex3EXO IRC GIF.gif ]]
| [[File:ZKWEXO IRC.PNG|ZKWEXO IRC.PNG]]
|-
| ENDO DA reaction
| [[File:Zkwex3ENDO IRC GIF.gif]]
| [[File:EX3 ENDO IRC.PNG|none ]]
|-
| Cheletropic
| [[File:Zkwex3CHE IRC GIF.gif]]
| [[File:ZkwCHE IRC.PNG|none ‎ ]]
|-
|}

=== Activation and reaction energies ===
The following energies' units are converted from Hartree. (1 Kjmol-1 = 3.8088 X10-4 Hartree)
{| class="wikitable"
! style="background: #EDEDED; color: black;" | Molecule
! style="background: #EDEDED; color: black;" | Exo approach
! style="background: #EDEDED; color: black;" | Endo approach
! style="background: #EDEDED; color: black;" | Cheletropic
|-
| xylylene
| +469.287
| +469.287
| +469.287
|-
| SO2
| -313.143
| -313.143
| -313.143
|-
|Transition State
| +
| +
| +
|-
| Product
| +
| +
| -
|-
| Activation Energy/kjmol<sup>-1</sup>
| +
| +
| +
|-
| Reaction Energy/kjmol<sup>-1</sup>
| -
| -
| -
|+ Table 9.Activation and reaction energies at PM6 Level/kjmol<sup>-1</sup>
|-
|}

File:Zkwex3EXO IRC GIF.gif

2017-12-15T13:40:15Z

Kz1015:

File:Zkwex3ENDO IRC GIF.gif

2017-12-15T13:39:20Z

Kz1015:

Rep:Mod:KZ1015TS

2017-12-15T13:38:19Z

Kz1015: /* IRC calculation */

=''' Transition states and reactivity '''=
== Introduction ==

In this experiment, we used three pericyclic reactions to understand the transition states. Transition states could be identified through the potential energy surface, which shows that the energy of a molecule acts as a function
of molecule's geometry. Generally, the number of geometric degrees of freedom of the non-linear molecule is equal to the dimensionality of its PES. This obey the equatoin (3N-6), where N= number of atoms.

In the PES, reactants and products locate at minimum points while the saddle(maximum) points represents the transition state. At saddle points, the gradient equals to zero and all forces vanish. Since the value of first derivatives of both minimum and maximum points are equal to zero, the second derivatives is needed to differentiate these two points. When the second derivatives is positive, it suggests the minimum point and once the geometry is changed, the energy will increase. In contrast, negative second derivatives leads to the transition state and the energy will decrease in the pathway to the product.

For non-linear molecules, their vibration modes also associate with the equation 3N-6 and each mode has its own force constant. After doing the optimisaition calculations, there should be only one imaginary frequency. It proves that we have the transition state structure because the imaginary frequency aries from the negative curvature of the 3N-6 dimensions of the PES at transition state.

=== Method ===
In the following three exercises, all the transition states were obtained through optimisation of products. First, drawing the product structure in the GaussView and let the structure being optimised to minimum at semi-empirical PM6 level. Then, breaking the bonds that were formed during the reaction and adjust and 'freeze' those bonds to a certain length. For instance, setting C-C=2.2 Å, C-O=2.0 Å and C-S=2.4 Å. At the same time, fixing the coordinates of the atoms that related to the breaking bonds. After these, the structure was optimised again at PM6 level followed by a futher optimisation, which was run to obtain the TS. Once we got the TS, there should be only one imaginary frequency and a perfect IRC figure was obtained to make sure that the TS was correct (gradient = 0 at TS).

== Exercise 1 ==
For exercise 1, butadiene and ethlyene were used to do diels-alder reaction.

=== Optimization ===
{| class="wikitable"
! center; style="background: #EDEDED; color: black;" | Butadiene
! center; style="background: #EDEDED; color: black;" | Ethlyene
! center; style="background: #EDEDED; color: black;" | Transition State
! center; style="background: #EDEDED; color: black;" | Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; vibration 2;rotate x -20; </script>
<uploadedFileContents>ZKW_BUTADIENE_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; vibration 2;rotate x -20; </script>
<uploadedFileContents>ZKW_Ethlyene1_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1 Transition.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_PRODUCT_IRC.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|+ Table 1. optimisation at PM6 level
|}

=== IRC and frequency calculation analysis ===
The figure below suggests that the correct TS is got because only one imaginary frequency was obtained and when the value of IRC in RMS gradient along IRC equals to zero, the gradient=0 as well. In addition, we found that the bond rupture and bond formation happened at the same time, which means it is a synchronous procedure.
{| class="wikitable" border="1"
|-
| [[File:EX1 PRODUCT3 IRC.PNG|350px|thumb|center |]] || [[File:EX1 PRODUCT3 VIBRATION.PNG|350px|thumb|center |]]
|-
|}

=== Molecular orbital analysis ===
The following table shows the HOMO/LUMO of reactants and transition state.
{| class="wikitable" border="1"
|+ Table 2. HOMO/LUMO and MO diagrams
! !! Butadiene !!Ethylene!!Transition state!!Transition state
|+
| HOMO || [[File:EX1 BUTDIENE HOMO11.png|thumb|150px|centre|HOMO of Butadiene, MO11]]|| [[File:EX1 ALKENE HOMO6.png|thumb|150px|centre|HOMO of Ethylene, MO6]]|| [[File:EX1 TS HOMO17.png|thumb|150px|centre|HOMO of the TS, MO17]]||[[File:EX1 TS HOMO 1 16.png|thumb|150px|centre|HOMO-1 of the TS, MO16]]
|-
| LUMO || [[File:EX1 BUTDIENE LUMO12.png|thumb|150px|centre|LUMO of Butadiene, MO12]] || [[File:EX1 ALKENE LUMO7.png|thumb|150px|centre|LUMO of Ethylene, MO7]]|| [[File:EX1 TS LUMO18.png|thumb|150px|centre|LUMO of the TS, MO18]]||[[File:EX1 TS LUMO+1 19.png|thumb|150px|centre|LUMO+1 of the TS, MO19]]
|}

Only the orbitals that have the same symmetry can combine with each other to give the transition state MO because if the orbitals are miss matching, the overlap will be zero.
Figure below was the idealized MO diagram for the reaction between butadiene and ethylene.
The HOMO - LUMO interaction are summarised below: (S and AS are symmetric and asymmetric respectively)
Ethylene LUMO (MO7, AS) - Butadiene HOMO (MO11, AS) ---> TS LUMO+1 (MO19, AS)
Ethylene LUMO (MO7, AS) - Butadiene HOMO (MO11, AS) ---> TS HOMO-1 (MO16, AS)
Ethylene HOMO (MO6, S) - Butadiene LUMO (MO12, S) ---> TS LUMO (MO18, S)
Ethylene HOMO (MO6, S) - Butadiene LUMO (MO12, S) ---> TS HOMO (MO17, S)

The effect arise from the symmetry of the orbital on the orbital overlap integral:
symmetric-antisymmetric interaction ---> Zero
symmetric-symmetric interaction ---> Non-zero
antisymmetric-antisymmetric interaction ---> Non-zero

{|
|
|[[File:EX1_MO_FIG.PNG|thumb|600px|left|MO diagram]]
|}
In this experiment, butadiene and ethylene were doing [4+2] cycloaddition, which is a pericyclic chemical reaction. For pericyclic reactions, we have to obey the Woodward-Hoffmann Rules. The rules state that in order to make the reaction to be thermal allowed, the sum of (4q+2)s and (4r)a must be odd, where 's' represents suprafacial, 'a' stands for antarafacial and q,r are integers from 0. If the sum of (4q+2)s and (4r)a is an even number, then the reaction will be forbidden. According to the MO, we know that the cycloaddition between butadiene and ethylene was thermal allowed because :
(4q + 2)s + (4r)a
= 1 + 0
= 1 ----> odd number, q=0,r=0.

=== Bond lengths analysis ===
The typical C-C bond lengths are shown below:
sp<sup>3</sup> C- sp<sup>3</sup> C 1.54Å
sp<sup>2</sup> C- sp<sup>2</sup> C 1.47Å
sp<sup>3</sup> C- sp<sup>2</sup> C 1.50Å

{| class="wikitable" border="1"
|+ Table 3. C-C Bond lengths changes during the reaction
! molecules !! Bond lenghts !!molecules!!Bond lengths
|+
| [[File:C1-C4-2.PNG|thumb|150px|centre]]||
*reactant ethylene
*C1=C4 1.33Å
|| [[File:BUT C-C2.PNG|thumb|150px|centre]]||
*reactant butadiene
*C12=C14 1.33Å
*C12-C10 1.47Å
*C10-C7 1.33Å
|-
|| [[File:PRODUCT C-C-2.PNG|thumb|150px|centre]]||
*Product
*C7-C1 1.54Å sp3-sp3
*C1-C4 1.53Å sp3-sp3
*C4-C14 1.54Å sp3-sp3
*C14-C12 1.50Å sp3-sp2
*C12=C10 1.34Å sp2-sp2
*C10-C7 1.50Å sp2-sp3
|| [[File:TS C-C-2.PNG|thumb|150px|centre]]||
*Transition state
*C1=C4 1.38Å bond rupture
*C12=C10 1.41Å bond formation
*C10=C7 1.38Å bond rupture
*C7-C1 2.11Å bond formation
*C12=C14 1.38Å bond rupture
*C14-C4 2.11Å bond formation
|}

The Van der Waals radius of the C atom is 1.7Å, so the expected VDW C-C bond length shoule be 3.4Å. After comparing, we can see that the length of the partly formed C-C bonds (C14-C4 and C7-C1) in TS are smaller than the expected one while larger than the typical sp<sup>3</sup> C- sp<sup>3</sup> C bond length. It shows that the bond is forming. In addition, in TS, a partial double bond is formed between C12 and C10, as a result, the length of C12-C10 is smaller than the standard sp<sup>2</sup> C- sp<sup>2</sup> C bonds.

== Exercise 2 ==
In exercise 2, we looked at the reaction between cyclohexadiene and 1,3-dioxole.
=== Optimisation at B3LYP/6-31G(d) level ===
{| class="wikitable"
!
! center; style="background: #EDEDED; color: black;" | Structure
! center; style="background: #EDEDED; color: black;" | Frequency

|-
|Cyclohexadiene
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18 </script>
<uploadedFileContents>Zkw CYCLO 631G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zkw CYCLO FRE.PNG|thumb|300px|center]]
|-

| 1,3-Dioxole
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>Zkw DIO 631G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:DIO FRE.PNG|thumb|300px|center]]
|-

|-
|Exo TS
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18 </script>
<uploadedFileContents>Zkw EXO TS 631G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:EXO TS FRE.PNG|thumb|300px|center]]
|-
|Exo Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18 </script>
<uploadedFileContents>ZKW EXO PRODUCT 631G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:EXO PRODUCT FRE.PNG|thumb|300px|center]]
|-
|Endo TS
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18 </script>
<uploadedFileContents>ZKW ENDO TS 631G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ENDO TS FRE.PNG|thumb|300px|center]]
|-
|Endo Product
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18 </script>
<uploadedFileContents>ZKWENDO PRODUCT 631G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ENDO PRODUCT FRE.PNG|thumb|300px|center]]
|}

=== HOMO/LUMO of Transition State ===
{| class="wikitable" border="1"
|+ Table 4. HOMO/LUMO of TS
! !! TS HOMO MO41 !!TS LUMO MO42!!TS HOMO-1 MO40!! TS LUMO+1 MO43
|+
| ENDO|| [[File:ENDO HOMO 41.png|thumb|150px|centre]]||[[File:ENDO LUMO 42.png|thumb|150px|centre]] || [[File:ENDO HOMO-1 40.png|thumb|150px|centre]]||[[File:ENDO LUMO+1 43.png|thumb|150px|centre]]
|-
| EXO|| [[File:ZKWEXO HOMO 41.png|thumb|150px|centre]]||[[File:EXO LUMO 42.png|thumb|150px|centre]] || [[File:EXO HOMO-1 40.png|thumb|150px|centre]]||[[File:EXO LUMO+1 43.png|thumb|150px|centre]]
|}

=== Molecular Orbital Analysis ===
{| class="wikitable" border="1"
|-
| [[File:EX2 ENDO MO.png|400px|thumb|center|Fig.1 MO diagram of ENDO TS ]] || [[File:屏幕快照 2017-12-13 23.29.47.png|400px|thumb|center|Fig.2 MO diagram of EXO TS]]
|}

There are two types of Diels–Alder reaction, one is the standard DA reaction, the other is inverse electron demand DA reaction. Generally, for most of the DA reactions, MOs of the electron rich diene would have higher energy levels than the MOs of electron poor dienophile. Then, according to the frontier molecular orbital theory, there are interactions between the HOMO of diene and LUMO of dienophile because their energy levels are close to each other. In contrast, for inverse electron demand DA reactions, the energy of diene's LUMO is more similar to the dienophile's HOMO. As a result, in the inverse situation, LUMO<sub>diene</sub> and HOMO<sub>dienophile</sub> are the frontier molecular orbitals.

In both MO diagrams (Fig.1 and Fig.2), the energy levels of HOMO/LUMO of the diene (cyclohexadiene) are lower than the ones of dienophile (1,3-dioxole). Also, the FMO are LUMO<sub>cyclohexadiene</sub>(MO 23) and HOMO<sub>1,3-dioxole</sub> (MO 19). The small energy gap between them lead to the strong interactio and favourable the bond formation. These indicate that cyclohexadiene and 1,3-dioxole will do an inverse electron demand DA reaction.

=== Thermochemistry - Reaction Energies and Barriers ===
The following energies' units are converted from Hartree. (1 Kjmol<sup>-1</sup> = 3.8088 X10<sup>-4</sup> Hartree)
{| class="wikitable" border="1"
|+ Table 5. Energies of reactants, products, TS
!Molecules!!Energies under B3LYP/631G(d) mode / Kjmol<sup>-1</sup>
|+
|Cyclohexadiene||-6.12582 x 10<sup>5</sup>
|-
|1,3-Dioxole||-7.01158 x 10<sup>5</sup>
|-
|ENDO TS|| -1.313614 x 10<sup>6</sup>
|-
|ENDO product||-1.313815 x 10<sup>6</sup>
|-
|EXO TS||-1.3136 x 10<sup>6</sup>
|-
|EXO product||-1.3138 x 10<sup>6</sup>
|}

In order to get the reaction energy and activation energy, we need to use the following equations:
Reaction energy = Product's energy - Reactants' energies
Activation energy = TS's energy - Reactants' energies

{| class="wikitable" border="1"
|+ Table 6. E<sub>activation</sub> and E<sub>reaction</sub> of Endo/Exo product
!!!Activation Energy / Kjmol<sup>-1</sup>!!Reaction Energy / Kjmol<sup>-1
|+
|Exo Product||+140.0||-60.0
|-
|Endo Product||+126.0||-75.0
|}

After comparing the data in table.6 we can see that the Exo product has more positive E<sub>activation</sub> than the Endo one, with +14Kjmol<sup>-1</sup>. At the same time, the E<sub>reaction</sub> of Endo product has more negative value (-15Kjmol) than the Exo one.
The lower the activation energy, the faster the reactants can reach the TS and fewer energy is needed. Therefore, smaller E<sub>activation</sub> means the product is kinetically favourable and in this exercise, endo product is the kinetically favourable one.
The reaction energy represents the stability of the product. More negative the reaction energy is, more heat is released to the environment to form the stable product. As a result, the endo product is thermodynamically favoured as well.

=== Secondary Orbital Interaction ===
Both secondary orbital interaction and primary orbital interaction can be seen in the endo TS while in exo TS, only primary orbital interaction presents. The secondary orbital interaction indicates that the lone paired electrons in p orbitals on oxygen will overlap with the LUMO<sub>diene</sub>. As a result, the endo approaching is more preferred. Also, because of the SOI, the activation energy is decreased and then, the TS is stabilised. When the dienophile doing exo approach, sterics effect arose, which lead to a larger reaction barrier energy.

== Exercise 3 ==
Exercise 3 is the DA cycloaddition of Xylylene and SO<sub>2</sub>.

=== Optimisation at PM6 level ===
{| class="wikitable"
! center; style="background: #EDEDED; color: black;" | Xylylene
! style="background: #EDEDED; color: black;" | EXO TS
! style="background: #EDEDED; color: black;" | ENDO TS
! style="background: #EDEDED; color: black;" | Cheletropic TS
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 34; vibration 2;rotate x -20; </script>
<uploadedFileContents>XYL PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; vibration 2;rotate x -20; </script>
<uploadedFileContents>EXO PM6-3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; vibration 2;rotate x -20; </script>
<uploadedFileContents>ZkwENDO PM6-3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 58; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ex3CHE PM6-3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! center; style="background: #EDEDED; color: black;" | SO<sub>2</sub>
! style="background: #EDEDED; color: black;" | Exo Product
! style="background: #EDEDED; color: black;" | Endo Product
! style="background: #EDEDED; color: black;" | Cheletropic Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; vibration 2;rotate x -20; </script>
<uploadedFileContents>ZKWSO2PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; vibration 2;rotate x -20; </script>
<uploadedFileContents>EXO PM6-1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 28; vibration 2;rotate x -20; </script>
<uploadedFileContents>ZkwENDO PM6-1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; vibration 2;rotate x -20; </script>
<uploadedFileContents>ZkwCHE PM6-1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|+ Table 7. Optimisation of reactants, transition states, products at PM6 Level
|}

=== IRC calculation ===
{| class="wikitable"
! style="background: #EDEDED; color: black;" |Reaction
! style="background: #EDEDED; color: black;" | gif
! style="background: #EDEDED; color: black;" | IRC
|-
| EXO DA reaction
| [[File:EXO IRC GIF.gif ]]
| [[File:ZKWEXO IRC.PNG|ZKWEXO IRC.PNG]]
|-
| ENDO DA reaction
| [[File:ENDO IRC GIF.gif ]]
| [[File:EX3 ENDO IRC.PNG|none ]]
|-
| Cheletropic
| [[File:Zkwex3CHE IRC GIF.gif]]
| [[File:ZkwCHE IRC.PNG|none ‎ ]]
|-
|}

=== Activation and reaction energies ===
The following energies' units are converted from Hartree. (1 Kjmol-1 = 3.8088 X10-4 Hartree)
{| class="wikitable"
! style="background: #EDEDED; color: black;" | Molecule
! style="background: #EDEDED; color: black;" | Exo approach
! style="background: #EDEDED; color: black;" | Endo approach
! style="background: #EDEDED; color: black;" | Cheletropic
|-
| xylylene
| +469.287
| +469.287
| +469.287
|-
| SO2
| -313.143
| -313.143
| -313.143
|-
|Transition State
| +
| +
| +
|-
| Product
| +
| +
| -
|-
| Activation Energy/kjmol<sup>-1</sup>
| +
| +
| +
|-
| Reaction Energy/kjmol<sup>-1</sup>
| -
| -
| -
|+ Table 9.Activation and reaction energies at PM6 Level/kjmol<sup>-1</sup>
|-
|}