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Rep:Zw4415:TSexercise

2018-03-14T01:43:17Z

Zw4415:

=Introduction=

===The Transition State===

According to '''Computational Quantum Chemistry''' the reaction coordinate was functionalised by all 3N<sub>atoms</sub>-6 internal coordinates.

Potenyial energy surface describes the energy of a specific system where energy was tabulated by a set of reaction coordinates. [1]

The reactant and product with stationary structure are the minimum points on the potential energy surface.It could be calculated by :

[[File:Zinan_Wang_eq1.png|thumb|center|Equation. 1 [1] ]]

where '''R''' is a set of all internal coordinates and q is normal coordinates which is a linear combination of all internal coordinates.

The transition state is the point with the highest energy along the reaction pathway. The second derivative should be all positive except the one along the reaction coordinate.
Thus it could be calculated as below.
[[File:Zinan_Wang_eq2.png|thumb|center|Equation. 2 [1] ]]
[[File:Zinan_Wang_eq3.png|thumb|center|Equation. 3 [1] ]]

===The computational method===
In this exercise, PM6 and B3LYP/6-31G(d) methods have been used to calculate the optimized structure of the reactants, products and the transition state. PM6 method is generally a faster method to give a rough approximation of the structure. A more precise optimization could be carried out by B3LYP with basis set of 6-31G(d) while it often takes quite a long time.

===Freqrency check===
All the normal modes for stationary structure ,thus the reactants and products, should have positive values as they represent the minimum energy points on the PES.
For all the transition state structures, only 1 negative value should be seen. It is because when calculating from a harmonic oscillator with negative force constant (The negative value of the second derivative along the reaction coordinate), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate the imaginary number (e.g. 526.7i).

===IRC check===
IRC was obtained with the same basis set used to calculate the transition structrue. The gradient of the energy graph (thus the first derivative along the reaction coordinate) shows 0 at the Transition state, reactants and product, which confirms the success of obtaining transition state.

=Exercise 1: Reaction of Butadiene with Ethylene=
In exercise 1, the simplest Diels-Alder reaction between butadiene and ethene was calculated.

The net reaction was visualized by the bond length measurment which represent the change of bond order.

===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level with frequency checked to only have one negative value at around -930.

[[File: Zinan_Wang_EX1_IRC.PNG|thumb|The IRC for optimized transition state|300px]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]
The MO energy level of both reactant was obtained by Energy calculation using PM6 method. For this specific Diels-Alder reaction between butadiene and ethene with no substituents, the electrons are in normal demand (Diene being electron rich and ethene being electron poor).

The Transition state MO generated by both reactant has higher energy then the HOMO of ethene. That is due to the fact that it is MO for transition state (not the product) which is the highest energy point along the reaction pathway.

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 Å indicating the formation of a sp3-sp3 carbon bond in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

PM6 IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

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

This is a reaction between cyclohexadiene and 1,3-Dioxole. There are 2 pathways of Diels-Alder reaction, Endo and Exo. For both pathway, reactants, TS and products were approximated using PM6 method then reoptimized by B3LYP method with 6-31G(d) basis set. Frequencies were checked, Gibbs free energies were extracted and MO diagrams were constructed and adjusted.

===Visualized HOMOs and LUMOs,frequency check and Gibbs free energies===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy (Hatree)
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|<jmol>
<jmolApplet>
<title>HOMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<title>LUMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|<jmol>
<jmolApplet>
<title>HOMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

According to the frequency calculation, all transition states are showing only 1 negative value and all the other species are showing all positive frequencies which confirms the success in obtaining the optimized structures.

===MO diagram===

Firstly the a single point energy calculation was carried out for two reactants being separated for 20 a.u.(i.e. assume no interaction)
The MO diagram for the resulting file was shown below
[[File:Zinan_Wang_EX2_REACT1and2.PNG|thumb|center|800px|The MOs from single point energy calculation ]]
The value of the each energy level was used to draw the corresponded MO diagram.
The energy levels for the MO of TS are higher than the final product as expected, as the TS represent the highest energy along the reaction coordination.

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp) / Hartree
|0.062817 (164.926034 kJ/mol)
|0.060358 (158.469929 kJ/mol)
|-
|Reaction energies (at room temp) /Hartree
|<nowiki>-0.024815</nowiki> (<nowiki>-65.1517825</nowiki> kJ/mol)
|<nowiki>-0.026185</nowiki> (<nowiki>-68.7487175</nowiki> kJ/mol)
|}

The reaction barrier and reaction energy are both lower for the Endo-pathway.
Therefore the endo pathway is both kinetic and thermodynamic favored.

From the single point calculation, the energy of the HOMO of the dieneophile (1,3-Dioxole) is higher than that of the diene (Cyclohexadiene) which shows that the dieneophile is more electron rich than the diene, thus inverse electron demand.

===Secondary orbital interactions===

In the endo position, there are 2 oxygen p orbitals from oxygen lone pair which has the silimar energy and same symmetry of the cyclohexadiene LUMO, therefore they would have non-zero overlap integral. This interaction would lower the energy of LUMO producing a stabalising effect for the whole structrue. Thus more thermodynamically favored.

In the exo position, the two orbitals mentioned above were too far apart, thus almost no overlap integral. Moreover, there is a steric clash between the ring structure of 1,3-Dioxole and the half of the ring structure of cyclohexadiene, which rise up the energy of the net structure, thus less stable.

===.log Files for Exercise 2===

B3LYP/6-31G(d) optimized cyclohexadiene:[[File:ZINAN_WANG_EX2_REACT1_OPT_B3LYP.LOG]]

B3LYP/6-31G(d) optimized 1,3-dioxole:[[File:Zinan_Wang_EX2_REACT2_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Exo TS:[[File:ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log]]

B3LYP/6-31G(d) optimized Endo TS:[[File:ZINAN_WANG_EX2_TS_ENDO_OPT_B3LYP_CHRIS.LOG]]

B3LYP/6-31G(d) optimized Exo product:[[File:Zinan_Wang_EX2_PRODUCT_EXO_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Endo product:[[File:ZINAN_WANG_EX2_PRODUCT_ENDO_OPT_B3LYP.LOG]]

=Exercise 3: Diels-Alder vs Cheletropic=

In exercise 3, xylylene and SO<sub>2</sub> are used as the reactant.
They could react through 3 pathways: Exo and Endo hetero-Diels Alder reaction or the Cheletropic reaction.
Energy barrier and reaction energy for each pathway has been calculated and plotted.

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.

The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is most thermodynamic favored.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

===.log Files for Exercise 3===

PM6 Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

PM6 Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

PM6 Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

PM6 Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

PM6 Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

PM6 Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

PM6 Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

PM6 Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

=Conclusion=

In this computational lab, 3 pericyclic reactions were investigated. Gaussian was used to optimized the structure of the reactants, products and transition states using either PM6 or B3LYP method with IRC and frequency checked to confirm the transition states. Gibbs free energy was extracted from the log file for each species and the reaction barriers and reaction energies were calculated from them. The kinetic favored pathway were determined by the lowest reaction barrier and thermodynamic favored pathway was determined by the lowest reaction energy.

This computational method could be carried out for more reactions to determine the reaction route under different conditions.

=Reference=

[1] J. J. W. McDouall, in Computational Quantum Chemistry: Molecular Structure and Properties in Silico, The Royal Society of Chemistry, London,
2013, ch. 1, pp. 1-62.

Rep:Zw4415:TSexercise

2018-03-14T00:52:53Z

Zw4415: /* Freqrency check */

=Introduction=

===The Transition State===

According to '''Computational Quantum Chemistry''' the reaction coordinate was functionalised by all 3N<sub>atoms</sub>-6 internal coordinates.[1]

Potenyial energy surface describes the energy of a specific system where energy was tabulated by a set of reaction coordinates.

The reactant and product with stationary structure are the minimum points on the potential energy surface.It could be calculated by :

[[File:Zinan_Wang_eq1.png|thumb|center|Equation. 1 [1] ]]

where '''R''' is a set of all internal coordinates and q is normal coordinates which is a linear combination of all internal coordinates.

The transition state is the point with the highest energy along the reaction pathway. The second derivative should be all positive except the one along the reaction coordinate.
Thus it could be calculated as below.
[[File:Zinan_Wang_eq2.png|thumb|center|Equation. 2 [1] ]]
[[File:Zinan_Wang_eq3.png|thumb|center|Equation. 3 [1] ]]

===The computational method===
In this exercise, PM6 and B3LYP/6-31G(d) methods have been used to calculate the optimized structure of the reactants, products and the transition state. PM6 method is generally a faster method to give a rough approximation of the structure. A more precise optimization could be carried out by B3LYP with basis set of 6-31G(d) while it often takes quite a long time.

===Freqrency check===
All the normal modes for stationary structure ,thus the reactants and products, should have positive values as they represent the minimum energy points on the PES.
For all the transition state structures, only 1 negative value should be seen. It is because when calculating from a harmonic oscillator with negative force constant (The negative value of the second derivative along the reaction coordinate), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate the imaginary number (e.g. 526.7i).

===IRC check===
IRC was obtained with the same basis set used to calculate the transition structrue. The gradient of the energy graph (thus the first derivative along the reaction coordinate) shows 0 at the Transition state, reactants and product, which confirms the success of obtaining transition state.

=Exercise1=
===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level first with frequency checked to only have one negative value at around -930. Followed by B3LYP/6-31G(d) method and the resulting structure have one negative frequency at -526.7.

[[File: Zinan_Wang_EX1_IRC.PNG|thumb|center|The IRC for optimized transition state|800px ]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]
The Transition state MO has higher energy than the fragment molecular orbitals.

That is due to the fact that it is a MO for the transition state which is the highest energy point along the reaction pathway.

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 Å indicating the formation of a sp3-sp3 carbon bond in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

PM6 IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

=Exercise2=

===Visualized HOMOs and LUMOs,frequency check and Gibbs free energies===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|<jmol>
<jmolApplet>
<title>HOMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<title>LUMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|<jmol>
<jmolApplet>
<title>HOMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

According to the frequency calculation, all transition states are showing only 1 negative value and all the other species are showing all positive frequencies which confirms the success in obtaining the optimized structures.

===MO diagram===

Firstly the a single point energy calculation was carried out for two reactants being separated for 20 a.u.(i.e. assume no interaction)
The MO diagram for the resulting file was shown below
[[File:Zinan_Wang_EX2_REACT1and2.PNG|thumb|center|800px|The MOs from single point energy calculation ]]
The value of the each energy level was used to draw the corresponded MO diagram.
The energy levels for the MO of TS are higher than the final product as expected, as the TS represent the highest energy along the reaction coordination.

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp) / Hartree
|0.062817 (164.926034 kJ/mol)
|0.060358 (158.469929 kJ/mol)
|-
|Reaction energies (at room temp) /Hartree
|<nowiki>-0.024815</nowiki> (<nowiki>-65.1517825</nowiki> kJ/mol)
|<nowiki>-0.026185</nowiki> (<nowiki>-68.7487175</nowiki> kJ/mol)
|}

The reaction barrier and reaction energy are both lower for the Endo-pathway.
Therefore the endo pathway is both kinetic and thermodynamic favored.

From the single point calculation, the energy of the HOMO of the dieneophile (1,3-Dioxole) is higher than that of the diene (Cyclohexadiene) which shows that the dieneophile is more electron rich than the diene, thus inverse electron demand.

===.log Files for Exercise 2===

B3LYP/6-31G(d) optimized cyclohexadiene:[[File:ZINAN_WANG_EX2_REACT1_OPT_B3LYP.LOG]]

B3LYP/6-31G(d) optimized 1,3-dioxole:[[File:Zinan_Wang_EX2_REACT2_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Exo TS:[[File:ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log]]

B3LYP/6-31G(d) optimized Endo TS:[[File:ZINAN_WANG_EX2_TS_ENDO_OPT_B3LYP_CHRIS.LOG]]

B3LYP/6-31G(d) optimized Exo product:[[File:Zinan_Wang_EX2_PRODUCT_EXO_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Endo product:[[File:ZINAN_WANG_EX2_PRODUCT_ENDO_OPT_B3LYP.LOG]]

=Exercise3=
In exercise 3, xylylene and SO<sub>2</sub> are used as the reactant.
They could react through 3 pathways: Exo and Endo hetero-Diels Alder reaction or the Cheletropic reaction.
Energy barrier and reaction energy for each pathway has been calculated and plotted.

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.
The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is thermodynamic pathway of reaction.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

===.log Files for Exercise 3===

PM6 Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

PM6 Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

PM6 Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

PM6 Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

PM6 Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

PM6 Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

PM6 Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

PM6 Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

=Conclusion=

In this computational lab, 3 pericyclic reactions were investigated. Gaussian was used to optimized the structure of the reactants, products and transition states using either PM6 or B3LYP method with IRC and frequency checked to confirm the transition states. Gibbs free energy was extracted from the log file for each species and the reaction barriers and reaction energies were calculated from them. The kinetic favored pathway were determined by the lowest reaction barrier and thermodynamic favored pathway was determined by the lowest reaction energy.

This computational method could be carried out for more reactions to determine the reaction route under different conditions.

=Reference=

[1] J. J. W. McDouall, in Computational Quantum Chemistry: Molecular Structure and Properties in Silico, The Royal Society of Chemistry, London,
2013, ch. 1, pp. 1-62.

Rep:Zw4415:TSexercise

2018-03-14T00:48:54Z

Zw4415:

=Introduction=

===The Transition State===

According to '''Computational Quantum Chemistry''' the reaction coordinate was functionalised by all 3N<sub>atoms</sub>-6 internal coordinates.[1]

Potenyial energy surface describes the energy of a specific system where energy was tabulated by a set of reaction coordinates.

The reactant and product with stationary structure are the minimum points on the potential energy surface.It could be calculated by :

[[File:Zinan_Wang_eq1.png|thumb|center|Equation. 1 [1] ]]

where '''R''' is a set of all internal coordinates and q is normal coordinates which is a linear combination of all internal coordinates.

The transition state is the point with the highest energy along the reaction pathway. The second derivative should be all positive except the one along the reaction coordinate.
Thus it could be calculated as below.
[[File:Zinan_Wang_eq2.png|thumb|center|Equation. 2 [1] ]]
[[File:Zinan_Wang_eq3.png|thumb|center|Equation. 3 [1] ]]

===The computational method===
In this exercise, PM6 and B3LYP/6-31G(d) methods have been used to calculate the optimized structure of the reactants, products and the transition state. PM6 method is generally a faster method to give a rough approximation of the structure. A more precise optimization could be carried out by B3LYP with basis set of 6-31G(d) while it often takes quite a long time.

===Freqrency check===
All the normal modes for stationary structure ,thus the reactants and products, should have positive values as they represents the minimum energy point on the PES.
For all the transition state structures, only 1 negative value should be seen. It is because when calculating form a harmonic oscillator with negative force constant (The negative value of the second derivative along the reaction coordinate), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate the imaginary number (e.g. 526.7i).

===IRC check===
IRC was obtained with the same basis set used to calculate the transition structrue. The gradient of the energy graph (thus the first derivative along the reaction coordinate) shows 0 at the Transition state, reactants and product, which confirms the success of obtaining transition state.

=Exercise1=
===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level first with frequency checked to only have one negative value at around -930. Followed by B3LYP/6-31G(d) method and the resulting structure have one negative frequency at -526.7.

[[File: Zinan_Wang_EX1_IRC.PNG|thumb|center|The IRC for optimized transition state|800px ]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]
The Transition state MO has higher energy than the fragment molecular orbitals.

That is due to the fact that it is a MO for the transition state which is the highest energy point along the reaction pathway.

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 Å indicating the formation of a sp3-sp3 carbon bond in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

PM6 IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

=Exercise2=

===Visualized HOMOs and LUMOs,frequency check and Gibbs free energies===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|<jmol>
<jmolApplet>
<title>HOMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<title>LUMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|<jmol>
<jmolApplet>
<title>HOMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

According to the frequency calculation, all transition states are showing only 1 negative value and all the other species are showing all positive frequencies which confirms the success in obtaining the optimized structures.

===MO diagram===

Firstly the a single point energy calculation was carried out for two reactants being separated for 20 a.u.(i.e. assume no interaction)
The MO diagram for the resulting file was shown below
[[File:Zinan_Wang_EX2_REACT1and2.PNG|thumb|center|800px|The MOs from single point energy calculation ]]
The value of the each energy level was used to draw the corresponded MO diagram.
The energy levels for the MO of TS are higher than the final product as expected, as the TS represent the highest energy along the reaction coordination.

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp) / Hartree
|0.062817 (164.926034 kJ/mol)
|0.060358 (158.469929 kJ/mol)
|-
|Reaction energies (at room temp) /Hartree
|<nowiki>-0.024815</nowiki> (<nowiki>-65.1517825</nowiki> kJ/mol)
|<nowiki>-0.026185</nowiki> (<nowiki>-68.7487175</nowiki> kJ/mol)
|}

The reaction barrier and reaction energy are both lower for the Endo-pathway.
Therefore the endo pathway is both kinetic and thermodynamic favored.

From the single point calculation, the energy of the HOMO of the dieneophile (1,3-Dioxole) is higher than that of the diene (Cyclohexadiene) which shows that the dieneophile is more electron rich than the diene, thus inverse electron demand.

===.log Files for Exercise 2===

B3LYP/6-31G(d) optimized cyclohexadiene:[[File:ZINAN_WANG_EX2_REACT1_OPT_B3LYP.LOG]]

B3LYP/6-31G(d) optimized 1,3-dioxole:[[File:Zinan_Wang_EX2_REACT2_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Exo TS:[[File:ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log]]

B3LYP/6-31G(d) optimized Endo TS:[[File:ZINAN_WANG_EX2_TS_ENDO_OPT_B3LYP_CHRIS.LOG]]

B3LYP/6-31G(d) optimized Exo product:[[File:Zinan_Wang_EX2_PRODUCT_EXO_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Endo product:[[File:ZINAN_WANG_EX2_PRODUCT_ENDO_OPT_B3LYP.LOG]]

=Exercise3=
In exercise 3, xylylene and SO<sub>2</sub> are used as the reactant.
They could react through 3 pathways: Exo and Endo hetero-Diels Alder reaction or the Cheletropic reaction.
Energy barrier and reaction energy for each pathway has been calculated and plotted.

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.
The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is thermodynamic pathway of reaction.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

===.log Files for Exercise 3===

PM6 Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

PM6 Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

PM6 Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

PM6 Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

PM6 Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

PM6 Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

PM6 Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

PM6 Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

=Conclusion=

In this computational lab, 3 pericyclic reactions were investigated. Gaussian was used to optimized the structure of the reactants, products and transition states using either PM6 or B3LYP method with IRC and frequency checked to confirm the transition states. Gibbs free energy was extracted from the log file for each species and the reaction barriers and reaction energies were calculated from them. The kinetic favored pathway were determined by the lowest reaction barrier and thermodynamic favored pathway was determined by the lowest reaction energy.

This computational method could be carried out for more reactions to determine the reaction route under different conditions.

=Reference=

[1] J. J. W. McDouall, in Computational Quantum Chemistry: Molecular Structure and Properties in Silico, The Royal Society of Chemistry, London,
2013, ch. 1, pp. 1-62.

Rep:Zw4415:TSexercise

2018-03-13T23:48:36Z

Zw4415:

=Introduction=

===The transition state===

According to '''Computational Quantum Chemistry''' the reaction coordinate was functionalised by all 3N<sub>atoms</sub>-6 internal coordinates.[1]

Potenyial energy surface describes the energy of a specific system where energy was tabulated by a set of reaction coordinates.

The reactant and product with stationary structure are the minimum points on the potential energy surface.It could be calculated by :

[[File:Zinan_Wang_eq1.png|thumb|center|Equation. 1 [1] ]]

where '''R''' is a set of all internal coordinates and q is normal coordinates which is a linear combination of all internal coordinates.

The transition state is the point with the highest energy along the reaction pathway. The second derivative should be all positive except the one along the reaction coordinate.
Thus it could be calculated as below.
[[File:Zinan_Wang_eq2.png|thumb|center|Equation. 2 [1] ]]
[[File:Zinan_Wang_eq3.png|thumb|center|Equation. 3 [1] ]]

gradient and the curvature

It is because when calculating form a harmonic oscillator with negative force constant (the bond yet to be formed in this case), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate that imaginary number (e.g. 526.7i). Success IRC was obtained at PM6 level as shown below where gradient was 0 at the Transition state, reactants and product.

=Exercise1=
===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level first with frequency checked to only have one negative value at around -930. Followed by B3LYP/6-31G(d) method and the resulting structure have one negative frequency at -526.7.

[[File: Zinan_Wang_EX1_IRC.PNG|thumb|center|The IRC for optimized transition state|800px ]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]
The Transition state MO has higher energy than the fragment molecular orbitals.

That is due to the fact that it is a MO for the transition state which is the highest energy point along the reaction pathway.

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 Å indicating the formation of a sp3-sp3 carbon bond in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

PM6 IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

=Exercise2=

===Visualized HOMOs and LUMOs,frequency check and Gibbs free energies===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|<jmol>
<jmolApplet>
<title>HOMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<title>LUMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|<jmol>
<jmolApplet>
<title>HOMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

According to the frequency calculation, all transition states are showing only 1 negative value and all the other species are showing all positive frequencies which confirms the success in obtaining the optimized structures.

===MO diagram===

Firstly the a single point energy calculation was carried out for two reactants being separated for 20 a.u.(i.e. assume no interaction)
The MO diagram for the resulting file was shown below
[[File:Zinan_Wang_EX2_REACT1and2.PNG|thumb|center|800px|The MOs from single point energy calculation ]]
The value of the each energy level was used to draw the corresponded MO diagram.
The energy levels for the MO of TS are higher than the final product as expected, as the TS represent the highest energy along the reaction coordination.

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp) / Hartree
|0.062817 (164.926034 kJ/mol)
|0.060358 (158.469929 kJ/mol)
|-
|Reaction energies (at room temp) /Hartree
|<nowiki>-0.024815</nowiki> (<nowiki>-65.1517825</nowiki> kJ/mol)
|<nowiki>-0.026185</nowiki> (<nowiki>-68.7487175</nowiki> kJ/mol)
|}

The reaction barrier and reaction energy are both lower for the Endo-pathway.
Therefore the endo pathway is both kinetic and thermodynamic favored.

From the single point calculation, the energy of the HOMO of the dieneophile (1,3-Dioxole) is higher than that of the diene (Cyclohexadiene) which shows that the dieneophile is more electron rich than the diene, thus inverse electron demand.

===.log Files for Exercise 2===

B3LYP/6-31G(d) optimized cyclohexadiene:[[File:ZINAN_WANG_EX2_REACT1_OPT_B3LYP.LOG]]

B3LYP/6-31G(d) optimized 1,3-dioxole:[[File:Zinan_Wang_EX2_REACT2_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Exo TS:[[File:ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log]]

B3LYP/6-31G(d) optimized Endo TS:[[File:ZINAN_WANG_EX2_TS_ENDO_OPT_B3LYP_CHRIS.LOG]]

B3LYP/6-31G(d) optimized Exo product:[[File:Zinan_Wang_EX2_PRODUCT_EXO_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Endo product:[[File:ZINAN_WANG_EX2_PRODUCT_ENDO_OPT_B3LYP.LOG]]

=Exercise3=
In exercise 3, xylylene and SO<sub>2</sub> are used as the reactant.
They could react through 3 pathways: Exo and Endo hetero-Diels Alder reaction or the Cheletropic reaction.
Energy barrier and reaction energy for each pathway has been calculated and plotted.

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.
The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is thermodynamic pathway of reaction.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

===.log Files for Exercise 3===

PM6 Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

PM6 Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

PM6 Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

PM6 Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

PM6 Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

PM6 Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

PM6 Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

PM6 Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

=Conclusion=

File:Zinan Wang eq3.png

2018-03-13T23:45:11Z

Zw4415:

File:Zinan Wang eq2.png

2018-03-13T23:44:39Z

Zw4415:

File:Zinan Wang eq1.png

2018-03-13T23:32:51Z

Zw4415:

Rep:Zw4415:TSexercise

2018-03-13T22:54:18Z

Zw4415: /* Introduction */

=Introduction=

A minimum and transition state in the context of a potential energy surface.

gradient and the curvature

=Exercise1=
===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level first with frequency checked to only have one negative value at around -930. Followed by B3LYP/6-31G(d) method and the resulting structure have one negative frequency at -526.7.
It is because when calculating form a harmonic oscillator with negative force constant (the bond yet to be formed in this case), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate that imaginary number (e.g. 526.7i). Success IRC was obtained at PM6 level as shown below where gradient was 0 at the Transition state, reactants and product.
[[File: Zinan_Wang_EX1_IRC.PNG|thumb|center|The IRC for optimized transition state|800px ]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]
The Transition state MO has higher energy than the fragment molecular orbitals.

That is due to the fact that it is a MO for the transition state which is the highest energy point along the reaction pathway.

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 Å indicating the formation of a sp3-sp3 carbon bond in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

PM6 IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

=Exercise2=

===Visualized HOMOs and LUMOs,frequency check and Gibbs free energies===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|<jmol>
<jmolApplet>
<title>HOMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<title>LUMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|<jmol>
<jmolApplet>
<title>HOMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

According to the frequency calculation, all transition states are showing only 1 negative value and all the other species are showing all positive frequencies which confirms the success in obtaining the optimized structures.

===MO diagram===

Firstly the a single point energy calculation was carried out for two reactants being separated for 20 a.u.(i.e. assume no interaction)
The MO diagram for the resulting file was shown below
[[File:Zinan_Wang_EX2_REACT1and2.PNG|thumb|center|800px|The MOs from single point energy calculation ]]
The value of the each energy level was used to draw the corresponded MO diagram.
The energy levels for the MO of TS are higher than the final product as expected, as the TS represent the highest energy along the reaction coordination.

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp) / Hartree
|0.062817 (164.926034 kJ/mol)
|0.060358 (158.469929 kJ/mol)
|-
|Reaction energies (at room temp) /Hartree
|<nowiki>-0.024815</nowiki> (<nowiki>-65.1517825</nowiki> kJ/mol)
|<nowiki>-0.026185</nowiki> (<nowiki>-68.7487175</nowiki> kJ/mol)
|}

The reaction barrier and reaction energy are both lower for the Endo-pathway.
Therefore the endo pathway is both kinetic and thermodynamic favored.

From the single point calculation, the energy of the HOMO of the dieneophile (1,3-Dioxole) is higher than that of the diene (Cyclohexadiene) which shows that the dieneophile is more electron rich than the diene, thus inverse electron demand.

===.log Files for Exercise 2===

B3LYP/6-31G(d) optimized cyclohexadiene:[[File:ZINAN_WANG_EX2_REACT1_OPT_B3LYP.LOG]]

B3LYP/6-31G(d) optimized 1,3-dioxole:[[File:Zinan_Wang_EX2_REACT2_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Exo TS:[[File:ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log]]

B3LYP/6-31G(d) optimized Endo TS:[[File:ZINAN_WANG_EX2_TS_ENDO_OPT_B3LYP_CHRIS.LOG]]

B3LYP/6-31G(d) optimized Exo product:[[File:Zinan_Wang_EX2_PRODUCT_EXO_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Endo product:[[File:ZINAN_WANG_EX2_PRODUCT_ENDO_OPT_B3LYP.LOG]]

=Exercise3=
In exercise 3, xylylene and SO<sub>2</sub> are used as the reactant.
They could react through 3 pathways: Exo and Endo hetero-Diels Alder reaction or the Cheletropic reaction.
Energy barrier and reaction energy for each pathway has been calculated and plotted.

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.
The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is thermodynamic pathway of reaction.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

===.log Files for Exercise 3===

PM6 Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

PM6 Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

PM6 Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

PM6 Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

PM6 Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

PM6 Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

PM6 Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

PM6 Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

=Conclusion=

Rep:Zw4415:TSexercise

2018-03-13T21:38:57Z

Zw4415: /* .log Files for Exercise 1 */

=Introduction=

=Exercise1=
===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level first with frequency checked to only have one negative value at around -930. Followed by B3LYP/6-31G(d) method and the resulting structure have one negative frequency at -526.7.
It is because when calculating form a harmonic oscillator with negative force constant (the bond yet to be formed in this case), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate that imaginary number (e.g. 526.7i). Success IRC was obtained at PM6 level as shown below where gradient was 0 at the Transition state, reactants and product.
[[File: Zinan_Wang_EX1_IRC.PNG|thumb|center|The IRC for optimized transition state|800px ]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]
The Transition state MO has higher energy than the fragment molecular orbitals.

That is due to the fact that it is a MO for the transition state which is the highest energy point along the reaction pathway.

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 Å indicating the formation of a sp3-sp3 carbon bond in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

PM6 IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

=Exercise2=

===Visualized HOMOs and LUMOs,frequency check and Gibbs free energies===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|<jmol>
<jmolApplet>
<title>HOMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<title>LUMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|<jmol>
<jmolApplet>
<title>HOMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

According to the frequency calculation, all transition states are showing only 1 negative value and all the other species are showing all positive frequencies which confirms the success in obtaining the optimized structures.

===MO diagram===

Firstly the a single point energy calculation was carried out for two reactants being separated for 20 a.u.(i.e. assume no interaction)
The MO diagram for the resulting file was shown below
[[File:Zinan_Wang_EX2_REACT1and2.PNG|thumb|center|800px|The MOs from single point energy calculation ]]
The value of the each energy level was used to draw the corresponded MO diagram.
The energy levels for the MO of TS are higher than the final product as expected, as the TS represent the highest energy along the reaction coordination.

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp) / Hartree
|0.062817 (164.926034 kJ/mol)
|0.060358 (158.469929 kJ/mol)
|-
|Reaction energies (at room temp) /Hartree
|<nowiki>-0.024815</nowiki> (<nowiki>-65.1517825</nowiki> kJ/mol)
|<nowiki>-0.026185</nowiki> (<nowiki>-68.7487175</nowiki> kJ/mol)
|}

The reaction barrier and reaction energy are both lower for the Endo-pathway.
Therefore the endo pathway is both kinetic and thermodynamic favored.

From the single point calculation, the energy of the HOMO of the dieneophile (1,3-Dioxole) is higher than that of the diene (Cyclohexadiene) which shows that the dieneophile is more electron rich than the diene, thus inverse electron demand.

===.log Files for Exercise 2===

B3LYP/6-31G(d) optimized cyclohexadiene:[[File:ZINAN_WANG_EX2_REACT1_OPT_B3LYP.LOG]]

B3LYP/6-31G(d) optimized 1,3-dioxole:[[File:Zinan_Wang_EX2_REACT2_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Exo TS:[[File:ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log]]

B3LYP/6-31G(d) optimized Endo TS:[[File:ZINAN_WANG_EX2_TS_ENDO_OPT_B3LYP_CHRIS.LOG]]

B3LYP/6-31G(d) optimized Exo product:[[File:Zinan_Wang_EX2_PRODUCT_EXO_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Endo product:[[File:ZINAN_WANG_EX2_PRODUCT_ENDO_OPT_B3LYP.LOG]]

=Exercise3=
In exercise 3, xylylene and SO<sub>2</sub> are used as the reactant.
They could react through 3 pathways: Exo and Endo hetero-Diels Alder reaction or the Cheletropic reaction.
Energy barrier and reaction energy for each pathway has been calculated and plotted.

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.
The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is thermodynamic pathway of reaction.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

===.log Files for Exercise 3===

PM6 Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

PM6 Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

PM6 Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

PM6 Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

PM6 Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

PM6 Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

PM6 Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

PM6 Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

=Conclusion=

Rep:Zw4415:TSexercise

2018-03-13T21:38:30Z

Zw4415: /* HOMO, LUMO,frequency check and Gibbs free energy */

=Introduction=

=Exercise1=
===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level first with frequency checked to only have one negative value at around -930. Followed by B3LYP/6-31G(d) method and the resulting structure have one negative frequency at -526.7.
It is because when calculating form a harmonic oscillator with negative force constant (the bond yet to be formed in this case), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate that imaginary number (e.g. 526.7i). Success IRC was obtained at PM6 level as shown below where gradient was 0 at the Transition state, reactants and product.
[[File: Zinan_Wang_EX1_IRC.PNG|thumb|center|The IRC for optimized transition state|800px ]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]
The Transition state MO has higher energy than the fragment molecular orbitals.

That is due to the fact that it is a MO for the transition state which is the highest energy point along the reaction pathway.

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 Å indicating the formation of a sp3-sp3 carbon bond in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

=Exercise2=

===Visualized HOMOs and LUMOs,frequency check and Gibbs free energies===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|<jmol>
<jmolApplet>
<title>HOMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<title>LUMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|<jmol>
<jmolApplet>
<title>HOMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

According to the frequency calculation, all transition states are showing only 1 negative value and all the other species are showing all positive frequencies which confirms the success in obtaining the optimized structures.

===MO diagram===

Firstly the a single point energy calculation was carried out for two reactants being separated for 20 a.u.(i.e. assume no interaction)
The MO diagram for the resulting file was shown below
[[File:Zinan_Wang_EX2_REACT1and2.PNG|thumb|center|800px|The MOs from single point energy calculation ]]
The value of the each energy level was used to draw the corresponded MO diagram.
The energy levels for the MO of TS are higher than the final product as expected, as the TS represent the highest energy along the reaction coordination.

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp) / Hartree
|0.062817 (164.926034 kJ/mol)
|0.060358 (158.469929 kJ/mol)
|-
|Reaction energies (at room temp) /Hartree
|<nowiki>-0.024815</nowiki> (<nowiki>-65.1517825</nowiki> kJ/mol)
|<nowiki>-0.026185</nowiki> (<nowiki>-68.7487175</nowiki> kJ/mol)
|}

The reaction barrier and reaction energy are both lower for the Endo-pathway.
Therefore the endo pathway is both kinetic and thermodynamic favored.

From the single point calculation, the energy of the HOMO of the dieneophile (1,3-Dioxole) is higher than that of the diene (Cyclohexadiene) which shows that the dieneophile is more electron rich than the diene, thus inverse electron demand.

===.log Files for Exercise 2===

B3LYP/6-31G(d) optimized cyclohexadiene:[[File:ZINAN_WANG_EX2_REACT1_OPT_B3LYP.LOG]]

B3LYP/6-31G(d) optimized 1,3-dioxole:[[File:Zinan_Wang_EX2_REACT2_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Exo TS:[[File:ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log]]

B3LYP/6-31G(d) optimized Endo TS:[[File:ZINAN_WANG_EX2_TS_ENDO_OPT_B3LYP_CHRIS.LOG]]

B3LYP/6-31G(d) optimized Exo product:[[File:Zinan_Wang_EX2_PRODUCT_EXO_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Endo product:[[File:ZINAN_WANG_EX2_PRODUCT_ENDO_OPT_B3LYP.LOG]]

=Exercise3=
In exercise 3, xylylene and SO<sub>2</sub> are used as the reactant.
They could react through 3 pathways: Exo and Endo hetero-Diels Alder reaction or the Cheletropic reaction.
Energy barrier and reaction energy for each pathway has been calculated and plotted.

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.
The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is thermodynamic pathway of reaction.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

===.log Files for Exercise 3===

PM6 Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

PM6 Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

PM6 Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

PM6 Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

PM6 Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

PM6 Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

PM6 Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

PM6 Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

=Conclusion=

Rep:Zw4415:TSexercise

2018-03-13T21:35:36Z

Zw4415: /* Bond length measurement */

=Introduction=

=Exercise1=
===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level first with frequency checked to only have one negative value at around -930. Followed by B3LYP/6-31G(d) method and the resulting structure have one negative frequency at -526.7.
It is because when calculating form a harmonic oscillator with negative force constant (the bond yet to be formed in this case), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate that imaginary number (e.g. 526.7i). Success IRC was obtained at PM6 level as shown below where gradient was 0 at the Transition state, reactants and product.
[[File: Zinan_Wang_EX1_IRC.PNG|thumb|center|The IRC for optimized transition state|800px ]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]
The Transition state MO has higher energy than the fragment molecular orbitals.

That is due to the fact that it is a MO for the transition state which is the highest energy point along the reaction pathway.

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 Å indicating the formation of a sp3-sp3 carbon bond in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

=Exercise2=

===HOMO, LUMO,frequency check and Gibbs free energy===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|<jmol>
<jmolApplet>
<title>HOMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<title>LUMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|<jmol>
<jmolApplet>
<title>HOMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

According to the frequency calculation, all transition states are showing only 1 negative value and all the other species are showing all positive frequencies which confirms the success in obtaining the optimized structures.

===MO diagram===

Firstly the a single point energy calculation was carried out for two reactants being separated for 20 a.u.(i.e. assume no interaction)
The MO diagram for the resulting file was shown below
[[File:Zinan_Wang_EX2_REACT1and2.PNG|thumb|center|800px|The MOs from single point energy calculation ]]
The value of the each energy level was used to draw the corresponded MO diagram.
The energy levels for the MO of TS are higher than the final product as expected, as the TS represent the highest energy along the reaction coordination.

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp) / Hartree
|0.062817 (164.926034 kJ/mol)
|0.060358 (158.469929 kJ/mol)
|-
|Reaction energies (at room temp) /Hartree
|<nowiki>-0.024815</nowiki> (<nowiki>-65.1517825</nowiki> kJ/mol)
|<nowiki>-0.026185</nowiki> (<nowiki>-68.7487175</nowiki> kJ/mol)
|}

The reaction barrier and reaction energy are both lower for the Endo-pathway.
Therefore the endo pathway is both kinetic and thermodynamic favored.

From the single point calculation, the energy of the HOMO of the dieneophile (1,3-Dioxole) is higher than that of the diene (Cyclohexadiene) which shows that the dieneophile is more electron rich than the diene, thus inverse electron demand.

===.log Files for Exercise 2===

B3LYP/6-31G(d) optimized cyclohexadiene:[[File:ZINAN_WANG_EX2_REACT1_OPT_B3LYP.LOG]]

B3LYP/6-31G(d) optimized 1,3-dioxole:[[File:Zinan_Wang_EX2_REACT2_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Exo TS:[[File:ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log]]

B3LYP/6-31G(d) optimized Endo TS:[[File:ZINAN_WANG_EX2_TS_ENDO_OPT_B3LYP_CHRIS.LOG]]

B3LYP/6-31G(d) optimized Exo product:[[File:Zinan_Wang_EX2_PRODUCT_EXO_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Endo product:[[File:ZINAN_WANG_EX2_PRODUCT_ENDO_OPT_B3LYP.LOG]]

=Exercise3=
In exercise 3, xylylene and SO<sub>2</sub> are used as the reactant.
They could react through 3 pathways: Exo and Endo hetero-Diels Alder reaction or the Cheletropic reaction.
Energy barrier and reaction energy for each pathway has been calculated and plotted.

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.
The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is thermodynamic pathway of reaction.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

===.log Files for Exercise 3===

PM6 Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

PM6 Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

PM6 Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

PM6 Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

PM6 Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

PM6 Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

PM6 Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

PM6 Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

=Conclusion=

Rep:Zw4415:TSexercise

2018-03-13T21:34:15Z

Zw4415: /* MO diagram for the formation of the butadiene/ethene transition state */

=Introduction=

=Exercise1=
===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level first with frequency checked to only have one negative value at around -930. Followed by B3LYP/6-31G(d) method and the resulting structure have one negative frequency at -526.7.
It is because when calculating form a harmonic oscillator with negative force constant (the bond yet to be formed in this case), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate that imaginary number (e.g. 526.7i). Success IRC was obtained at PM6 level as shown below where gradient was 0 at the Transition state, reactants and product.
[[File: Zinan_Wang_EX1_IRC.PNG|thumb|center|The IRC for optimized transition state|800px ]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]
The Transition state MO has higher energy than the fragment molecular orbitals.

That is due to the fact that it is a MO for the transition state which is the highest energy point along the reaction pathway.

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 indicated a sp3-sp3 carbon bond has formed in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

=Exercise2=

===HOMO, LUMO,frequency check and Gibbs free energy===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|<jmol>
<jmolApplet>
<title>HOMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<title>LUMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|<jmol>
<jmolApplet>
<title>HOMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

According to the frequency calculation, all transition states are showing only 1 negative value and all the other species are showing all positive frequencies which confirms the success in obtaining the optimized structures.

===MO diagram===

Firstly the a single point energy calculation was carried out for two reactants being separated for 20 a.u.(i.e. assume no interaction)
The MO diagram for the resulting file was shown below
[[File:Zinan_Wang_EX2_REACT1and2.PNG|thumb|center|800px|The MOs from single point energy calculation ]]
The value of the each energy level was used to draw the corresponded MO diagram.
The energy levels for the MO of TS are higher than the final product as expected, as the TS represent the highest energy along the reaction coordination.

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp) / Hartree
|0.062817 (164.926034 kJ/mol)
|0.060358 (158.469929 kJ/mol)
|-
|Reaction energies (at room temp) /Hartree
|<nowiki>-0.024815</nowiki> (<nowiki>-65.1517825</nowiki> kJ/mol)
|<nowiki>-0.026185</nowiki> (<nowiki>-68.7487175</nowiki> kJ/mol)
|}

The reaction barrier and reaction energy are both lower for the Endo-pathway.
Therefore the endo pathway is both kinetic and thermodynamic favored.

From the single point calculation, the energy of the HOMO of the dieneophile (1,3-Dioxole) is higher than that of the diene (Cyclohexadiene) which shows that the dieneophile is more electron rich than the diene, thus inverse electron demand.

===.log Files for Exercise 2===

B3LYP/6-31G(d) optimized cyclohexadiene:[[File:ZINAN_WANG_EX2_REACT1_OPT_B3LYP.LOG]]

B3LYP/6-31G(d) optimized 1,3-dioxole:[[File:Zinan_Wang_EX2_REACT2_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Exo TS:[[File:ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log]]

B3LYP/6-31G(d) optimized Endo TS:[[File:ZINAN_WANG_EX2_TS_ENDO_OPT_B3LYP_CHRIS.LOG]]

B3LYP/6-31G(d) optimized Exo product:[[File:Zinan_Wang_EX2_PRODUCT_EXO_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Endo product:[[File:ZINAN_WANG_EX2_PRODUCT_ENDO_OPT_B3LYP.LOG]]

=Exercise3=
In exercise 3, xylylene and SO<sub>2</sub> are used as the reactant.
They could react through 3 pathways: Exo and Endo hetero-Diels Alder reaction or the Cheletropic reaction.
Energy barrier and reaction energy for each pathway has been calculated and plotted.

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.
The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is thermodynamic pathway of reaction.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

===.log Files for Exercise 3===

PM6 Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

PM6 Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

PM6 Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

PM6 Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

PM6 Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

PM6 Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

PM6 Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

PM6 Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

=Conclusion=

Rep:Zw4415:TSexercise

2018-03-13T21:33:05Z

Zw4415:

=Introduction=

=Exercise1=
===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level first with frequency checked to only have one negative value at around -930. Followed by B3LYP/6-31G(d) method and the resulting structure have one negative frequency at -526.7.
It is because when calculating form a harmonic oscillator with negative force constant (the bond yet to be formed in this case), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate that imaginary number (e.g. 526.7i). Success IRC was obtained at PM6 level as shown below where gradient was 0 at the Transition state, reactants and product.
[[File: Zinan_Wang_EX1_IRC.PNG|thumb|center|The IRC for optimized transition state|800px ]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]
The formed MO has the energy higher than the original molecular orbitals. That is due to the fact that it is a MO for the transition state, the highest energy point along the reaction pathway.

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 indicated a sp3-sp3 carbon bond has formed in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

=Exercise2=

===HOMO, LUMO,frequency check and Gibbs free energy===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|<jmol>
<jmolApplet>
<title>HOMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<title>LUMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|<jmol>
<jmolApplet>
<title>HOMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

According to the frequency calculation, all transition states are showing only 1 negative value and all the other species are showing all positive frequencies which confirms the success in obtaining the optimized structures.

===MO diagram===

Firstly the a single point energy calculation was carried out for two reactants being separated for 20 a.u.(i.e. assume no interaction)
The MO diagram for the resulting file was shown below
[[File:Zinan_Wang_EX2_REACT1and2.PNG|thumb|center|800px|The MOs from single point energy calculation ]]
The value of the each energy level was used to draw the corresponded MO diagram.
The energy levels for the MO of TS are higher than the final product as expected, as the TS represent the highest energy along the reaction coordination.

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp) / Hartree
|0.062817 (164.926034 kJ/mol)
|0.060358 (158.469929 kJ/mol)
|-
|Reaction energies (at room temp) /Hartree
|<nowiki>-0.024815</nowiki> (<nowiki>-65.1517825</nowiki> kJ/mol)
|<nowiki>-0.026185</nowiki> (<nowiki>-68.7487175</nowiki> kJ/mol)
|}

The reaction barrier and reaction energy are both lower for the Endo-pathway.
Therefore the endo pathway is both kinetic and thermodynamic favored.

From the single point calculation, the energy of the HOMO of the dieneophile (1,3-Dioxole) is higher than that of the diene (Cyclohexadiene) which shows that the dieneophile is more electron rich than the diene, thus inverse electron demand.

===.log Files for Exercise 2===

B3LYP/6-31G(d) optimized cyclohexadiene:[[File:ZINAN_WANG_EX2_REACT1_OPT_B3LYP.LOG]]

B3LYP/6-31G(d) optimized 1,3-dioxole:[[File:Zinan_Wang_EX2_REACT2_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Exo TS:[[File:ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log]]

B3LYP/6-31G(d) optimized Endo TS:[[File:ZINAN_WANG_EX2_TS_ENDO_OPT_B3LYP_CHRIS.LOG]]

B3LYP/6-31G(d) optimized Exo product:[[File:Zinan_Wang_EX2_PRODUCT_EXO_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Endo product:[[File:ZINAN_WANG_EX2_PRODUCT_ENDO_OPT_B3LYP.LOG]]

=Exercise3=
In exercise 3, xylylene and SO<sub>2</sub> are used as the reactant.
They could react through 3 pathways: Exo and Endo hetero-Diels Alder reaction or the Cheletropic reaction.
Energy barrier and reaction energy for each pathway has been calculated and plotted.

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.
The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is thermodynamic pathway of reaction.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

===.log Files for Exercise 3===

PM6 Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

PM6 Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

PM6 Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

PM6 Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

PM6 Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

PM6 Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

PM6 Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

PM6 Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

=Conclusion=

Rep:Zw4415:TSexercise

2018-03-13T21:32:20Z

Zw4415: /* Exercise3 */

=Introduction=

=Exercise1=
===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level first with frequency checked to only have one negative value at around -930. Followed by B3LYP/6-31G(d) method and the resulting structure have one negative frequency at -526.7.
It is because when calculating form a harmonic oscillator with negative force constant (the bond yet to be formed in this case), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate that imaginary number (e.g. 526.7i). Success IRC was obtained at PM6 level as shown below where gradient was 0 at the Transition state, reactants and product.
[[File: Zinan_Wang_EX1_IRC.PNG|thumb|center|The IRC for optimized transition state|800px ]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]
The formed MO has the energy higher than the original molecular orbitals. That is due to the fact that it is a MO for the transition state, the highest energy point along the reaction pathway.

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 indicated a sp3-sp3 carbon bond has formed in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

=Exercise2=

===HOMO, LUMO,frequency check and Gibbs free energy===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|<jmol>
<jmolApplet>
<title>HOMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<title>LUMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|<jmol>
<jmolApplet>
<title>HOMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

According to the frequency calculation, all transition states are showing only 1 negative value and all the other species are showing all positive frequencies which confirms the success in obtaining the optimized structures.

===MO diagram===

Firstly the a single point energy calculation was carried out for two reactants being separated for 20 a.u.(i.e. assume no interaction)
The MO diagram for the resulting file was shown below
[[File:Zinan_Wang_EX2_REACT1and2.PNG|thumb|center|800px|The MOs from single point energy calculation ]]
The value of the each energy level was used to draw the corresponded MO diagram.
The energy levels for the MO of TS are higher than the final product as expected, as the TS represent the highest energy along the reaction coordination.

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp) / Hartree
|0.062817 (164.926034 kJ/mol)
|0.060358 (158.469929 kJ/mol)
|-
|Reaction energies (at room temp) /Hartree
|<nowiki>-0.024815</nowiki> (<nowiki>-65.1517825</nowiki> kJ/mol)
|<nowiki>-0.026185</nowiki> (<nowiki>-68.7487175</nowiki> kJ/mol)
|}

The reaction barrier and reaction energy are both lower for the Endo-pathway.
Therefore the endo pathway is both kinetic and thermodynamic favored.

From the single point calculation, the energy of the HOMO of the dieneophile (1,3-Dioxole) is higher than that of the diene (Cyclohexadiene) which shows that the dieneophile is more electron rich than the diene, thus inverse electron demand.

===.log Files for Exercise 2===

B3LYP/6-31G(d) optimized cyclohexadiene:[[File:ZINAN_WANG_EX2_REACT1_OPT_B3LYP.LOG]]

B3LYP/6-31G(d) optimized 1,3-dioxole:[[File:Zinan_Wang_EX2_REACT2_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Exo TS:[[File:ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log]]

B3LYP/6-31G(d) optimized Endo TS:[[File:ZINAN_WANG_EX2_TS_ENDO_OPT_B3LYP_CHRIS.LOG]]

B3LYP/6-31G(d) optimized Exo product:[[File:Zinan_Wang_EX2_PRODUCT_EXO_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Endo product:[[File:ZINAN_WANG_EX2_PRODUCT_ENDO_OPT_B3LYP.LOG]]

=Exercise3=
In exercise 3, xylylene and SO<sub>2</sub> are used as the reactant.
They could react through 3 pathways: Exo and Endo hetero-Diels Alder reaction or the Cheletropic reaction.
Energy barrier and reaction energy for each pathway has been calculated and plotted.

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.
The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is thermodynamic pathway of reaction.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

===.log Files for Exercise 3===

PM6 Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

PM6 Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

PM6 Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

PM6 Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

PM6 Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

PM6 Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

PM6 Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

PM6 Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

Rep:Zw4415:TSexercise

2018-03-13T21:31:56Z

Zw4415: /* Exercise3 */

=Introduction=

=Exercise1=
===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level first with frequency checked to only have one negative value at around -930. Followed by B3LYP/6-31G(d) method and the resulting structure have one negative frequency at -526.7.
It is because when calculating form a harmonic oscillator with negative force constant (the bond yet to be formed in this case), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate that imaginary number (e.g. 526.7i). Success IRC was obtained at PM6 level as shown below where gradient was 0 at the Transition state, reactants and product.
[[File: Zinan_Wang_EX1_IRC.PNG|thumb|center|The IRC for optimized transition state|800px ]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]
The formed MO has the energy higher than the original molecular orbitals. That is due to the fact that it is a MO for the transition state, the highest energy point along the reaction pathway.

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 indicated a sp3-sp3 carbon bond has formed in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

=Exercise2=

===HOMO, LUMO,frequency check and Gibbs free energy===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|<jmol>
<jmolApplet>
<title>HOMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<title>LUMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|<jmol>
<jmolApplet>
<title>HOMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

According to the frequency calculation, all transition states are showing only 1 negative value and all the other species are showing all positive frequencies which confirms the success in obtaining the optimized structures.

===MO diagram===

Firstly the a single point energy calculation was carried out for two reactants being separated for 20 a.u.(i.e. assume no interaction)
The MO diagram for the resulting file was shown below
[[File:Zinan_Wang_EX2_REACT1and2.PNG|thumb|center|800px|The MOs from single point energy calculation ]]
The value of the each energy level was used to draw the corresponded MO diagram.
The energy levels for the MO of TS are higher than the final product as expected, as the TS represent the highest energy along the reaction coordination.

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp) / Hartree
|0.062817 (164.926034 kJ/mol)
|0.060358 (158.469929 kJ/mol)
|-
|Reaction energies (at room temp) /Hartree
|<nowiki>-0.024815</nowiki> (<nowiki>-65.1517825</nowiki> kJ/mol)
|<nowiki>-0.026185</nowiki> (<nowiki>-68.7487175</nowiki> kJ/mol)
|}

The reaction barrier and reaction energy are both lower for the Endo-pathway.
Therefore the endo pathway is both kinetic and thermodynamic favored.

From the single point calculation, the energy of the HOMO of the dieneophile (1,3-Dioxole) is higher than that of the diene (Cyclohexadiene) which shows that the dieneophile is more electron rich than the diene, thus inverse electron demand.

===.log Files for Exercise 2===

B3LYP/6-31G(d) optimized cyclohexadiene:[[File:ZINAN_WANG_EX2_REACT1_OPT_B3LYP.LOG]]

B3LYP/6-31G(d) optimized 1,3-dioxole:[[File:Zinan_Wang_EX2_REACT2_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Exo TS:[[File:ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log]]

B3LYP/6-31G(d) optimized Endo TS:[[File:ZINAN_WANG_EX2_TS_ENDO_OPT_B3LYP_CHRIS.LOG]]

B3LYP/6-31G(d) optimized Exo product:[[File:Zinan_Wang_EX2_PRODUCT_EXO_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Endo product:[[File:ZINAN_WANG_EX2_PRODUCT_ENDO_OPT_B3LYP.LOG]]

=Exercise3=

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]
In exercise 3, xylylene and SO<sub>2</sub> are used as the reactant. They could react through 3 pathways: Exo and Endo hetero-Diels Alder reaction or the Cheletropic reaction.
Energy barrier and reaction energy for each pathway has been calculated and plotted.

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.
The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is thermodynamic pathway of reaction.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

===.log Files for Exercise 3===

PM6 Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

PM6 Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

PM6 Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

PM6 Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

PM6 Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

PM6 Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

PM6 Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

PM6 Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

Rep:Zw4415:TSexercise

2018-03-13T21:26:58Z

Zw4415: /* .log File for Exercise 3 */

=Introduction=

=Exercise1=
===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level first with frequency checked to only have one negative value at around -930. Followed by B3LYP/6-31G(d) method and the resulting structure have one negative frequency at -526.7.
It is because when calculating form a harmonic oscillator with negative force constant (the bond yet to be formed in this case), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate that imaginary number (e.g. 526.7i). Success IRC was obtained at PM6 level as shown below where gradient was 0 at the Transition state, reactants and product.
[[File: Zinan_Wang_EX1_IRC.PNG|thumb|center|The IRC for optimized transition state|800px ]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]
The formed MO has the energy higher than the original molecular orbitals. That is due to the fact that it is a MO for the transition state, the highest energy point along the reaction pathway.

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 indicated a sp3-sp3 carbon bond has formed in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

=Exercise2=

===HOMO, LUMO,frequency check and Gibbs free energy===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|<jmol>
<jmolApplet>
<title>HOMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<title>LUMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|<jmol>
<jmolApplet>
<title>HOMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

According to the frequency calculation, all transition states are showing only 1 negative value and all the other species are showing all positive frequencies which confirms the success in obtaining the optimized structures.

===MO diagram===

Firstly the a single point energy calculation was carried out for two reactants being separated for 20 a.u.(i.e. assume no interaction)
The MO diagram for the resulting file was shown below
[[File:Zinan_Wang_EX2_REACT1and2.PNG|thumb|center|800px|The MOs from single point energy calculation ]]
The value of the each energy level was used to draw the corresponded MO diagram.
The energy levels for the MO of TS are higher than the final product as expected, as the TS represent the highest energy along the reaction coordination.

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp) / Hartree
|0.062817 (164.926034 kJ/mol)
|0.060358 (158.469929 kJ/mol)
|-
|Reaction energies (at room temp) /Hartree
|<nowiki>-0.024815</nowiki> (<nowiki>-65.1517825</nowiki> kJ/mol)
|<nowiki>-0.026185</nowiki> (<nowiki>-68.7487175</nowiki> kJ/mol)
|}

The reaction barrier and reaction energy are both lower for the Endo-pathway.
Therefore the endo pathway is both kinetic and thermodynamic favored.

From the single point calculation, the energy of the HOMO of the dieneophile (1,3-Dioxole) is higher than that of the diene (Cyclohexadiene) which shows that the dieneophile is more electron rich than the diene, thus inverse electron demand.

===.log Files for Exercise 2===

B3LYP/6-31G(d) optimized cyclohexadiene:[[File:ZINAN_WANG_EX2_REACT1_OPT_B3LYP.LOG]]

B3LYP/6-31G(d) optimized 1,3-dioxole:[[File:Zinan_Wang_EX2_REACT2_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Exo TS:[[File:ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log]]

B3LYP/6-31G(d) optimized Endo TS:[[File:ZINAN_WANG_EX2_TS_ENDO_OPT_B3LYP_CHRIS.LOG]]

B3LYP/6-31G(d) optimized Exo product:[[File:Zinan_Wang_EX2_PRODUCT_EXO_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Endo product:[[File:ZINAN_WANG_EX2_PRODUCT_ENDO_OPT_B3LYP.LOG]]

=Exercise3=

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.
The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is thermodynamic pathway of reaction.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

===.log Files for Exercise 3===

PM6 Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

PM6 Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

PM6 Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

PM6 Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

PM6 Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

PM6 Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

PM6 Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

PM6 Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

Rep:Zw4415:TSexercise

2018-03-13T21:26:48Z

Zw4415: /* .log files for Exercise 2 */

=Introduction=

=Exercise1=
===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level first with frequency checked to only have one negative value at around -930. Followed by B3LYP/6-31G(d) method and the resulting structure have one negative frequency at -526.7.
It is because when calculating form a harmonic oscillator with negative force constant (the bond yet to be formed in this case), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate that imaginary number (e.g. 526.7i). Success IRC was obtained at PM6 level as shown below where gradient was 0 at the Transition state, reactants and product.
[[File: Zinan_Wang_EX1_IRC.PNG|thumb|center|The IRC for optimized transition state|800px ]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]
The formed MO has the energy higher than the original molecular orbitals. That is due to the fact that it is a MO for the transition state, the highest energy point along the reaction pathway.

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 indicated a sp3-sp3 carbon bond has formed in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

=Exercise2=

===HOMO, LUMO,frequency check and Gibbs free energy===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|<jmol>
<jmolApplet>
<title>HOMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<title>LUMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|<jmol>
<jmolApplet>
<title>HOMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

According to the frequency calculation, all transition states are showing only 1 negative value and all the other species are showing all positive frequencies which confirms the success in obtaining the optimized structures.

===MO diagram===

Firstly the a single point energy calculation was carried out for two reactants being separated for 20 a.u.(i.e. assume no interaction)
The MO diagram for the resulting file was shown below
[[File:Zinan_Wang_EX2_REACT1and2.PNG|thumb|center|800px|The MOs from single point energy calculation ]]
The value of the each energy level was used to draw the corresponded MO diagram.
The energy levels for the MO of TS are higher than the final product as expected, as the TS represent the highest energy along the reaction coordination.

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp) / Hartree
|0.062817 (164.926034 kJ/mol)
|0.060358 (158.469929 kJ/mol)
|-
|Reaction energies (at room temp) /Hartree
|<nowiki>-0.024815</nowiki> (<nowiki>-65.1517825</nowiki> kJ/mol)
|<nowiki>-0.026185</nowiki> (<nowiki>-68.7487175</nowiki> kJ/mol)
|}

The reaction barrier and reaction energy are both lower for the Endo-pathway.
Therefore the endo pathway is both kinetic and thermodynamic favored.

From the single point calculation, the energy of the HOMO of the dieneophile (1,3-Dioxole) is higher than that of the diene (Cyclohexadiene) which shows that the dieneophile is more electron rich than the diene, thus inverse electron demand.

===.log Files for Exercise 2===

B3LYP/6-31G(d) optimized cyclohexadiene:[[File:ZINAN_WANG_EX2_REACT1_OPT_B3LYP.LOG]]

B3LYP/6-31G(d) optimized 1,3-dioxole:[[File:Zinan_Wang_EX2_REACT2_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Exo TS:[[File:ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log]]

B3LYP/6-31G(d) optimized Endo TS:[[File:ZINAN_WANG_EX2_TS_ENDO_OPT_B3LYP_CHRIS.LOG]]

B3LYP/6-31G(d) optimized Exo product:[[File:Zinan_Wang_EX2_PRODUCT_EXO_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Endo product:[[File:ZINAN_WANG_EX2_PRODUCT_ENDO_OPT_B3LYP.LOG]]

=Exercise3=

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.
The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is thermodynamic pathway of reaction.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

===.log File for Exercise 3===

PM6 Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

PM6 Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

PM6 Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

PM6 Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

PM6 Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

PM6 Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

PM6 Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

PM6 Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

Rep:Zw4415:TSexercise

2018-03-13T21:25:01Z

Zw4415: /* .log files for Exercise 2 */

=Introduction=

=Exercise1=
===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level first with frequency checked to only have one negative value at around -930. Followed by B3LYP/6-31G(d) method and the resulting structure have one negative frequency at -526.7.
It is because when calculating form a harmonic oscillator with negative force constant (the bond yet to be formed in this case), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate that imaginary number (e.g. 526.7i). Success IRC was obtained at PM6 level as shown below where gradient was 0 at the Transition state, reactants and product.
[[File: Zinan_Wang_EX1_IRC.PNG|thumb|center|The IRC for optimized transition state|800px ]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]
The formed MO has the energy higher than the original molecular orbitals. That is due to the fact that it is a MO for the transition state, the highest energy point along the reaction pathway.

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 indicated a sp3-sp3 carbon bond has formed in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

=Exercise2=

===HOMO, LUMO,frequency check and Gibbs free energy===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|<jmol>
<jmolApplet>
<title>HOMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<title>LUMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|<jmol>
<jmolApplet>
<title>HOMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

According to the frequency calculation, all transition states are showing only 1 negative value and all the other species are showing all positive frequencies which confirms the success in obtaining the optimized structures.

===MO diagram===

Firstly the a single point energy calculation was carried out for two reactants being separated for 20 a.u.(i.e. assume no interaction)
The MO diagram for the resulting file was shown below
[[File:Zinan_Wang_EX2_REACT1and2.PNG|thumb|center|800px|The MOs from single point energy calculation ]]
The value of the each energy level was used to draw the corresponded MO diagram.
The energy levels for the MO of TS are higher than the final product as expected, as the TS represent the highest energy along the reaction coordination.

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp) / Hartree
|0.062817 (164.926034 kJ/mol)
|0.060358 (158.469929 kJ/mol)
|-
|Reaction energies (at room temp) /Hartree
|<nowiki>-0.024815</nowiki> (<nowiki>-65.1517825</nowiki> kJ/mol)
|<nowiki>-0.026185</nowiki> (<nowiki>-68.7487175</nowiki> kJ/mol)
|}

The reaction barrier and reaction energy are both lower for the Endo-pathway.
Therefore the endo pathway is both kinetic and thermodynamic favored.

From the single point calculation, the energy of the HOMO of the dieneophile (1,3-Dioxole) is higher than that of the diene (Cyclohexadiene) which shows that the dieneophile is more electron rich than the diene, thus inverse electron demand.

===.log files for Exercise 2===

B3LYP/6-31G(d) optimized cyclohexadiene:[[File:ZINAN_WANG_EX2_REACT1_OPT_B3LYP.LOG]]

B3LYP/6-31G(d) optimized 1,3-dioxole:[[File:Zinan_Wang_EX2_REACT2_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Exo TS:[[File:ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log]]

B3LYP/6-31G(d) optimized Endo TS:[[File:ZINAN_WANG_EX2_TS_ENDO_OPT_B3LYP_CHRIS.LOG]]

B3LYP/6-31G(d) optimized Exo product:[[File:Zinan_Wang_EX2_PRODUCT_EXO_OPT_B3LYP.log]]

B3LYP/6-31G(d) optimized Endo product:[[File:ZINAN_WANG_EX2_PRODUCT_ENDO_OPT_B3LYP.LOG]]

=Exercise3=

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.
The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is thermodynamic pathway of reaction.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

===.log File for Exercise 3===

PM6 Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

PM6 Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

PM6 Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

PM6 Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

PM6 Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

PM6 Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

PM6 Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

PM6 Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

File:Zinan Wang EX2 PRODUCT EXO OPT B3LYP.log

2018-03-13T21:24:48Z

Zw4415:

File:ZINAN WANG EX2 TS EXO OPT B3LYP MO.log

2018-03-13T21:23:22Z

Zw4415: Zw4415 uploaded a new version of File:ZINAN WANG EX2 TS EXO OPT B3LYP MO.log

File:ZINAN WANG EX2 PRODUCT ENDO OPT B3LYP.LOG

2018-03-13T21:22:53Z

Zw4415:

File:ZINAN WANG EX2 TS ENDO OPT B3LYP CHRIS.LOG

2018-03-13T21:22:19Z

Zw4415:

File:ZINAN WANG EX2 REACT1 OPT B3LYP.LOG

2018-03-13T21:21:45Z

Zw4415:

File:Zinan Wang EX2 REACT2 OPT B3LYP.log

2018-03-13T21:20:55Z

Zw4415:

Rep:Zw4415:TSexercise

2018-03-13T21:16:35Z

Zw4415: /* .log File for Exercise 3 */

=Introduction=

=Exercise1=
===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level first with frequency checked to only have one negative value at around -930. Followed by B3LYP/6-31G(d) method and the resulting structure have one negative frequency at -526.7.
It is because when calculating form a harmonic oscillator with negative force constant (the bond yet to be formed in this case), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate that imaginary number (e.g. 526.7i). Success IRC was obtained at PM6 level as shown below where gradient was 0 at the Transition state, reactants and product.
[[File: Zinan_Wang_EX1_IRC.PNG|thumb|center|The IRC for optimized transition state|800px ]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]
The formed MO has the energy higher than the original molecular orbitals. That is due to the fact that it is a MO for the transition state, the highest energy point along the reaction pathway.

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 indicated a sp3-sp3 carbon bond has formed in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

=Exercise2=

===HOMO, LUMO,frequency check and Gibbs free energy===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|<jmol>
<jmolApplet>
<title>HOMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<title>LUMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|<jmol>
<jmolApplet>
<title>HOMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

According to the frequency calculation, all transition states are showing only 1 negative value and all the other species are showing all positive frequencies which confirms the success in obtaining the optimized structures.

===MO diagram===

Firstly the a single point energy calculation was carried out for two reactants being separated for 20 a.u.(i.e. assume no interaction)
The MO diagram for the resulting file was shown below
[[File:Zinan_Wang_EX2_REACT1and2.PNG|thumb|center|800px|The MOs from single point energy calculation ]]
The value of the each energy level was used to draw the corresponded MO diagram.
The energy levels for the MO of TS are higher than the final product as expected, as the TS represent the highest energy along the reaction coordination.

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp) / Hartree
|0.062817 (164.926034 kJ/mol)
|0.060358 (158.469929 kJ/mol)
|-
|Reaction energies (at room temp) /Hartree
|<nowiki>-0.024815</nowiki> (<nowiki>-65.1517825</nowiki> kJ/mol)
|<nowiki>-0.026185</nowiki> (<nowiki>-68.7487175</nowiki> kJ/mol)
|}

The reaction barrier and reaction energy are both lower for the Endo-pathway.
Therefore the endo pathway is both kinetic and thermodynamic favored.

From the single point calculation, the energy of the HOMO of the dieneophile (1,3-Dioxole) is higher than that of the diene (Cyclohexadiene) which shows that the dieneophile is more electron rich than the diene, thus inverse electron demand.

===.log files for Exercise 2===

=Exercise3=

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.
The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is thermodynamic pathway of reaction.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

===.log File for Exercise 3===

PM6 Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

PM6 Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

PM6 Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

PM6 Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

PM6 Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

PM6 Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

PM6 Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

PM6 Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

Rep:Zw4415:TSexercise

2018-03-13T21:16:01Z

Zw4415: /* Exercise2 */

=Introduction=

=Exercise1=
===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level first with frequency checked to only have one negative value at around -930. Followed by B3LYP/6-31G(d) method and the resulting structure have one negative frequency at -526.7.
It is because when calculating form a harmonic oscillator with negative force constant (the bond yet to be formed in this case), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate that imaginary number (e.g. 526.7i). Success IRC was obtained at PM6 level as shown below where gradient was 0 at the Transition state, reactants and product.
[[File: Zinan_Wang_EX1_IRC.PNG|thumb|center|The IRC for optimized transition state|800px ]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]
The formed MO has the energy higher than the original molecular orbitals. That is due to the fact that it is a MO for the transition state, the highest energy point along the reaction pathway.

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 indicated a sp3-sp3 carbon bond has formed in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

=Exercise2=

===HOMO, LUMO,frequency check and Gibbs free energy===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|<jmol>
<jmolApplet>
<title>HOMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<title>LUMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|<jmol>
<jmolApplet>
<title>HOMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

According to the frequency calculation, all transition states are showing only 1 negative value and all the other species are showing all positive frequencies which confirms the success in obtaining the optimized structures.

===MO diagram===

Firstly the a single point energy calculation was carried out for two reactants being separated for 20 a.u.(i.e. assume no interaction)
The MO diagram for the resulting file was shown below
[[File:Zinan_Wang_EX2_REACT1and2.PNG|thumb|center|800px|The MOs from single point energy calculation ]]
The value of the each energy level was used to draw the corresponded MO diagram.
The energy levels for the MO of TS are higher than the final product as expected, as the TS represent the highest energy along the reaction coordination.

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp) / Hartree
|0.062817 (164.926034 kJ/mol)
|0.060358 (158.469929 kJ/mol)
|-
|Reaction energies (at room temp) /Hartree
|<nowiki>-0.024815</nowiki> (<nowiki>-65.1517825</nowiki> kJ/mol)
|<nowiki>-0.026185</nowiki> (<nowiki>-68.7487175</nowiki> kJ/mol)
|}

The reaction barrier and reaction energy are both lower for the Endo-pathway.
Therefore the endo pathway is both kinetic and thermodynamic favored.

From the single point calculation, the energy of the HOMO of the dieneophile (1,3-Dioxole) is higher than that of the diene (Cyclohexadiene) which shows that the dieneophile is more electron rich than the diene, thus inverse electron demand.

===.log files for Exercise 2===

=Exercise3=

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.
The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is thermodynamic pathway of reaction.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

===.log File for Exercise 3===

Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

Rep:Zw4415:TSexercise

2018-03-13T21:14:42Z

Zw4415: /* MO diagram for the formation of the butadiene/ethene transition state */

=Introduction=

=Exercise1=
===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level first with frequency checked to only have one negative value at around -930. Followed by B3LYP/6-31G(d) method and the resulting structure have one negative frequency at -526.7.
It is because when calculating form a harmonic oscillator with negative force constant (the bond yet to be formed in this case), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate that imaginary number (e.g. 526.7i). Success IRC was obtained at PM6 level as shown below where gradient was 0 at the Transition state, reactants and product.
[[File: Zinan_Wang_EX1_IRC.PNG|thumb|center|The IRC for optimized transition state|800px ]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]
The formed MO has the energy higher than the original molecular orbitals. That is due to the fact that it is a MO for the transition state, the highest energy point along the reaction pathway.

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 indicated a sp3-sp3 carbon bond has formed in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

=Exercise2=

===HOMO, LUMO,frequency check and Gibbs free energy===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|<jmol>
<jmolApplet>
<title>HOMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<title>LUMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|<jmol>
<jmolApplet>
<title>HOMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

According to the frequency calculation, all transition states are showing only 1 negative value and all the other species are showing all positive frequencies which confirms the success in obtaining the optimized structures.

===MO diagram===

Firstly the a single point energy calculation was carried out for two reactants being separated for 20 a.u.(i.e. assume no interaction)
The MO diagram for the resulting file was shown below
[[File:Zinan_Wang_EX2_REACT1and2.PNG|thumb|center|800px|The MOs from single point energy calculation ]]
The value of the each energy level was used to draw the corresponded MO diagram.
The energy levels for the MO of TS are higher than the final product as expected, as the TS represent the highest energy along the reaction coordination.

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp) / Hartree
|0.062817 (164.926034 kJ/mol)
|0.060358 (158.469929 kJ/mol)
|-
|Reaction energies (at room temp) /Hartree
|<nowiki>-0.024815</nowiki> (<nowiki>-65.1517825</nowiki> kJ/mol)
|<nowiki>-0.026185</nowiki> (<nowiki>-68.7487175</nowiki> kJ/mol)
|}

The reaction barrier and reaction energy are both lower for the Endo-pathway.
Therefore the endo pathway is both kinetic and thermodynamic favored.

From the single point calculation, the energy of the HOMO of the dieneophile (1,3-Dioxole) is higher than that of the diene (Cyclohexadiene) which shows that the dieneophile is more electron rich than the diene, thus inverse electron demand.

=Exercise3=

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.
The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is thermodynamic pathway of reaction.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

===.log File for Exercise 3===

Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

File:Zinan Wang MO TS T.jpg

2018-03-13T21:12:55Z

Zw4415: Zw4415 uploaded a new version of File:Zinan Wang MO TS T.jpg

Rep:Zw4415:TSexercise

2018-03-13T20:51:44Z

Zw4415: /* HOMO, LUMO,frequency check and Gibbs free energy */

=Introduction=

=Exercise1=
===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level first with frequency checked to only have one negative value at around -930. Followed by B3LYP/6-31G(d) method and the resulting structure have one negative frequency at -526.7.
It is because when calculating form a harmonic oscillator with negative force constant (the bond yet to be formed in this case), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate that imaginary number (e.g. 526.7i). Success IRC was obtained at PM6 level as shown below where gradient was 0 at the Transition state, reactants and product.
[[File: Zinan_Wang_EX1_IRC.PNG|thumb|center|The IRC for optimized transition state|800px ]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 indicated a sp3-sp3 carbon bond has formed in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

=Exercise2=

===HOMO, LUMO,frequency check and Gibbs free energy===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|<jmol>
<jmolApplet>
<title>HOMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<title>LUMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|<jmol>
<jmolApplet>
<title>HOMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

According to the frequency calculation, all transition states are showing only 1 negative value and all the other species are showing all positive frequencies which confirms the success in obtaining the optimized structures.

===MO diagram===

Firstly the a single point energy calculation was carried out for two reactants being separated for 20 a.u.(i.e. assume no interaction)
The MO diagram for the resulting file was shown below
[[File:Zinan_Wang_EX2_REACT1and2.PNG|thumb|center|800px|The MOs from single point energy calculation ]]
The value of the each energy level was used to draw the corresponded MO diagram.
The energy levels for the MO of TS are higher than the final product as expected, as the TS represent the highest energy along the reaction coordination.

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp) / Hartree
|0.062817 (164.926034 kJ/mol)
|0.060358 (158.469929 kJ/mol)
|-
|Reaction energies (at room temp) /Hartree
|<nowiki>-0.024815</nowiki> (<nowiki>-65.1517825</nowiki> kJ/mol)
|<nowiki>-0.026185</nowiki> (<nowiki>-68.7487175</nowiki> kJ/mol)
|}

The reaction barrier and reaction energy are both lower for the Endo-pathway.
Therefore the endo pathway is both kinetic and thermodynamic favored.

From the single point calculation, the energy of the HOMO of the dieneophile (1,3-Dioxole) is higher than that of the diene (Cyclohexadiene) which shows that the dieneophile is more electron rich than the diene, thus inverse electron demand.

=Exercise3=

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.
The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is thermodynamic pathway of reaction.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

===.log File for Exercise 3===

Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

Rep:Zw4415:TSexercise

2018-03-13T20:48:41Z

Zw4415: /* MO diagram */

=Introduction=

=Exercise1=
===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level first with frequency checked to only have one negative value at around -930. Followed by B3LYP/6-31G(d) method and the resulting structure have one negative frequency at -526.7.
It is because when calculating form a harmonic oscillator with negative force constant (the bond yet to be formed in this case), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate that imaginary number (e.g. 526.7i). Success IRC was obtained at PM6 level as shown below where gradient was 0 at the Transition state, reactants and product.
[[File: Zinan_Wang_EX1_IRC.PNG|thumb|center|The IRC for optimized transition state|800px ]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 indicated a sp3-sp3 carbon bond has formed in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

=Exercise2=

===HOMO, LUMO,frequency check and Gibbs free energy===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|<jmol>
<jmolApplet>
<title>HOMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<title>LUMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|<jmol>
<jmolApplet>
<title>HOMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

[[Category:]]===MO diagram===

Firstly the a single point energy calculation was carried out for two reactants being separated for 20 a.u.(i.e. assume no interaction)
The MO diagram for the resulting file was shown below
[[File:Zinan_Wang_EX2_REACT1and2.PNG|thumb|center|800px|The MOs from single point energy calculation ]]
The value of the each energy level was used to draw the corresponded MO diagram.
The energy levels for the MO of TS are higher than the final product as expected, as the TS represent the highest energy along the reaction coordination.

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp) / Hartree
|0.062817 (164.926034 kJ/mol)
|0.060358 (158.469929 kJ/mol)
|-
|Reaction energies (at room temp) /Hartree
|<nowiki>-0.024815</nowiki> (<nowiki>-65.1517825</nowiki> kJ/mol)
|<nowiki>-0.026185</nowiki> (<nowiki>-68.7487175</nowiki> kJ/mol)
|}

The reaction barrier and reaction energy are both lower for the Endo-pathway.
Therefore the endo pathway is both kinetic and thermodynamic favored.

From the single point calculation, the energy of the HOMO of the dieneophile (1,3-Dioxole) is higher than that of the diene (Cyclohexadiene) which shows that the dieneophile is more electron rich than the diene, thus inverse electron demand.

=Exercise3=

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.
The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is thermodynamic pathway of reaction.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

===.log File for Exercise 3===

Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

Rep:Zw4415:TSexercise

2018-03-13T20:40:05Z

Zw4415: /* MO diagram */

=Introduction=

=Exercise1=
===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level first with frequency checked to only have one negative value at around -930. Followed by B3LYP/6-31G(d) method and the resulting structure have one negative frequency at -526.7.
It is because when calculating form a harmonic oscillator with negative force constant (the bond yet to be formed in this case), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate that imaginary number (e.g. 526.7i). Success IRC was obtained at PM6 level as shown below where gradient was 0 at the Transition state, reactants and product.
[[File: Zinan_Wang_EX1_IRC.PNG|thumb|center|The IRC for optimized transition state|800px ]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 indicated a sp3-sp3 carbon bond has formed in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

=Exercise2=

===HOMO, LUMO,frequency check and Gibbs free energy===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|<jmol>
<jmolApplet>
<title>HOMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<title>LUMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|<jmol>
<jmolApplet>
<title>HOMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

===MO diagram===

Firstly the a single point energy calculation was carried out for two reactants being separated for 20 a.u.(i.e. assume no interaction)
The MO diagram for the resulting file was shown below
[[File:Zinan_Wang_EX2_REACT1and2.PNG|thumb|center|800px|The MOs from single point energy calculation ]]
The value of the each energy level was used to draw the corresponded MO diagram.
The energy levels for the MO of TS are higher than the final product as expected, as the TS represent the highest energy along the reaction coordination.

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp) / Hartree
|0.062817 (164.926034 kJ/mol)
|0.060358 (158.469929 kJ/mol)
|-
|Reaction energies (at room temp) /Hartree
|<nowiki>-0.024815</nowiki> (<nowiki>-65.1517825</nowiki> kJ/mol)
|<nowiki>-0.026185</nowiki> (<nowiki>-68.7487175</nowiki> kJ/mol)
|}

Only 1 'negative' frequency was shown in the table, thus confirms that the transition states were successfully obtained.

=Exercise3=

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.
The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is thermodynamic pathway of reaction.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

===.log File for Exercise 3===

Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

Rep:Zw4415:TSexercise

2018-03-13T20:39:47Z

Zw4415: /* MO diagram */

=Introduction=

=Exercise1=
===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level first with frequency checked to only have one negative value at around -930. Followed by B3LYP/6-31G(d) method and the resulting structure have one negative frequency at -526.7.
It is because when calculating form a harmonic oscillator with negative force constant (the bond yet to be formed in this case), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate that imaginary number (e.g. 526.7i). Success IRC was obtained at PM6 level as shown below where gradient was 0 at the Transition state, reactants and product.
[[File: Zinan_Wang_EX1_IRC.PNG|thumb|center|The IRC for optimized transition state|800px ]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 indicated a sp3-sp3 carbon bond has formed in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

=Exercise2=

===HOMO, LUMO,frequency check and Gibbs free energy===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|<jmol>
<jmolApplet>
<title>HOMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<title>LUMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|<jmol>
<jmolApplet>
<title>HOMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

===MO diagram===

Firstly the a single point energy calculation was carried out for two reactants being separated for 20 a.u.(i.e. assume no interaction)
The MO diagram for the resulting file was shown below
[[File:Zinan_Wang_EX2_REACT1and2.PNG|thumb|center|The MOs from single point energy calculation ]]
The value of the each energy level was used to draw the corresponded MO diagram.
The energy levels for the MO of TS are higher than the final product as expected, as the TS represent the highest energy along the reaction coordination.

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp) / Hartree
|0.062817 (164.926034 kJ/mol)
|0.060358 (158.469929 kJ/mol)
|-
|Reaction energies (at room temp) /Hartree
|<nowiki>-0.024815</nowiki> (<nowiki>-65.1517825</nowiki> kJ/mol)
|<nowiki>-0.026185</nowiki> (<nowiki>-68.7487175</nowiki> kJ/mol)
|}

Only 1 'negative' frequency was shown in the table, thus confirms that the transition states were successfully obtained.

=Exercise3=

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.
The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is thermodynamic pathway of reaction.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

===.log File for Exercise 3===

Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

File:Zinan Wang EX2 EXO TS MO.jpg

2018-03-13T20:37:32Z

Zw4415: Zw4415 uploaded a new version of File:Zinan Wang EX2 EXO TS MO.jpg

File:Zinan Wang EX2 ENDO TS MO.jpg

2018-03-13T20:37:09Z

Zw4415: Zw4415 uploaded a new version of File:Zinan Wang EX2 ENDO TS MO.jpg

File:Zinan Wang EX2 REACT1and2.PNG

2018-03-13T19:55:32Z

Zw4415:

Rep:Zw4415:TSexercise

2018-03-13T19:45:49Z

Zw4415: /* HOMO, LUMO,frequency check and Gibbs free energy */

=Introduction=

=Exercise1=
===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level first with frequency checked to only have one negative value at around -930. Followed by B3LYP/6-31G(d) method and the resulting structure have one negative frequency at -526.7.
It is because when calculating form a harmonic oscillator with negative force constant (the bond yet to be formed in this case), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate that imaginary number (e.g. 526.7i). Success IRC was obtained at PM6 level as shown below where gradient was 0 at the Transition state, reactants and product.
[[File: Zinan_Wang_EX1_IRC.PNG|thumb|center|The IRC for optimized transition state|800px ]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 indicated a sp3-sp3 carbon bond has formed in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

=Exercise2=

===HOMO, LUMO,frequency check and Gibbs free energy===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|<jmol>
<jmolApplet>
<title>HOMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<title>LUMO Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Exo TS</title>
<color>white</color>
<size>280</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|<jmol>
<jmolApplet>
<title>HOMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>HOMO-1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>LUMO+1 Endo TS</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

===MO diagram===

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp) / Hartree
|0.062817 (164.926034 kJ/mol)
|0.060358 (158.469929 kJ/mol)
|-
|Reaction energies (at room temp) /Hartree
|<nowiki>-0.024815</nowiki> (<nowiki>-65.1517825</nowiki> kJ/mol)
|<nowiki>-0.026185</nowiki> (<nowiki>-68.7487175</nowiki> kJ/mol)
|}

Only 1 'negative' frequency was shown in the table, thus confirms that the transition states were successfully obtained.

=Exercise3=

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.
The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is thermodynamic pathway of reaction.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

===.log File for Exercise 3===

Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

Rep:Zw4415:TSexercise

2018-03-13T19:41:16Z

Zw4415: /* HOMO, LUMO,frequency check and Gibbs free energy */

=Introduction=

=Exercise1=
===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level first with frequency checked to only have one negative value at around -930. Followed by B3LYP/6-31G(d) method and the resulting structure have one negative frequency at -526.7.
It is because when calculating form a harmonic oscillator with negative force constant (the bond yet to be formed in this case), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate that imaginary number (e.g. 526.7i). Success IRC was obtained at PM6 level as shown below where gradient was 0 at the Transition state, reactants and product.
[[File: Zinan_Wang_EX1_IRC.PNG|thumb|center|The IRC for optimized transition state|800px ]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 indicated a sp3-sp3 carbon bond has formed in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

=Exercise2=

===HOMO, LUMO,frequency check and Gibbs free energy===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|<jmol>
<jmolApplet>
<title>HOMO Exo TS</title>
<color>white</color>
<size>180</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

|
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|<jmol>
<jmolApplet>
<title>HOMO Endo TS</title>
<color>white</color>
<size>180</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

===MO diagram===

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp) / Hartree
|0.062817 (164.926034 kJ/mol)
|0.060358 (158.469929 kJ/mol)
|-
|Reaction energies (at room temp) /Hartree
|<nowiki>-0.024815</nowiki> (<nowiki>-65.1517825</nowiki> kJ/mol)
|<nowiki>-0.026185</nowiki> (<nowiki>-68.7487175</nowiki> kJ/mol)
|}

Only 1 'negative' frequency was shown in the table, thus confirms that the transition states were successfully obtained.

=Exercise3=

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.
The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is thermodynamic pathway of reaction.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

===.log File for Exercise 3===

Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

Rep:Zw4415:TSexercise

2018-03-13T19:37:54Z

Zw4415: /* HOMO, LUMO,frequency check and Gibbs free energy */

=Introduction=

=Exercise1=
===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level first with frequency checked to only have one negative value at around -930. Followed by B3LYP/6-31G(d) method and the resulting structure have one negative frequency at -526.7.
It is because when calculating form a harmonic oscillator with negative force constant (the bond yet to be formed in this case), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate that imaginary number (e.g. 526.7i). Success IRC was obtained at PM6 level as shown below where gradient was 0 at the Transition state, reactants and product.
[[File: Zinan_Wang_EX1_IRC.PNG|thumb|center|The IRC for optimized transition state|800px ]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 indicated a sp3-sp3 carbon bond has formed in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

=Exercise2=

===HOMO, LUMO,frequency check and Gibbs free energy===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|<jmol>
<jmolApplet>
<title>HOMO Exo TS</title>
<color>white</color>
<size>180</size>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>

|
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|<jmol>
<jmolApplet>
<title>HOMO Endo TS</title>
<color>white</color>
<size>180</size>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

===MO diagram===

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp) / Hartree
|0.062817 (164.926034 kJ/mol)
|0.060358 (158.469929 kJ/mol)
|-
|Reaction energies (at room temp) /Hartree
|<nowiki>-0.024815</nowiki> (<nowiki>-65.1517825</nowiki> kJ/mol)
|<nowiki>-0.026185</nowiki> (<nowiki>-68.7487175</nowiki> kJ/mol)
|}

Only 1 'negative' frequency was shown in the table, thus confirms that the transition states were successfully obtained.

=Exercise3=

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.
The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is thermodynamic pathway of reaction.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

===.log File for Exercise 3===

Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

Rep:Zw4415:TSexercise

2018-03-13T19:35:24Z

Zw4415: /* HOMO, LUMO,frequency check and Gibbs free energy */

=Introduction=

=Exercise1=
===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level first with frequency checked to only have one negative value at around -930. Followed by B3LYP/6-31G(d) method and the resulting structure have one negative frequency at -526.7.
It is because when calculating form a harmonic oscillator with negative force constant (the bond yet to be formed in this case), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate that imaginary number (e.g. 526.7i). Success IRC was obtained at PM6 level as shown below where gradient was 0 at the Transition state, reactants and product.
[[File: Zinan_Wang_EX1_IRC.PNG|thumb|center|The IRC for optimized transition state|800px ]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 indicated a sp3-sp3 carbon bond has formed in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

=Exercise2=

===HOMO, LUMO,frequency check and Gibbs free energy===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|<jmol>
<jmolApplet>
<title>HOMO Exo TS</title>
<color>white</color>
<size>180</size>
<uploadedFileContents>ZINAN_WANG_EX2_TS_EXO_OPT_B3LYP_MO</uploadedFileContents>
</jmolApplet>
</jmol>

|
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|<jmol>
<jmolApplet>
<title>HOMO Endo TS</title>
<color>white</color>
<size>180</size>
<uploadedFileContents>Zinan_Wang_EX2_TS_ENDO_OPT_B3LYP_MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

===MO diagram===

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp) / Hartree
|0.062817 (164.926034 kJ/mol)
|0.060358 (158.469929 kJ/mol)
|-
|Reaction energies (at room temp) /Hartree
|<nowiki>-0.024815</nowiki> (<nowiki>-65.1517825</nowiki> kJ/mol)
|<nowiki>-0.026185</nowiki> (<nowiki>-68.7487175</nowiki> kJ/mol)
|}

Only 1 'negative' frequency was shown in the table, thus confirms that the transition states were successfully obtained.

=Exercise3=

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.
The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is thermodynamic pathway of reaction.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

===.log File for Exercise 3===

Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

File:ZINAN WANG EX2 TS EXO OPT B3LYP MO.log

2018-03-13T19:34:58Z

Zw4415:

File:Zinan Wang EX2 TS ENDO OPT B3LYP MO.log

2018-03-13T19:33:30Z

Zw4415:

Rep:Zw4415:TSexercise

2018-03-13T19:16:54Z

Zw4415: /* MO diagram */

=Introduction=

=Exercise1=
===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level first with frequency checked to only have one negative value at around -930. Followed by B3LYP/6-31G(d) method and the resulting structure have one negative frequency at -526.7.
It is because when calculating form a harmonic oscillator with negative force constant (the bond yet to be formed in this case), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate that imaginary number (e.g. 526.7i). Success IRC was obtained at PM6 level as shown below where gradient was 0 at the Transition state, reactants and product.
[[File: Zinan_Wang_EX1_IRC.PNG|thumb|center|The IRC for optimized transition state|800px ]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 indicated a sp3-sp3 carbon bond has formed in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

=Exercise2=

===HOMO, LUMO,frequency check and Gibbs free energy===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|
|
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|
|
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

===MO diagram===

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp) / Hartree
|0.062817 (164.926034 kJ/mol)
|0.060358 (158.469929 kJ/mol)
|-
|Reaction energies (at room temp) /Hartree
|<nowiki>-0.024815</nowiki> (<nowiki>-65.1517825</nowiki> kJ/mol)
|<nowiki>-0.026185</nowiki> (<nowiki>-68.7487175</nowiki> kJ/mol)
|}

Only 1 'negative' frequency was shown in the table, thus confirms that the transition states were successfully obtained.

=Exercise3=

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.
The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is thermodynamic pathway of reaction.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

===.log File for Exercise 3===

Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

Rep:Zw4415:TSexercise

2018-03-13T19:16:04Z

Zw4415: /* MO diagram */

=Introduction=

=Exercise1=
===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level first with frequency checked to only have one negative value at around -930. Followed by B3LYP/6-31G(d) method and the resulting structure have one negative frequency at -526.7.
It is because when calculating form a harmonic oscillator with negative force constant (the bond yet to be formed in this case), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate that imaginary number (e.g. 526.7i). Success IRC was obtained at PM6 level as shown below where gradient was 0 at the Transition state, reactants and product.
[[File: Zinan_Wang_EX1_IRC.PNG|thumb|center|The IRC for optimized transition state|800px ]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 indicated a sp3-sp3 carbon bond has formed in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

=Exercise2=

===HOMO, LUMO,frequency check and Gibbs free energy===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|
|
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|
|
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

===MO diagram===

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp) / Hartree
|0.062817 (164.926034 kJ/mol)
|0.060358 (158.469929 kJ/mol)
|-
|Reaction energies (at room temp) /Hartree
|-0.024815 (-65.1517825 kJ/mol)
|-0.026185 (-68.7487175 kJ/mol)
|}

Only 1 'negative' frequency was shown in the table, thus confirms that the transition states were successfully obtained.

=Exercise3=

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.
The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is thermodynamic pathway of reaction.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

===.log File for Exercise 3===

Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

Rep:Zw4415:TSexercise

2018-03-13T19:11:20Z

Zw4415: /* HOMO, LUMO,frequency check and Gibbs free energy */

=Introduction=

=Exercise1=
===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level first with frequency checked to only have one negative value at around -930. Followed by B3LYP/6-31G(d) method and the resulting structure have one negative frequency at -526.7.
It is because when calculating form a harmonic oscillator with negative force constant (the bond yet to be formed in this case), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate that imaginary number (e.g. 526.7i). Success IRC was obtained at PM6 level as shown below where gradient was 0 at the Transition state, reactants and product.
[[File: Zinan_Wang_EX1_IRC.PNG|thumb|center|The IRC for optimized transition state|800px ]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 indicated a sp3-sp3 carbon bond has formed in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

=Exercise2=

===HOMO, LUMO,frequency check and Gibbs free energy===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|<nowiki>-233.324375</nowiki>
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|
|
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|
|
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

===MO diagram===

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp)
|
|
|-
|Reaction energies (at room temp)
|
|
|}

Only 1 'negative' frequency was shown in the table, thus confirms that the transition states were successfully obtained.

=Exercise3=

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.
The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is thermodynamic pathway of reaction.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

===.log File for Exercise 3===

Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

Rep:Zw4415:TSexercise

2018-03-13T18:52:03Z

Zw4415: /* HOMO, LUMO,frequency check and Gibbs free energy */

=Introduction=

=Exercise1=
===TS analysis===
All reactants and product were optimized at PM6 level.
Transition state were obtained at PM6 level first with frequency checked to only have one negative value at around -930. Followed by B3LYP/6-31G(d) method and the resulting structure have one negative frequency at -526.7.
It is because when calculating form a harmonic oscillator with negative force constant (the bond yet to be formed in this case), frequency was obtained as a imaginary number. The negative value in the frequency table thus illustrate that imaginary number (e.g. 526.7i). Success IRC was obtained at PM6 level as shown below where gradient was 0 at the Transition state, reactants and product.
[[File: Zinan_Wang_EX1_IRC.PNG|thumb|center|The IRC for optimized transition state|800px ]]

===MO diagram for the formation of the butadiene/ethene transition state===
[[File:Zinan_Wang_MO_TS_T.jpg|thumb|x800px|center|MO diagram for the formation of the cyclohexene]]

===Visualised MOs for HOMO and LUMO===
{| class="wikitable" style="border: none; background: none;"
|+|Table 1: Visualised MOs
! colspan="2"| cis-Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<title>HOMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO diene</title>
<color>white</color>
<size>180</size>
<script>frame 24; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_DIENE_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO ethene</title>
<color>white</color>
<size>180</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_ETHENE_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>LUMO TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 TS</title>
<color>white</color>
<size>180</size>
<script>frame 60; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZW4415_EX1_TS_OPT_PM6_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram
|-
|[[File:Zinan_Wang_MO_DI_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_DI_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_ENE_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO1.jpg|center]]
|[[File:Zinan_Wang_MO_TS_HOMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO.jpg|center]]
|[[File:Zinan_Wang_MO_TS_LUMO1.jpg|center]]
|}

For a reaction to take place the interacting orbitals must have the same symmetry (a-a/s-s), also both orbitals should be in the similar energy level.
For both symmetric-symmetric interaction and antisymmetric-antisymmetric interaction, the overlap integral is non zero. For symmetric-antisymmetric interactions the overlap integral is zero.

===Bond length measurement===
The Van der Waals radii of carbon is around 1.7 Å.
A typical sp3-sp3 carbon bond length is about 1.54 Å, and a typical sp2-sp2 carbon bond length is about 1.33 Å.

{| class="wikitable"
!
!cis-Butadiene
!Ethene
!Transition State
!Product
!Bond length
!Bond order
|-
|
|[[File:Zinan_Wang_EX1_di_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_ene_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_TS_BOND.PNG|x200px]]
|[[File:Zinan_Wang_EX1_P_BOND.PNG|x200px]]
|
|
|-
|C1-C2
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11484
|1.53580
|decrease
|forming
|-
|C2-C3
|<nowiki>-</nowiki>
|1.32731
|1.38205
|1.53764
|increase
|breaking
|-
|C3-C4
|<nowiki>-</nowiki>
|<nowiki>-</nowiki>
|2.11485
|1.53579
|decrease
|forming
|-
|C4-C5
|1.33529
|<nowiki>-</nowiki>
|1.37977
|1.49261
|increase
|breaking
|-
|C5-C6
|1.46826
|<nowiki>-</nowiki>
|1.41113
|1.33306
|decrease
|forming
|-
|C6-C1
|1.33537
|<nowiki>-</nowiki>
|1.37972
|1.49261
|increase
|breaking
|}

At transition state, the partially formed bond length is about 2.11 Å, which is smaller than 2 times the van der Waals radii of carbon atom while still longer than a typical sp3-sp3 C-C single bond. That means the electrons from both atoms have been interacting (but yet to form a bond) at the transition state, after which the distance decreased to 1.54 indicated a sp3-sp3 carbon bond has formed in the product.

===Bond vibration at reaction path===

As seen in this bond formation vibration, two bonds are forming synchronously.

[[File:Zinan_Wang_EX1_TS_vibration.gif|center|thumb|800px|The bond vibration at reaction path.]]

===.log Files for Exercise 1===
PM6 optimized s-cis-Butadiene: [[File:ZW4415_EX1_DIENE_OPT_PM6_4.LOG]]

PM6 optimized ethene: [[File:ZW4415_EX1_ETHENE_OPT_PM6.LOG]]

PM6 optimized transition state: [[File:ZW4415_EX1_TS_OPT_PM6_2.LOG]]

PM6 optimized product: [[File:ZW4415_EX1_PRODUCT_OPT_PM6.LOG]]

IRC: [[File:ZW4415_EX1_TS_IRC_PM6_2_2.LOG]]

=Exercise2=

===HOMO, LUMO,frequency check and Gibbs free energy===

{| class="wikitable"
!
!HOMO
!LUMO
!frequency check
!Gibbs Free Energy
|-
|Cyclohexadiene
|<jmol>
<jmolApplet>
<title>HOMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO Cyclohexadiene</title>
<color>white</color>
<size>280</size>
<script>frame 12; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT1_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT1.PNG]]
|
|-
|1,3-Dioxole
|<jmol>
<jmolApplet>
<title>HOMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 14; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO 1,3-Dioxole</title>
<color>white</color>
<size>280</size>
<script>frame 6; mo 15; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>ZINAN_WANG_EX2_REACT2_OPT_PM6_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|[[File:ZINAN_WANG_EX2_REACT2.PNG]]
|<nowiki>-267.068132</nowiki>
|-
|Exo transition state
|
|
|[[File:Zinan_Wang_EX2_EXO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.329169</nowiki>
|-
|Exo product
|
|
|[[File:Zinan_Wang_EX2_EXO_P_FRQ.PNG]]
|<nowiki>-500.417322</nowiki>
|-
|Endo transition state
|
|
|[[File:Zinan_Wang_EX2_ENDO_TS_FRQ_B3LYP.PNG]]
|<nowiki>-500.332149</nowiki>
|-
|Endo product
|
|
|[[File:Zinan_Wang_EX2_ENDO_P_FRQ.PNG]]
|<nowiki>-500.418692</nowiki>
|}

===MO diagram===

{| class="wikitable"
!
!EXO
!ENDO
|-
|The MO diagram for TS formation
|[[File:Zinan_Wang_EX2_EXO_TS_MO.jpg|500px]]
|[[File:Zinan_Wang_EX2_ENDO_TS_MO.jpg|500px]]
|-
|Reaction barriers (at room temp)
|
|
|-
|Reaction energies (at room temp)
|
|
|}

Only 1 'negative' frequency was shown in the table, thus confirms that the transition states were successfully obtained.

=Exercise3=

[[File:Zinan_Wang_EX3_Scheme.jpg|thumb|center|600px|The reaction scheme for Exercise 3]]

===Reaction energy calculation===
The Gibbs free energy for each reactants, transition states and products were extracted form the .log file at 'Thermochemistry' section and converted to kJ/mol.

{| class="wikitable"
!
!Gibbs free energy (Hatree)
!Gibbs free energy (kJ/mol)
|-
|Xylylene
|0.178134
|467.6908
|-
|SO<sub>2</sub>
|<nowiki>-0.118614</nowiki>
|<nowiki>-311.4211</nowiki>
|-
|'''EXO TS'''
|0.092078
|241.7508
|-
|'''ENDO TS'''
|0.090558
|237.76
|-
|'''Cheletropic TS'''
|0.099062
|260.0873
|-
|EXO product
|0.021456
|56.33273
|-
|ENDO product
|0.021696
|56.96285
|-
|Cheletropic product
|<nowiki>-0.000002</nowiki>
|<nowiki>-0.00525</nowiki>
|}

===Reaction coordinations===
{| class="wikitable"
!
!Exo DA reaction
!Endo DA reaction
!Cheletropic reaction
|-
|Reaction coordinate from IRC
(click to see animation)
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.gif|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.gif|400px]]
|-
|IRC energy calculation
|[[File:Zinan_Wang_EX3_irc_EXO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_ENDO_PM6.PNG|400px]]
|[[File:Zinan_Wang_EX3_irc_Chele_PM6.PNG|400px]]
|-
|Reaction barriers (kJ/mol)
|85.4811
|81.4903
|103.8176
|-
|Reaction energy (kJ/mol)
|<nowiki>-99.9370</nowiki>
|<nowiki>-99.3069</nowiki>
|<nowiki>-156.275</nowiki>
|}

From the reaction barriers calculated, the Endo path has slightly lower reaction barrier than the Exo path. These two DA reaction path also has the silimar reaction energy. Although the most kinetic path is the Endo, the Exo is a strong competing pathway.
The Cheletropic reaction has the highest reaction barrier while the lowest reaction energy, thus it is thermodynamic pathway of reaction.

[[File:Zinan_Wang_EX3_Reactionenergy.jpg|thumb|center|600px|The reaction profile]]

===.log File for Exercise 3===

Optimized Xylylene:[[File:ZINAN_WANG_EX3_REACT1_OPT_PM6.LOG]]

Optimized SO2:[[File:ZINAN_WANG_EX3_SO2_OPT_PM6.LOG]]

Optimized EXO product:[[File:ZINAN_WANG_EX3_P_EXO_OPT_PM6.LOG]]

Optimized EXO TS:[[File:ZINAN_WANG_EX3_TS_EXO_PM6.LOG]]

Optimized ENDO product:[[File:ZINAN_WANG_EX3_P_ENDO_OPT_PM6.LOG]]

Optimized ENDO TS:[[File:ZINAN_WANG_EX3_TS_ENDO_PM6.LOG]]

Optimized Cheletropic product:[[File:ZINAN_WANG_EX3_P_CHELE_OPT_PM6.LOG]]

Optimized Cheletropic TS:[[File:ZINAN_WANG_EX3_TS_CHELE_PM6.LOG]]

File:Zinan Wang EX2 ENDO TS FRQ B3LYP.PNG

2018-03-13T18:10:46Z

Zw4415: Zw4415 uploaded a new version of File:Zinan Wang EX2 ENDO TS FRQ B3LYP.PNG

File:Zinan Wang EX2 ENDO P FRQ.PNG

2018-03-13T18:10:29Z

Zw4415:

File:Zinan Wang EX2 EXO TS FRQ B3LYP.PNG

2018-03-13T18:10:03Z

Zw4415: Zw4415 uploaded a new version of File:Zinan Wang EX2 EXO TS FRQ B3LYP.PNG

File:Zinan Wang EX2 EXO P FRQ.PNG

2018-03-13T18:09:07Z

Zw4415:

Rep:Zw4415:TSexercise

2018-03-13T18:05:16Z

Zw4415: /* MO diagram */